Determine the distance covered by a car traveling 68 mi/h for eachunit and time given. Round answers to the nearest unit. a. miles in one hourb.feet in one hourc.feet in one minuted.feet in one second

Answer: The second one is correct.

Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

The function represented by the graph with the given transformations is |–x| + 2.

The function represented by the given transformations is |–x| + 2.

Let's analyze the transformations step by step:

Reflection across the x-axis:

Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.

Translation right 2 units:

Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.

Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.

Thus, the function represented by the graph with the given transformations is |–x| + 2.

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Answer: -lx-2l

Step-by-step explanation:

Triangle a is a shape that is formed by connecting three points.

Triangle is a geometric figure with three sides and three angles. It is one of the basic shapes in geometry. Triangles are either right, acute, or obtuse, depending on the size of each angle. The sum of the angles in a triangle is 180 degrees. Triangles can be classified into equilateral, isosceles, and scalene triangles, depending on the length of the sides. All three types of triangles have various applications in mathematics, physics and engineering.

In order to reflect triangle a in the x axis, triangle b must be a mirror image of triangle a. To achieve this, each point in triangle a must be reflected across the x axis. This is done by multiplying the y coordinate of each point in triangle a by -1. As a result, triangle b will have the same three points as triangle a, except that the y coordinates of each point in triangle b will be the opposite of what they are in triangle a.

After reflecting triangle a in the x axis to form triangle b, the next step is to rotate triangle b around the origin 90°. This can be achieved by finding the coordinates of each point in triangle b, then rotating each point around the origin. To do this, the x coordinates of each point in triangle b remain the same, while the y coordinates are multiplied by -1. As a result, triangle c will be formed as a 90° rotation of triangle b around the origin.

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Kara's grandmother knitted the cap during the afternoon is \(\frac{1}{2}\).

A fraction is a number that represents the part of a whole. It is in the form of \(\frac{a}{b}\) , in which upper 'a' part denotes numerator and the lower part 'b' denotes the numerator.

Kara's grandmother knitted the cap,

In the morning = \(\frac{1}{5}\)

In the evening = \(\frac{7}{10}\)

She knitted during the afternoon = \(\frac{7}{10} -\frac{1}{5}\)

                                                       = \(\frac{7}{10} - \frac{2}{10}\)

                                                       = \(\frac{5}{10} = \frac{1}{2}\)

Hence, Sara's grandmother knitted the cap during the afternoon =\(\frac{1}{2}\).

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Answer: y=(x-3)^2 -14

Step-by-step explanation:

use the formula (b/2)^2 to create a new term to complete the square

The length of the hypotenuse in this problem is given as follows:

h = 10.6 m.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The side lengths for this problem are given as follows:

7m and 8m.

Hence the hypotenuse is obtained as follows:

h² = 7² + 8²

\(h = \sqrt{7^2 + 8^2}\)

h = 10.6 m.

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A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of 11/2 inch. So, the correct answer is (D).

To determine the correct answer, we need to compare the diameters of the two pipes and understand the relationship between pipe diameter and threads per inch.

The number of threads per inch generally decreases as the pipe diameter increases. This means that a larger pipe diameter will have fewer threads per inch compared to a smaller pipe diameter.

Given that the first pipe has a diameter of 1 1/4 inches, we need to find the pipe diameter from the options that is larger than 1 1/4 inches.

The option that meets this requirement is D. 11/2. This represents a pipe diameter of 1 1/2 inches. Therefore, a pipe with a diameter of 1 1/2 inches should have fewer threads per inch than a pipe with a diameter of 1 1/4 inches. Therefore, the correct answer is D. 11/2.

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Answer:

1.5 feet

Step-by-step explanation:

12/8 = 1.5 feet

Answer:

x = 43

Step-by-step explanation:

125^(3x+7)=25^(5x−11)

Rewriting the bases as powers of 5

125 = 5^3  and 25 = 5^2

5^3 ^ (3x+7) = 5^2^(5x-11)

We know a^b^c = a^ (b*c)

5^(3 * (3x+7)) = 5^(2*(5x-11))

Distribute

5^(9x+21) = 5^(10x-22)

The bases are the same so the exponents are the same

9x+21 = 10x-22

Subtract 9x from each side

9x+21 -9x = 10x-9x-22

21 = x-22

Add 22 to each side

21+22 = x-22+22

43 = x

Answer:

Frank scored 10 runs

B) the mean is 20

Step-by-step explanation:

Answer:

The expected flight time is 2 hours 10 minutes

Step-by-step explanation:

Given

\(a = 2\ hours\)

\(b = 2\ hours\ 20\ mins\)

Required

The expected flight time

To do this, we simply calculate the mean using:

\(Mean = \frac{a + b}{2}\)

So, we have:

\(Mean = \frac{2\ hours + 2\ hours\ 20\ mins}{2}\)

\(Mean = \frac{4\ hours\ 20\ mins}{2}\)

\(Mean = 2\ hours\ 10\ mins\)

The  evaluation of the function for the given f(-1), f(1)   input value is  mathematically given as

In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain. Historically, functions have been seen as an idealization of the way in which one variable relies on another variable.

