The equatiοn fοr H, the number οf times Nοah’s beats in m minutes is H = k * m
What is the equivalent expressiοn?Expressiοns that perfοrm the same functiοn regardless οf appearance are said tο be equivalent. If twο algebraic expressiοns are equivalent, then they have the same value when the same variable value is used.
Assuming yοu meant "Nοah's heart beats", the equatiοn fοr H, the number οf times Nοah's heart beats in m minutes can be given by:
H = k * m
where k is a cοnstant that represents the number οf heartbeats per minute.
The value οf k may vary depending οn the individual and their physical cοnditiοn.
Hence, the equatiοn fοr H, the number οf times Nοah’s beats in m minutes
is H = k * m
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Complete Question;
A persons resting heart rate is typically between 60 and 100 beats per minute. Nοah looks at his watch, and counts 8 heartbeats in 10 seconds.
Is his heart rate typical? Explain how you know.
Write an equation for h, the number of times Noahs heart beats (at this rate) in m minutes.
convert to slope intercept (y=mx+b)
Four high jumpers listed their highest jump in the chart.
Which person jumped the highest?
anna: 2.1 yards
javier 72 inches
charles 5 feet 11 inches
yelena 74 inches
Responses?
Based on the given information, Yelena jumped the highest with a jump of 74 inches (6.17 feet).
What is measurement?Measurement is the process of assigning a numerical value to a physical quantity, such as length, mass, time, temperature, or volume. It is a fundamental aspect of science, engineering, and everyday life. In order to measure something, we need a unit of measurement, which is a standard reference quantity that is used to express the measurement. For example, meters or feet are commonly used units for length, while grams or pounds are used for mass.
To compare the high jumps of the four athletes, we need to convert all the measurements to the same unit.
Anna: 2.1 yards = 6.3 feet
Javier: 72 inches = 6 feet
Charles: 5 feet 11 inches = 71 inches = 5.92 feet
Yelena: 74 inches = 6.17 feet
So, Yelena jumped the highest with a jump of 74 inches (6.17 feet).
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Choose the list that shows the investment with the least risk to the one with the highest risk.
A. Mutual Funds, Savings Bonds, Stock Market
B. Savings Bonds, Mutual Funds, Stock Market
C. Savings Bonds, Stock Market, Mutual Funds
D. Stock Market, Mutual Funds, Savings Bonds
The best choice is B. Saving Bonds, Stock Market, Mutual
Why do you use the word "investment"?Investments are defined as assets bought or invested in with the goal of increasing wealth and setting aside funds from salary or capital gains. The main goal of an investment is to generate extra income or to make money on an investment over a certain amount of time.
Generally speaking, the following is the order of investments from the lowest risk to the greatest risk:
Bonds for savings, mutual funds, and the stock market
As a result, list B is the one that runs from investment with the lowest risk to investment with the greatest risk. Stock market, mutual funds, and savings bonds.
The sequence of mutual fund investments, Savings Bonds, and Stock Market in Option A is not in decreasing order of danger.
Savings Bonds, the stock market, and mutual funds are listed in Option C's order, and this is also not from lowest to greatest risk.
Stock markets, mutual funds, and savings bonds are listed in Option D's order of greatest to lowest risk.
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please help !!
Determine the length of side FE
18
20
21
26
the length of EF is 11 units.
How to solve similar triangles?
Since triangles DEF and GHF are both right triangles, we can use the Pythagorean theorem to find the length of EF.
Let's first find the lengths of DE and EF.
DE = DF + FE = 13 + x, where x is the length of FE.
GF = DE - DG = (13 + x) - 4 = 9 + x.
GH = 4.
Now, using the Pythagorean theorem in triangle GHF, we have:
GH² + HF² = GF²
4²+ HF² = (9 + x)²
16 + HF² = 81 + 18x + x²
And in triangle DEF, we have:
DE²+ EF² = DF²
(13 + x)² + EF² = 13²
169 + 26x + x²+ EF² = 169
Simplifying the above equation, we get:
EF²= -26x - x²
Substituting this into the equation we got from the GHF triangle, we have:
16 + HF² = 81 + 18x + x² - EF²
16 + HF² = 81 + 18x + x²+ 26x + x²
HF² = 97 + 44x + 2x²
Now, using the fact that HE + EF = HF, we have:
8 + x = √(97 + 44x + 2x²)
Squaring both sides and simplifying, we get:
4x² + 16x - 225 = 0
Solving this quadratic equation, we get:
x = (-16 ± √(16² - 44(-225)))/(2*4) = (-16 ± 34)/8
Since x has to be positive, we take the positive solution:
x = 3
Therefore, EF = HE + FE = 8 + 3 = 11.
