the discontinuities of a rational function involves finding the values of x that make the denominator equal to zero, while finding the asymptotes of a rational function involves examining the behavior of the function as x approaches certain values.
Describe the function.
There will be questions on every subject, including created and real places as well as algebraic variable design, on the midterm test. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.
To find the discontinuities of a rational function, we need to determine where the function is undefined. In general, a rational function is a function of the form:
f(x) = p(x) / q(x)
where p(x) and q(x) are polynomials in x, and q(x) is not the zero polynomial. The rational function f(x) is undefined at any value of x that makes the denominator q(x) equal to zero, since division by zero is undefined.
Therefore, to find the discontinuities of a rational function, we need to solve the equation q(x) = 0. The values of x that make q(x) equal to zero are called the "zeros" or "roots" of the denominator q(x). These values of x are the discontinuity points of the function, since the function is undefined at those points.
On the other hand, to find the asymptotes of a rational function, we need to examine the behavior of the function as x approaches certain values. In general, a rational function may have three types of asymptotes: horizontal, vertical, and oblique (also called slant).
Vertical asymptotes occur when the function approaches positive or negative infinity as x approaches a certain value, typically where the denominator q(x) equals zero.
Horizontal asymptotes occur when the function approaches a constant value as x approaches positive or negative infinity.
Oblique asymptotes occur when the degree of the numerator is exactly one greater than the degree of the denominator. In this case, the function approaches a straight line (i.e., a slant asymptote) as x approaches positive or negative infinity.
To summarize, finding the discontinuities of a rational function involves finding the values of x that make the denominator equal to zero, while finding the asymptotes of a rational function involves examining the behavior of the function as x approaches certain values.
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IJ is dilated by a scale factor of 2 to form I' J'. I' J' measures 58. What is the measure of IJ?
The measure of IJ is 29, when IJ is dilated by a scale factor of 2 to form I' J', and I' J' measures 58. Geometric figures in two or three dimensions can be expanded and contracted using dilation mathematics.
What is meant by dilation?Dilation refers to the change in size without a change in shape of an object. The scale factor may also cause the object's size to either increase or decrease.
Dilation is hence the process of resizing or altering an object. It is a transformation that makes the objects smaller or larger by applying the provided scale factor. It is a transformation that makes the objects smaller or larger by applying the provided scale factor. The pre-image is the original figure, while the image is the new figure created as a result of dilation. Dilation comes in two varieties:
As an object experiences expansion, its size expands.
Contraction is the process of a thing getting smaller.
Given:
I'J' is IJ with the scale factor of 2.
so (IJ) × 2= (I'J)
(IJ) × 2 = 58
58 ÷ 2 = 29
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The new, larger coral reef tank will thrill visitors by providing a floor-to-ceiling view of sea creatures swimming through the reef. In the old version of the exhibit, 576,000 gallons of water circulated through the tank over 24 hours. if the volume of the new exhibit is 3 1/2 times larger than the old one, how many gallons per hour will be circulated?
Flow rate =[tex]V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex] gallons per hour (rounded to the nearest gallon) will be circulated.
What is meant by rate?
In general, a rate is a measure of how quickly something changes over time or with respect to some other quantity. It is typically expressed as a ratio of two quantities, where the numerator represents the amount of change and the denominator represents the time or other quantity over which the change occurs.
