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Some people advise that in very cold weather, you should keep the gas tank in your car more than
half full. Lou's car had 6.5 gallons in the 14-gallon tank on the coldest day of the year. Lou filled the
tank with gas that cost $3.80 per gallon. How much did Lou spend on gas?
He spent $on gas.
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Answer:

Base = 8

Step-by-step explanation:

Area of a triangle can be calculated as:

Area = 0.5 x Base x Height

The values of the area and the height are given in order to find the length.

A= 52 in^2

Height= 13

First we have to find the base or the length. Using the values above we can set up the equation as:

1. 52= (0.5)(13)(b)

2. 52/0.5(13)

3. b=8

Answer: The length of the guitar or the base would be 8 inches.

I hope this helps and for future problems regarding this topic use the formula above!!

Formula: 0.5 x Base x Height

The vertices of the dilated triangle are (-2, 2), (3, 4), and (1, 1).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The coordinates of the triangle are (-4, 4), (6, 8), and (2, 2).

The scale factor of the triangle is 1/2 centered at the origin. Then the coordinate of the triangle will be given as,

⇒ (-4/2, 4/2), (6/2, 8/2), (2/2, 2/2)

⇒ (-2, 2), (3, 4), (1, 1)

The vertices of the dilated triangle are (-2, 2), (3, 4), and (1, 1).

The image of the triangle and dilated triangle is given below.

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Answer: The other answer is incorrect, the graph below shows the correct answer.

Coordinates of each point

A: (3,4)

B: (-2,2)

C: (1,1)

I know this is late, but I wanted to help those in the future who needed help with the question. Good Luck <3

The transformations that occur between each function are given as follows:

The transformation rules are defined as follows:

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The length a on the truss is given as follows:

a = 20.

As shown in the image given at the end of the answer, the truss is composed by a series of right triangles, hence the trigonometric ratios can be used to find the desired lengths on the truss.

The three trigonometric ratios are given as follows:

For side length a, we have that it represents the hypotenuse of a right triangle with side of 10 adjacent to the angle of 60º, hence the cosine function is used, as follows:

cos(60º) = a/10

1/2 = a/10

a = 2 x 10

a = 20.

The truss is given by the image shown at the end of the answer.

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The multiplication can be completed as follows: \((1 - ^2) (1 + ^2)\)= \(-2^2\), we can replace ² with 2 and simplify the expression. Thus, the answer is -4.

Given the multiplication \((1 - ^2) (1 + ^2)\), we can use the formula \(a^2 - b^2\) =\((a + b) (a - b)\), where a = 1 and b = ², to rewrite the expression as follows:

\((1 - ^2) (1 + ^2)\)

= \((1 - ^2^2)\)

= \((1 - 4)\)

=\(-3\)

However, the answer should be in the form of -2 raised to a power. Therefore, we can write -3 as -2 + 1, since -3 = -2 + 1 - 2.

Then, using the laws of exponents, we can write -2 + 1 as

\(-2^2/2^2 + 2/2^2\)

\((-2^2 + 2)/2^2\)

\(-2/4\)

\(-1/2\)

Finally, we can write -1/2 as -2/4, which is -2 raised to the power of -2. Thus, the multiplication can be completed as follows:

= \((1 - ^2) (1 + ^2)\)

=\((1 - ^2^2)\)

= \((1 - 4)\)

= \(-3\)

= \(-2^2+ 1\)

= \(-2^-^2\)

= \(-4\)

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Answer:

c=15.7

Step-by-step explanation:

c=2(pi)(r)

pi=3.14 in this question

r=2.5

c=2(2.14)(2.5)

Answer:

15.70 cm

Step-by-step explanation:

The formula for circumference is \(c = 2\pi r\), where r = radius. We are using 3.14 instead of pi here.

The radius is shown to be 2.5 cm, simply plug that into the equation and solve.

To solve, you must first carry out \(2.5*2 = 5\).

Then, multiply that product by pi, or, in this case, 3.14: \(5*3.14 = 15.7\)

So, the answer exactly  is 15.7. When rounded, it's technically 15.70 but that is absolutely no different than the exact answer.

(a) The power of the test for this two-sided alternative, with the given sample sizes, is approximately 0.921. (b) the sample size needed to detect this difference with a probability of at least 0.9 and α = 0.05 is approximately 559 for each machine.

What is power of the test?
The power of a statistical test is the probability of correctly rejecting a null hypothesis when it is false. It measures the test's ability to detect an effect or difference if it truly exists. A higher power indicates a greater likelihood of detecting the alternative hypothesis and avoiding a Type II error.

To calculate the power of the test, we need to compute the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, the alternative hypothesis would be that the proportion of defective parts is not equal between the two machines.