So the length of EF is 11 units.
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find the minors of the matrix A 1*3
Answer:
A 1x3 matrix only has one entry, so there is only one minor, which is the determinant of the matrix itself.
For example, if A = [a, b, c], then the minor of A is simply:
|A| = det(A) = a
Since the determinant of a 1x1 matrix is just its single entry.
Step-by-step explanation:
What is the solution to the equation below?
√x-1=x-13
OA. 14
OB. 15
O C. 17
D. 16
The solution for the equation √(x-1) = x - 13 is x = 17, the correct option is C.
How to solve this equation?We have the following equation.
√(x-1) = x - 13
If we apply the square exponent in both sides, we will get:
x - 1 = (x - 13)²
x - 1 = x² - 26x + 169
x² - 27x + 170 = 0
Using the quadratic formula we get:
[tex]x = \frac{27 pm \sqrt{(-27)^2 - 4*170*1} }{2} \\\\x = \frac{27 pm 7}{2}[/tex]
We only care for the positive solution, which is:
x = (27 + 7)/2 = 17
The correct option is C.
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The solution to the given equation is 14 by squaring both sides of the equation and simplifying. Therefore, the solution to the equation is option A.
Explanation:To solve the equation √x-1=x-13, we first square both sides to eliminate the square root.
That results in the equation x - 2*x +1 = x - 13. Simplify this to get -x + 14 = 0. Further simplifying, x = 14 is the solution. Therefore, the solution to the equation is 14 (option A).
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(2x^3 -3x^2 +4x -1) /(x+2)
Quotient ➔ 2x² - 7x + 18
Remainder ➔ - 37
━━━━━━━━━━━━━━━━━━━━━━
SolutioN ::
ㅤ
➸ Attachment[tex]\begin{gathered} \\ \\ \qquad{\rule{120pt}{7pt}} \\ \\ \end{gathered}[/tex]
VerificatioN ::
ㅤ
➸ Taking the product of Divisor and Quotient as LHS[tex]\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf {x(2x^{2} - 7x + 18) + 2(2x^{2} - 7x + 18) + ( - 37)} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^{3} - 7x^{2} + 18x + 4x^{2} - 14x + 36 - 37} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^{3} - 7x^{2} + 4x^{2} + 18x - 14x - 1} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf \pink{2x^{3} - 3x^{2} + 4x - 1} \\ \\ \end{gathered}[/tex]
➸ Taking Dividend as RHS[tex]\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf \pink{2x^{3} - 3x^{2} + 4x - 1} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {LHS = RHS} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \underline{\boxed{\sf{Verified}}} \; \pmb{\red{\bigstar}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ {\underline{\rule{150pt}{10pt}}} \end{gathered}[/tex]
[tex]\blue{\huge {\mathrm{DIVIDING \; POLYNOMIALS}}}[/tex]
[tex]\\[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]
[tex]\sf \dfrac{(2x^3 -3x^2 +4x -1)}{(x+2)}[/tex][tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
Through the computations performed, we came to the conclusion that the quotient is [tex]\blue{\bold{2x^2 - 7x + 18}}[/tex] and the remainder is [tex]\red{\bold{-37}}[/tex].[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]
[tex]\qquad\begin{aligned}\sf \blue{2x^2 - 7x + 18} \:\:\:\:\:\:\:\:\:\: &\\\sf x + 2 \: \: ) \overline{2x^3 - 3x^2+4x-1} \quad&\\\sf \: \: \underline{ - 2x^3 - 4x^2 \qquad\qquad \: \: \: \: } \\\sf - 7x^2 + 4x \qquad \: \: \: \\\sf \:\:\: \underline{ - 7x^2 + 14x \qquad \: } \\ \sf 18x - 1 \: \: \: \\ \underline{ \sf{ - 18x - 36 \: }} \\ \sf \red{ - 37} \end{aligned}[/tex]
[tex]{===========================================}[/tex]
[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]
Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 4 , −3 is the only other zero, leading coefficient is 2 .
