Imagine that the price per gallon of gas with a $7 car wash is $3. 19 and the price without the car wash is $3. 39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?

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Question 9. The Angles (3 + 5x) and (x + 15) are forming linear pair, so

Question 10. Angle 58° + Angle (2x + 4) = 90, so

Question 11. 5x = 70°

Question 12. Angle 106° and Angle (2x +4) forms linear pair, so

Answer:

9. \(x=27\)

10. \(x=14\)

11. \(x=14\)

12. \(x=35\)

Step-by-step explanation:

9. \(3+5x+x+15=6x+18\)

==>> \(6x+18=180\); subtract 18 from 180 giving you 162, and finally 162 divided by 6 equals 27.

10.  \(90+58 = 148\\180 - 148 = 32\\2(14)+4=32\)

11. 70 and 5x are congruent so, \(180-70=110; 110/5 = 35\)

12. \(180-106=74; 74-4 = 70; 70/2 = 35\)

Joaquin will need 1 and two fifths cups to make his famous chocolate chip cookies for his friend's birthday party

To solve this problem we will use a rule of three with the problem information:

5 people-------- 1/4 cup of butter

28 people -------- x

Applying the rule of three we get:

x = ( 28 people * 1/4 cup of butter) / 5 people

x = 1,4 cup of butter

x = 1 + 2/5 cup of butter = 1 and two fifths cups

It describes the proportionality of 3 known data and an unknown data. When you have more than 3 known facts that are involved in the proportionality, it is known as a compound rule. The rule of three is also known as a direct proportions.

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The company should use a warranty period that is equal to 67,467.5 miles.

To determine the warranty period, we need to find the value of the tire life that corresponds to 95% of the tires. We can use the standard normal distribution table to find the value of the z-score that corresponds to the 95th percentile. This value is approximately 1.645.

Now, we can use the formula for the normal distribution to find the tire life value that corresponds to the z-score of 1.645. This formula is:

X = μ + zσ

Where X is the tire life value, μ is the mean of the distribution (65,000 miles), z is the z-score (1.645), and σ is the standard deviation of the distribution (1500 miles).

Plugging in the values, we get:

X = 65,000 + 1.645(1500)

X = 67,467.5

This means that 95% of the tires will have a life of at least 67,467.5 miles.

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For the linera regression equation with dependent variable is monthly expenses for medical care while his independent variable is number of family members. See the above Excel output.

a) The prediction equation is y = 110.47 + 16.83x.

b) Based on his model, each additional family member increases the predicted costs by 16.83 times.

Linear regression equation is used to predict the dependent variable value based on the value of one or more independent variables. We have y, the dependent variable as monthly expenses for medical care and x, the independent variable as number of family members. From the Excel output are present in above figure and we need to find the predicted regression equation. The prediction linear regression equation is written as

a) From the above data the prediction equation is y = 110.47 + 16.83x --(1)

where, y --> monthly expenses

x --> number of family members

b) Based on this model, with an unit increase in family member, the predicted cost increases by 16.83 times. Hence, the required value is 16.83.

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Complete question:

Bob White is conducting research on monthly expenses for medical care, including over-the-counter medicine. His dependent variable is monthly expenses for medical care while his independent variable is number of family members. above is his Excel output.

a) What is the prediction equation?

(b) Based on his model, each additional family member increases the predicted costs by how much?

The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.

In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:

Each term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.

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The full question is:

How many terms are in the following expression 6 + 2 x - 4 y + 5 z

The solution of the trigonometric equation is θ = π/6 radian

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

2cosθ = √3

Divide both sides by 2:

cosθ = (√3)/2

θ = cos⁻¹[(√3)/2]

θ = 30°

Convert 30° to radian by multiplying it with π/180. That is:

θ = 30 × π/180

θ = π/6 radian

Thus, the solution is θ = π/6 radian

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Answer:

196

Step-by-step explanation:

Formula for the nth term

Taking n = 64

Answer:

\(a_{64}=196\)

Step-by-step explanation:

Arithmetic sequence

General form of an arithmetic sequence: \(a_n=a+(n-1)d\)

where:

Given:

Substituting these into the equation to find the nth term:

\(\implies a_n=7+(n-1)3\)

\(\implies a_n=3n+4\)

To find the 64th term, substitute n = 64 into the formula:

\(\implies a_{64}=3(64)+4=196\)

20,000 pounds equals to 10 US ton.

Value conversion from Pound to US Ton

Add the value and the conversion ratio together.

