Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2600. What was the rate charged per hour by each mechanic if the sum of the two rates was $155
per hour?

The biggest length stick that will fit is 16.49 units long.

The length stick which will fit into Elaina's 12* 8*8 tank can be found using the Pythagorean theorem.

The diagonal length, of tank will be equal to square root of the sum of the squares of its length, width and height.

So, the diagonal length of the tank, using Pythagorean theorem, is

= √(12² + 8² + 8²)

= √(144 + 64 + 64)

= √272

≈ 16.49.

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Answer:

[tex]The[/tex] [tex]Answer[/tex] [tex]Is:[/tex] [tex]\frac{3}{9}[/tex] [tex]&[/tex]& [tex]\frac{5}{15}[/tex]

Step-by-step explanation:

Divide by 4 , 2nd fraction Divide by 5:

3/4 ≠ 4/5

5/6 ≠ 6/5 We can already see it.

Divide by 3. . .

2/4 ≠ 3/4

Divide by 3 , 2nd fraction Divide by 5:

1/3 = 1/3 [tex]Perfect![/tex]

The answer is, [tex]\frac{3}{9}[/tex] & [tex]\frac{5}{15}[/tex]

Answer:

Based on the information given, we know that the domain of g is -20 ≤ x ≤ 5 and the range is -5 ≤ g(x) ≤ 45. We also know that g(0) = -2 and g(-9) = 6.

A. g(-4) = -11: This statement could be true or false, as there is not enough information to determine its validity.

B. g(0) = 2: This statement is false, since we know that g(0) = -2.

C. g(7) = -1: This statement could be true or false, as there is not enough information to determine its validity.

D. g(-13) = 20: This statement is false, since -13 is outside the domain of g (-20 ≤ x ≤ 5).

Step-by-step explanation:Therefore, the statement that could be true for g is A. g(-4) = -11 or C. g(7) = -1.

The possible outcomes for each of the given events are:

A --> {1, 3, 5}

B --> {4, 5, 6}

For a regular number cube, the sample space (possible outcomes) is:

S = {1, 2, 3, 4, 5, 6}

Now we have two events.

A = rolling an odd number

Here the outcomes can be any of the odd numbers in the sample space, so the possible outcomes are:

A --> {1, 3, 5}

The second event is:

B = the number rolled is greater than 3. Again, the outcomes are thevalues in the sample space that are larger than 3, these are:

B --> {4, 5, 6}

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The claim is: Testing if the time spent completing the obstacle course is improved by the energy drink

The null and the alternate hypotheses are added below

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

The table

Also, we have the following statistical question

Is there sufficient evidence at α = 0.05 to conclude that the students did better the second time?

This means that the null hypothesis are

H1: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

The alternate hypothesis is the opposite of the null hypothesis

So, we have

H2: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

Lastly, the claim is that

Testing if the time spent completing the obstacle course is improved by the energy drink

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Answer:

they are correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sampling distribution of the sample mean for samples of size n is approximately normal with mean μ and standard deviation σ/sqrt(n), where μ is the mean of the population, σ is the standard deviation of the population, and sqrt(n) is the square root of the sample size.

In this case, the population mean is μ = 112 and the population standard deviation is σ = 22. We are interested in the sampling distribution of the sample mean for samples of size n = 16.

The mean of the sampling distribution of the sample mean is the same as the population mean, which is μ = 112.

The standard deviation of the sampling distribution of the sample mean is σ/sqrt(n) = 22/sqrt(16) = 5.5.

Therefore, the sampling distribution of the sample mean for samples of size 16 is approximately normal with mean 112 and standard deviation 5.5.

Answer:

Step-by-step explanation:

D is the correct answer.

Answer:

D

Step-by-step explanation:

By reading the graph, place the art museum at location (5,5). Then check all the locations to see which statement is true.

A is not true because the art museum is located 4 units east and 1 unit north from the coliseum.

B is not true because the art museum is located 3 units east and 3 units north of the smith's tower.

C is not true because the art museum is located 1 unit east and 2 units north of the state capital.

This is why D is the correct answer.

Answer:

4/5

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given a figure, consisting of a right triangle with a circle cut out of it.

To Calculate : area of the shaded region below,

First Let's find the Area of the right triangle:

Area(triangle) = 1/2 × Base × Height

= 1/2 × 56 × 56

= 1/2 × 3136

= 3136/2

= 1568 m².

Now, We are diameter of the circle = 20 m

Radius of the circle = 20/2 = 10 m

Acc. to question we have to use 3.14 as an

approximation for pi.

Area (circle) = 3.14 × 10 × 10

Area (circle) = 3.14 × 100

Area (circle) = 314 m²

Area of shaded region = Area of triangle - Area of circle =

= 1568 m² - 314 m²

= 1.254 square meters

Therefore, The approximate area of the shaded region is 1.254 square meters.

Option (a) is the required answer.