If the new exhibit is 3 1/2 times larger than the old one, then its volume is:
[tex]V_{new} = 3.5 * V_{old[/tex]
We know that in the old exhibit, 576,000 gallons of water circulated over 24 hours. Therefore, the flow rate of water in gallons per hour is:
576,000 gallons / 24 hours = 24,000 gallons per hour
To find the flow rate in the new exhibit, we need to divide the total volume of water by the number of hours. Since we want the flow rate in gallons per hour, we can write:
Flow rate = [tex]V_{new[/tex] / time
Plugging in the values we have:
Flow rate = (3.5 * [tex]V_{old[/tex]) / time
We don't know the time yet, but we do know that the flow rate should be the same as in the old exhibit, which was 24,000 gallons per hour. So we can set up an equation:
24,000 = (3.5 * [tex]V_{old[/tex]) / time
To solve for time, we can multiply both sides by time:
24,000 * time = 3.5 * [tex]V_{old[/tex]
Then we can divide both sides by 24,000:
time = (3.5 * [tex]V_{old[/tex]) / 24,000
Plugging in [tex]V_{old[/tex] = 576,000, we get:
time = (3.5 * 576,000) / 24,000 = 84 hours
Therefore, in the new exhibit, 3.5 times larger than the old one, the flow rate of water in gallons per hour will be:
[tex]Flow rate = V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex]gallons per hour (rounded to the nearest gallon).
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Answer:
To find out how many gallons per hour will be circulated in the new exhibit, we need to first determine the volume of the old exhibit. Given that 576,000 gallons of water circulated through the old tank over 24 hours, we can calculate the amount of water circulated per hour.
To do this, we divide the total gallons by the number of hours:
576,000 gallons / 24 hours = 24,000 gallons per hour
Now, we know that the new exhibit is 3 1/2 times larger than the old one. To find the volume of the new exhibit, we multiply the volume of the old exhibit by 3 1/2.
Let's assume the volume of the old exhibit is x gallons.
The volume of the new exhibit is 3 1/2 times larger than the old one, so the volume of the new exhibit is 3 1/2 * x.
To calculate the new volume, we need to convert the mixed fraction 3 1/2 into an improper fraction. It equals 7/2.
So, the volume of the new exhibit is 7/2 * x.
Now, we can determine the amount of water circulated per hour in the new exhibit.
To find this, we multiply the volume of the new exhibit by the rate of circulation per hour in the old exhibit (24,000 gallons/hour):
(7/2 * x) * 24,000 gallons/hour = (7 * 24,000 * x) / 2 gallons/hour = 168,000x gallons/hour
Therefore, the number of gallons per hour that will be circulated in the new exhibit is 168,000x, where x represents the volume of the old exhibit.
Please note that the actual value of x (the volume of the old exhibit) is not given in the question, so we can't determine the exact number of gallons per hour. However, we can express it as a multiple of the volume of the old exhibit.
Step-by-step explanation:
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Rectangle ABCD is congruent to rectangle A′′B′′C′′D′′ . Which sequence of transformations could have been used to transform rectangle ABCD to produce rectangle A′′B′′C′′D′′ ? Responses Rectangle ABCD was translated 2 units left and then 3 units down. , , rectangle A B C D, , , , was translated 2 units left and then 3 units down. Rectangle ABCD was reflected across the y-axis and then across the x-axis. , , rectangle A B C D, , , , was reflected across the y -axis and then across the x -axis. Rectangle ABCD was rotated 180° around the origin and then translated 7 units down. , , rectangle A B C D, , , , was rotated 180° around the origin and then translated 7 units down. Rectangle ABCD was translated 8 units left and then 7 units down.
Rectangle ABCD was translated 8 units left and then 7 units down.
We can see vertex A(2,4) of rectangle ABCD moves to A"(-6,-3), in a way that A translated 8 units left (-8)and 7 units down(-7) to A".
A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.
Vertex is a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet. The plural of a vertex is vertices.
A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints.
that is (2-8,4-7)=(-6,-3)
Similarly the other vertices of rectangle ABCD moves to form rectangle A"B"C"D"
B (2,2) → B" (-6,-5)
C (6,2) → C" (-2,-5)
D(6,4) → D" (-2,-3)
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You don’t have to do this it’s just bonus but you can do it if you want
Note that given the perimeter of the Rhombus above, KN will be 35.03 inches
What is the explanation for the above response?Since JKLM is a rhombus, all sides have the same length. Let's call this length "x".