1 pound = 0.0005 US ton

20,000 pounds worth

20,000 pounds × value of one US ton

20,000 × 0.0005

10 tons

Therefore, 20,000 pounds equals to 10 US ton.

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Answer:

P=60

Step-by-step explanation:

P=2(l+w)

P=2(14+16)

P=2(30)

P=60

Perimeter of a rectangle with 16in length and 14in width is 60 in.

Perimeter of a rectangle = 2(l+b)

here l = length and b= width

Given : l= 16 in and b= 14 in

perimeter = 2(l+b)

= 2(16+14)

= 2(30)

=60 inches.

The perimeter of rectangle is 60 inches

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Yes, the statement "if x is rational and y is irrational, then x + y is irrational" is true.

To understand why, let's break it down step by step:

1. First, let's define what it means for a number to be rational or irrational:
  - A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
  - An irrational number is a number that cannot be expressed as the ratio of two integers.

2. Given that x is rational and y is irrational, we can express x and y as follows:
  - x = a/b, where a and b are integers and b is not zero.
  - y = c, where c is an irrational number.

3. Now, let's consider the sum x + y:
  - x + y = (a/b) + c

4. To prove that x + y is irrational, we'll assume the contrary, that is, x + y is rational. This means we can express x + y as the ratio of two integers:
  - x + y = p/q, where p and q are integers and q is not zero.

5. We can rewrite this equation as follows:
  - (a/b) + c = p/q

6. Rearranging the equation, we get:
  - (a/b) = (p/q) - c

7. Since (p/q) is a rational number and c is an irrational number, the right side of the equation (p/q) - c would be the difference between a rational and an irrational number.

8. However, the difference between a rational number and an irrational number is always irrational. Therefore, the right side of the equation is irrational.

9. This contradicts our assumption that (a/b) is rational, leading us to conclude that x + y must be irrational.

In conclusion, if x is rational and y is irrational, then x + y is always irrational.

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The parameter is the percentage of coworkers who use the company's healthcare.

In statistics, the parameter is a numeric measurement that defines the characteristics of the population. It is generally denoted with Greek letters. In the provided scenario,

Ralph wants to estimate the percentage of coworkers that use the company's healthcare. He asks a randomly selected group of 200 coworkers whether or not they use the company's healthcare. Here, the parameter is the percentage of coworkers who use the company's healthcare.

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Answer:

\((6a-7)5a=30a^2-35a\)

Step-by-step explanation:

Message if you want a detailed explanation.

The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.

Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.

For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.

For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.

For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.

Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.

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Answer: 37/3 is the answer

Step-by-step explanation:

Answer:

5 is the answer

Step-by-step explanation:

Answer:

The total price is $9.30

Step-by-step explanation:

Price of the orders of popcorn= $5.25

Price of the drinks= $4.05

Answer:

$13 overpayment

Step-by-step explanation:

We can find the amount Trevor should pay each month by dividing the $26,555 by 36 months:

               ($26,555/(36 months)) = $737.64 per month

Since Trevor decide to round up to the nearest dollar, he will pay $738 each month.  That's an overpayment of $0.361 each month.

After 36 months of overpaying by $0.361 each month, Trevor will have overpaid:

  ($0.36/month)*(36 months) = $13 overpayment

Answer:

Rectangles! Nice.

Step-by-step explanation:

This is a very simple problem. Let's first represent the width of the rectangle as the variable x.

Then, we know that the length of the triangle is x+2. See where I'm going with this?

The formula for the perimeter of an rectangle is \(P=2*Length+2*Width\).

All we have to do next is just input our values for the length and width, and you'll be golden!

\(56=2(x+2)+2(x)\\56=4x+4\)

Next to subtract 4 from both sides and then to divide by 4!

\(52=4x\\x=13\)

There's your answer! Don't know why Brainly is bugged right now.

NOTE: If you can't read the answer above, the width is 13cm. This also means that the length is 15cm.

Hope this helps!

Stay safe!

Answer:

refer to the picture for step by step answer

hope it helps

Answer:

9

hope it's helpful ❤❤❤❤

THANK YOU

#

Answer:

Step-by-step explanation:

The total area under the standard normal is 0.0760.

What is the standard normal?

A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.

Here, we have

Given: the total area under the standard normal curve to the left of z = -1.48 or to the right of z = 2.48.

= P(z < -1.48 or z > 2.48)

= P(z < -1.48) + P(z > 2.48)

= 0.0694 + 0.0066

= 0.0760

Hence, the total area under the standard normal is 0.0760.

