The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
-6x - 5 < 10 - x
-6x + 15 < 10 - 5x
Therefore, the first and second options are the correct representations.
For the number line, we first need to solve the inequality for x:
-3(2x - 5) < 5(2 - x)
-6x + 15 < 10 - 5x
-x < -5
x > 5
Using this solution, we can plot the open circle at 5 and the bold line pointing to the right on a number line from -3 to 3 in increments of 1. This matches the first option provided. The second option represents a number line with an open circle at -5 and a bold line pointing to the left, which does not correctly represent the solution to the inequality.
What exponential function can be used to determine the number of transistors in a car that doubles every TWO years? The year is 1974 and there are 4100 transistors. For this function to work, we should be able to find the amount of transistors in a car in the year 1989,1993,1997 etc. (or any odd number of years).
(also I asked this earlier just without the year part)
We can use the exponential function [tex]N(t) = N0 * 2^(t/2)[/tex] to determine the number of transistors in a car that doubles every two years.
An exponential function with the following form can be used to calculate the number of transistors in an automobile whose number doubles every two years:
[tex]N(t) = N0 * 2^(t/2)[/tex]
Where t is the amount of time in years after the initial measurement, N0 is the number of transistors at the start, and N(t) is the number of transistors at time t.
We can use this technique to determine the number of transistors in the car in any odd year since 1974, when there were 4100 in it.
For instance, we may insert in t = 15 to determine the quantity of transistors in 1989:
transistors N(15) = 4100 * 2(15/2) = 261,632
Similarly, we may enter t = 19 to calculate the number of transistors in 1993:
522,724 transistors are found in N(19) = 4100 * 2(19/2)
In 1997, we can enter t = 23:
1,045,449 transistors make up N(23) = 4100 * 2(23/2)
In summary, we may calculate the number of transistors in an automobile whose number doubles every two years using the exponential equation [tex]N(t) = N0 * 2(t/2)[/tex]. We can determine the number of transistors in a car in any odd year with an initial measurement of 4100 transistors in 1974.
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What is the solution to this equation: 9 - x = -47?
46. around 1910, the indian mathematician srinivasa ramanujan discovered the formula william gosper used this series in 1985 to compute the first million digits of . verify that the series is convergent. how many correct decimal places of do you get if you use just the first term of the series? what if you use two terms?
a) The series 1/pi = 2sqrt(2)/9801 × summation n=0 to infinity of (4n)!(1103+26390n)/((n!)^4*396^4n) is convergent by the ratio test.
b) If we use just the first term of the series, we get an approximation of pi to one correct decimal place: pi ≈ 6533.008.
If we use two terms of the series, we get an approximation of pi to 14 correct decimal places: pi ≈ 3.14159265358979324.
a) To verify the convergence of the given series, we can use the ratio test.
Let's take the limit of the ratio of the (n+1)th term to the nth term as n approaches infinity:
limit as n approaches infinity of [(4(n+1))!(1103+26390(n+1))/((n+1)!^4396^4(n+1))] / [(4n)!(1103+26390n)/(n!)^4396^4n]
= [(4n+4)(4n+3)(4n+2)(4n+1)(1103+26390n+26390)/(n+1)^4*396^4]
= [(4n+1)^4(1103+26390n+26390)/(n+1)^4*396^4]
= (4n+1)^4(1103+26390n+26390)/(n+1)^4(396^4)
= (4n+1)^4(1103/n+26390+26390/n)/(396^4)
As n approaches infinity, the terms inside the parentheses approach constant values, and we can ignore the n-dependent terms in the numerator and denominator. Thus, the limit simplifies to
= (4^4 × 1103) / (396^4) = 1/(\pi)
Since the limit is less than 1, the series converges by the ratio test.
b) If we use just the first term of the series, we get
1/pi ≈ (2sqrt(2)/9801)×(4!/396^4) = 1.2337 x 10^-4
Taking the reciprocal of both sides, we get
pi ≈ 807104 / 1.2337 ≈ 6533.008
This approximation gives us only one correct decimal place of pi.
If we use two terms of the series, we get
1/pi ≈ (2sqrt(2)/9801)[(4!(1103)+(8!26390))/(396^4(1!^4))]
= 3.1415927300133055 x 10^-1
Taking the reciprocal of both sides, we get
pi ≈ 3.14159265358979324
This approximation gives us 14 correct decimal places of pi.