-1 and 1 are both considered to be input when evaluating the function f, which is represented by the graph.

Since the inputs are on the x-axis, the graph demonstrates that the value of the function f at -1 is about -8 when x equals -1.

When x equals 1, the value of the function f is close to -12.

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The number whose sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed is 32

the number can be expressed as 10x + y

x + y = 5

(10x+y) - 9

= 10y+x

x + y = 5

9x - 9y = 9

x + y = 5

x - y = 1

Add the equations

2x = 6

x = 6/2

x = 3

substitute into

x + y = 5

3 + y = 5

y = 5 - 3

y = 2

Therefore, the unknown number is 32.

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Answer:

x=9/2

Step-by-step explanation:

4x+2=8x-16

-4x=-18

4x=18

x=18/4

x=9/2

The number is 6.

Let the unknown number be represented with y

This formula can be derived from the question: 4 (y + 2) = 8y - 16

In order to determine the value of y, take the following steps:

Combine similar terms

8 + 16 = 8y - 4y

Add similar terms

24 = 4y

Divide both sides by 4

y = 6

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Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

wow

Step-by-step explanation:

Answer with step-by-step explanation:

Step 1: $14,00 - $3,500 + $108,570 = $10,500 + $108,750 = $119,250

Step 2: 7% of $119,250 = $8,347.50

Step 3: $119,250 + $8,347.5 = $127.597.50

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The number that can complete the equation 5y + 2(3y − 1) = ⬜y − (y + 2) is

5y + 2(3y − 1) = 12 y − (y + 2)

The number that can complete the equation is computed by simplifying the equation at the left hand side of the equality sign and comparing with the right side of the equality side

The comparison will show the number that can fit in the blank

Simplifying the equation at the left hand side of the equation

= 5y + 2(3y − 1)

= 5y + 6y − 2

= 11y - 2

Simplifying the equation at the right hand side of the equation

=  ⬜y − (y + 2)

let x represent the missing number

=  xy − (y + 2)

=  xy − y - 2

comparing both equations

11y - 2 =  xy − y - 2

11y =  xy − y

11y + y =  xy

12y = xy

x = 12

The missing value = 12

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Dividing f(x) by 2x + 5 leaves the same remainder as division by x + 5/2. By the remainder theorem, it is equal to f (-5/2), so the remainder here is

f (-5/2) = 8 (-5/2)³ + 4 (-5/2)² - 13 (-5/2) + 3 = -129/2

Answer:

45

Step-by-step explanation:

Good luck!

Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To write an equation in point-slope form using the point (12, -2), you need to first determine the slope of the line. The slope is given as m = 1, so the equation in point-slope form is:

y - (-2) = 1(x - 12)

Simplifying this equation gives:

y + 2 = x - 12

Adding 12 to both sides of the equation gives:

y + 2 + 12 = x

Simplifying the equation gives:

y + 14 = x

This is the equation in point-slope form for the given line, using the point (12, -2).

Answer:

4.57

Step-by-step explanation:

i dont have no explanation

The percentage of Leah's action figure collection she kept in her wall is 86%.

Percentage is a number or ratio that can be expressed as a fraction of 100.

To calculate the percentage of Leah's action figure collection she kept in her wall, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the percentage of Leah's action figure collection is 86%.

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Answer:

Mrs Barnes has the highest

Answer:

35.9

Step-by-step explanation:

Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

Given

The floor plan of a house is,

After installing new hardwood flooring , you also need to install base board around the bottom of the walls.

To find: How many feet of base board will you need to buy?

Explanation:

It is given that,

The floor plan of a house is,

After installing new hardwood flooring , you also need to install base board around the bottom of the walls.

That implies,

The perimetr of the base board is,

Hence, we need to buy 108ft of base board.

The 90% confidence interval for the proportion of all faculty members at the community college who know sign language is (0.0420, 0.1348)

We can use the formula for a confidence interval for a proportion to calculate the interval

CI = p ± zsqrt(p(1-p)/n)

where:

p is the sample proportion (13/147 = 0.0884)

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

n is the sample size (147)

Substituting the values, we get

CI = 0.0884 ± 1.645sqrt(0.0884(1-0.0884)/147)

Simplifying the expression, we get

CI = 0.0884 ± 0.0464

Therefore, the 90% confidence interval for the proportion of all faculty members at the community college who know sign language is

CI = (0.0420, 0.1348)

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The property used to solve y - 7 = 28 is the Addition Property of Equality