Angle B is 50 degrees in measurement.
One method to find the measure of angle b is to use the properties of angles in a triangle. We know that the sum of the angles in a triangle is 180 degrees. We also know that angles a and c have measures of 50 degrees and 80 degrees respectively. Therefore, we can find the measure of angle b by subtracting the sum of angles a and c from 180 degrees:
angle b = 180 degrees - angle a - angle c
angle b = 180 degrees - 50 degrees - 80 degrees
angle b = 50 degrees
Therefore, angle b has a measure of 50 degrees. Another method to find the measure of angle b is to use trigonometry, such as the sine or cosine rule, depending on the given information.
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What is one method to find the measure of angle B?
A. use the Pythagorean theorem to find BC, then solve the equation tan(B)=8/BC
B. because of the 30-60-90 triangle theorem, you know the measure of angle B is 60
C. solve the equation cos(B)=8/89(square rooted)
Mr. Kelly buys a total of 40 boxes of pens and pencils for his class. Each box of
pens costs $5. Each box of pencils costs $2. Mr. Kelly spends a total of $131 on
the pens and pencils.
Which equations form a system of equations that can be used to determine the
number of boxes of pens, x, and the number of boxes of pencils, y, that Mr. Kelly
buys? Select two correct answers.
A. x+y = 40
B. x+y = 131
C. 5x+2y = 40
D. 2x + 5y = 40
E. 5x + 2y = 131
F.2x + 5y = 131
The correct equations that form a system of equations to determine the number of boxes of pens, x, and the number of boxes of pencils, y, that Mr. Kelly buys are:
A. x+y = 40 (since he buys a total of 40 boxes)
E. 5x + 2y = 131 (since he spends a total of $131)
Therefore, the correct answers are A and E.
Mr. And Mrs. White and their son, Herbert, ignore the warnings about the danger of the supernatural. This foreshadowing helps develop the theme
The foreshadowing of Mr. and Mrs. White and Herbert ignoring the warnings about the danger of the supernatural helps to build suspense and create a sense of foreboding, thus helping to establish the theme of the story.
If that is the case, then yes, the White family ignoring the warnings about the danger of the supernatural helps develop the theme of the story. The story explores the consequences of tempting fate and meddling with the unknown, as the family's wishes on the cursed monkey's paw lead to tragic and horrifying outcomes.
The foreshadowing of danger through warnings and ominous hints, such as the Sergeant-Major's tales and the paw's sinister appearance, underscores the gravity of the situation and the potential consequences of the family's actions. However, the White family disregards these warnings and ultimately pays the price for their curiosity and greed.
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According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays. Suppose 190 executives are randomly surveyed.
Appendix A Statistical Tables a. What is the probability that fewer than 85 of the executives believe employees are most productive on Tuesdays? b. What is the probability that more than 95 of the executives believe employees are most productive on Tuesdays? c. What is the probability that more than 79 of the executives believe employees are most productive on Tuesdays?
Therefore , the solution of the given problem of probability comes out to be P = 0.8236 , P= 0.0155 and P = 0.0203
What precisely is probability?The calculation of the probability that a statement is true or that a particular event will happen is the main objective of the patterns in the form known as hyperparameters. Chance can be represented by any number from range 0 and 1, where 1 typically signifies certainty and 0 typically signifies potential. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
Based on the survey findings, let p represent the likelihood that an executive thinks workers are most productive on Tuesdays: p = 0.48
Suppose there were n leaders who were surveyed: n = 190
Using Appendix A and the binomial distribution method, we can calculate:
=> P(X < 85) = P(X ≤ 84) = 0.0155
b. To determine the likelihood that more than 95 of the executives think that workers are most effective on Tuesdays, use Appendix A and the complement rule.
=> P(X > 95) = 1 - P(X ≤ 95) = 1 - 0.9797 = 0.0203
c. We need to compute P(X > 79) to determine the likelihood that more than 79 executives think workers are most productive on Tuesdays. This can be done using the complement rule and Appendix
A:
=> P(X > 79) = 1 - P(X ≤ 79) = 1 - 0.1764 = 0.8236
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If the total surface area of a cube is 302.46 in², which best describes the length of an edge of the cube?
