Mr. Cox took a taxi from his home to the airport. The taxi driver charged an initial fee of $6 plus $3 per mile. The total fare was $24, not including the tip. How many miles did Mr. Cox travel on his ride? (7.EE.4a)


A 2

B 6

C 8

D 10

Based on this, a 90% confidence interval for the proportion, p. of adult residents who are parents in this county is 0.787 < p < 0.873.

The point estimate for the proportion is calculated by dividing the number of adults with kids by the total sample size. In this case, the point estimate is 166/200 = 0.83.

To construct the confidence interval, we can use the formula:

[tex]p \pm z \times \sqrt{\frac{p \times (1 - p )}{n}}[/tex]

Where:

p is the point estimate

z is the z-score corresponding to the desired confidence level (90% confidence corresponds to a z-score of approximately 1.645)

n is the sample size

Substituting the values into the formula, we get:

[tex]= 0.83 \pm 1.645 \times \sqrt{\frac{0.83 \times (1-0.83)}{200}}[/tex]

Calculating the values, we can obtain the 90% confidence interval for the proportion of adult residents who are parents.

To construct a 90% confidence interval for the proportion of adult residents who are parents in the county, we can use the sample proportion and the standard error formula. Out of the 200 adult residents sampled, 166 had kids.

we calculate the sample proportion, p-hat:

p-hat = 166 / 200

         = 0.83

Next, we calculate the standard error using the formula:

SE = √((p-hat × (1 - p-hat)) / n)

SE = √((0.83 × (1 - 0.83)) / 200) ≈ 0.025

To construct the confidence interval, we use the formula:

p-hat ± (z × SE)

where, z is the z-score corresponding to the desired confidence level.

For a 90% confidence interval, the z-score is approximately 1.645.

Substituting the values into the formula, we get:

= 0.83 ± (1.645 × 0.025)

Calculating the upper and lower bounds:

Lower bound = 0.83 - (1.645 × 0.025) ≈ 0.787

Upper bound = 0.83 + (1.645 × 0.025) ≈ 0.873

Therefore, the 90% confidence interval for the proportion of adult residents who are parents in the county is approximately 0.787 < p < 0.873.

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Answer:

[tex] \sin(m < q) = \frac{7}{9} \\ \sin(m < q) =(0.77777777778) \\ m < q = { \sin 0.77777777778}^{ - 1} \\ m < q = (51.05755873102)[/tex]

The principal should reject her original hypothesis, as the lower bound of the interval is less than 110.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 20 - 1 = 19 df, is t = 2.8609.

The parameters for this problem are given as follows:

[tex]\overline{x} = 108, s = 10, n = 20[/tex]

Then the lower bound of the interval is given as follows:

[tex]108 - 2.8609 \times \frac{10}{\sqrt{20}} = 101.6[/tex]

The upper bound of the interval is given as follows:

[tex]108 + 2.8609 \times \frac{10}{\sqrt{20}} = 114.4[/tex]

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The radius of the circle is 144 units.

To find the radius of the circle, we can use the formula that relates the circumference of a circle to its radius and the central angle intercepted by an arc.

The formula is:

Arc length = 2πr * (θ/360)

Where:

Arc length is the length of the intercepted arc

r is the radius of the circle

θ is the central angle in degrees

In this case, we are given that the arc length is 48π and the central angle is 120°. Let's substitute these values into the formula and solve for r:

48π = 2πr * (120/360)

Simplifying the equation:

48 = 2r * (120/360)

48 = r * (1/3)

r = 48 * 3

r = 144

Therefore, the radius of the circle is 144 units.

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Answer:

27 1/6

Step-by-step explanation:

14 + 12=26

4+3=7

26 7/6= 27 1/6

9514 1404 393

Answer:

  (d)  512√3

Step-by-step explanation:

The area (A) of a regular hexagon can be computed from its side length (s) using the formula ...

  A = (3√3)/2·s²

Here, the side length is given as ...

  s = 32√3/3 = 32/√3

Then the area is ...

  [tex]A=\dfrac{3\sqrt{3}}{2}\cdot\left(\dfrac{32}{\sqrt{3}}\right)^2=\dfrac{3\sqrt{3}\cdot1024}{2\cdot3}=\boxed{512\sqrt{3}}[/tex]

The area of the hexagon is 512√3 square units.