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The given question is incomplete, the complete question is:
Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula:
1/pi = 2sqrt(2)/9801 * summation n=0 to infinity of (4n)!(1103+26390n)/((n!)^4*396^4n)
William Gosper used this series in 1985 to compute the first 17 million digits of pi.
a) Verify that the series in convergent.
b) How many correct decimal places of pi do you get if you use just the first term of the series? What if you use two terms?
The net shown folds to form a rectangular prism. Determine the lateral surface area of the prism
Answer: To find the lateral surface area of the rectangular prism formed by folding the net, we need to identify the faces that make up the sides of the prism.
In the net, we can see that the two rectangles on the top and bottom will form the bases of the prism, and the four rectangles around the sides will form the lateral faces.
The dimensions of the net are labeled in the diagram as follows:
a = 8 cm
b = 6 cm
c = 10 cm
To find the lateral surface area of the prism, we need to calculate the area of each of the four rectangles around the sides and then add them up.
The dimensions of the rectangles are:
8 cm by 10 cm (on the front and back)
6 cm by 10 cm (on the sides)
So the area of each of the four rectangles is:
8 cm x 10 cm = 80 cm²
6 cm x 10 cm = 60 cm²
Adding up the areas of the four rectangles, we get:
80 cm² + 80 cm² + 60 cm² + 60 cm² = 280 cm²
Therefore, the lateral surface area of the rectangular prism formed by folding the net is 280 square centimeters.
Step-by-step explanation:
An exam has two papers, Paper 1 and Paper 2
Paper 1 has 65 marks.
Paper 2 has 75 marks.
The pass mark is of the total number of marks.
Stephanie gets 80% of the marks for Paper 1
How many of the marks for Paper 2 must Stephanie get in order to get the pass mark?
ANSWER:
Therefore, Stephanie cannot pass the exam even if she gets full marks in Paper 2.
Step-by-step explanation:
Pass mark = 65 + 75 = 140
Stephanie got 80% of the marks for Paper 1, which is:
0.8 x 65 = 52
To pass the exam, Stephanie must get a total of 140 marks, and she already has 52 from Paper 1. Therefore, she needs to get the remaining marks from Paper 2:
140 - 52 = 88
So, Stephanie must get at least 88 marks out of 75 in Paper 2 to pass the exam. However, this is not possible as the maximum marks for Paper 2 are 75.
A rectangular prism has a volume of 6 cubic inches. It is dilated using a scale factor of 2, what is the volume of the dilated rectangular prism?
Answer:
48 cubic inches.
Step-by-step explanation:
The volume of a rectangular prism is given by the formula:
Volume = length x width x height
Since the rectangular prism has a volume of 6 cubic inches, we can write:
6 = length x width x height
When the prism is dilated using a scale factor of 2, each of its dimensions (length, width, and height) is multiplied by 2. Therefore, the new dimensions of the prism are:
2 x length, 2 x width, and 2 x height
The volume of the dilated prism can be calculated as:
Volume of dilated prism = (2 x length) x (2 x width) x (2 x height)
= 2³ x length x width x height
= 8 x (length x width x height)
Since the original rectangular prism had a volume of 6 cubic inches, we know that:
length x width x height = 6
Substituting this value into the equation for the volume of the dilated prism, we get:
Volume of dilated prism = 8 x 6 = 48 cubic inches
Therefore, the volume of the dilated rectangular prism is 48 cubic inches.
Solve for x someone please
The length of the third side is x= 8 (nearest rounded to the tenth).
What is the midpoint theorem?The line segment in a triangle connecting the midway of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.
By using the midpoint theorem, we get
The line is parallel to its third side x and is also half the length of the third side, therefore we can write
X= [tex]\frac{1}{2} * 15[/tex]
X = 7.5
Rounded the value nearest tenth
X = 8
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Mr. Rodriguez is packing bags of snacks for his children’s lunchboxes. He plans to use 20 blueberries and 30 grapes. Each snack bag will have the same number of blueberries and grapes. How many bags can he make if each bag needs to be the same?
5 bags
10 bags
50 bags
60 bags
As a result, Mr. Rodriguez can produce 10 sacks, each containing two blueberries and three grapes.
So, 10 bags must be the solution.