The length of the edge of the cube with the given total surface area is 7.1 inches.
What is total surface area?The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a form with a curved base and surface is equal to the sum of the two areas.
Let us suppose the length of an edge of the cube = l.
The total surface are of the cube is given as:
TSA = 6l²
Substituting TSA = 302.46 we have:
302.46 = 6l²
l² = 50.41
l = 7.1 in.
Hence, the length of the edge of the cube with the given total surface area is 7.1 inches.
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5.8 Khomo and Peter bought a house for R575 000 as an investment. Khomo payed R245 000 and Peter payed the rest. They sold the house 5 years later and made a profit of R234 500.if they share the profit in the same ratio as their respective investments,how much profit will peter recieve
Answer:
133,380
Step-by-step explanation:
Cost of house 575,000
Khomo paid 245,000
Peter paid 575,000 - 245,000 = 330,000
Ratio of Khomo to Peter = 245,000 : 330,000 = 49:66
Profit made = 234,500
Khomos share is 49/ 115 x 234,00 = 0.43 x 234,000 = 100,620
Peters share is 66/115 x 234,000 = =0.57 x 234,000 = 133,380
Surface area of the prism
Answer: 450
Step-by-step explanation:
9x10x5
Rewrite the expression as a product of two factors x²+x-2
we will multiply x by both terms in the parentheses, giving us x²+2x. Then, we will subtract 1 from this expression, leaving us with x²+2x-1. Therefore, the expanded expression is x²+2x-1.
x(x+2) - 1To rewrite the expression x²+x-2 as a product of two factors, we will use algebraic factoring. First, we will factor out the greatest common factor from the expression, which is x. We do this by dividing each term in the expression by x, leaving us with x+2 and -1. The expression can now be written as x(x+2) - 1. This expression is the product of two factors x and (x+2) - 1.
x²+2x-1 To expand the expression x(x+2) - 1, we will use the distributive property. First, we will multiply x by both terms in the parentheses, giving us x²+2x. Then, we will subtract 1 from this expression, leaving us with x²+2x-1. Therefore, the expanded expression is x²+2x-1.
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Find a formula for the exponential function passing through the points (5, 32567 ) and (4, 16
189). Use exact values, not decimals. f(x)=
As a result, the exponential function travelling between the points (5, 32567) and (4, 16189) has the following formula: function [tex]f(x) = 14000 * (1.007044628)^x[/tex]
what is function?Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.
f(x) = a * bx, where a and b are unknown constants. We have two places through which the function passes, which implies we have two equations:
[tex]f(5) = a * b^5 = 32567 f(4) = a * b^4 = 16189[/tex]
When we divide these two equations, we get:
[tex]b^5 / b^4 = 32567 / 16189 b = (32567 / 16189)^(1/1) = 1.007044628[/tex]
We may solve for a by substituting this value of b in any of the equations:
[tex]a = 16189 / b^4 = 16189 / (1.007044628)^4 = 14000[/tex]
As a result, the exponential function travelling between the points (5, 32567) and (4, 16189) has the following formula:
[tex]f(x) = 14000 * (1.007044628)^x[/tex]
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Simplify: 5x2 +7y -6z, 4y + 3x2
, 9x2 +2z2
, 2z2
– 9y, 2y – 2x2
Answer:
Step-by-step explanation:
i don't know
Geometry: Find the unknown lengths of these isosceles right triangles (ASAP!!)
22=4 square root 2
Step-by-step explanation:
Using Pythagorean Theory
A quantity m varies jointly with p and r. When p is 2 and r is 4, m is 1. What is the constant of variation?
One-eighth
One-half
2
8
The constant of variation is [tex]\frac{1}{8}[/tex].
What is variation?The discrepancy among an ideal and real scenario is referred to as the Law of Variation. The most frequent manifestations of variation or variability are changes in the data, anticipated results, or minor changes in the quality of the output.
