a car traveling at 48 mph overtakes a cyclist who, riding at 12 MPH has a 3 hour head start. how far from the starting point does the car overtake the cyclist.

The image and the net that represents the solid figure is attached

From the question, we have the following parameters that can be used in our computation:

rectangular prism

When the rectangular prism is splitted into nets, we have the following shapes

Shapes = 6 rectangular faces

This means that the net that represents the solid figure has 6 rectangular faces

Using the above as a guide, we have the following:

The net of the solid figure is the image 4

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Answer:

Account A:

[tex]4750 {e}^{.0375 \times 7} = 6175.84[/tex]

Account B:

[tex]5100 {(1 + \frac{.03875}{12}) }^{12 \times 5} = 6188.41[/tex]

Account B has a larger balance.

A higher slope indicates a stronger relationship between the variables, and the sign (positive or negative) indicates the direction of the relationship (positive: both variables increase together, negative: one variable increases while the other decreases).

When comparing the slopes of the regression lines for two models, you're essentially looking at the differences in their unstandardized coefficients. These coefficients represent the change in the dependent variable for each unit change in the independent variable, keeping all other variables constant.

In the unstandardized model you mentioned, the slope of 0.96 means that for every one-unit increase in the independent variable, the dependent variable is expected to increase by 0.96 units, on average. This helps us understand the strength and direction of the relationship between the two variables in the model.

To compare the slopes between two models, simply examine their unstandardized coefficients.

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The margin of error for a 95% confidence interval can be calculated using the formula: Margin of error = (z-score) x (standard deviation)

where the z-score is the number of standard deviations corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval) and the standard deviation is calculated as:
Standard deviation = sqrt[(population proportion) x (1 - population proportion) / sample size]
We know from the given information that the lower limit of the 95% confidence interval is 62% and the upper limit is 73.1%. Therefore, the midpoint of the interval is:
Midpoint = (lower limit + upper limit) / 2 = (62% + 73.1%) / 2 = 67.55%
Using this midpoint as an estimate for the population proportion, we can solve for the standard deviation:
Standard deviation = sqrt[(0.6755) x (1 - 0.6755) / n]
where n is the sample size (which is not given). Since we don't know the sample size, we can't calculate the standard deviation directly. However, we can use the fact that the margin of error is half the width of the confidence interval to estimate the sample size:
Margin of error = (upper limit - lower limit) / 2
Plugging in the given values, we get:
Margin of error = (73.1% - 62%) / 2 = 5.55%
Now we can solve for the standard deviation:
Standard deviation = sqrt[(0.6755) x (1 - 0.6755) / (sample size)]
Using the margin of error as an estimate for the standard deviation, we can solve for the sample size:
5.55% = 1.96 x sqrt[(0.6755) x (1 - 0.6755) / (sample size)]
Solving for sample size, we get:
sample size = 610.05
Rounding up to the nearest whole number, we get a sample size of 611. Therefore, the margin of error for this 95%confidence interval is approximately 5.55%, assuming a sample size of 611.

Given a 95% confidence interval for a population proportion with limits (62%, 73.1%), you are asked to find the margin of error.
Step 1: Calculate the midpoint of the interval.
Midpoint = (Lower limit + Upper limit) / 2
Midpoint = (62% + 73.1%) / 2
Midpoint = 135.1% / 2
Midpoint = 67.55%
Step 2: Determine the margin of error.
Margin of error = (Upper limit - Midpoint) or (Midpoint - Lower limit)
Margin of error = (73.1% - 67.55%) or (67.55% - 62%)
Margin of error = 5.55%
The margin of error for the given 95% confidence interval of the population proportion with limits (62%, 73.1%) is 5.55%.

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Note that the complete statement is:

Note that the translation is -4 units in the x -direction (to the left), and4 units in the y- direction (upwards). That is (-4, 4) Units.

A translation moves  a form up, down, or from side to side, but it has n effect on its appearance . A transformation is an example of translation. A transformation is a method of modifying a shape's size or location. Every point in the shape is translated in the same direction by the same amount.

To go from ⊕ A to   ⊕ B, we can use a combination of translation and  reflection.

We can see that the center of  ⊕ A is at (1,0), and the c  enter of ⊕ B is at (-3,4).

