1.
A boy throws a rock from his bedroom window. The height of the rock is a function of time and can be
modeled by the equation h(t) = 15 + 7t - 16t2. Height is measured in feet and time is measure in
seconds. The graph of this function is shown.
a. Evaluate h(0) and explain what it means in context.
b. Estimate the value of h(t) = 0 and explain what it means in context.
c. What does the equation h(1) = 6 mean?
height (ft)
d. Estimate and state the vertex h(t)and explain its meaning in context.
time (sec)
shift
(intel
Inside

Answer:

8

Step-by-step explanation:

The box contains a total of 4 x 12 = 48 eggs.

If we arrange these eggs in 6 rows, we need to divide the total number of eggs by 6:

48 ÷ 6 = 8

Therefore, there will be 8 eggs in each row.

There are 52 weeks of data included in this frequency distribution.

The given frequency distribution displays the weekly sales of a certain brand of television at an electronics store.

We need to find the number of weeks of data included in this frequency distribution.From the given data, we can see that the frequency column represents the number of televisions sold per week.

To find the number of weeks of data included, we need to sum up the frequency column. Summing up the frequency column gives us:12 + 5 + 5 + 5 + 25 = 52

Therefore, there are 52 weeks of data included in this frequency distribution.

The given frequency distribution displays the weekly sales of a certain brand of television at an electronics store. We need to find the number of weeks of data included in this frequency distribution.

From the given data, we can see that the frequency column represents the number of televisions sold per week. To find the number of weeks of data included, we need to sum up the frequency column. Summing up the frequency column gives us:

12 + 5 + 5 + 5 + 25 = 52

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Answer:96

Step-by-step explanation:

[tex]Area=\frac{d1 d2}{2}[/tex]

[tex]Area=\frac{(6+6)(8+8)}{2}[/tex]

[tex]Area=96[/tex]

The rate of change of y = cos x with respect to time is approximately -1.46 cm/sec.

This problem involves finding the rate of change of the dependent variable (y = cos x) with respect to the independent variable (x) at a given rate of change of the independent variable (dx/dt = 4 cm/sec).

Using the chain rule of differentiation, we have:

dy/dt = dy/dx * dx/dt

Taking the derivative of y = cos x with respect to x, we get:

dy/dx = -sin x

Substituting the given value of dx/dt = 4 cm/sec and the value of sin x can be obtained using the identity cos² x + sin² x = 1 and the given value of cos x = cos 0 = 0.95, we get:

dy/dt = dy/dx * dx/dt

= (-sin x) * 4

= (-√(1 - cos² x)) * 4 [Using the identity sin x = √(1 - cos² x)]

= (-√(1 - 0.95²)) * 4

≈ -1.46 cm/sec

Therefore, the rate of change of y = cos x with respect to time is approximately -1.46 cm/sec.

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Answer:

Step-by-step explanation:

You want the remainder of a number when divided by 3 if (1) the sum of digits is 5, and (2) the remainder from division by 9 is 5.

The sum of digits of a 2-digit number will be 5 if that number is one of ...

  {14, 23, 32, 41, 50}

In every case, the remainder when divided by 3 is 2. Effectively, it is the remainder of 5 when that is divided by 2.

In addition to the numbers listed above, 2-digit numbers with a sum of digits of 14 will also have a remainder of 5 when divided by 9. This adds five more numbers to the list:

  {59, 68, 77, 86, 95} . . . . have remainders of 5 when divided by 9

The remainders when divided by 3 are all 2 for these numbers as well.

__

Additional comment

The process of (recursively) summing the digits of a positive integer is called "casting out 9s". It effectively finds the modulo 9 value of the number, with the exception that a sum of 9 corresponds to a modulo 9 value of 0.

Since 9 is divisible by 3, the modulo 3 value of a number will be the modulo 3 value of the modulo 9 value. In other words, if the sum of digits is 5, or the remainder from division by 9 is 5, then the mod 3 value is 5 mod 3 = 2.

The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.

Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.

This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.

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The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.

Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.

This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.

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Complete questions as follows-
What value makes the expressions equivalent?
6(3x+5) and 15x+□+3x

A. 5
B.11
C.15
D.30

Answer:

no the didn't hear the question

Answer:

I am pretty sure the answer is that the question can't be heard

Step-by-step explanation:

Answer:

1. 1/2

2. -4/1

3. 1/1

Step-by-step explanation:

Answer:

1 y=2/1+2

2 y=.25x+3

3 y=x-2

Step-by-step explanation:

Step-by-step

y=mx+b

1. 2

2. .25

3. 1

The percentage change in the birth rate of a nation from 1990 to 2000 is -35%.