Answer:

The A matches the table x+3

Answer:

system is:

y = 1/2x

y = 1/2x - 2

No Solution to this system

Step-by-step explanation:

In the given situation, "angle 4 is the angle of elevation from the radar tower to the person" is the description of angle 4.In trigonometry, an angle of elevation or inclination is the angle between the horizontal and the line of sight of an observer looking upwards. An angle of depression is the angle between the horizontal and the line of sight of an observer looking downwards.

In the given situation, angle 4 refers to the angle formed between the horizontal and the line of sight from the radar tower to the person. As the angle is formed while looking upwards from the radar tower to the person, it is called the angle of elevation. Hence, the correct description of angle 4 in this situation is "angle 4 is the angle of elevation from the radar tower to the person."

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Answer:

Hi! The answer to your question is B) He can walk 12 miles in 1 minute.

To find Unit rate divide the biggest number by the smallest; Example: [tex]120/10[/tex]

Step-by-step explanation:

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Hope this helps!!

- Brooklynn Deka

Answer:

The answer is postulate

Answer:  h < 6

Step-by-step explanation:

3h - 5 < 13

3h < 18

h < 6

Answer:

h<6

Step-by-step explanation:

Answer:

if x is 16 then 3/4(16) - 12

when you simplify 4 by 16

3(4)-12

12-12=0

mode is 4 and the median is also 4

mode is the number that appears the most which is 4 and median is the number that is in the middle when you line up all the numbers in order  (0,2,2,3,3,4,4,4,4,5,5,5,6,6,10)

Answer:

0.25

Step-by-step explanation:

4/16 --> 1/4 and 1/4 = 0.25

Answer:

mean = 5+9+9+6+6+11+8+4/7 = 8.29

median = 6

mode = 6

range = 11 - 4 = 7

Answer:

Step-by-step explanation:

5 , 9 , 6 , 6 , 11 , 8 , 4

Mean = sum of all data ÷ number of data

         [tex]= \frac{5+9+6+6+11+8+4}{7}\\\\= \frac{49}{7}\\\\= 7[/tex]

Median: To find median, arrange in ascending order and medianis the middle term

4 , 5 , 6 , 6 , 8 , 9 , 11

Middle term = 4th term

Median = 6

Mode: a number that appears most often is mode

6 appears 2 times

Mode = 6

Range:

Range = maximum value - minimum value

          = 11 - 4

          = 7

Answer:

The ratio of perimeter of ABCD to perimeter of WXYZ = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

First, we have to determine the multiplicative factor of the dimensions for both figures.

Considering sides AB and WX,

multiplicative factor = [tex]\frac{12}{8}[/tex]

                                = 1.5

So that:

XY = 6 x 1.5 = 9

YZ = 7 x 1.5 = 10.5

ZW = 7 x 1.5 = 10.5

Perimeter of ABCD = 6 + 7 + 7 + 8

                                = 28

Perimeter of WXYZ = 9 + 10.5 + 10.5 + 12

                                 = 42

The ratio of the perimeters of the two quadrilaterals can be determined as;

ratio = [tex]\frac{perimeter of ABCD}{Perirmeter of WXYZ}[/tex]

       = [tex]\frac{28}{42}[/tex]

       = [tex]\frac{2}{3}[/tex]

The ratio of the perimeter of ABCD to perimeter of WXYZ is [tex]\frac{2}{3}[/tex].

Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The p-value is 0.024.

The null and alternative hypotheses for the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level are:

H0: p = 0.7 (null hypothesis

)H1: p ≠ 0.7 (alternative hypothesis)

The test is a two-tailed test because the alternative hypothesis includes not equal to (<>) which means either p is less than 0.7 or greater than 0.7

Based on a sample of 500 people, 62% owned cats.

This means that the sample proportion, p = 0.62.

To calculate the p-value, we will use the z-test statistic.

The formula for calculating the z-test statistic is given as:

z = (p - P) / √(PQ/n) where P is the hypothesized proportion (P = 0.7), Q is the complement of P (Q = 1 - P), and n is the sample size.

Using the given values in the formula, we have; z = (0.62 - 0.7) / √(0.7 × 0.3 / 500) = -2.52

The p-value for a two-tailed test at 0.02 level of significance is obtained from the standard normal table.

The area in both tails beyond the z-score of 2.52 is 0.012.