The pοlynοmial functiοn with a fifth degree, 2 as a zerο οf multiplicity 4, −3 as the οnly οther zerο, and a leading cοefficient οf 2 is:
[tex]f(x) = 2(x-2)^4(x+3) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080[/tex]
What is Polynomial Function?
A pοlynοmial functiοn is a mathematical functiοn οf the fοrm [tex]f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0[/tex], where the coefficients[tex]a_n, a_{n-1}, ..., a_1, a_0[/tex] are constants, x is the variable, and n is a non-negative integer. It is a functiοn that can be graphed as a smοοth curve with nο breaks οr jumps.
If 2 is a zerο οf multiplicity 4, then the pοlynοmial functiοn must have the factοr[tex](x-2)^4[/tex].
If −3 is the οnly οther zerο, then the pοlynοmial functiοn must alsο have the factοr (x+3).
The pοlynοmial functiοn with these properties and a leading cοefficient οf 2 can be written as:
[tex]f(x) = 2(x-2)^4(x+3)[/tex]
Expanding this polynomial gives:
[tex]f(x) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080[/tex]
Therefore, the polynomial function with a fifth-degree, 2 as a zero of multiplicity 4, −3 as the only other zero, and a leading coefficient of 2 is:
[tex]f(x) = 2(x-2)^4(x+3) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080[/tex]
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The sum of a number times 10 and 20 is at most -19.
The solution to the problem is that the number "x" must be less than or equal to -3.9 in order for the sum of "a number times 10 and 20" to be at most -19.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.
Let's use algebra to solve this problem.
Let's call the number we're trying to find "x".
The sum of "a number times 10 and 20" can be written as "10x + 20".
So, we can translate the statement "the sum of a number times 10 and 20 is at most -19" into an equation:
10x + 20 ≤ -19
Now we can solve for x:
10x + 20 ≤ -19
Subtract 20 from both sides:
10x ≤ -39
Divide both sides by 10:
x ≤ -3.9
Therefore, the solution to the problem is that the number "x" must be less than or equal to -3.9 in order for the sum of "a number times 10 and 20" to be at most -19.
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Ron and Jim are making sandwiches for a party. Ron make 2 times as many sandwiches as Jim. Together they make a total of 42 sandwiches.
14 because 14+28=42.
A point at (-5,7) is reflected across the x-axis. The new point is then reflected across the y-axis. What ordered pair names the third point?explain.
Answer:
Step-by-step explanation:
Reflecting a point across the x-axis negates the y-coordinate, so the point (-5, 7) reflected across the x-axis becomes (-5, -7).
Reflecting a point across the y-axis negates the x-coordinate, so the point (-5, -7) reflected across the y-axis becomes (5, -7).
Therefore, the third point is (5, -7).
a
3. Woody and Buzz each bought a pink bear for
$50.
• Woody sold his bear for 10% more than the
original price.
• Buzz sold his bear for 30% more than the original
price.
Enter how much more money, in dollars, Buzz
earned for his pink bear than Woody received for his
bear.
Buzz earned $65 - $55 = $10 more than Woody for his pink bear.
How to calculate earnings?
Woody sold his bear for $50 + 10% of $50 = $55.
Buzz sold his bear for $50 + 30% of $50 = $65.
Therefore, Buzz earned $65 - $55 = $10 more than Woody for his pink bear.
To determine how much more money Buzz earned than Woody for their pink bears, we first needed to calculate the selling price for each of them.
We know that both of them bought their bears for $50. Woody sold his bear for 10% more, which means his selling price was $50 + 10% of $50 = $55. Buzz sold his bear for 30% more, which means his selling price was $50 + 30% of $50 = $65. Therefore, Buzz earned $65 - $55 = $10 more than Woody for his pink bear.
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Matt is 3 times as old as his brother Nick. Oscar is 5 years younger than
Nick.
Write an expression in simplest form that represents the sum (+) of their
ages.
Answer:
(4x - 5) years old
Step-by-step explanation:
Nick = x years old
Matt = (3 x X)
=3x years old
Oscar = (x - 5) years old
total age = x + 3x + (x - 5)
= (4x - 5) years old
A company makes steel rods shaped like cylinders. Each rod has a diameter of 6 centimeters and a height of 20 centimeters. If the company used 30520.8cm3 of steel, how many rods did it make?
As a result, the company produced number of rods are **56** rods.
What exactly is radius?
A radius is a section of a straight line in geometry that connects a circle's or sphere's center to its edge or surface Its length is divided by the circle's diameter by two.