Answer:

the line is passing through 1 for y and -4 for x

Step-by-step explanation:

The function y = 1/4 + 1 contains all the information you need. The + 1 indicates the y intercept, so it is given. Since the slope of the line is 1/4, the graph would pass through (-4, 0) and (0, 1) as starting from a point would go up one unit and right 4 units.

3.) The quantity of students that are in the P.E class would be = 31 students.

4.) The number of students that ran 1 mile in under 9 minutes would be = 6 students.

For question 3.)

To calculate the quantity of students, all the values in the frequency column is added together. That is;

Total number of students= 6+2+8+6+9 = 31 students.

For question 4.)

To calculate the number of students that ran 1 mile in less than 9 minutes would be the time range of 8.00-8.59 minutes = 6 students.

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Answer:

The range is 37

Step-by-step explanation:

highest - lowest = range

64-27= 37

Hope it helped! :)

If principal of $3900 is invested at 4.25% interest, compounded annually, the investment will be worth approximately $4,756.89 after 5 years.

To calculate the future value of the investment, we use the formula for compound interest:

A = [tex]P(1 + r/n)^{(n*t)[/tex]

where A is the future value, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $3900, r = 4.25%, n = 1 (compounded annually), and t = 5. Plugging these values into the formula, we get:

A = 3900(1 + 0.0425/1)⁵

A = 3900(1.0425)⁵

A ≈ $4,756.89

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Answer:

30 square units

Step-by-step explanation:

The area of a rectangle is its length multiplied by its width.

We can see that the length of Rectangle A is 6 units, and its width is 5 units.

Multiplying these together to get the rectangle's area:

6 units × 5 units = 30 square units

Answer:

Beth has $752

Step-by-step explanation:

First we lay out what we know:

Beth: 3x+20

Will: x

Dennis: x+20

Next we write the equation:

3x+20+20+x+x=1260

Then we add any numbers that can be added to each other:

5x+40=1260

Then we solve,

We first minus 40 from both sides of the equation,

5x+40=1260

-40 -40

---------------------

5x=. 1220

Last we divide 1220 by 5,

5x=1220

÷5. ÷ 5

----------------

x=244

Now that we know that x is 244 we fill in the blanks,

Beth: 732+20

Will: 244

Dennis: 244+20

Then we just solve the equations,

Beth: 732+20=752

Will: 244

Dennis: 244+20=264

That's it,

if you want to check your work you can add them all up and if they equal 1260 it's correct.

752+244+264=1260

Your welcome, have a good day/night.

The result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.

In linear algebra, we often use scalars and vectors to perform various operations. Scalars are just ordinary numbers that can be used to multiply or divide vectors. On the other hand, vectors are quantities that have both magnitude and direction.

In this problem, we are given three vectors, u, v, and w, and we are asked to find the result of multiplying 5u by the difference between 3v and 4w.

First, let's calculate 3v - 4w. Since v = 4i - 2j and w = -2j, we can substitute these values to get,

3v - 4w = 3(4i - 2j) - 4(-2j)

= 12i - 6j + 8j

= 12i + 2j

Next, we need to find the scalar product of 5u and 12i + 2j. To find the scalar product of two vectors, we need to multiply the corresponding components and add up the products.

Therefore: 5u(3v - 4w) = 5u(12i + 2j)

= 5(-4i + j)(12i + 2j)

= -20i(12i) + 5i(2j) + 60j(i) - 10j(j)

= -240i + 10j + 60j + 10

= -240i + 70j + 10

So, the result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.

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The angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z are

180 degrees

540 degrees

900 degrees

The transformation rule for an angle of 180 degrees is simply a reflection or a flip. This means that any object or figure that undergoes this transformation will be flipped over a line or axis.

The rule is (x, y) will become (-x, -y)

Where 540 degrees = 360 + 180

where 900 degrees = 360 + 360 + 180

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The time taken for the pebble to hit the water is 1.41 seconds.

The time taken for the pebble to hit the water is calculated by using the equation of the motion as follows;

h = -16t² + 5

where;

when the height is 27 ft, the time of motion is calculated as;

-27 = -16t² + 5

16t² = 5  + 27

16t² = 32

t² = 32/16

t² = 2

t = √2

t = 1.41 seconds

Thus, the time of motion is determined by applying the equation of motion as shown above.

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The ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.

A circle is a two-dimensional shape that is defined as the set of all points in a plane that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference, and the distance across the circle passing through the center is called the diameter.

The circumference of a circle with radius r is given by the formula:

C = 2πr

The area of a circle with radius r is given by the formula:

A = π×r²

Therefore, the ratio of the circumference of a circle with radius r to its area is:

C/A = (2πr) / (πr²)

Simplifying the expression by canceling out π and r from the numerator and denominator, we get:

C/A = 2/r

Therefore, the ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.

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The complete question is:

Find the following ratio.

The ratio of circumference of circle with radius r to its area.

Answer:  Joe's property tax bill is based on the assessed value of the house, not the purchase price.

To calculate his annual property tax bill, we first need to calculate the assessed value of the house that will be used to determine the tax. The assessed value is given as $280,000.

