A company charges $60 per day plus $0.50 per mile for truck rentals. If Greg rents a truck for 3 days and drives 150 miles, how much will the company charge?

1500(1+0.04)^3 = 1687.30

1687.30(1+0.05) = 1771.67 to the nearest pound: 1772

Answer:

C. 60° and 80°

Step-by-step explanation:

Sum of triangle = 180°

Therefore,

8x + 4 + 6x - 2 + 10x + 10 = 180

Add like terms

8x + 6x + 10x + 4 - 2 + 10 = 180

24x + 12 = 180

24x = 180 - 12

24x = 168

x = 168/24

x = 7

Find each measure of the angles by substitute x = 7 into each expression

8x + 4 = 8(7) + 4 = 60°

6x - 2 = 6(7) - 2 = 40°

10x + 10 = 10(7) + 10 = 80°

The answer is 60° and 80°

Option D is the correct answer. The probability that a test correctly rejects a false null hypothesis is called the significance level.

The significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant.

The probability of making a type II error (failing to reject the null hypothesis when it is actually false) is called β (beta). The quantity (1 - β) is called power, the significance level is the probability of rejecting the null hypothesis when it is true.

For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.

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60  milliliters of 13% vinegar and 150 milliliters of 6% vinegar will give him 300ml of 12% vinegar.

This is further explained below.

Generally, The ratio of their amounts is inversely proportional to the variations in their cost from the mean value when varied quantities of various components are combined to generate a mixture of a mean value, according to the rule of alligation.

In conclusion, How much of each brand is

\(x=\frac{13-8}{8-6}\\\\x=5/2\)

For every 2 measures of the 13% vinegar, the Chef needs to add 5 measures of the 6% vinegar (meaning a ratio of 2:5)

2/7 *210=60  milliliters of 13% vinegar

and

150 milliliters of 6% vinegar will give him 300ml of 12% vinegar.

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Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 center is  0.275

 \(SE = 0.063\)

b

 center is  0.275

 \(SE = 0.020\)

Step-by-step explanation:

considering question a

From the question we are told that

   The sample size is  n  =  50

 The proportion of  US adults are college graduates is  p = 0.275

Generally the center is equivalent to the proportion so the center is  0.275

Generally the standard error is  

      \(SE =  \sqrt{\frac{p *  (1- p)}{ n} }\)

=>   \(SE =  \sqrt{\frac{0.275 *  (1- 0.275)}{ 50} }\)

=>   \(SE = 0.063\)

considering question b

    The sample size is  n  =  500

      The proportion of  US adults are college graduates is  p = 0.275

     Generally the center is equivalent to the proportion so the center is  0.275

     Generally the standard error is  

      \(SE =  \sqrt{\frac{p *  (1- p)}{ n} }\)

=>   \(SE =  \sqrt{\frac{0.275 *  (1- 0.275)}{ 500} }\)

=>   \(SE = 0.020\)

In the sampling distribution, the center of the sampling distribution is 0.275 and the standard error is 0.063.

A sampling distribution simply means the probability distribution that is gotten from a larger number of samples that are drawn from a population.

In this case, the center of the sampling distribution is 0.275 and the standard error is 0.063. The standard error will be:

= [p × (1 - p)]/n

= [0.275 × (1 - 0.275)]/50

= 0.0039875

= ✓0.0039875

= 0.063

Also, when the sample is 500, the center of the sampling distribution is 0.275 and the standard error is 0.020.

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Answer:

It will take 41.7 years for this investment to triple in value.

Step-by-step explanation:

Here is the formula for simple interest

\(A=P(1+rt)\)

Lets solve for \(t\).

Divide both sides by \(P\).

\(\frac{A}{P}=rt+1\)

Subtract 1 from both sides.

\(\frac{A}{P}-1=rt\)

Divide both sides by \(r\).

\(\frac{\frac{A}{P}-1}{r} =t\)

To write \(-1\) as a fraction with a common denominator, multiply by \(\frac{P}{P}\) .

\(\frac{\frac{A}{P}-1*\frac{P}{P}}{r} =t\)

\(\frac{\frac{A}{P}*\frac{-P}{P}}{r} =t\)

Combine the numerators over the common denominator.

\(\frac{\frac{A-P}{P} }{r} =t\)

Multiply the numerator by the reciprocal of the denominator.

\(t=\frac{A-P}{Pr}\)

We are given

\(P=3800\\r=0.048\)

We need to find what amount is triple his money.

\(3800*3=11400\)

\(A=11400\)

Substitute our numbers into the equation for \(t\).

\(t=\frac{11400-3800}{3800*0.048}\)

Factor 3800 out of 11400.

\(t=\frac{3800*3-3800}{3800*0.048}\)

Factor 3800 out of −3800.

\(t=\frac{3800*3-3800*-1}{3800*0.048}\)

Factor 3800 out of \(3800*3-3800*-1\).

\(t=\frac{3800*(3-1)}{3800*0.048}\)

Cancel the common factor of 3800.