Also, since JL and KM are diagonals of the rhombus, they bisect each other at point N. This means that JN = NL and KN = NM.
We know that JN = 16 inches, and we need to find KN. To do this, we need to first find x, the length of the sides.
The perimeter of the rhombus is 72 inches, so we can write:
4x = 72
Dividing both sides by 4, we get:
x = 18
Now we can use the Pythagorean theorem to find NM (which is equal to KN):
(NM)² = (JN)² + (JM)²
We know that JN = 16, and we can find JM using the fact that JL and KM are perpendicular bisectors of each other:
JM = √[(2x)² - x²] = sqrt(3x²) = x √(3)
Substituting x = 18 and simplifying, we get:
(NM)² = 16² + (18 √(3))²
(NM)² = 256 + 972
(NM)² = 1228
NM = √(1228) = 35.03
Therefore, KN is approximately 35.0 inches (to the nearest tenth).
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Polynomial expressions of [tex]2^{nd}[/tex] degree with one unknown (only [tex]x[/tex]) have [tex]2[/tex] roots. We use the formula below to determine these roots;
[tex]x_{1}=\frac{-b+\sqrt{b^2-4(ac)} }{2a}[/tex][tex]x_{2}=\frac{-b-\sqrt{b^2-4(ac)} }{2a}[/tex]This formula is valid for equations of the form [tex]ax^2+bx+c[/tex]. We can convert the equation given in the question into this format to get the result;
[tex]ax^2+bx+c = 8x^2+16x+3=0[/tex]Hence, the value of [tex]a[/tex]: [tex]8[/tex],
the value of [tex]b[/tex]: [tex]16[/tex],
the value of [tex]c[/tex]: [tex]3[/tex].
Now, we can find the roots of this equation by using this formula;
[tex]x_{1}=\frac{-16+\sqrt{160} }{16} = \frac{-4+\sqrt{10}}{4}[/tex][tex]x_{2}=\frac{-16-\sqrt{160} }{16}=\frac{-4-\sqrt{10}}{4}[/tex]Which shows all the like terms in the expression? 4 x minus 3 + 7 x + 1 –3 and 1; 4x and –3 –3 and 1; 4x and 7x 4x and 1; 7x and –3 4x and –3; 1 and 7x. and Quick because it's a test
the mean wait time for a drive-through chain is 193.2 seconds with a standard deviation of 29.5 seconds. what is the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds? (write answer round to whole number like 91%).
The probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.
To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means is approximately normal for large sample sizes.
First, we need to calculate the standard error of the mean (SEM) using the formula
SEM = standard deviation / sqrt(sample size)
SEM = 29.5 / sqrt(45) = 4.4
Next, we can standardize the sample mean using the formula
z = (x - μ) / SEM
where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.
For the lower limit, we have
z = (185.7 - 193.2) / 4.4 = -1.70
For the upper limit, we have
z = (206.5 - 193.2) / 4.4 = 3.02
We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.
The probability of z being between -1.70 and 3.02 is approximately 0.9429 or 94%. Therefore, the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.
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Classify each polynomial on the left by degree
The greatest power of "p" in this situation is 4, which is the coefficient of p4. Consequently, the polynomial has a degree of 4.
What is a polynomial?Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates.
This equation is provided:
1) [tex]$2p^{4}+p^{3}$[/tex]
The greatest power of the polynomial's variable "p" must be identified to categorize this polynomial by degree.
Therefore, the polynomial [tex]$2p^{4}+p^{3}$[/tex] is a polynomial of the fourth degree.
2) [tex]$2x^{2}$[/tex]
The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.
The greatest power of "x" in this situation is 2, which is the coefficient of . Consequently, the polynomial has a degree of 2.
Therefore, the polynomial [tex]2x^2[/tex] is a polynomial of the second degree.
3) [tex]$-5n^{4}+10n-10$[/tex]
The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.