To move from the center of ⊕ A to the center of ⊕ B, we need to translate by -4 units in the x-  direction and 4 units in the y-  direction. This will move the center of ⊕A to the point ( -3,   4), which is the center of ⊕   B.

hence, the translation is -4 units in the x -direction (to the left), and4 units in the y- direction (upwards). That is (-4, 4) Units.

NOte that ⊕ mean circle.

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The simplified value of the expression given as 7^(3 +12)/7^5  is 7^10

From the question, we have the following parameters that can be used in our computation:

7^3+^12-^75

Expess properly

So, we have the following representation

7^(3 +12)/7^5

Evaluate the sum of the exponents

So, we have the following representation

7^15/7^5

When the exponents are simplified, we have

7^10

Hence, the simplified expression of 7^(3 +12)/7^5  is 7^10

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The solution to the system of equations is w = 0 and z = -2

Given equations are 3w - 4z = 8   ...(1)

2w + 3z = - 6          ...(2)

By multiplying the first equation by 3 and the second equation by 4, we get:

9w - 12z = 24        ...(3)

8w + 12z = -24      ....(4)

Adding equation (1) and (2)

17w + 0 = 0

w = 0

Putting the value of w in first equation

3(0) - 4z = 8

- 4z = 8

z = - 2

Therefore, the solution to the system of equations is w = 0 and z = -2

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Answer: A. 11 yards

Step-by-step explanation:

To find the distance between the bike rack at (-6, 1) and the bench at (5, 1), we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the coordinates of the bike rack and (x2, y2) is the coordinates of the bench.

Substituting the values, we get:

d = sqrt((5 - (-6))^2 + (1 - 1)^2)

d = sqrt((11)^2 + 0^2)

d = sqrt(121)

d = 11

Therefore, the distance between the bike rack and the bench is 11 yards. So, the correct answer is A.

Answer: 11 yards

Step-by-step explanation:

Bill has a total of 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. To find the number of possible outfits he can wear to work, we can use the multiplication principle.

First, we need to determine how many choices Bill has for his top and bottom. He can either wear a jumpsuit or a combination of pants and a shirt. Therefore, he has 3 + (5 x 8) = 43 choices for his top and bottom.

Next, we can use the multiplication principle to determine the total number of possible outfits he can wear. Since he has 43 choices for his top and bottom, and each outfit combination is independent of the others, we can multiply the number of choices for his top and bottom by the number of one-piece jumpsuits he has.

Therefore, Bill has a total of 43 x 3 = 129 possible outfits he can wear to work.

In summary, Bill has 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. He can wear either a jumpsuit or pants and a shirt to work. Using the multiplication principle, we determined that he has a total of 129 possible outfits he can wear.

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The area of the figure is 102 square inches.

To find the area of the figure, we need to first calculate the area of the rectangle and then the area of the triangle and add them together.

Area_rectangle = length x width

= 15 in. x 5 in. = 75 in²

The base of the triangle is the same as the length of the rectangle minus the distance from the vertex.

i.e. 15 in. - 3 in. = 9 in.

The height of the triangle is 11 in - 5 in = 6 in

Area_triangle = (1/2) x base x height

= (1/2) x 9 in. x 6 in. = 27 in²

Therefore, the required total area is the sum of the area of the rectangle and the area of the triangle

Total_area = Area_rectangle + Area_triangle

= 75 in² + 27 in² = 102 in²

So, the area of the figure is 102 square inches.

Hence, option d is correct.

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The solution to the equation 3/5x = 2 is x = 10/3.

What is equation?

An equation is a mathematical statement that asserts that two expressions are equal. An equation typically contains one or more variables (letters that represent unknown or varying quantities), along with constants and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

To solve the equation 3/5x = 2, we need to isolate x on one side of the equation.

First, we can simplify the left side of the equation by multiplying both sides by the reciprocal of 3/5, which is 5/3, as follows:

(5/3)(3/5)x = (5/3)2

This simplifies to:

x = 10/3

Therefore, the solution to the equation 3/5x = 2 is x = 10/3.

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We can estimate that about 31.5% + 43% = 74.5% of the observations are between 50 and 90.

To find out what percent of the observations are between 50 and 90, we need to first calculate the interquartile range (IQR).