Which meaning of "common factor" is the best?The largest number that can split evenly into two other numbers is known as the greatest common factor in mathematics. For instance, the number 6 is the most frequent factor between 12 and 30. The greatest common denominator is another name for the greatest common component.
We must find the GCF, or greatest common factor, between 20 and 30 to calculate how many bags Mr. Rodriguez can produce. This is necessary because each bag must contain the same quantity of blueberries and grapes, requiring that they both have a similar factor of 20 or 30.
1, 2, 4, 5, 10, and 20 are the elements that make up 20.
1, 2, 3, 5, 6, 10, 15, and 30 make up the number 30.
1, 2, 5, and 10 are the common variables between 20 and 30.
Since the quantity of blueberries and grapes in each bag must be the same, we can split both 20 and 30 by the GCF of 10, which is 10.
The correct number of bags needed is 10 .
This results in:
2 blueberries are in each container of 20/10.
3 grapes per container (30/10)
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your university is upgrading the computers on campus. a national student survey revealed that 62% of college students preferred pcs to macs. a recent poll of 200 social science majors at your university revealed that 82% of students preferred macs to pcs. how do social science majors at your university compare to national mac computer preference norms for college students? what is the correct statistical decision?
The social science majors at your university compare to national mac computer preference norms for college students statistical decision is 5.83.
The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
Finding valid inferences about big groups and general occurrences from the behaviour and other observable features of small samples is a major challenge for statisticians, or persons who study statistics. These tiny samples are representative of a small subset of a larger group or a small number of isolated occurrences of a widespread phenomena.
Proportion of students who preferred PC's to Mac (P) = 0.62
Sample size (n) = 200
Sample proportion of students who prefer Mac's to PCs = 0.82
To compare the proportion of students with Mac preference for college students a Z-test for single proportion will e conducted. The hypothesis is formulated as follows:
H o: There is no significant difference in the national proportion and college preference
H1 : There is a significant difference in the national proportion and college preference
The test statistic is computed below:
[tex]z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]
[tex]z=\frac{0.82-0.62}{\sqrt{\frac{0.62(1-0.62)}{200} } }[/tex]
= 5.8272
Thus, the value of the test statistic is 5.83.
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How many hours after the culture was started and the maximum population is approximately what?
Check the picture below, so that's the picture of a parabolic path with a certain initial velocity.
so anyhow, not to bore you to death, the maximum or peak point occurs at the vertex, as you see in the picture, and the x-coordinate is how long it took to get there.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ P(t)=\stackrel{\stackrel{a}{\downarrow }}{-1698}t^2\stackrel{\stackrel{b}{\downarrow }}{+85000}t\stackrel{\stackrel{c}{\downarrow }}{+10000} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 85000}{2(-1698)}~~~~ ,~~~~ 10000-\cfrac{ (85000)^2}{4(-1698)}\right) \implies \left( - \cfrac{ 85000 }{ -3396 }~~,~~10000 - \cfrac{ 7225000000 }{ -6792 } \right)[/tex]
[tex]\left( \cfrac{ -21250 }{ -849 } ~~~~ ,~~~~ 10000 +\cfrac{ 903125000 }{ 849 } \right) \\\\\\ \left( \cfrac{ 21250 }{ 849 } ~~~~ ,~~~~ \cfrac{ 911615000 }{ 849 } \right) ~~ \approx ~~ (\stackrel{ hrs }{25}~~,~~\stackrel{ population }{1,074,000})[/tex]
What are the factors of 6x2 + 37x - 60? a. 3x - 4 and 2x + 15 b. 3x + 4 and 2x - 15 c. 2(x - 2) and 3(x + 5) d. 2(x + 2) and 3(x - 5)
The factors of 6[tex]x^{2}[/tex]+ 37x - 60 are 2(x - 2) and 3(x + 5), which is answer c.
To factor the polynomial 6[tex]x^{2}[/tex] + 37x - 60, we need to find two numbers whose product is -360 (the product of the leading coefficient and the constant term) and whose sum is 37 (the coefficient of the linear term).
One way to do this is to list all the possible factor pairs of -360 and look for a pair that adds up to 37. Some of the factor pairs are:
1, -360
2, -180
3, -120
4, -90
5, -72
6, -60
8, -45
9, -40
10, -36
12, -30
15, -24
18, -20
We can see that 15 and -24 add up to 37, so we can use them as the coefficients of the linear term. To get the correct sign, we need to use -24 and 15 instead of 15 and -24.