Percentage change is the relative difference between two values expressed as a percentage of one of the values, where the value of the latter is used as the reference point.

It can be calculated by using the following formula:

Percentage change = ((new value - old value) / old value) x 100

Given the birth rate of a nation in 1990 as 20 and the birth rate in 2000 as 13, the percentage change can be calculated as follows: Percentage change = ((13 - 20) / 20) x 100= (-7 / 20) x 100= -0.35 x 100= -35%

Hence, the percentage change is -35%.

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5.4 out of the 12 adult Australian sheep dogs in the sample weigh 65 pounds or more, on average.

We can start by calculating the likelihood that a single adult Australian sheep dog weighs 65 pounds or more using the provided estimate of 45%. If p represents the percentage of adult dogs weighing 65 pounds or more, the following is the result:

p = 0.45

Next, we may calculate the median number of dogs weighing 65 pounds or more using the sample size of 12. If X represents the proportion of dogs in the sample that weigh 65 pounds or more, X will follow a binomial distribution with n = 12 and p = 0.45 as its parameters.

The formula for X's mean or expected value is:

E(X) = np

When we change the values of n and p, we obtain:

E(X) = 12(0.45) = 5.4

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Justin's speed on his way to his parents' house was 42 mph. Therefore, his speed on his way back home was 18 mph slower, or 18 mph.

Let's use x mph to represent the pace at which Justin was travelling to his parents' house. Then, as he travelled 24 mph slower owing to the terrible weather, his speed on the way back would be (x - 24) mph.

By dividing the distance he drove by his speed, one may determine how long it took Justin to drive to his parents' house, or:

Time is a function of both speed and distance.

Similar to how long it would take Justin to drive back home:

Time is a function of distance and speed (x - 24)

Justin drove for a total of 12 hours, so we can construct the following equation:

420/x + 420/(x-24) = 12

By multiplying both sides of the equation by x(x-24), we may simplify the equation and find the value of x. After some algebraic fiddling, we arrive at:

[tex]x^2 - 24x - 840 = 0[/tex]

We can find the value of x by using the quadratic formula:

[tex]x = (24 +- \sqrt{(242 + 41840)}) / 2[/tex] or x = -18

We can determine that Justin was travelling at a speed of 42 mph as he made his way to his parents' home because the speed cannot be negative. Thus, he travelled at a speed of 18 mph less on the way back home.

We can confirm the following to see if the solution is accurate:

420/42 + 420/18 = 10 + 23.33 = 33.33

Justin did, in fact, drive for a total of 12 hours, proving that our answer is accurate.

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Answer:

Step-by-step

To make 100 to 250, you need to multiply 100 by 2.5 to make 250. In the similar way you need to multiply 80 by 2.5 which equals 200 which is the answer

Answer:

759=165% of last quarters members so you could divide by 1.65(move the decimal place twice to the left) so you get 460 people were there last quarter

Step-by-step explanation:

A pyramid with a base having n sides will have n + 1 faces, excluding the base. So, the pyramid that shares the same base as the prism will have 16 + 1 = 17 faces.

Let's say the base of the pyramid is a polygon with n sides. There are n faces in the pyramid (excluding the base), each of which is a triangle. Since there is just one base, the number of faces in the pyramid is n + 1.A prism is a polyhedron that is formed when two congruent polygons are joined by parallelograms. As a result, a prism with a polygon base has two polygons as bases and a number of rectangular faces equal to the number of sides of the polygon, which in this scenario is n.There are 2 bases and n rectangular faces in total for the prism. Since the number of edges in the prism is 99, we may express this as:Edges in prism = (Number of edges in each rectangular face × Number of rectangular faces) + (Number of edges in each base × Number of bases)= [tex]4n + 2n = 6n = 99n = 16.5[/tex] faces are in the pyramid = 16 + 1 = 17 faces.

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Therefore, the observed value of the test statistic for testing the null hypothesis H0: p = 0.5 versus the alternative hypothesis H1: [tex]p > 0.5[/tex]is z= 1.8. The correct answer is (e) z=[tex]0.59— 0.5/√0.5(0.5)/100.[/tex]

In this particular question, the observed value of the test statistic for testing the null hypothesis H0: p = 0.5 versus the alternative hypothesis H1: p > 0.5 is to be determined. The question provides a random sample of 100 likely voters in a small city, which produced 59 voters in favor of Candidate A. The formula for calculating the test statistic is as follows:

z= (p- P) / sqrt[P(1-P) / n]

where p is the sample proportion, P is the hypothesized population proportion, and n is the sample size.