The types of variation are given below-
Where a variable is a fixed multiple of another, this is known as direct variation. For instance, my income varies directly (or proportionally) with the amount of hours I put in.When one of the variables rises, the other one falls—this is known as inverse and indirect variation (product is constant). For instance, the length of time an air conditioner is operating has an indirect (equal or inverse) impact mostly on temperature in my home.Joint variation occurs when at least two factors are directly associated. For instance, a triangle's base and height are both related to the triangle's area.According to the question;
A quantity m varies jointly with p and r which shows that p and r in joint variation with m.
m ---> pr
m = kpr
where, k is the constant of variation.
m = 1, p = 2, r = 4.
Substitute the values in the relation,
1 = k(2)(4)
1 = 8k
k = 1/8
Therefore, the constant of variation is [tex]\frac{1}{8}[/tex].
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The constant of variation is 1/8, which is option A.
What is variation?
The way in which a quantity changes or varies with respect to another quantity. There are two types of variation: direct variation and inverse variation. Direct variation occurs when two quantities change in the same direction. In other words, if one quantity increases, the other quantity also increases.
y = kx, where y and x are the two quantities, and k is a constant of proportionality.
Inverse variation occurs when two quantities change in opposite directions. In other words, if one quantity increases, the other quantity decreases.
y = k/x, where y and x are the two quantities, and k is a constant of proportionality.
If m varies jointly with p and r, we can write the relationship as:
m = k * p * r
where k is the constant of variation.
We are given that when p is 2 and r is 4, m is 1. Substituting these values into the equation, we get:
1 = k * 2 * 4
Simplifying this equation, we get:
k = 1 / (2 * 4)
k = 1/8
Therefore, the constant of variation is 1/8, which is option A.
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A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and the second brand is 70% pure antifreeze. In ord gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
5 gallons of 70% antifreeze, 1 gallon of 45% antifreeze
Step-by-step explanation:
Many different combinations can be made to equal 65% pure antifreeze.
Essentially, this problem is asking us to find a combination that fits a mean of 65%. So, multiply 5 by 70 to get 350, and 1 x 45 to get 45. Add 350 + 45 together to get 395, and divide by the total amount of gallons used - 6.
395/6 = 65, which is the target value.
Find the value of $x$ . Write your answer in simplest form.
A right triangle is shown. The measure of one of the interior angles is 45 degrees. The length of one of the legs is 1 unit. The length of the hypotenuse is x units.
$x=$
Answer:
The length of the hypotenuse is $x=\sqrt{2}$ units. ($x=\√2$)
Explanation:
If one of the angles of a right triangle is 45 degrees, then the other acute angle is also 45 degrees. Let's label the other leg of the triangle as $y$ units.
Using the Pythagorean Theorem, we have:
$1^2 + y^2 = x^2$
Simplifying:
$1 + y^2 = x^2$
We can also use the fact that the ratio of the sides of a 45-45-90 triangle is $1:1:\sqrt{2}$ to write:
$\frac{x}{1}=\sqrt{2}$
Simplifying:
$x=\sqrt{2}$
Now, substituting this value of $x$ into our equation $1 + y^2 = x^2$, we have:
$1 + y^2 = (\sqrt{2})^2$
Simplifying:
$1 + y^2 = 2$
$y^2 = 1$
$y = 1$ (since we're looking for a positive length)
Therefore, the length of the hypotenuse is $x=\sqrt{2}$ units.
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Because of your amazing work maximizing the revenue for the math club, the basketball team wants you to help them. They want to know how much admission they should charge for their games to make the most money. The team manager tells you that when they charged $5 per ticket, they sold 600 tickets, but when they tried to charge $20 per ticket, they sold no tickets.
1. You can assume the relationship between the price of the ticket and the number of tickets sold is linear. Write a linear function “n” that models the number of tickets sold “n(p),” as a function of the price of a ticket, “p.”
2. To calculate revenue, you multiply the price of the ticket by the number of tickets sold. Write a function “r” that models the revenue generated by selling tickets, “r(p),” as a function of the price of the ticket, “p.”
3. Use your function “r” from question 2 to recommend a ticket price to the basketball team. Support your recommendation by explaining how much revenue they could generate from your ticket price versus a higher or lower price.