The greatest power of "n" in this situation is 4, which is the coefficient of . Consequently, the polynomial has a degree of 4.
Therefore, the polynomial [tex]n^4[/tex] is a polynomial of the fourth degree.
4) 6n
The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.
The greatest power of "n" in this situation is 1, which is the coefficient of [tex]n^1[/tex]. Consequently, the polynomial has a degree of 1.
Therefore, the polynomial [tex]n^1[/tex] is a polynomial of one degree.
5) -6
The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.
The polynomial in this instance doesn't have a component. It has a value of 6 and is a constant word. A constant word is thought to have a degree of zero.
Therefore, equation 6 is a zero-degree polynomial.
6) [tex]$x^{3}-3$[/tex]
The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.
The greatest power of "x" in this situation is 3, which is the coefficient of . Consequently, the polynomial has a degree of 3.
Therefore, the polynomial [tex]x^3[/tex] is a polynomial of the third degree.
7) [tex]$2n^{5}$[/tex]
The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.
The greatest power of "n" in this situation is 5, which is the coefficient of . Consequently, the polynomial has a degree of 5.
Therefore, the polynomial [tex]n^5[/tex] is a polynomial of the fifth degree.
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2. the top-selling red and voss tire is rated 60000 miles, which means nothing. in fact, the distance the tires can run until wear out is a normally distributed random variable with a mean of 71000 miles and a standard deviation of 5000 miles. a. what is the probability that the tire wears out before 60000 miles? b. what is the probability that a tire lasts more than 81000 miles?
a. The probability that the top-selling Red and Voss tire wears out before 60,000 miles can be found by calculating the Z-score and using a standard normal distribution table. The Z-score formula is: Z = (X - μ) / σ, where X is the distance (60,000 miles), μ is the mean (71,000 miles), and σ is the standard deviation (5,000 miles).
Z = (60,000 - 71,000) / 5,000 = -11,000 / 5,000 = -2.2. Using a standard normal distribution table, the probability is approximately 0.0139 or 1.39%.
b. To find the probability that a tire lasts more than 81,000 miles, calculate the Z-score: Z = (81,000 - 71,000) / 5,000 = 10,000 / 5,000 = 2. Using the standard normal distribution table, the probability of a Z-score less than 2 is approximately 0.9772. Since we want the probability of the tire lasting more than 81,000 miles, we need to find the complement: 1 - 0.9772 = 0.0228 or 2.28%.
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2plus 2 is 4 everybody knows that
A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.
The final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
The initial balance of the checking account is $350.
If the customer makes two withdrawals, one $50 more than the other, let's assume the smaller withdrawal amount is x. Then, the larger withdrawal amount will be x + $50.
So, the new balance of the checking account after these two withdrawals would be:
$350 - x - (x + $50) = $350 - 2x - $50 = $300 - 2x
After this, the customer makes a deposit of $75, which would increase the balance of the checking account to:
$300 - 2x + $75 = $375 - 2x
Therefore, the final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.
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Complete question:
Write an expression for the new balance using as few terms as possible. A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.
Mrs. Morales wrote a test with 18 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. The maximum number of points possible on the test is 100. Write an equation in slope-intercept form to represent the total number of points on the test. If necessary, write any fraction in decimal form. (Please help ASAP its due tmrw)
By answering the presented question, we may conclude that As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.
what is slope intercept?In mathematics, the slope-intercept form of a linear equation is an that the equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point on the line where it intersects the y-axis. Since it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line crosses the y-axis.
Let x denote the number of spelling and y the number of vocabulary questions. Because there are a total of 18 questions, we know:
x + y = 18
5x + 10y = 15 points
We must solve for y 5x + 10y = 100 to put this equation in slope-intercept form.
10y = -5x + 100
y = (-1/2)x + 10
As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.