So we have:
6[tex]x^{2}[/tex] + 37x - 60 = 6[tex]x^{2}[/tex] + 15x - 24x - 60
= 3x(2x + 5) - 12(2x + 5)
= (3x - 12)(2x + 5)
= 6(x - 2)(x + 5)
Therefore, the factors of 6[tex]x^{2}[/tex] + 37x - 60 are 2(x - 2) and 3(x + 5), which is answer c.
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1. 4x^2+21x-18
2. 2x^2-13x-45
3. 3x^2+22x-16
factor the polynomial
HOW CAN I SOLVE THIS ASAP?? ( looking for the surface area )
Answer:
125
Step-by-step explanation:
Calculate the area of all the triangles (base x height/2) and add to the area of the square.
Help please with this question
The value of angle C in the cyclic quadrilateral is determined as 61⁰.
What is opposite angles of a cyclic quadrilateral?In a cyclic quadrilateral, opposite angles are the pair of angles that are opposite to each other, meaning they are located at the ends of a diagonal that divides the quadrilateral into two triangles.
The key property of a cyclic quadrilateral is that its four vertices lie on a circle. This means that opposite angles of a cyclic quadrilateral are supplementary, meaning they add up to 180 degrees.
The value of angle C is calculated as follows;
m ∠ C = 180 - m ∠A ( opposite angles of cylic quadrilateral )
m ∠ C = 180 - 119
m ∠ C = 61⁰
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would it be reasonable to use the least squares regression line to predict the final grade for a student who missed 15 class periods? why or why not?
To use the least squares regression line to predict the final grade for a student who missed 15 class periods. It depends on the relationship between the number of missed class periods and the final grade.
If there is a strong linear relationship between these variables, then it would be reasonable to use the least squares regression line to predict the final grade for a student who missed 15 class periods. However, if there is a weak or nonlinear relationship between these variables, then the prediction may not be reliable.
Even if there is a strong linear relationship between the variables, there may be other factors that affect a student's final grade that are not accounted for in the regression model. Therefore, it's always important to interpret the results of a regression analysis with caution and consider other sources of information as well.
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answerrrrr pleaseeeeeeeeeeeeeeeeeeeeeeee <3..
the scale factor for the dilation is 1.0625. According to the given question
how to find scale factor?
To find the scale factor for the dilation that transforms quadrilateral QRST to Q'R'ST, we need to compare the corresponding side lengths of the two figures. Since the figures are similar, the corresponding sides are proportional to each other.
Let the scale factor be represented by k. Then, we have:
|QR| / |Q'R'| = |RS| / |R'S'| = |ST| / |S'T'| = k
We can use the given information about the coordinates of the vertices to calculate the lengths of the sides.
|QR| = √((4-(-2))² + (1-(-4))²) = √(85)
|RS| = √((2-4)²+ (7-1)²) = √(40)
|ST| = √(((-4)-2)² + (1-7)²) = √(72)
|Q'R'| = √(((-4)-(-8))²+ ((-1)-(-7))²) = √(80)
|R'S'| = √(((-8)-(-2))² + ((-7)-1)²) = √(170)
|S'T'| = √(((-2)-(-4))² + (1-7)²) = √(20)
Therefore, we have:
√(85) /√(80) = √(40) / √(170) =√(72) / √(20) = k
Simplifying, we get:
k = √(85/80) = √(17/16) = 1.0625
Thus, the scale factor for the dilation is 1.0625.
Note: It's important to keep track of the order of the vertices when calculating the lengths of the sides. In this case, we assumed that the vertices were listed in clockwise order around the quadrilateral.
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Triangle ABC is rotated 90° counterclockwise about the origin to produce triangle A'B'C'. Then, triangle A'B'C' is dilated by a scale factor of 1/2 with respect to the origin to produce A''B''C''.
Write coordinates of each vertex in the final image.
A"
B"
C"
Answer:
Step-by-step explanation:
Help with this question
The answers are:
a). The required monthly percentage rate of APR of 19% is 1.59%.
b). The Monthly percentage rate is 2.08%
c). Oscar pays $0.96 more than Felix.
What was his monthly percentage rate?a). Felix received a card with an APR of 19%; it is unknown what his monthly percentage rate was.