\(t=\frac{3-1}{0.048}\)

Simplify.

\(t=\frac{2}{0.048}\)

\(t=41.666\)

Merry Christmas!

Answer: The breaking point

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

6 / 2 = 3 hours

Answer: C = 170

Step-by-step explanation: 45+45+40+40 = 170

Answer:

Your answer is: B) 175ft

Step-by-step explanation:

To fid the perimeter you need to add all the sides together. Don't forget to add the sides that are not labeled, as well as the extra 5ft.

45+45+40+40+5=175

Let there are d number of deers in the forest when biologist capture 55 deers.

So the ratio of deer that are tagged is,

After two week, the number of deer for the sample are 40 and out of which tagged are 8.

So the ratio for the tagged deer is,

Sine the ratio of tagged deer is same for both cases.

So proportion for the total number of deers is,

As a result, the 95% CI for the population mean of shear strength is (31.053, 74.767).

The mean is a measure of central tendency in statistics that represents the average value of a group of numerical data. It is computed by summing all of the values in the dataset and dividing the total by the number of values. The mean is frequently used as a simple summary statistic to indicate a data set's middle location.

In this case, a) get the sample mean by combining all of the data and dividing by the total number of observations:

(22.2 + 40.4 + 16.4 + 73.7 + 36.6 + 109.9) / 11 = 52.91

As a result, the sample mean shear strength is 52.91.

b) The sample variance may be calculated using the following formula:

Sample variance = (xi - x)2 / (n - 1) where (xi - x) is the sample size.

The sample size is n, and 2 is the total of the squared deviations between each observation xi and the sample mean x.

We may compute the sample variance using the sample mean given in component (a) as follows:

[Sample variance] (30.0 - 52.91)

² + (44.0 - 52.91) (44.0 - 52.91)

² + (33.1 - 52.91) (33.1 - 52.91)

² + (66.7 - 52.91) (66.7 - 52.91)

² + (81.5 - 52.91) (81.5 - 52.91)

² + (22.2 - 52.91) (22.2 - 52.91)

² + (40.4 - 52.91) (40.4 - 52.91)

² + (16.4 - 52.91) (16.4 - 52.91)

² + (73.7 - 52.91) (73.7 - 52.91)

² + (36.6 - 52.91) (36.6 - 52.91)

² + (109.9 - 52.91) (109.9 - 52.91)

²] / (11 - 1) (11 - 1)

1012.0259 is the sample variance.

As a result, the shear strength sample variance is 1012.0259.

c) In order to obtain the sample median, we must first organize the data from least to largest:

16.4, 22.2, 30.0, 33.1, 36.6, 40.4, 44.0, 66.7, 73.7, 81.5, 109.9

When the number of observations is odd, the sample median is the middle value, which is:

40.4 is the sample median.

As a result, the sample median shear strength is 40.4. d) Confidence interval = sample mean * (s / (n))

We may compute the sample standard deviation using the numbers from sections (a) and (b) as follows:

Standard deviation of the sample = (1012.0259) = 31.817

When we enter the values into the formula, we get:

Interval of confidence = 52.91 2.228 * (31.817 / (11))

The confidence interval is 52.91 21.857.

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Answer:

1. 118

2. 2^2×5^2

3. 167

4. 10

Step-by-step explanation:

For number 3 i use BODMAS method and 4 you replace the given b=6 in the equation.

to figure out this equation, all you need to do is combine like terms!

x = 1x

4x = 4x

6x = 6x

1x + 4x + 6x = 11x

Hope this helped! :D

Answer:

11x is the answer

Step-by-step explanation:

the x by it self is a 1

There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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To verify if the relation is a function, it must be verified if from each value of x only one arrow departs.

A relation represents a function when each input value is mapped to a single output value.

In mapping notation, with the arrows, it must be verified if there is no input from which more than one arrow departs.

The problem is incomplete, hence the general procedure to verify if the relation is a function was presented.

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Answer:

Step-by-step explanation:

The first two questions are answered here

Use the equation for exterior angle

Exterior angle  = sum of non-adjacent interior angles

Answer:

x = 26° degrees the work bellow is correct i double checked it :)

Step-by-step explanation:

Hello !

Answer:

\(\Large \boxed{\sf length=13cm}\)

Step-by-step explanation:

The volume of a pyramid is given by \(\sf V_{pyramid}=\frac{1}{3} \times B\times h\) where B is the area of the base and h is the height.

This is a rectangular pyramid. We have where \(\sf B=l\times w\) l is the length and w is the width (breadth).

So \(\sf V_{pyramid}=\frac{1}{3} \times l\times w\times h\)

Given :

Let's replace h, w, l, \(\sf V_{pyramid}\) with their values in the previous formula :

\(\sf 728=\frac{1}{3} \times x\times 8 \times 21\\728=56x\)

Let's solve for x !