1. Linear function: n(p) = -40p + 800
2. r(p) = P. n(p)
3. Total revenue = $4000
What is the slope of a linear function?There are numerous formulas for deriving a line's equation using linear functions, depending on the available data.
With the exception of vertical lines, which are not functions, any line may have its equation found using a formula for a linear function.
In the question,
We can assume, we have two points:
(5, 600) and (20,0)
The slope:
0-600/20-5
= -40
So, n(p) = -40 (p-20)
n(p) = -40p +800
Now solving,
r(p) = P. n(p)
= -40p² + 800p
Now to calculate the revenue,
r'(p) = -2 × 40p + 800
= -80p + 800
Order r'(p) = 0
⇒ P = 10
The highest price is: $10.
Revenue = -40 × ($10) ² + 800 × $10 = $4000
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Deandre wants to measure the height of a tree. He sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 33 ft from the tree, and Deandre is standing 10.2 ft from the mirror, as shown in the figure. His eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
First person to answer gets brainilest.Do what the picture says!!!!
Answer:
please mark as brainliest
Answer:Good question
Step-by-step explanation:
The sum of two numbers is 58 and the difference is 20. What are the numbers?
Larger number:
Smaller number:
Answer:
Larger number: 39
Smaller number: 19
Step-by-step explanation:
Write two equations and solve the system of equations.
One number can be x. The other number can be y.
"sum" means adding.
x + y = 58
"difference" means subtracting.
x - y = 20
Take both equations, stack them and add them together from the top down.
x + y = 58
x - y = 20
_________
2x = 78
Divide by 2
x = 39
Use either original equation to find the other number.
x + y = 58
39 + y = 58
subtract 39
y = 19
The bigger number is 39 and the smaller number is 19.
During gym class, there were 7 teams in the four-square match. Each team was made of 5 third-graders.
Which shows how many students were in the four-square match in all?
1. 5 times 5
2. 5 minus 7
3. 7 times 5
4. 7 plus 5
7 times 5 shows the number of students in the four-square match. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
It is stated that the four fundamental operations, often known as "arithmetic operations," can explain all real numbers. Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.
We are given that there were 7 teams in the four-square match and each team was made of 5 third-graders.
Now, in order to find the total students, we will use the multiplication operation.
From this, we get 7 times 5 which represents the total students.
Hence, 7 times 5 shows the number of students in the four-square match.
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Question Darryl plays a card game with his sister. He uses a 52 card deck and she chooses 1 card. If she chooses the 4 of hearts, she will win $10 and if she chooses any spade, she loses $2. If any other card is drawn, they break even. What is the expected value for Darryl's sister? Round to the nearest cent. Do not round until your final calculation. Note: within a deck of cards, there are 4 equal suits: hearts, clubs, diamonds, and spades.
The expected value for Darryl's sister is -$0.31. This means that on average, she can expect to lose 31 cents per game played with the 52 card deck.
The expected value for Darryl's sister can be calculated by multiplying the probability of each outcome by the value of that outcome and then summing those products.
Probability of choosing the 4 of hearts: 1/52
Probability of choosing any spade: 13/52
Probability of choosing any other card: 38/52
Expected value = (1/52)($10) + (13/52)(-$2) + (38/52)($0)
Expected value = $0.19 - $0.50 + $0
Expected value = -$0.31
Therefore, the expected value for Darryl's sister is -$0.31. This means that on average, she can expect to lose 31 cents per game played with the 52 card deck.
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Explain. What should the format of a problem be if using the Factoring Method? Can this method be applied for any quadratic problems? What are the limitations? Why do we make each factor equal to zero?
The factoring method is a technique used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. To use the factoring method, we need to find two numbers that multiply to give c and add to give b. We then use these two numbers to factor the quadratic expression into two binomials, set each binomial equal to zero, and solve for x.
The format of a problem that can be solved using the factoring method should be in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The quadratic expression should be factorable into two binomials.
The factoring method can be applied to any quadratic problem that is in the correct format and is factorable. However, not all quadratic equations can be factored. In cases where the quadratic expression cannot be factored, we need to use other methods such as the quadratic formula or completing the square.