APR = 19%
Given that APR is increased monthly throughout the year,
Monthly rate = 19% / number of months in year
Monthly rate = 19% / 12
Monthly rate = 1.59%
Therefore, 1.59% is the minimum monthly percentage rate for an APR of 19%.
b) Oscar received a credit card with a 21% APR.
Monthly percentage rate = 21%/12 = 1.75%
c). We are informed that for a particular month, each of them had an average daily amount of $800.
Thus;
Felix's payments in full = 800 * 1.63%
Felix's payments in full = $13.04
Amount Oscar issued = 800 * 1.75%
Amount Oscar issued = $14
Variation in Payments = $14 - $13.04 = $0.96
Thus, Oscar pays $0.96 more than Felix.
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22 is what percent of 48?
Rouns to the nearest hundredth if necessary.
%218.18
first you add then subtract do the math work coordinate planes and such graphing math problems
The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.
The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.
Approximately 841 men weigh more than 165 pounds, and 841 men weigh less than 135 pounds. This is due to the fact that the area under the normal curve between the z-scores of -1 and 1 is 0.8413, or 84.13%.
what is standard deviations ?Standard deviation is a measure of how spread out a set of data is. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Standard deviation can be used to measure the variability of a set of data points or to compare different sets of data. It is a useful tool for understanding how a set of data is distributed, as it gives an indication of how much of the data is close to the mean and how much is far away from it.
To calculate these values, we can use the z-score formula to calculate the standard deviation from the mean weight. The z-score formula is z = (x - μ)/σ, where x is a data point, μ is the mean, and σ is the standard deviation. Thus, for men weighing more than 165 pounds, z = (165 - 150)/15 = 1, and for men weighing less than 135 pounds, z = (135 - 150)/15 = -1.
We can then use the z-score to calculate the probability of finding a man with a weight less than or equal to 165 pounds and greater than or equal to 135 pounds. This probability is equal to the area under the normal curve between the z-scores of -1 and 1. From a normal table, we can find that the area under the normal curve between -1 and 1 is 0.8413, which is equal to 84.13%.
Therefore, the number of men weighing more than 165 pounds is equal to 0.8413 * 1,000, which is approximately 841 men, and the number of men weighing less than 135 pounds is equal to 0.8413 * 1,000, which is also approximately 841 men.
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Complete questions as follows-
The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.
From the data, we can conclude that the number of men weighing more than 165 pounds is about , and the number of men weighing less than 135 pounds is about .
sphere a has radius 2 cm. sphere b has radius 4 cm what is there volumes
The volume of sphere a is 32π/3 cubic cm, and the volume of sphere b is 256π/3 cubic cm.
What is volume of sphere?
The volume of a sphere is given by the formula:
V = (4/3)πr³
where r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159.
The volume of a sphere can be calculated using the formula:
V = (4/3)π[tex]r^3[/tex]
where r is the radius of the sphere and π is the mathematical constant pi.
Using this formula, we can find the volumes of spheres a and b as follows:
Volume of sphere a:
V = (4/3)π([tex]2^3[/tex]) = (4/3)π(8) = 32π/3 cubic cm
Volume of sphere b:
V = (4/3)π([tex]4^3[/tex]) = (4/3)π(64) = 256π/3 cubic cm
Therefore, the volume of sphere a is 32π/3 cubic cm, and the volume of sphere b is 256π/3 cubic cm.
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In the following image, AB is parallel to DC, and BC is a transversal intersecting both parallel lines. The measure of angle ABC is 118°, and the measure of DAB is 132
The measure of angle BCD is 62 degrees.
When a transversal intersects two parallel lines, alternate interior angles are congruent.
This is given by the Alternate Interior Angles Theorem. Likewise, when two parallel lines are cut by a transversal, consecutive interior angles add up to 180 degrees.
This is given by the Consecutive Interior Angles Theorem.
In the following image, AB is parallel to DC, and BC is a transversal intersecting both parallel lines.
The measure of angle ABC is 118°, and the measure of DAB is 132.
Given that AB is parallel to DC, and BC is a transversal intersecting both parallel lines.
The measure of angle ABC is 118°, and the measure of DAB is 132.
We need to find the measure of angle BCD.
By the Consecutive Interior Angles Theorem, we know that angle BCD + angle ABC = 180 degrees
Therefore, angle BCD = 180 - angle ABC angle BCD = 180 - 118angle BCD = 62 degrees
Therefore, the measure of angle BCD is 62 degrees.