Substituting the given values into the formula, we get:

z= [tex](0.59- 0.5) / sqrt[0.5(0.5) / 100][/tex]

z= [tex]0.09 / 0.05[/tex]

z=[tex]1.8[/tex]

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The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.

Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)

P(x > 77.83) = 1 - P(x < 77.83)

P(x > 77.83) = 1 - 0.9234

P(x > 77.83) = 0.0766

Answer: 37.7mm

Step-by-step explanation:

c = 2πr

c = 2π(6)

c ≈ 37.7

Psychologists have raised concerns about the accuracy and validity of ____ personality tests, as they are not standardized. This means that the same test administered to two different people can yield different results, making it difficult to interpret. Moreover, results may be inconsistent, meaning the same test administered at different times could produce different results. This lack of consistency can lead to inaccurate interpretations and can render the tests less useful. Furthermore, there is a lack of standardization of criteria and methodologies used to evaluate personality tests, which could lead to misinterpretations of results.
In order to address these issues, it is important to use standardized personality tests, which are tested and validated to ensure consistent and accurate results. This will ensure that the tests yield consistent results and can be interpreted accurately.

Additionally, researchers must adhere to established guidelines and criteria to ensure that the results are reliable and valid. This will enable professionals to confidently use the tests and make accurate interpretations of the results.

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The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.

To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.

In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.

Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.

By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.

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Answer:

Step-by-step explanation:

3x^16

Answer:

3x^16

Step-by-step explanation:

Answer: If adding predictor variables to a regression model never reduces r2, you can include all the available predictor variables in the model, as long as they have a significant correlation with the dependent variable. However, having too many variables in a model may lead to overfitting, resulting in poor model generalization. In addition, some predictor variables may not be useful, while others may be collinear. As a result, it is usually recommended to use a stepwise regression method, which selects the best subset of predictor variables that improve the model's performance, without including irrelevant or collinear variables.r2 adj: R2 adj is the adjusted R2 value of a regression model. R2 adj is a statistical measure of how well the regression model fits the observed data. It is similar to the R2 value, but takes into account the number of predictor variables in the model, in addition to the sample size. The adjusted R2 value increases when a new predictor variable improves the model's fit, but decreases when the new predictor variable does not improve the model's fit or is collinear with other predictor variables.

The adjusted R2 value ranges from 0 to 1, with higher values indicating better model fit.

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The point c satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5] is: c = 1.4697

The conclusion of the Mean Value Theorem says that there is a number

c in the interval (1, 5) such that:

f'(c) = (f(5) - f(1))/(5 - 1)

We are given the function f(x) = x⁻⁸

Thus:

f(1) = 1⁻⁸ = 1

f(5) = 5⁻⁸ = 0.00000256

Thus:

f'(c) = (0.00000256 - 1)/4

= -0.25

f'(c) = -8x⁻⁹

Thus:

-8c⁻⁹ = -0.25

c⁻⁹  = 0.25/8

c⁻⁹ = 0.03125

c = 0.03125^(-1/9)

c = 1.4697

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Yes, if is a critical point of a function with continuous second derivatives, then it is a stationary point.

This means that the function's derivative is equal to 0 at that point and it is neither increasing or decreasing.

A stationary point is a point on the graph of a function where the function's derivative is equal to 0. This is an important property of a function and it can be used to determine the properties of the function.

At a stationary point, the rate of change of the function is equal to 0, so the function is neither increasing or decreasing. In other words, the function is neither increasing or decreasing at that point.

This property can be used to analyze the function and determine its characteristics. For example, it can be used to identify local minima or maxima.

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The value of x for the given inequality to justify the equation to get the desired result of the equation is x < - 4 .

Define inequality:

In mathematics, inequality refers to a statement that compares two values or expressions, indicating that one value or expression is greater than or less than the other. An inequality can be represented using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to). For example, "2x + 3 > 5" is an inequality that states that the expression "2x + 3" is greater than "5". Inequalities are often used in algebra, calculus, and other branches of mathematics to represent relationships between variables or to solve equations.

What about equation in the relation?

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation consists of two expressions, separated by an equals sign "=" and it states that the value of one expression is equal to the value of the other expression. The expressions in an equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used in many areas of mathematics to describe relationships between variables, to solve problems, and to make predictions. For example, the equation "x + 3 = 7" states that the value of the expression "x + 3" is equal to "7".

According to the given information:

For the following equation we have that,

⇒ - 8x < 32

⇒ -x < [tex]\frac{32}{8}[/tex]

⇒ -x < [tex]4[/tex]

⇒ x < [tex]- 4[/tex]

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The sum of the volume of the square prism and the square pyramid is 672 cubic inches.