The annual property tax bill is then calculated as follows:

Tax bill = assessed value x tax rate

Tax bill = $280,000 x 0.029

Tax bill = $8,120

Therefore, Joe's annual property tax bill for this house is $8,120.

Answer:

Step-by-step explanation:

Based on the information given, it is not possible to determine whether the sample may be biased or not.

However, there is a possibility that the sample may be biased if the company's computer database does not accurately represent its entire customer base. For example, if the database contains only a specific type of customers, such as those who frequently make large purchases, then the sample may not be representative of the company's entire customer base. In this case, the survey results may not accurately reflect the opinions of all the company's customers.

It is also important to consider other factors such as how the survey was conducted and how the questions were framed, as these can also affect the validity of the survey results

The proportion relation obtained from the similar triangles indicates that the x/3 = 10/x

Similar triangles are triangles that have the same shape but their sizes may vary.

The proportion equation from the image based on the ratio of the corresponding sides of the similar right triangles can be found as follows;

The side x is the hypotenuse side of the smallest right triangle

The ratio x/3, is equivalent to the ratio of the hypotenuse side to the shortest side of the right triangle

The corresponding ratio in the medium triangle is ((x² - 3²) + 7²)/(x² - 3²)

((x² - 3²) + 7²)/(x² - 3²) = (x² + 40)/(x² - 3²)

The corresponding ratio in the large similar right triangle is (7 + 4)/x = 10/x

Therefore, the corresponding ratio is; x/3 = 10/x

The proportion is; x/3 = 10/x

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Answer:

45w + 180 = 900

45w = 720

w = 16 weeks

The sum of the arithmetic sequence is 987

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

For example, the sequence, 2,4,6,8,10... is an arithmetic sequence.

The sum of an arithmetic sequence is given as;

Sn=n/2[2a+(n−1)d]. Where d is the common difference and a is the first term.

the last term is 87

therefore;

87= 7+(n-1) 4

87= 7+4n-4

91-7 = 4n

84 = 4n

n = 84/4

n = 21

therefore 87 is the 21st term

Sn=n/2[2a+(n−1)d]

= 21/2(2×7+(21-1)4

= 21/2 ( 14+80)

= 21×94/2

= 987

therefore the sum of the arithmetic sequence is 987

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These are absolute value expressions evaluated under different conditions:

|x + 3| if x > 5:

Here x is greater than 5, so x + 3 will also be positive. In this case, |x + 3| = x + 3.

|x + 3| if x > 2:

Similar to the above, x is greater than 2, so x + 3 will be positive. Thus, |x + 3| = x + 3.

|x + 3| if x = 2:

In this case, x + 3 = 2 + 3 = 5, and the absolute value of 5 is just 5. Thus, |x + 3| = 5.

|x - 3| if x > 5:

If x is greater than 5, then x - 3 will be positive. Hence, |x - 3| = x - 3.

|120 + x| if x < -120:

Since x is less than -120, 120 + x will be negative. But the absolute value of a negative number is its positive counterpart, so |120 + x| = -(120 + x).

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Joey’s monthly payment is solved to be

C. $79.70

20% down 600 to calculate the monthly payment on a 3 000 car we would pay 2 400.

the interest rate is 12% per annum which equates to 1% per month the term of the loan is three years which equates to 36 months we can use a formula to calculate the monthly payments

[tex]Monthly salary = (P * r * (1 + r)^n) / ((1 + r)^n - 1) .[/tex]

where

P is the principal (premium),

r is the monthly interest rate, and

n is the number of months.

Plug in the prices and we have:

[tex]Monthly salary = (2400 * 0.01 * (1 + 0.01)^{36} ) / ((1 + 0.01)^{36} - 1)[/tex]

= $79.65 per square foot

So Joey’s monthly payment would be $79.65.

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If Frank spends $90 on his $1800 monthly income, then 95 percent of monthly check does not go toward food.

Let's say Frank spends $90 on food and has a monthly income of $1800. We can calculate the percentage of his monthly check that does not go towards food as follows:

Percentage = (Total Income - Food Expenses) / Total Income

Percentage = (1800 - 90) / 1800

Percentage = 0.95 = 95%

Therefore, 95% of Frank's monthly check does not go towards food.

Here are the steps in detail:

Subtract the food expenses from the total income to get the amount of money that is not spent on food.

Divide the amount of money that is not spent on food by the total income to get the percentage.

In this case, the amount of money that is not spent on food is $1800 - $90 = $1710. The percentage of the monthly check that is not spent on food is $1710 / $1800 = 0.95 = 95%.

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Step-by-step explanation:

X component  = 4.5 - 2.1  =   2.4

Y component  = 7.8 - 2.1  =    5.7

Find magnitude using Pythagorean theorem

  m^2 = 2.4^2 + 5.7^2

    magnitude  = 6.18    units

Remember for a right triangle   tangent Φ = opposite leg / adjacent leg

    angle = arctan ( 5.7 / 2.4 )   = 67.2 degrees