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PLEASE HELP ME I DONT KNOW WHAT IM DOING I GOT IT WRONG LIKE 20 TIMES PLEASE EXPLAIN HOW TO DO THIS STEP BY STEP
Answer:
m = 5
n = 2
c = 7
Step-by-step explanation:
Use the property of degrees (when dividing two same based numbers with different degree indicators, the degree indicators are subtracted)
[tex] \frac{ {9}^{ - 3} }{ {9}^{2} } = \frac{1}{ {9}^{m} } [/tex]
[tex] {9}^{ - 3 - 2} = {9}^{ - 5} [/tex]
[tex] {9}^{ - 5} = \frac{1}{ {9}^{m} } [/tex]
If the degree indicator is negative, the number is written as a fraction (1 in the numerator) and the degree indicator is raised to the denominator with a positive sign:
m = 5
.
[tex] \frac{ {x}^{ - 4} }{ {x}^{ - 6} } = {x}^{n} [/tex]
[tex] {x}^{ - 4 - ( - 6) } = {x}^{ - 4 + 6} = {x}^{2} [/tex]
n = 2
.
[tex] \frac{ ({ - 11})^{7} }{ ( { - 11})^{0} } = ( { - 11})^{c} [/tex]
Raising any number to the zero power makes it one
[tex] \frac{ ({ - 11})^{7} }{1} = ({ - 11})^{c} [/tex]
When dividing by 1, the number does not change
[tex]( { - 11})^{7} = ({ - 11})^{c} [/tex]
c = 7
Is Y=8.35x proportional or non proportional
The equation Y=8.35x represents a proportional relationship between Y and x.
What is proportion?
In mathematics, two quantities are said to be proportional if they vary in a way that can be expressed as a ratio or fraction. Specifically, if two quantities x and y are proportional, this means that as x increases or decreases, y also increases or decreases by the same factor.
The equation Y=8.35x represents a proportional relationship between Y and x.
In a proportional relationship, when one variable (x) increases or decreases, the other variable (Y) changes by a constant factor. This constant factor is known as the constant of proportionality.
In the given equation, Y and x are directly proportional to each other, with a constant of proportionality of 8.35. This means that if x is multiplied by any factor, Y will also be multiplied by the same factor. For example, if x is doubled, Y will also be doubled (since 2 times 8.35 is 16.7).
Therefore, the equation Y=8.35x represents a proportional relationship between Y and x.
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a forecast is defined as a(n) . a. quantitative method used when historical data on the variable of interest are either unavailable or not applicable b. prediction of future values of a time series c. outcome of a random experiment
A forecast is defined as a(n) prediction of future values of a time series which is option B.
Using past data as inputs, forecasting is a process that produces accurate predictions of the future course of trends. Companies use forecasting to decide how to spend their budgets and make plans for forthcoming costs. Often, this is based on the anticipated demand for the provided goods and services.
Forecasting is a tool used by investors to predict if certain events, such sales projections, would raise or lower the price of a company's stock. For businesses that require a long-term view on operations, forecasting also offers an essential benchmark.
To predict how trends, like as the GDP or unemployment, will change in the upcoming quarter or year, equity analysts utilise forecasting. Lastly, statisticians may examine the probable effects of a change in business operations via forecasting. Data may be gathered, for example, on how altering company hours affects consumer happiness or how changing particular work conditions affects staff productivity.
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5 1/3 yards long and 2 1/6 yards wide. What’s the area
The area of the rectangle has a width of 5 1/3 yards long and 2 1/6 yards wide is 104/9 square yards or 11.56 square yards.
What is the equation to determine the rectangle's area?When calculating a rectangle's area, we multiply the length by the breadth of the rectangle.
What is a mixed fraction?A mixed fraction is one that is expressed by its quotient and remainder.