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There are 28 students whose last names begin with the letters G, H, J, or K. Information about the probability of randomly selecting one of these students is listed below • probability of selecting a student whose last name begins with G: 7 • probability of selecting a student whose last name begins with G or H: 5 14 O How many of these students have a last name that begins with H?
A4
B5
C6
D7
5
We know that there are 28 students in total, so:
G + H + J + K = 28
We also know the following probabilities:
P(G) = 7/28
P(G or H) = 5/14
The probability of selecting a student whose last name begins with G or H can be expressed as:
P(G or H) = P(G) + P(H) - P(G and H)
Since the events "selecting a student whose last name begins with G" and "selecting a student whose last name begins with H" are mutually exclusive (a student cannot have a last name that begins with both G and H), P(G and H) = 0. Therefore, we have:
5/14 = 7/28 + P(H)
Simplifying the equation, we get:
P(H) = 5/14 - 7/28 = 5/28
So the probability of selecting a student whose last name begins with H is 5/28. To find the number of students whose last name begins with H, we can multiply this probability by the total number of students:
H = P(H) x 28 = 5/28 x 28 = 5
Therefore, there are 5 students whose last name begins with H.
*IG: whis.sama_ent*
Find the missing angles in these diagrams. All shapes a regular (ignore my pen marks)
(Image attached)
The missing angle in the triangle is 70 degrees.
The missing angle in the quadrilateral is 120 degrees.
For the first diagram, since all the sides of the hexagon are equal, all the interior angles must also be equal. Therefore, each angle measures 120 degrees.
For the second diagram, we can start by finding the missing angle in the triangle.
Since the sum of the angles in a triangle is 180 degrees,
we can subtract the known angles from 180 to find the missing angle:
180 - 60 - 50 = 70
To find the missing angle in the quadrilateral, we can start by noticing that opposite angles in a parallelogram are equal.
Therefore, we can use the fact that the angle marked 60 degrees is opposite the missing angle:
Missing angle = 180 - 60 = 120
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A freezer is at -14°C and then it is unplugged. It gets warmer by 3°C an hour. It is checked once an hour and when it gets above 0 °C, it is plugged back in. After it is plugged in again, it gets colder by 4°C per hour.
Copy and complete the table to show the sequence of temperatures for the first 8 hours after it was unplugged.
What is the temperature of the freezer (in °C) 8 hours after it was unplugged?
After 8 hours, the freezer is at a temperature of 8°C.The temperature sequence for the first 8 hours after the freezer was unplugged is as follows:
Time (hours) Temperature (°C)
0 -14
1 -11
2 -8
3 -5
4 -2
5 1
6 0
7 4
8 8
Temperature is a physical quantity that expresses the degree of hotness or coldness of an object or a living being.
The direction in which heat energy will spontaneously flow from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature) is indicated by temperature, and it is expressed in terms of any of several arbitrary scales
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The depth, d
, of a lake is 73 m, truncated to an integer.
Write the error interval for d
in the form a
≤ d
< b
.
The error interval for the depth of the lake would be:
72.5 m ≤ d < 73.5 m
Since the depth of the lake is given as 73 m, truncated to an integer, the actual depth could be anywhere between 72.5 m and 73.5 m. This is because if the depth is between 72.5 m and 73 m, it would be rounded down to 73 m, and if it is between 73 m and 73.5 m, it would be rounded up to 73 m.
This error interval takes into account the rounding that occurred when the depth was truncated to an integer and gives a range of possible depths that the lake could be within.