Divide both sides by 56 :

\(\sf \frac{56x}{56} =\frac{728}{56}\\ \boxed{\sf x=13cm}\)

Have a nice day ;)

Answer:

\(\huge\boxed{\dfrac{5}{12}x-5}\)

Step-by-step explanation:

\(\left(\dfrac{3}{4}x-1\right)-\left(\dfrac{1}{3}x+4\right)=\dfrac{3}{4}x-1-\dfrac{1}{3}x-4=\left(\dfrac{3}{4}x-\dfrac{1}{3}x\right)+(-1-4)\\\\=\left(\dfrac{3\cdot3}{4\cdot3}x-\dfrac{1\cdot4}{3\cdot4}x\right)+(-5)=\left(\dfrac{9}{12}x-\dfrac{4}{12}x\right)-5=\dfrac{9-4}{12}x-5\\\\=\dfrac{5}{12}x-5\)

the fraction of the class that are boys is 4/9. And the fraction of the class that are girls is 5/9.

What is ratio?

A ratio is a comparison of two or more quantities that are related in some way. It expresses the relationship between these quantities in terms of the number of times one quantity contains another. Ratios are usually expressed as a fraction, where the numerator represents the first quantity and the denominator represents the second quantity. For example, the ratio of boys to girls in a class of 40 students may be expressed as 2:3 or 2/3, meaning there are 2 boys for every 3 girls. Ratios can also be expressed in other forms, such as percentages or decimals. Ratios are commonly used in mathematics, science, engineering, and everyday life to compare quantities and make predictions or decisions.

A fraction is a number that represents a part of a whole or a ratio of two quantities. It consists of two numbers, a numerator and a denominator, separated by a line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or in the comparison. Fractions are used in many areas, such as mathematics, science, engineering, cooking, and everyday life. They can be added, subtracted, multiplied, and divided, and can be converted to decimals or percentages.

a) The total ratio of boys to girls in the class is 4+5 = 9. Therefore, the fraction of the class that are boys is 4/9.

b) The question is unclear as it seems to be asking for the same answer as in part (a). If you meant to ask for the fraction of the class that are girls, you can use the same approach: the fraction of the class that are girls is 5/9.

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The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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Answer:

C becausee I'm trying to help

Answer:

Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.

Step-by-step explanation:

The given equation is:

-x + 3y = 11

To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.

Let's suppose we have another equation with x, for example:

2x + 5y = 7

We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:

-2x + 6y = 22 (multiply the first equation by -2)

2x + 5y = 7 (the second equation)

Now we can add the two equations to eliminate x:

-2x + 2x + 6y + 5y = 22 + 7

Simplifying the equation, we get:

11y = 29

Dividing both sides by 11, we get:

y = 29/11

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 3y = 11

Substituting y = 29/11, we get:

-x + 3(29/11) = 11

Simplifying the equation, we get:

-x + 87/11 = 11

Subtracting 87/11 from both sides, we get:

-x = 11 - 87/11

Multiplying both sides by -1, we get:

x = 87/11 - 11

Simplifying the equation, we get:

x = (87 - 121)/11

x = -34/11

The height of the kite from the ground when the angle is 50 degrees is 232 feet.

The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.

Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.

To find the height of the kite above the ground we use the trigonometric identity of tangent.

Thus, we have:

tan(50°) = h/200

Now, using cross multiplication:

h = 200 tan(50°) ≈ 232 feet

Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.

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Answer:

y = 36

Step-by-step explanation:

given y varies directly  with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition when x = 5 , y = 15

15 = 5k ( divide both sides by 5 )

3 = k

y = 3x ← equation of variation

when x = 12 , then

y = 3 × 12 = 36

Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.

To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.

First, let's simplify the equation:

2^x - 2 = 8^4

We know that 8 can be expressed as 2^3, so we can rewrite the equation as:

2^x - 2 = (2^3)^4

Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:

2^x - 2 = 2^(34)

Simplifying the right side of the equation:

2^x - 2 = 2^12

Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:

x = 12

Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.

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The Interest (simple interest) will be less on Loan A.

What exactly is simple interest?

Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.

The simple interest formula is as follows:

SI=P*R*T/100

SI stands for simple interest.

P stands for principal.

R is the interest rate (in percentage)

T denotes the length of time (in years)

The following formula is used to compute the total amount:

Amount (A) = Principal (P) x Simple Interest (SI)

Now,

For A Principal=$10000, Time = 3 years, Rate=5%

then interest paid=10000*3*5/100

=300*5=$1500

For B  Principal=$10000, Time = 5 years, Rate=8%

Interest=10000*5*8/100

=500*8

=$4000

That means SI(B)>SI(A)

Hence,  

          The Interest will be less on Loan A.

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The sum total by the given data is equals to $658,880.

We are given that;

Percent=15%

Amount= $98,880

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:

15% = 0.15

To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:

$98,880 / 0.15 = $98,880 x 1/0.15

To multiply by 100, we can move the decimal point two places to the right. This gives us:

$98,880 x 1/0.15 x 100 = $658,880

Therefore, by the percentage the answer will be $658,880.

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