Area = length * breadth
Given: Length = [tex]5 \frac{1}{3}[/tex] yards
breadth = [tex]2 \frac{1}{6}[/tex] yards
First, we need to convert a mixed number into the improper fraction
[tex]5 \frac{1}{3}[/tex] = [tex]\frac{(5*3) + 1}{3}[/tex] = [tex]\frac{16}{3}[/tex]
[tex]2 \frac{1}{6} = \frac{(2*6) +1}{6} =\frac{13}{6}[/tex]
Therefore the area of the rectangle = Length * width
= [tex]\frac{16}{3} * \frac{13}{6}[/tex]
=[tex]\frac{104}{9}[/tex]
=[tex]\frac{104}{9} yards^{2}[/tex]
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Complete question:
The rectangle has [tex]5\frac{1}{3}[/tex] yards long and [tex]2 \frac{1}{6} \\[/tex] yards wide. What’s the area
What is the value of x? sin64°=cosx enter your answer in the box. x = °
Answer:Sin and cosine of the acute angle are complementary trigonometric functions. This means that between these trigonometric functions, the rule of complementary acute angles applies: sin64° = cos(90°-64°) = cos26°
So, if we have given cos64° = cosx and we want to determine the value of the acute angle x, given the complementarity of the angles to 90 degrees, the required value of the angle x is 26°.
The answer is: x = 26°
Step-by-step explanation:
Please help and explain
Answer:
The first box is 4 and the second box is 4
The solution is
([tex]\frac{3}{2}[/tex],1)
Step-by-step explanation:
y = 2x -2 Subtract 2x from both sides
-2x + y = -2 Multiply all the way through by - 2
4x - 2y = 4 You are doing this so that you can add it to the first equation 4x + 2y = 8
4x + 2y = 8
(+) 4x - 2y = 4
8x = 12 Divide both sides by 8
x = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]
To find y substitute [tex]\frac{3}{2}[/tex] for x and solve for y
y = 2x - 2
y = [tex]\frac{2}{1}[/tex] x [tex]\frac{3}{2}[/tex] - 2
y = 3 - 2
y = 1
Helping in the name of Jesus.
Answer:
Part A = 4x - 2y = 4
Part B = (1.5, 1)
Step-by-step explanation:
Part A:
y = 2x - 2
2y = 4x -4
4x - 4 = 2y
4x - 2y = 4
Part B:
4x + 2y = 8
2y = 8 - 4x
y = (8 - 4x)/2
y = 2x -2
(8 - 4x)/2 = 2x -2
8 - 4x = 4x - 4
8x = 12
x = 1.5
4x + 2y = 8
4(1.5) + 2y = 8
6 + 2y = 8
2y = 2
y = 1
(1.5, 1)
please help!!!!!!!!!!!
Therefore, the value of tan N rounded to the nearest hundredth is approximately 0.85.
What is triangle?A triangle is a basic geometrical shape that is formed by connecting three non-collinear points in a plane using straight line segments. The three points are called the vertices of the triangle, and the line segments connecting them are called the sides. The angles formed between the sides of a triangle are also an important characteristic of the triangle. Triangles come in many different shapes and sizes, and they have many interesting properties and applications in mathematics, science, engineering, and other fields.
Since the opposite side of angle N is √67 and the adjacent side is √92, we can use the following formula for tangent:
tan(N) = opposite / adjacent
tan(N) = √67 / √92
We can simplify this expression by rationalizing the denominator:
tan(N) = (√67 / √92) * (√92 / √92)
tan(N) = √(67*92) / 92
tan(N) = √6164 / 92
tan(N) = 78.43 / 92
tan(N) ≈ 0.85 (rounded to the nearest hundredth)
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Room and board charged for on-campus students at the local college have increased 3.15 each year since 2000. In 2000, students paid 4,291 for room and board.
Write a function to model the cost of C after t years since 2000
If the trend continues, how much would a student expect to pay for room and board in 2017? Express your answer as a decimal rounded to the nearest hundredth
1) A function to model the cost of C after t years since 2000 is [tex]C = 4,291(1 + 0.0315)^t[/tex]
2)If the trend continues, a student expect to pay for room and board in 2017 is $7862.35 .