The main limitation of the factoring method is that it only works for quadratic equations that can be factored into two binomials. If the quadratic equation cannot be factored or if it has complex roots, then the factoring method cannot be used to solve the problem.
We make each factor equal to zero because if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x to find the roots of the quadratic equation.
IF YOU GET THIS ONE QUESTION RIGHT, I'LL GIVE BRAINLIEST
Solve this equation.
√(x-10)^2=x-10
A tapered bar is 10. 0 inches long. The diameter of the circular cross section decreases linearly from 4. 0 inches at one end to 2. 0 inches at the other end. Determine the equation that expresses the cross-sectional area of the bar as a function of the position, x, along the length. The area of a circle is given by A=πr2.
what is the meaning of the cross-sectional area of the bar ? ( with drawing )
π/4 [2 + 1/5x] is the equation that expresses the cross-sectional area of the bar as a function of the position, x, along the length. The area of a circle is given by A=πr2.
Let us now consider a uniformly tapering circular bar having length,
L = 10 inches
and having diameter,
d₁ = 2 inches
at one end and
d₂ = 4 inches
at the other end, therefore we know that d₂ > d₁
let us consider a very short section xx of length kx and diameter dx, situated at a distance x from end A
now diameter, dx = d₁ + (d₂ - d₁)x
= d₁ + kx
where k = d₂ - d₁/ L
= 4-2/10 = 2/10 = 1/5
cross section area of the given circular bar 1
π/4 d₁²
π/4(d₁+Kx)
π/4 [2 + 1/5x]
here the cross section over 1x function of the given position of x, along the length.
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pinworm: in a prior sample of u.s. adults, the center for disease control (cdc), found that 11% of the people in this sample had pinworm but the margin of error for the population estimate was too large. they want an estimate that is in error by no more than 1.5 percentage points at the 95% confidence level. enter your answers as whole numbers. (a) what is the minimum sample size required to obtain this type of accuracy? use the prior sample proportion in your calculation. the minimum sample size is u.s. adults. (b) what is the minimum sample size required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion? the minimum sample size is u.s. adults.
A minimum sample size of 1399 is required assuming a prior knowledge of the sample proportion of 11%, and a minimum sample size of 960 is required if no prior knowledge of the sample proportion is assumed.
To obtain an estimate of the percentage of U.S. adults with pinworm with an error of no more than 1.5 percentage points at a 95% confidence level, a minimum sample size of 1399 is required, assuming prior knowledge of the sample proportion of 11%.
However, if no prior knowledge of the sample proportion is assumed, a minimum sample size of 960 is required.
To calculate the minimum sample size, the formula n = (Z² * p * (1-p)) / E² is used, where n is the sample size, Z is the Z-value for the desired confidence level (1.96 for 95% confidence), p is the prior sample proportion, and E is the desired margin of error.
Therefore, assuming a prior knowledge of the sample proportion of 11%, a sample size of 1399 was needed. If no prior knowledge was assumed, a minimum sample size of 960 was required.
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(-7+3)4 with work shown
Answer: -16
Step-by-step explanation:
First, we need to solve the parentheses by performing the operation inside them. (-7 + 3) equals -4, so we can substitute that in the expression to get:
(-7 + 3)4 = -4 × 4
Next, we can perform the multiplication operation:
-4 × 4 = -16
Therefore, (-7 + 3)4 = -16.
Answer:
-16
Step-by-step explanation:
First, you distribute 4 into the equation, basically multiplying, so 4 * 3 is 12, then 4 * -7 is -28. Add them together so -28 + 12 is -16
Hope this helps <3
1)Sketch the function f(x)=1 /(x−2)^3 −8.
Calculate and show the x-intercepts and y-intercepts, as well as
the horizontal and vertical asymptotes. Must show all the steps in
the calculations in order to receive credit.
2) Calculate the average rate of change of f(x)=2x^3−3x^2−4x
from x=1 to x=3. Must show all the steps in the calculations in order to receive credit.
1) f(x) = 1/(x - 2)^3 - 8
2)f(x) from x = 1 to x = 3 is 15.5.