Each rod has a diameter of 6 centimeters, hence the radius is 3 centimeters. Each rod has a 20-centimeter height.
The following formula can be used to determine a cylinder's volume:
V = πr²h
where V stands for volume, r for radius, which is equal to half of the diameter, and h for height.
Adding these values to the formula yields the following results:
V = π(3)²(20) (20)
V = 180π
The volume of each rod is therefore 180 cubic centimeters.
30520.8 cubic centimeters of steel were used to make how many rods?
To find out,
divide the total volume of steel by the volume of each rod:
30520.8 / (180π) ≈ **56** rods
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The length of o a rectangle is 12 cm and its width is 2 cm less than ¾ of its length
Draw an illustration pls
Answer:
Certainly, here's an illustration:
----------------------
| |
2cm | |
| | 12cm
| |
----------------------
<---- ¾ of 12cm --->
(9cm - 2cm)
= 7cm
In this illustration, the rectangle is represented by a box with a length of 12cm and a width of 7cm. The width is calculated by taking ¾ of the length (which is 9cm) and subtracting 2cm from it. The dimensions of the rectangle are shown inside the box, with the length indicated by the vertical line and the width indicated by the horizontal line.
A company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 7m and a diameter of 8m. The container will be made from steel (including its top and bottom). If the steel costs 29$ for each square meter, how much will the steel cost in total? Use 3.14 for pi, and do not round your answer.
Step-by-step explanation:
Two ends' area = 2 * pi r^2 r is radius = 1/2 diameter = 4m
2 * 3.14 * (4^2) = 100.48 m^2
Sidewall is cicumfernce ( = pi *d) times the height ( =7m)
3.14 * 8 *7=175.84 m^2
Cost = (100.48 +175.84) m^2 * $ 29 /m^2 = $ 8013.28
Roy has decided to visit the new ice cream shop around the corner. When he goes in, he sees 14 big buckets full of ice cream behind the counter, each containing a different flavor. There are 5 flavors that contain chocolate.
If he closes his eyes and picks out a bucket at random, what is the probability that the flavor he picks will contain chocolate?
A. 2/7
B. 5/14
C. 4/19
D. 3/7
The correct option is B. 5/14, which is equivalent to approximately 0.357 or 35.7%
The probability of selecting a chocolate ice cream bucket is calculated by dividing the number of chocolate ice cream buckets by the total number of buckets:
P(chocolate) = number of chocolate ice cream buckets / total number of buckets
P(chocolate) = 5 / 14
P(chocolate) = 0.35714285714285715
To simplify the fraction, we can express it as a decimal or a percentage:
P(chocolate) ≈ 0.357 or P(chocolate) ≈ 35.7%
Therefore, the probability of selecting a chocolate ice cream bucket is approximately 0.357 or 35.7%. The probability of selecting a chocolate ice cream bucket can be calculated by dividing the number of chocolate ice cream buckets by the total number of buckets. The number of chocolate ice cream buckets is 5, and the total number of buckets is 14. Therefore, the probability of selecting a chocolate ice cream bucket is: 5/14
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60% of the students in a class are boys. If there are 16 girls in the class, how many boys are there
Answer: Let the total number of students in the class be x.
Then the number of boys in the class is 60% of x, or 0.6x.
And the number of girls in the class is 16.
We can write an equation based on the information given:
0.6x + 16 = x
Solving for x:
0.4x = 16
x = 40
Therefore, there are 0.6x = 24 boys in the class.
Step-by-step explanation:
Two functions g and f are defined in the figure below.
The domain of fog is: Domain of fog = {x ∈ R | 3 ≤ g(x) ≤ 9}
The range of fog is: Range of fog = {1, 2, 5}
What is domain and range?The domain of a function is the set of all possible input values (usually denoted by x) for which the function is defined.
The range of a function is the set of all possible output values (usually denoted by y) that the function can produce for its corresponding inputs in the domain.
(a) Domain of fog:
The domain of fog is the set of all inputs for which the composition is defined. Since g is defined for all values in its domain, and f is defined for all values in the range of g, the domain of fog is the set of all values in the domain of g for which g(x) is in the domain of f.
(b) Range of fog:
The range of fog is the set of all possible outputs of the composition. Since g is defined for all values in its domain, and f is defined for all values in the range of g, the range of fog is the set of all possible outputs of f when its input is an output of g.