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Here we need to use exponential function formula to find the cost function . Then,
=> [tex]f(x)=a(1+r)^t[/tex]
Where a is cost for room in 2000 and r is rate of change.
Then model the cost of room and board C after t years since 2000, we can use the formula:
=> [tex]C = 4,291(1 + 0.0315)^t[/tex]
where 0.0315 represents the annual increase of 3.15% expressed as a decimal.
Now we have to find the cost of room and board in 2017, we need to substitute t = 17 (since 2017 is 17 years after 2000) into the function and round the result to the nearest hundredth.
So,[tex]C = 4,291\times(1 + 0.0315)^{17}[/tex]
=>C = 7,862.35
Therefore, a student would expect to pay approximately $7862.35 for room and board in 2017 if the trend continued.
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Given that 5 sin x + 4 cos x = 0, find the value of tan x
We can start by rearranging the equation 5 sin x + 4 cos x = 0 by dividing both sides by cos(x):
5
sin
�
cos
�
+
4
=
0
5
cosx
sinx
+4=0
Recall that $\frac{\sin x}{\cos x} = \tan x$. So we can substitute this in:
5
tan
�
+
4
=
0
5tanx+4=0
Now we can solve for $\tan x$:
\begin{align*}
5 \tan x + 4 &= 0 \
5 \tan x &= -4 \
\tan x &= \frac{-4}{5}
\end{align*}
Therefore, the value of $\tan x$ is $\boxed{\frac{-4}{5}}$.
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Solving the given inequality, we get the value of x to be,
x ≥ 16.
What is an inequality?In a mathematical equation with an inequality, both sides must be equal. In inequality, we don't use equations but rather compare two values. The signs greater than (or greater than or equal to), less than (or less than or equal to), or not equal to are used in place of the equal sign.
Here in the question, we have the inequality:
x - 4 ≥ 12
Now to simplify this we will add 4 on both sides,
⇒ x - 4 + 4 ≥ 12 + 4
⇒ x ≥ 16
So, this implies that the value of x is greater than or equal to 16.
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Calvin wants to know the proportion of students at his school who plan to
attend college. he interviews a random sample of students at his school.
he finds that 70% of the students in the sample plan to attend college.
what conclusion can he draw from the sample?
Answer:
30% of students do not plan to attend college.
The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 510 and a standard deviation of 270. If a college requires a student to be in the top 30 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?
answer:(round to the nearest integer)
The minimum score that a student must obtain to be in the top 30% of students taking the national standardized examination for college admission is approximately 658.4.
To find the minimum score that a student must obtain to be in the top 30% of students taking the test, we need to find the score that corresponds to the 70th percentile of the distribution.
Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 70th percentile is approximately 0.52.
We can use the formula for transforming a score from a normal distribution to a standard normal distribution to find the corresponding score in the original distribution:
z = (x - mu) / sigma
where z is the z-score, x is the score in the original distribution, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.
Rearranging this formula, we get:
x = mu + z * sigma
Substituting the values we have, we get:
x = 510 + 0.52 * 270
x = 658.4
Therefore, to be among the top 30% of test-takers and be eligible for admission to the college, a student must score at least 658.4 on the exam.
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Hakeem gave out a survey to some students in his school about their favorite color. 325 of those surveyed said their favorite color was red. If 65% of the students surveyed said their favorite color was red, how many students were surveyed in total?
Answer: Let's say the total number of students surveyed is "x".
We know that 65% of the students surveyed said their favorite color was red, which means that 325 students said their favorite color was red.
We can set up a proportion to solve for "x":
65/100 = 325/x
To solve for "x", we can cross-multiply:
65x = 32500
Dividing both sides by 65, we get:
x = 500
Therefore, Hakeem surveyed 500 students in total.