Therefore, the p-value is:

p-value = 2 × 0.012 = 0.024

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Answer:

I belive the answer is A

Step-by-step explanation:

So any answer with 22t would make sense, so you have A and C. In C though, it is subtracting 22, but since 6195 is the total it would have to include the 22 so it is A.

Answer:

67-32=a

if his mom is 67 and he is 32 years younger 67 minus 32 would equal a which is his age

It is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space. Let's explain why.

Let A be an m × n matrix, and let x be a nonzero vector in the null space of A, so Ax = 0. We can also say that x is in the null space of A transpose. So x is an element of N(AT).Let’s prove the contradiction that arises from the initial claim by assuming that 3,1,2 is a row vector in the row space of A and 2,1,1 is a column vector in N(AT).We have that A[3 1 2]T = 0 and 2,1,1 is in the null space of A transpose. We also know that if a vector v is in the row space of A, then there exists a vector y such that v = A*y, where y is a column vector. So in this case, we can say that 3,1,2 is in the row space of A if there is a column vector y such that A * y = [3 1 2]T. But if that's the case, then we have the following equation: A* y = [3 1 2]. This can be written as: TA* = [3 1 2]If we then take the transpose of both sides, we have: A* y = [3 1 2]T and TA = [3 1 2]. However, this implies that TA* = TA, which can only be true if A is a symmetric matrix. But A is an m × n matrix, where m and n are not equal, so A cannot be a symmetric matrix. Therefore, it is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space.

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The average fixed cost of each case will be $25

Average fixed cost = fixed cost / number of cases.

$4500/ 180= $25

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Yes, if ƒ is differentiable on (0, 1), then ƒ is uniformly continuous on (0, 1).

In mathematics, the concept of differentiability plays a crucial role in understanding the behavior of functions. If a function ƒ is differentiable on the interval (0, 1), it means that the derivative ƒ'(x) exists for every point x in that interval.

The answer states that if a function is differentiable on (0, 1), then it is uniformly continuous on the same interval.

To understand this result, we need to consider the properties of differentiability and uniform continuity.

Differentiability implies that the function has a well-defined tangent line at every point within the interval. This implies that the function cannot exhibit abrupt changes or discontinuities, as it must be smooth and continuous.

Uniform continuity, on the other hand, deals with the behavior of a function as the input values get arbitrarily close to each other. It ensures that the function does not exhibit extreme fluctuations or rapid oscillations.

If a function is differentiable on (0, 1), then it satisfies the conditions required for uniform continuity. This is because the derivative of the function acts as a measure of its rate of change.

If the derivative is bounded (i.e., it does not become infinitely large or small), then the function can be guaranteed to be uniformly continuous.

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Answer:

(6, 4 )

Step-by-step explanation:

Given the 2 equations

9x - 2y = 46 → (1)

x + 2y = 14 → (2)

Adding the 2 equations term by term will eliminate the y- term

10x + 0 = 60

10x = 60 ( divide both sides by 10 )

x = 6

Substitute x = 6 into either of the 2 equations and solve for y

Substituting into (2)

6 + 2y = 14 ( subtract 6 from both sides )

2y = 8 ( divide both sides by 2 )

y = 4

solution is (6, 4 )

Answer:

80 minutes.

Step-by-step explanation:

do I need to explain? I hate explaining :(

If We consider the string w = [tex]CA^pG^pT^pC[/tex], then L ∉ RLs by pumping lemma.

To prove that L ∉ RLs using the RL pumping theorem, we assume L is a regular language and apply the pumping lemma for RLs. Let p be the pumping length of L.

We consider the string w = [tex]CA^pG^pT^pC[/tex], where |w| ≥ p. According to the pumping lemma, we can decompose w into uvxyz such that |vxy| ≤ p, |vy| > 0, and for all k ≥ 0, the string [tex]u(v^k)x(y^k)z[/tex] is also in L.

However, by examining the structure of L, we see that the number of A's and G's is dependent on each other and must match the number of T's.

Since pumping up or down would alter this balance, there is no way to satisfy the condition for all k, leading to a contradiction. Therefore, L cannot be a regular language, and we conclude that L ∉ RLs.

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12+85% is $22.20

80%x12=9.6

5%x12=0.6

9.6+0.6=10.2

12+10.2=22.20

 Answer: $22.20  

Answer:

$8.75

Step-by-step explanation:

Cost price= $9.75

Selling price= $1.00

profit= C.P-.SP

= 9.75-1.00

= $8.75