What is prism ?

A prism is a three-dimensional geometric shape that has two identical, parallel polygonal bases and rectangular sides that connect the bases. The sides are perpendicular to the bases and their shape depends on the shape of the base. For example, if the base is a square, the prism is called a square prism. If the base is a rectangle, the prism is called a rectangular prism. The height of the prism is the perpendicular distance between the bases.

According to the question:
First, let's calculate the volume of the square prism:

The formula for the volume of a square prism is V = lwh, where l is the length, w is the width, and h is the height.

In this case, the length (l) and width (w) of the prism are both equal to a, which is 10 inches, and the height (h) is 6 inches. So, we have:

V_prism = lwh = 10 x 10 x 6 = 600 cubic inches

Next, let's calculate the volume of the square pyramid:

The formula for the volume of a square pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.

In this case, the base of the pyramid is a square with side length b, which is 6 inches, so the area of the base is:

[tex]B = b^2 = 6^2 = 36 square inches[/tex]

The height of the pyramid is also 6 inches, so we have:

V_pyramid = (1/3)Bh = (1/3) x 36 x 6 = 72 cubic inches

Finally, the total volume is the sum of the volumes of the prism and pyramid:

V_total = V_prism + V_pyramid = 600 + 72 = 672 cubic inches

Therefore, the sum of the volume of the square prism and the square pyramid is 672 cubic inches.

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Answer: 7x - 7y + 21

Step-by-step explanation:

7( x - y + 3) = 7x - 7y + 21

(a) To test the hypotheses H0: µ = 115 and H1: µ > 115, we will conduct a one-sample t-test using the given information.

Step 1: Calculate the t-value.
t = (sample mean - population mean) / (standard deviation / √sample size)
t = (127.8 - 115) / (30 / √25)
t = 12.8 / 6
t = 2.13

Step 2: Determine the degrees of freedom (df).
df = sample size - 1
df = 25 - 1
df = 24

Step 3: Find the P-value.
Using a t-table or calculator, find the P-value corresponding to t = 2.13 and df = 24. The P-value is approximately 0.022.

Step 4: State the conclusion.
Since the P-value is less than the commonly used significance level of 0.05, we reject the null hypothesis (H0: µ = 115) and conclude that the mean score for older students is significantly higher than the mean score for the entire population.

(b) The two important assumptions for the t-test are:
1. The sample is randomly selected from the population.
2. The population is normally distributed.

The most important assumption for the validity of the conclusion in part (a) is the normality of the population. If the population is not normally distributed, the results of the t-test may not be valid, and the conclusion may be inaccurate.

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when the distance between the top of the rod and the foot of the wall is 152 inches, the distance between the bottom of the rod and the foot of the wall is decreasing at a rate of approximately 19.08 inches per second.

In this case, we are given that the distance between the top of the rod and the foot of the wall is decreasing at a rate of 9 inches per second. We want to find the rate at which the distance between the bottom of the rod and the foot of the wall is changing.

We can start by using the Pythagorean theorem to relate the three distances involved: the height of the rod (h), the distance between the top of the rod and the foot of the wall (x), and the distance between the bottom of the rod and the foot of the wall (y). Specifically, we have:

[tex]h^2 = x^2 + y^2[/tex]

To find the rate at which y is changing, we can take the derivative of both sides of this equation with respect to time (t), using the chain rule:

2h dh/dt = 2x dx/dt + 2y dy/dt

We are given that dh/dt = -9 inches per second (since h is decreasing). We also know that h = 172 inches and x = 152 inches (when y = 0). Substituting these values and solving for dy/dt, we get:

dy/dt = (h/x) * (dx/dt - (x/y) * dh/dt)

dy/dt = (172/152) * (-9 - (152/y) * 9)

dy/dt = -19.08 inches per second (rounded to two decimal places)

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Based on the attached figure, the volume of the composite figure is 408 cm³

A composite figure is a three-dimensional shape that is made up of two or more simpler shapes.

To find the volume of a composite figure, you need to break it down into its simpler shapes and then use the appropriate formulas to calculate the volume of each individual shape

The volume of the composite figure is:

Volume = area of base * height

Substituting:

Base area = (14 * 3) + (1/2)(5 + (14-6))(7 - 3) = 68 cm²; height = 6 cm

So, we have

Volume = area of base * height = 68 cm² * 6 cm = 408 cm³

This means that

The volume is 408 cm³

Hence, the volume is 408 cm³

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New car prices to fall within is $18,300 - $41,900

Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.

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