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). We can calculate Q1 and Q3 using the five-number summary:

Q1 = 35 + 0.25(50-35) = 42.5
Q3 = 70 + 0.25(90-70) = 77.5

So the IQR is: IQR = Q3 - Q1 = 77.5 - 42.5 = 35

Now we can use the IQR to estimate what percent of the observations are between 50 and 90. Since the data is roughly symmetric and follows a normal distribution, we can assume that about 50% of the data falls within one standard deviation of the mean. In this case, the IQR represents about one standard deviation of the data.

Therefore, we can estimate that about 68% of the observations fall within one IQR of the mean. Since the IQR spans from 35 to 77.5, we can estimate that about 68% of the observations fall between these values.

To estimate the percent of observations between 50 and 90, we need to determine how many standard deviations away from the mean these values are.

50 is (50 - 60)/35 = -0.29 standard deviations away from the mean.
90 is (90 - 60)/35 = 0.86 standard deviations away from the mean.

Using the empirical rule, we can estimate that about 63% of the observations fall within one standard deviation of the mean. Since 50 is less than one standard deviation away from the mean, we can estimate that less than 31.5% of the observations fall between 50 and the mean.

Similarly, we can estimate that about 86% of the observations fall within two standard deviations of the mean. Since 90 is less than two standard deviations away from the mean, we can estimate that less than 43% of the observations fall between the mean and 90.

Therefore, we can estimate that about 31.5% + 43% = 74.5% of the observations are between 50 and 90.

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To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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The volume of the resulting cone is  3, 336, 704m³

Given that the volume of a cone is 1216 m³. We need to find the volume of the resulting cone when the original cone is dilated by a scale factor of 14.

We know that the volume of a cone with radius of the base 'r' and height 'h' is given by;

Volume 1 = 1/3 πr²h =  1216 m³

After dilation, both the radius and height will be increased by 14 times, so the new volume of the resulting cone will be

Volume of dilation = 14³ ×  1/3 πr²h

Substitute the value

Volume of dilation = 14³ × 1216

Find the cube

Volume of dilation = 2744 × 1216

Multiply the values

Volume of dilation = 3, 336, 704m³

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The surface area of each of the hemisphere's are:

1) S.A = 1520.5 cm²

2) S.A = 929.4 ft²

3) S.A = 706.9 m²

4) S.A = 615.8 in²

5) S.A = 804.2 in²

6) S.A = 380.1 yd²

The formula for the area of a sphere is expressed as:

S.A = 4πr²

1) The radius is given as r = 11 cm

S.A = 4 * π * 11²

S.A = 1520.5 cm²

2) The radius is given as r = 8.6 ft

S.A = 4 * π * 8.6²

S.A = 929.4 ft²

3) The diameter is given as d = 15 m

Thus, radius: r = 15/2 = 7.5 m

S.A = 4 * π * 7.5²

S.A = 706.9 m²

4) The radius is given as r = 7 in

S.A = 4 * π * 7²

S.A = 615.8 in²

5) The radius is given as r = 8 cm

S.A = 4 * π * 8²

S.A = 804.2 in²

6) The diameter is given as d = 11 yards

Thus, radius: r = 11/2 = 5.5 yards

S.A = 4 * π * 5.5²

S.A = 380.1 yd²

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Answer: $24.50

Step-by-step explanation:

We know that each battery  pack contains 4 batteries.

This mean that to get 28 batteries, you would need 7 packs (28/4)

7 battery packs x $3.50 = $24.50

∴, 28 batteries will cost $24.50

The expression for the cost of 5 large Italian ices in terms of the cost of a medium Italian ice is "5d + 10" dollars.

To find the cost of 5 large Italian ices, we need to multiply the cost of one large Italian ice by 5. So, the expression for the cost of 5 large Italian ices is:

5 × (d + 2)

We can simplify this expression by using the distributive property of multiplication. This means that we can multiply the number outside the parentheses (5) by each term inside the parentheses (d and 2):

5 × (d + 2) = 5 × d + 5 × 2

Simplifying further, we get:

5d + 10

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How closely repeated values of the estimator are to one another is the optimal response to the missing information (ii).

The variance of an estimator is a measure of how much the estimates vary from one sample to another. Specifically, determines how closely repeated estimator values match one another. Option

Option (i) is not correct, because the variance of an estimator is not a measure of how close the estimator is to the true value, but rather a measure of how much it varies from one sample to another.

Option (iii) is also not correct, because the mean of the estimator is not necessarily equal to the true value, and the variance of the estimator measures how much the estimates vary from one sample to another, regardless of whether the mean of the estimator is close to the true value or not.