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Can you Solve these Problems ASAP
Find the set of solutions for each of the following absolute value inequalities
The set of solutions for each of the inequalities are given by:
(b) - 4.8 < m < 6.4
(e) x [tex]\geq[/tex] 5
(g) - 11.6 < z < 14
(h) either k < -19/3 or k > 7
Solving the given absolute value inequalities we get,
(b) The given inequality,
|2 - 5m/2| < 14
- 14 < 2 - 5m/2 < 14
-14 - 2 < -5m/2 < 14 - 2
-16 < -5m/2 < 12
-12 < 5m/2 < 16
-12*2 < 5m < 16*2
-24/5 < m < 32/5
- 4.8 < m < 6.4
(e) The given inequality,
2> - |(x-8)/5 + 3/5|
|(x-8)/5 + 3/5| > -2
|(x-8)/5 + 3/5| [tex]\geq[/tex] 0 [Since absolute value is always positive or zero]
(x-8)/5 + 3/5 [tex]\geq[/tex] 0
(x-8+3)/5 [tex]\geq[/tex] 0
x - 5 [tex]\geq[/tex] 0
x [tex]\geq[/tex] 5
(g) The given inequality,
|(5z - 6)/8| < 8
-8 < (5z - 6)/8 < 8
-64 < 5z - 6 < 64
-64 + 6 < 5z < 64 + 6
-58 < 5z < 70
-58/5 < z < 70/5
-58/5 < z < 14
- 11.6 < z < 14
(h) The given inequality,
|(3k - 1)/4| > 5
either, (3k - 1)/4 < -5
3k - 1 < -20
3k < -19
k < -19/3
or, (3k - 1)/4 > 5
3k - 1 > 20
3k > 20 + 1 = 21
k > 21/3
k > 7
Hence the solution sets are:
(b) - 4.8 < m < 6.4
(e) x [tex]\geq[/tex] 5
(g) - 11.6 < z < 14
(h) either k < -19/3 or k > 7
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Two parallel lines are graphed on a coordinate plane as shown. The lines are rotated about the origin. The graph of the image of the lines after the rotation is also shown.
Which conclusion is supported by the image of the lines?
The conclusion supported by the image of the lines is that when two parallel lines are rotated about the origin, they remain parallel to each other.
1. Observe the initial graph with two parallel lines.
2. Rotate the lines about the origin by the given angle.
3. Observe the image of the lines after the rotation.
4. Notice that the lines still maintain the same distance apart and do not intersect, meaning they are still parallel to each other.
If two lines do not intersect, they are said to be parallel.
The lines' slopes are identical. If m1=m2, then f(x) =m1x + b1 and
g(x)= m2x + b2 are parallel.
If m 1 = m 2, then f (x) = m 1 x + b 1 and g (x) = m 2 x + b 2 are parallel equations.
The coordinate axes are rotated about the origin (0,0) in counter clockwise direction through an angle of 60∘ .
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Which equation represents the graph of y = x² + 2x - 3 moved 3 units to the left?
A. y = x² + 2x - 6
B. y = (x+3)² + 2x - 3
C. y = (x + 3)² + 2(x+3)
D. y = (x+3)² + 2(x+3)-3
Equation A
Equation B
Equation C
Equation D
The equation that represents the graph of y = x² + 2x - 3 moved 3 units to the left is: D. y = (x+3)² + 2(x+3)-3
What is graph equation?
To move a function 3 units to the left, we need to replace x with (x + 3) in the equation. This is because, if we plug in x + 3 into the equation, we will get the same value as if we had plugged in x but moved 3 units to the left.
So, starting with the original equation y = x² + 2x - 3, we replace x with (x + 3):
y = (x + 3)² + 2(x + 3) - 3
Now, we can simplify this equation to get it into standard form:
y = x² + 8x + 18
Therefore, the equation that represents the graph of y = x² + 2x - 3 moved 3 units to the left is:
D. y = (x+3)² + 2(x+3)-3
which simplifies to:
y = x² + 8x + 18.
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Valley Bank has four tellers. It takes a teller 8 minutes to serve one customer. What is the capacity of the bank in customers per hour? A. 15 B. 10 C. 8 D. 30
Since there are four tellers, the capacity of the bank in customers per hour = 4 x 7.5 = 30.
What is the capacity of the bank in customers per hour?Valley Bank has four tellers. It takes a teller 8 minutes to serve one customer.
The correct option is D. 30.
We are given that
Valley Bank has four tellers. It takes a teller 8 minutes to serve one customer.
To calculate the capacity of the bank in customers per hour, we need to find how many customers each teller can serve in an hour. To do this, we first need to convert the time taken to serve one customer from minutes to hours.
1 minute = 1/60 hoursSo, time taken to serve one customer
= 8 minutes
= 8/60 hours
= 2/15 hours
One teller can serve one customer in 2/15 hours.In one hour, the number of customers one teller can serve = 1/(2/15) = 15/2 = 7.5 (customers/hour)
Therefore, the capacity of one teller in customers per hour is 7.5.
Now, we need to find the capacity of the bank in customers per hour. Since there are four tellers, the capacity of the bank in customers per hour = 4 x 7.5 = 30.
So, the correct option is D. 30.
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