Step-by-step explanation:
Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Step-by-step explanation:
To find the price of one tire patch, you could use the equation:
4x = 22.2 + 1.9
which simplifies to:
4x = 24.1
Then divide both sides by 4 to isolate x:
x = 6.025
So the equation that applies here is:
4x = 22.2 + 1.9
14. assuming p-value is 0.03, what is the conclusion of testing at the 0.10 level of significance whether the fruit drink distributor should sell this drink? a. based on the sample data, there isn't sufficient evidence to conclude that the average rating is more than 4.75. b. based on the sample data, there isn't sufficient evidence to conclude that the average rating is no more than 4.75. c. based on the sample data, there is sufficient evidence to conclude that the average rating is no more than 4.75. d. based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75. e. none of the above.
Based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75, thus the correct option is (d). The question is related to hypothesis testing in statistics.
If the p-value is 0.03 and the level of significance is 0.10, we reject the null hypothesis if the p-value is less than 0.10.
Since the null hypothesis is not specified in the question, we assume that it is that the average rating of the fruit drink is no more than 4.75.
Therefore, if the p-value is less than 0.10, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the average rating of the fruit drink is more than 4.75.
Since the p-value, in this case, is 0.03, which is less than the level of significance of 0.10, we would reject the null hypothesis and conclude that based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.
Therefore, the correct answer is (d) based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.
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Prior to going, Ben read that the lobster population in the area labeled NBHK is estimated to be 6, 817. What is the density of the lobster population in the area labeled NBHK?
A) 84 lobsters/mi^2
B) 756 lobsters/mi^2
C) 9.02 lobsters/mi^2
D) 81.15 lobsters/mi^2
The density of the lobster population in the area labeled NBHK is C) 9.02 lobsters/mi^2.
How to calculate the densityPopulation density refers to the number of people living in a given area, usually expressed as the number of individuals per square mile or kilometer.
To calculate population density, you can divide the total population of a given area by its land area. For example, if a city has a population of 1 million people and an area of 100 square miles, its population density would be 10,000 people per square mile.
The figure has two trapezoid and the areas are 306 and 756. Total area will be 1062 miles².
Lobster population will be:
= 6817 / 756
= 9
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as people exit the polling booth, researchers ask those between the ages of 20 and 40 how they voted on the various propositions on the ballot in order to predict election outcomes. this sampling method is called sampling.
The sampling method described in the question is called "quota sampling."
Quota sampling is a non-probability sampling technique in which researchers select participants based on pre-determined quotas or characteristics, such as age or gender. In this case, the researchers are selecting participants between the ages of 20 and 40.
However, this method may not be representative of the entire population as it does not guarantee that all subgroups within the population have an equal chance of being selected. Therefore, the results may be biased and not accurately reflect the opinions of the entire population.
Therefore, it is important to consider the limitations of quota sampling when interpreting the results
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Suma a doua nr naturale este 70.daca se împarte nr mare la cel mic , se obține cățel 4 di restul 10, sa se afle vele 2 numere
Answer:
Los dos números naturales son 12 y 58.
Step-by-step explanation:
Llamemos al número más pequeño "x" y al número más grande "y".
Del problema sabemos que:
x + y = 70 (ya que la suma de los dos números naturales es 70)
Cuando el número mayor se divide por el número menor, el cociente es 4 con un resto de 10. Esto se puede escribir como:
y = 4x + 10 (ya que 4 es el cociente y 10 es el resto)
Ahora podemos sustituir la segunda ecuación en la primera ecuación:
x + (4x + 10) = 70
Simplificando esta ecuación, obtenemos:
5x + 10 = 70
Restando 10 de ambos lados, obtenemos:
5x = 60
Dividiendo ambos lados por 5, obtenemos:
x = 12
Ahora que conocemos x, podemos volver a sustituirlo en una de las ecuaciones anteriores para encontrar y:
y = 4x + 10 = 4(12) + 10 = 58
Por lo tanto, los dos números naturales son 12 y 58.