Range of fog = {f(g(x)) | x ∈ R, 3 ≤ g(x) ≤ 9}
To determine the values in the range of fog, we need to evaluate f(g(x)) for each x in the domain of fog. We can do this by first determining the outputs of g for each value in its domain, and then evaluating f at those outputs.
The outputs of g for x = 4, 5, 7 are:
g(4) = 6
g(5) = 8
g(7) = 9
Since f is defined for all values in the range of g, we can evaluate f at each of these outputs to get:
f(g(4)) = f(6) = 5
f(g(5)) = f(8) = 2
f(g(7)) = f(9) = 1
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On your graph paper, plot points A(-5, -2), B(-3, -2), and D(-5, -4). Mark point C to make a square in the third quadrant. Name the coordinate rule that will rotate the rectangle to the fourth quadrant, with vertex C’ at point (4, -3).
After plotting the points A (-5, -2), B (-3, -2), and D (-5, -4) in the 4th quadrant as shown in the attached graph, we can see that to make the square we have to plot point C, at (-3, -4).
Define graphs?Simply said, the graph is a structured representation of the data. Because of this, it is simpler for us to understand the facts. Data is the term used to describe the numerical information obtained through observation.
The word data is derived from the Latin word datum, which meaning "something delivered."
After developing a research question, data are progressively obtained through observation. The information is then organised, categorised, and visually shown.
Here in the question,
After plotting the points A (-5, -2), B (-3, -2), and D (-5, -4) in the 4th quadrant as shown in the attached graph, we can see that to make the square we have to plot point C, at (-3, -4).
And the coordinate rule that will rotate the rectangle to the fourth quadrant, with vertex C’ at point (4, -3) is known as reflection.
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Solve the problems.
The number a is less than the number b by (1)/(5) of b. By what part of a is b greater than a ?
Answer:
B is greater than A by 1/4 of A
Step-by-step explanation:
Let's use the information given in the problem to write expressions for the values of a and b:
a = b - (1/5)b = (4/5)b
b is greater than a by the difference:
b - a = b - (4/5)b = (1/5)b
To express this difference as a fraction of a, we divide by a:
(b - a)/a = ((1/5)b)/((4/5)b) = 1/4
Therefore, b is greater than a by 1/4 of a.
pls help asap!
A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters.
What is the surface area of the prism?
five hundred fifty and one-fourth cm2
four hundred twelve and three-fourths cm2
two hundred seventy-five and one-eighth cm2
one hundred thirty-seven and nine-sixteenths cm2
The surface area of the prism from the net is 260.5 cm².
Calculating the surface areaThe rectangular prism has dimensions of length, width, and height given by 5 and three-fourths cm, 4 cm, and 11 and three-fourths cm respectively.
To find the surface area of the prism, we need to find the area of each of its six faces and then add them up.
So, we have
Area = 2 * (5 3/4 * 4 + 5 3/4 * 11 + 4 * 11)
Evaluate
Area = 260.5
Therefore, the surface area of the prism is 260.5 cm².
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I’m stuck I need you to do it
Answer: The length of the prism is 8 yards
Step-by-step explanation:
First, take the volume of the prism, divide it by the width (2 1/2). Once you get that divide that answer by height (5 3/4) getting you the length of the prism (8 yards)
Find the lower quartile and upper quartile of the data set.
lower quartile: 13
upper quartile: 27
About ?
minutes
Complete the statement about the data set.
About ?
minutes
of students ride the bus for less than 13 minutes.
of students ride the bus for less than 27 minutes.
help pls
About 25% of students ride the bus for less than 13 minutes.
About 75% of students ride the bus for less than 27 minutes.
What is median?Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.
In this case, the median is 21 minutes. This means that half of the students ride the bus for less than 21 minutes and half of the students ride the bus for more than 21 minutes.
The lower quartile (Q1) is the value that separates the lowest 25% of the data from the other 75%. In this case, the lower quartile is 13 minutes. This means that 25% of the students ride the bus for less than 13 minutes and 75% ride the bus for more than 13 minutes.
The upper quartile (Q3) is the value that separates the highest 25% of the data from the other 75%. In this case, the upper quartile is 27 minutes. This means that 75% of the students ride the bus for less than 27 minutes and 25% ride the bus for more than 27 minutes.