Option (iv) is also not correct, because it refers to the variance of the mean of the estimator, rather than the variance of the estimator itself.

The variance of the estimator's mean serves as a gauge of how much sample means fluctuate from one sample to the next.

As a result, the right response is ii, which refers to how closely related repeated estimator values are to one another.

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Complete Question:

Choose the best answer to fill in the blank. The variance of an estimator measures ____________.

i. how close the estimator is to the true value.

ii. how close repeated values of the estimator are to each other.

iii. how close the mean of the estimator is to the true value.

iv. how close repeated values of the mean of the estimator are to each other.

Answer:

A= 1320 u^2 P= 176 u

Step-by-step explanation

A= 1/2 (b)(h)

A=1/2 (48)(55)= 1320

P= a+b+c

48+55+73=176

Answer:

A= 1320 u^2 P= 176 u

Step-by-step explanation

A= 1/2 (b)(h)

A=1/2 (48)(55)= 1320

P= a+b+c

48+55+73=176

Step-by-step explanation:

The correct expression for "a does not equal b" is "a ≠ b". The symbol ≠ represents the inequality of "not equal to". This means that a and b are not the same and can have different values. It is important to note that the inequality symbol ≠ is used for non-equal values, while the equals symbol = is used for equal values.

In mathematics, inequalities are used to compare two values and show how they differ. They are represented by symbols such as <, >, ≤, and ≥, which stand for less than, greater than, less than or equal to, and greater than or equal to, respectively. These symbols help us understand the relationship between two values and can be used to solve problems involving numerical comparisons.

When it comes to choosing the correct inequality or expression, it is important to carefully analyze the given information and determine which symbol accurately represents the relationship between the values. In this case, since a does not equal b, the correct symbol to use is ≠. By choosing the correct inequality or expression, we can ensure that our mathematical statements are clear, accurate, and meaningful.

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the backboard is 14 feet tall.by using similar Triangle properties (Height of person) / (Length of person's shadow) = (Height of backboard) / (Length of backboard's shadow)

Let's use similar triangles to find the height of the backboard.

Step 1: Identify the given measurements.
The person is 7 feet tall and casts a shadow of 12 feet. The shadow of the backboard is 24 feet.

Step 2: Set up a proportion using similar triangles.
(Height of person) / (Length of person's shadow) = (Height of backboard) / (Length of backboard's shadow)
7 ft / 12 ft = (Height of backboard) / 24 ft

Step 3: Solve for the height of the backboard.
To find the height of the backboard, cross-multiply and solve for the unknown value.
7 ft * 24 ft = 12 ft * (Height of backboard)

Step 4: Calculate the height of the backboard.
7 ft * 24 ft = 168 ft²
168 ft² / 12 ft = (Height of backboard)
14 ft = (Height of backboard)

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The correct order of magnitudes is:

hurricane > tornado and 10 > 100

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

The diameter of a typical tornado is usually much smaller than that of a typical hurricane.

The diameter of a tornado can range from a few tens of meters to about 2 km, while the diameter of a hurricane can range from a few hundred kilometers to more than 1,000 km.

Therefore, the correct order of magnitudes for the diameter of a typical hurricane and a typical tornado, from largest to smallest, is:

10,000 (this is too large for both hurricanes and tornadoes)

1,000 (this is still too large for both hurricanes and tornadoes)

100 (this is a possible diameter for a tornado, but it's too small for a hurricane)

10 (this is a typical diameter for a tornado)

Hence, the correct order of magnitudes is:

hurricane > tornado and 10 > 100

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After one hour, approximately 364 people will have heard the news.

In general, if n people know the news, then the next round will add 3n new people who also know the news. Therefore, after k rounds (where k is the number of rounds that can fit in an hour), the total number of people who know the news will be:

n + 3n + 3²ⁿ + 3³ⁿ + ... + 3ˣⁿ

To simplify this expression, we can use the formula for the sum of a geometric series:

S = a(1 - rⁿ) / (1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term = n ,

the common ratio = 3

and the number of terms = x

Therefore, we can write:

S = n(1 - 3ˣ) / (1 - 3)

Simplifying further, we get:

S = (3ˣ - 1)n / 2

Now we can substitute the values we know:

n = 4

x = 6

Therefore:

S = (3⁶ - 1)4 / 2 = 364

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Complete Question:

Luisa has great news, she communicates it to 3 people. Each of them tells 3 more. This is how a chain is set up, since each new person who learns the news communicates it to three others. It takes one person approximately 10 minutes to communicate the news to three others. If an hour has passed, how many people have heard the news?