Question: Determine the total area under the standard normal curve to the left of z= -1.48 or to the right of z = 2.48.

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Answer:

a) 7.2 b) 10.4 c) 3.4 d) 3.6

Step-by-step explanation:

f(x) = 3(x - 1) - 0.4(9 - x)

a) f(2) + f(4)

First we will need to find f(2). Substitute 2 for x

f(2) = 3(2 - 1) - 0.4(9 - 2)

Use the distributive property

f(2) = (6 - 3) - (3.6 - 0.8)

f(2) = 3 - 2.8

f(2) = 0.2

Now we need to find f(4). It is the same process as we need for f(2), except x = 4 here

f(4) = 3(4 - 1) - 0.4(9 - 4)

f(4) = (12 - 3) - (3.6 - 1.6)

f(4) = 9 - 2

f(4) = 7

Now we add both answers together:

f(2) + f(4)

0.2 + 7 = 7.2

f(2) + f(4) = 7.2

b) f(5)

f(5) = 3(5 - 1) - 0.4(9 - 5)

f(5) = (15 - 3) - (3.6 - 2)

f(5) = 12 - 1.6

f(5) = 10.4

c) f(7) - f(6)

f(7) = 3(7 - 1) - 0.4(9 - 7)

f(7) = (21 - 3) - (3.6 - 2.8)

f(7) = 18 - 0.8

f(7) = 17.2

f(6) = 3(6 - 1) - 0.4(9 - 6)

f(6) = (18 - 3) - (3.6 - 2.4)

f(6) = 15 - 1.2

f(6) = 13.8

f(7) - f(6)

17.2 - 13.8 = 3.4

f(7) - f(6) = 3.4

d) f(3)

f(3) = 3(3 - 1) - 0.4(9 - 3)

f(3) = (9 - 3) - (3.6 - 1.2)

f(3) = 6 - 2.4

f(3) = 3.6

The values are

a) f(2) + f(4) = 7.2

b) f(5) = 10.4

c) f(7)-f(6) = 3.4

d) f(3) = 3.6

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.

Given:

f(x) = 3(x-1) - 0.4(9-x)

a) f(2) + f(4)

So, f(2)= 3(2-1) - 0.4(9 - 2)

f(2)= 3(1)- 0.4(7)

f(2)= 3 - 2.8

f(2)= 0.2

and, f(4)= 3(4-1) - 0.4(9 -4)

f(4)= 3(3)- 0.4(5)

f(4)= 9 - 2

f(4)= 7

Then,  f(2) + f(4)= 0.2 + 7 = 7.2

b) f(5)= 3(5-1) - 0.4(9 - 5)

f(5)= 3(4)- 0.4(4)

f(5)= 12 - 1.6

f(5)= 10.4

c)  f(7)-f(6)

So, f(7)= 3(7-1) - 0.4(9 - 7)

f(7)= 3(6)- 0.4(2)

f(7)= 18 - 0.8

f(7)= 17.2

and, f(6)= 3(6-1) - 0.4(9 -6)

f(6)= 3(5)- 0.4(3)

f(6)= 15 - 1.2

f(6)= 13.8

Then,   f(7)-f(6) = 17.2-13.8= 3.4

d) f(3)= 3(3-1) - 0.4(9 -3)

f(3)= 3(2)- 0.4(6)

f(4)= 6 - 2.4

f(4)= 3.6

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The surface area of the triangular prism is 27.4 ft².

The diagram above is a triangular base prism. Therefore, the surface area of the prism can be found as follows:

surface area of the prism = 2(area of the triangle) + 3(area of the rectangular face)

Therefore,

area of the rectangular face = 2 × 4

area of the rectangular face = 8 ft²

area of the triangular face = 1.7 ft²

Hence,

surface area of the prism = 2(1.7) + 3(8)

surface area of the prism = 3.4 + 24

surface area of the prism = 27.4 ft²

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The simplification of the given algebraic expression is; -³/₂x²

We are given the algebra expression as;

(3x³ + 15x²)/(-2x - 10)

Let us factorize the numerator to get;

(3x³ + 15x²) = 3x²(x + 5)

Similarly, let us factorize the denominator to get;

(-2x - 10) = -2(x + 5)

Thus, our original equation is now;

(3x³ + 15x²)/(-2x - 10) = [3x²(x + 5)]/-2(x + 5)

= -³/₂x²

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To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.

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

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))

First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.

Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.

Next, we calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380

Finally, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62

Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38

Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.

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