So, to answer the statement about the data set:
About 25% of students ride the bus for less than 13 minutes. (this is because the lower quartile separates the lowest 25% of the data from the other 75%)
About 75% of students ride the bus for less than 27 minutes. (this is because the upper quartile separates the highest 25% of the data from the other 75%)
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Help with math problems
(D) |k - 7| < - 6 has no solution is not a true statement because an absolute value can never be negative, so the inequality has no solution.
What is inequality?Inequality refers to the state of being unequal or not equal in some respect. It can refer to various forms of disparities or differences, such as differences in income, wealth, education, opportunities, health, or social status, among others. Inequality can occur between individuals, groups, communities, or nations, and it can be caused by various factors, such as discrimination, historical legacies, social structures, policies, or economic systems. Inequality is often considered a social problem because it can lead to social tension, unrest, and injustice, as well as undermine economic growth and human development.
(D) |k - 7| < - 6 has no solution is not a true statement because an absolute value can never be negative, so the inequality has no solution.
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Suppose that a cliff diver's height (in feet) after t seconds is given by the model
H(t)=-16t^2+32t+20 find the height after 1.25 seconds pls help me
The height of the cliff diver after 1.25 seconds is 35 feet.
Calculating Height :
The concept used is evaluating a function at a given input or value. In this case, we are evaluating the height function H(t) at t = 1.25 to find the height of the cliff diver after 1.25 seconds. The formula for the height function is given as H(t) = -16t^2 + 32t + 20.
Here we have
A cliff diver's height (in feet) after t seconds is given by the model
H(t)=-16t² +32t +20
Given time t = 1.25 seconds
To find the height after 1.25 seconds, we simply need to evaluate H(1.25) using the given formula:
H(1.25) = -16(1.25)² + 32(1.25) + 20
On Simplifying the expression we get:
H(1.25) = -16(1.5625) + 40 + 20
H(1.25) = -25 + 60
H(1.25) = 35
Therefore,
The height of the cliff diver after 1.25 seconds is 35 feet.
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A soccer team is planning to sell candy bars to spectators at their games. They will buy two-pound bags of candy. The number of candy bars per bag has mean 12 and standard deviation 2. They will sell each candy bar for $1.25. (Assume that all of the candy in a bag will be sold.)
1. What is the expected value and the standard deviation for the amount of money that would be made selling all of the candy in one bag of candy?
The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.
What exactly is a standard deviation?The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.
The expected value for the amount of money made selling all of the candy in one bag can be found by;
Expected value = mean number of candy bars per bag x price per candy bar
Expected value = 12 x $1.25 = $15
Formula for the standard deviation of a product of random variables:
[tex]SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}[/tex]
where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.
X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:
E(Y²) = $1.25² = $1.5625
E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148
Cov (X,Y) = 0 (because X and Y are independent)
Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:
[tex]SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))[/tex]
SD = √(592)
SD ≈ $24.33
Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.
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help me please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
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[tex]\sqrt[4]{-81}[/tex]
The fourth root of -81 is not a real number is 3√i.
What is imaginary number?A number that can be represented in the form a + bi is an imaginary number. In this case, a and b are real numbers, while I is the imaginary unit, which is equal to the square root of -1. In mathematics, imaginary numbers are used to expand on the real number system and to describe values that cannot be stated using real numbers.
Complex numbers, which are numbers of the type a + bi, where a and b are real numbers, are one of the principal applications for imaginary numbers. Several mathematical and scientific disciplines, such as electrical engineering, signal processing, and quantum physics, require complex numbers.
The value of -81 can be written as i²(3)⁴.
Taking the fourth root of the number we get 3√.
Hence, the fourth root of -81 is not a real number is 3√i.
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suppose a charity received a donation of 15.2 million. if this represents 56% of the charity's donation funds, what is the total amount of it's donated funds? round answer to nearest million dollars
Answer:
27 million dollars
Step-by-step explanation:
Let x be the total amount of the charity's donated funds. We know that the donation of 15.2 million represents 56% of x.
We can set up the following equation to solve for x:
15.2 million = 0.56x
Dividing both sides by 0.56, we get:
x = 15.2 million / 0.56 = 27.14 million
Therefore, the total amount of the charity's donated funds is approximately 27 million dollars.
Answer:
27 million
Step-by-step explanation:
create the equation
[tex]\frac{15200000}{x} =\frac{56}{100}[/tex], where x is equivalent to the total amount of donation funds
solve the equation by cross multiplying
[tex]x=2714285 \frac{5}{7}[/tex],
this can be simplified to 27 million