1) Sketch the function f(x) = 1/(x - 2)^3 - 8 and calculate its x-intercepts, y-intercepts, horizontal and vertical asymptotes.To sketch the function f(x) = 1/(x - 2)^3 - 8, we need to find the x-intercepts, y-intercepts, horizontal and vertical asymptotes. First, let's find the x-intercept. It's a point on the graph where the function intersects the x-axis, so y-coordinate should be zero.f(x) = 1/(x - 2)^3 - 8y = 0 = 1/(x - 2)^3 - 8⇒ 1/(x - 2)^3 = 8⇒ (x - 2)^3 = 1/8⇒ x - 2 = 1/2⇒ x = 2 + 1/2 = 5/2So, the x-intercept is (5/2, 0).Next, let's find the y-intercept. It's a point on the graph where the function intersects the y-axis, so x-coordinate should be zero.f(x) = 1/(x - 2)^3 - 8x = 0 = 1/(0 - 2)^3 - 8⇒ 1/(-2)^3 - 8 = -1/8 - 8 = -8 1/8So, the y-intercept is (0, -8 1/8).Next, let's find the horizontal asymptote. As x approaches infinity or negative infinity, the function approaches a certain value, which is the horizontal asymptote.To find the horizontal asymptote, we need to find the limit of f(x) as x approaches infinity.f(x) = 1/(x - 2)^3 - 8∴ as x → ∞, (x - 2)^3 → ∞⇒ 1/(x - 2)^3 → 0So, the horizontal asymptote is y = -8. To find the vertical asymptotes, we need to find the values of x that make the denominator of the fraction zero.f(x) = 1/(x - 2)^3 - 8x - 2 = 0 = (x - 2)^3⇒ x = 2So, the vertical asymptote is x = 2.Now, we can sketch the function as shown below. f(x) = 1/(x - 2)^3 - 8Answer:2) Calculate the average rate of change of f(x) = 2x^3 - 3x^2 - 4x from x = 1 to x = 3.To find the average rate of change of a function, we need to divide the change in the function by the change in the variable. In this case, the change in the variable is Δx = 3 - 1 = 2.f(x) = 2x^3 - 3x^2 - 4xf(1) = 2(1)^3 - 3(1)^2 - 4(1) = -5f(3) = 2(3)^3 - 3(3)^2 - 4(3) = 26So, the change in the function is Δf = f(3) - f(1) = 26 - (-5) = 31.Now, the average rate of change is given by,Δf/Δx = 31/2 = 15.5Therefore, the average rate of change of f(x) from x = 1 to x = 3 is 15.5.
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A runner sprinted for 447 feet . How many yards is this
Answer: 447/3
Feet to yards is every three feet is one yard
Step-by-step explanation:
447 divided by 3 equals 149 yards
The linear model represents the height f(x) of a water balloon thrown off a building over time, x, measured in seconds
a) Interval(s) of the domain in which the water balloon's height increasing is from x = 0 to x = 2.
b) Interval(s) of the domain in which the water balloon's height staying the same is from x = 2 to x = 4.
c) Interval(s) of the domain in which the water balloon's height decreasing the fastest is from x = 8 to x = 10.
d) The predicted height of the water balloon at 14 seconds is 82 feet.
a) The water balloon's height is increasing from x = 0 to x = 2 seconds, as the height goes from 26 feet to 34 feet.
b) The water balloon's height is staying the same from x = 2 seconds to x = 4 seconds, as the height remains at 34 feet.
c) The water balloon's height is decreasing the fastest from x = 8 seconds to x = 10 seconds, as the height drops from 30 feet to 0 feet over a span of only 2 seconds. During this interval, the balloon is likely hitting the ground.
d) To predict the height of the water balloon at 14 seconds, we need to find the corresponding value of f(x) on the linear model. Since the given ordered pairs only go up to x = 12 seconds, we need to use the equation of the line to extrapolate beyond that point.