The future amount at the end of 2 years for a $20,000 investment that yields 15% at the end of each year is $26,450. Option c is correct.

We need to replace the values with the formula for the future value of an investment when it earns a fixed interest rate. The formula is:

Where:

We can then substitute in the formula, which will be:

Therefore, based on the formula, we find that the future value of $20,000 after 2 years of investment at an interest rate of 15% will be $26,450.

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V satisfies all three properties, it is a subspace of F(R, R).

To show that V is a subspace of F(R, R), we need to show that V satisfies three properties:

The zero vector in V is the function f(x) = 0 for all x in R. This function is differentiable, so V is non-empty.

Let f and g be two functions in V. Then f' and g' exist and are real-valued functions. Since (f + g)' = f' + g', the sum of f and g is also differentiable. Thus, V is closed under vector addition.

Let f be a function in V and let c be a scalar. Then f' exists and is a real-valued function. Since (cf)' = cf', the scalar multiple of f is also differentiable. Thus, V is closed under scalar multiplication.

Since V satisfies all three properties, it is a subspace of F(R, R).

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Answer:

a)

[tex]p(x) = 10000( {.997}^{x} )[/tex]

b)

[tex]p(11) = 10000( {.997}^{11} ) = 9675[/tex]

c)

[tex]10000( {.997}^{x} ) = 8000[/tex]

[tex]x = 74.27 \: years[/tex]

The population will be 8,000 in about 74.27 years after 2005, or sometime in 2079.

Answer:

Factor x^2 - 4 into (x - 2)(x + 2). Cancel out the x + 2 factor. Then multiply.

[tex] \frac{9x + 14}{ {x}^{2} - 4} \times \frac{x + 2}{x + 1} [/tex]

[tex] \frac{9x + 14}{(x - 2)(x + 2)} \times \frac{x + 2}{x + 1} [/tex]

[tex] \frac{9x + 14}{(x - 2)(x + 1)} [/tex]

Answer: The value of the leading coefficient of the quadratic function f(x) = x^2 – 8x – 4 is 1.

Step-by-step explanation:

The leading coefficient of a quadratic function is the coefficient of the highest degree term of the function, which is the squared term x^2 in this case.

The given quadratic function f(x) = x^2 – 8x – 4 is already in standard form, where the coefficient of the squared term is 1. Therefore, the leading coefficient of the function is 1.

Answer:

1

Step-by-step explanation:

The answer above is correct.

The correct p-value for the test of H0: p = 0.25 versus H1: p > 0.25 is 0.375.

In this question, we are given two hypotheses:

H0: p = 0.25

H1: p < 0.25

The p-value for this test is 0.625. This means that if the null hypothesis is true, we would observe a sample proportion as extreme as, or more extreme than, the observed proportion with a probability of 0.625.

Now, we need to find the correct p-value for the alternative hypothesis:

H0: p = 0.25

H1: p > 0.25

Since the null hypothesis is that p = 0.25, the sampling distribution of the sample proportion is approximately normal with mean 0.25 and standard deviation √(0.25*(1-0.25)/n), where n is the sample size.

The observed sample proportion is not given in the question, so we cannot calculate the exact p-value. However, we can use the fact that the p-value is the area in the tail of the distribution beyond the observed sample proportion.

Since the alternative hypothesis is p > 0.25, the observed sample proportion is less than the null hypothesis value of 0.25. Therefore, the area in the right tail beyond the observed sample proportion is the complement of the original p-value of 0.625.

This means that the correct p-value for the test of H0: p = 0.25 versus H1: p > 0.25 is 1 - 0.625 = 0.375.

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The reference angle for a rotation of 334° is 26°.

A reference angle is the smallest acute angle between the terminal side of an angle and the x-axis. To find the reference angle of a given angle, you need to subtract the nearest multiple of 360° from the given angle until the resulting angle is between 0° and 360°.

In this case, 334° is greater than 360°, so you can subtract 360° from it once to get 334° - 360° = -26°. Since the reference angle is always positive, you can take the absolute value of -26° to get 26°. Therefore, the reference angle for a rotation of 334° is 26°.

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