We can first find the slope of the line using any two of the ordered pairs. Let's use (0, 26) and (2, 34):
slope = (34 - 26) / (2 - 0) = 4
Using the point-slope form of the equation, we can write the equation of the line as:
f(x) - 26 = 4(x - 0)
f(x) = 4x + 26
To predict the height at 14 seconds, we can simply substitute x = 14 into the equation:
f(14) = 4(14) + 26
f(14) = 82
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Complete question is:
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:
A linear model with ordered pairs at 0, 26 and 2, 34 and 4, 34 and 8, 30 and 10, 0 and 12, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet.
a) During what interval(s) of the domain is the water balloon's height increasing? (2 points)
b) During what interval(s) of the domain is the water balloon's height staying the same? (2 points)
c) During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points)
d) Use the constraints of the real-world situation to predict the height of the water balloon at 14 seconds. Use complete sentences to support your answer. (3 points)
Valerie's class is attempting to recreate Van Gogh's
"'The Starry Night" on a tapestry to cover one of the
walls in the media center. The original painting was
28. 7 inches by 36. 25 inches. If they use a scale
factor Sin. : 2ft. , approximately how many square
feet will the tapestry cover? Round to the nearest
tenth
If they use a scale factor Sin : 2ft. , approximately 14.43 square feet will the tapestry cover.
The tapestry will cover approximately 57.4 square feet.
To calculate this, first multiply the width and the length of the painting (in inches) to find the area of the painting in inches squared.
28.7 inches x 36.25 inches = 1040.375 inches squared
Then, convert the inches squared to feet squared by dividing by 144.
1040.375/144 inches squared = 7.21354 feet squared
Finally, multiply the area of the painting in feet squared by the scale factor (2 feet) to find the area of the tapestry in feet squared.
7.21354 feet squared x 2 feet = 14.42708 feet squared
Finally, round the answer to the nearest hundredth to get the answer:
14.43 feet squared, or 57.4 square feet
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You are designing an in-ground lap swimming pool with a volume of 2000 cubic feet. The width of the
pool should be 5 feet more than the depth, and the length should be 35 feet more than the depth. What
should the dimensions of the pool be?
The dimensions of the pool should be 8 feet deep, 13 feet wide, and 43 feet long.
How to calculate the dimension of the poolLet's assume that the depth of the pool is "x".
Given that the width is 5 feet more than the depth, then the width is x + 5.
Also, the length is 35 feet more than the depth, then the length is x + 35.
The volume of the pool is 2000 cubic feet, then:
length x width x depth = 2000
(x + 35) (x + 5) (x) = 2000
x^3 + 40x^2 + 175x - 2000 = 0
We can use trial and error or synthetic division to find that one of the roots of this cubic equation is x = 8.
Therefore, the depth of the pool is 8 feet.
The width is x + 5 = 8 + 5 = 13 feet.
The length is x + 35 = 8 + 35 = 43 feet.
So, the dimensions of the pool should be 8 feet deep, 13 feet wide, and 43 feet long.
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To evaluate their products, the manager of an assembly line inspects the first 100 batteries that are produced out of 30,000 total batteries produced that day. He displays the results in the graph at the right and then releases it to a local newspaper.
95 batteries are in excellent condition, three batteries do not hold charge, two batteries are broken or they have cracked casing.
5. Identify any sampling errors( ways in which the when/ who of the data collected can lead to biased results)
The sample is large enough, random, and representative of the population being studied to avoid biased results.
The following list of potential sampling flaws that can result in biassed results is based on the information provided:
Limited sample size: Of the 30,000 batteries produced that day, the manager only examined 100 of them. It's possible that this sample size is insufficient to adequately represent the full population of batteries. A bigger sample size can yield more reliable results.
Non-random sampling: It's unclear how the manager decided to test 100 batteries. The outcomes might be skewed if the selection wasn't random or if there was any bias throughout the selection procedure.
Selection from a non-representative subset of the population: It is unclear if the 100 batteries that were subjected to inspection were drawn at random from the full population of batteries manufactured that day or merely from a particular section of the production line. The results might not be representative of the whole population of batteries manufactured that day if the batteries were only collected from a portion of the production line.
Confirmation bias: The manager's inspection procedure may have been prejudiced inadvertently, looking for more of what they anticipated to see. For instance, the management might have been more inclined to identify more batteries as being in good condition if they had expected the batteries to be of high quality, which could have skewed the results.
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