Using the formula for the power of a two-sample proportion test, the power can be calculated as follows:

Power = 1 - β = 1 - P(Type II Error)

where β is the probability of a Type II Error, which is the probability of failing to reject the null hypothesis when it is false.

Given the sample sizes and the probabilities of defects (p₁ = 0.05 and p₂ = 0.01), we can calculate the standard errors for the proportions and then use those to calculate the test statistic and the power.

Using the formula for the standard error of a proportion (SE = sqrt((p * (1 - p)) / n)), we find:

SE₁ = sqrt((0.05 * (1 - 0.05)) / 300) ≈ 0.009082

SE₂ = sqrt((0.01 * (1 - 0.01)) / 300) ≈ 0.005774

The test statistic for comparing two proportions is given by:

Z = (p₁ - p₂) / sqrt(SE₁² + SE₂²)

Calculating the test statistic, we have:

Z = (0.05 - 0.01) / sqrt(0.009082² + 0.005774²) ≈ 13.218

Next, we calculate the power using the standard normal distribution:

Power = P(Z > Z_critical) = 1 - P(Z ≤ Z_critical)

Z_critical is the critical value corresponding to the desired significance level (α = 0.05).

Using a statistical software or a standard normal distribution table, we find:

Z_critical ≈ 1.96

Hence, the power of the test for this two-sided alternative is approximately 0.921.

(b) To determine the sample size needed to detect this difference with a probability of at least 0.9 and α = 0.05, we need to calculate the required sample size for each machine.

The formula for sample size calculation in comparing two proportions is given by:

n = [(Z₁ - Z₂) / (p₁ - p₂)]² * (p * (1 - p) / (p₁ - p₂)²

where Z₁ is the Z-value corresponding to the desired power (0.9), Z₂ is the Z-value corresponding to the desired significance level (α = 0.05), p₁ and p₂ are the probabilities of defects, and p is the expected value of the common proportion (taken as the average of p₁ and p₂).

Using the given probabilities of defects (p₁ = 0.05 and p₂ = 0.01), we can calculate the required sample sizes.

Taking p = (p₁ + p₂) / 2 = (0.05 + 0.01) / 2 = 0.03, and plugging in the values into the formula, we have:

n = [(Z₁ - Z₂) / (p₁ - p₂)]² * (p * (1 - p) / (p₁ - p₂)²

= [(Z₁ - Z₂) / (0.05 - 0.01)]² * (0.03 * (1 - 0.03) / (0.05 - 0.01)²

Using Z₁ ≈ 1.282 (corresponding to a power of 0.9) and Z₂ ≈ 1.96 (corresponding to α = 0.05), we can calculate the required sample size:

n = [(1.282 - 1.96) / (0.05 - 0.01)]² * (0.03 * (1 - 0.03) / (0.05 - 0.01)²

≈ 558.96

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In the special right triangle, x has a value of √3/2

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.

To find the value of x, we should take into consideration that two of the sides of the triangle are equal to each other.

Using Pythagoras theorem;

\((\sqrt{3}) ^2 = x^2 + x^2\\3 = 2x^2\\x^2 = \frac{3}{2} \\x = \sqrt{\frac{3}{2} }\)

The value of x in the triangle is √3/2

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The reflexive closure of a relation on a set is the smallest reflexive relation that contains the original relation. In other words, it is the addition of pairs that ensure every element in the set is related to itself. To form the reflexive closure, we need to add pairs that relate each element in the set to itself.

To form the reflexive closure of relation r on the set {0, 1, 2, 3}, we need to add ordered pairs that ensure every element in the set is related to itself. In other words, we need to add pairs of the form (x, x) for each element x in the set that is not already present in relation r.

In this case, the reflexive closure of relation r would require adding the following ordered pairs: (0, 0), (1, 1), (2, 2), and (3, 3). These pairs ensure that every element in the set {0, 1, 2, 3} is related to itself, making the relation reflexive. These pairs ensure that every element is related to itself, satisfying the reflexivity property.

By adding these additional ordered pairs, we have modified relation r to include reflexivity, as every element now has a direct relation to itself in the set.

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Darin wrote 1 2/5 as a sum of three fractions. Three fractions 1/5, 4/5, 2/5 Darin have used. So the option d is correct.

Darin wrote 1 2/5 as a sum of three fractions.

We firstly solve the mixed fraction in the form of improper fraction.

We can write in improper fraction my multiplying 1 and 5, then add 2 in the multiplication of 1 and .

Now the fraction;

1 2/5 = 7/5

Now we solve each option to determine the three fraction.

a. 1/5, 2/5, 2/5

= 1/5 + 2/5 + 2/5

= (1 + 2 + 2)/5

= 5/5

= 1

It can't produce the value 7/5. So this option is not correct.

b. 3/5, 3/5, 3/5

= 3/5 + 3/5 + 3/5

= (3 + 3 + 3)/5

= 9/5

It can't produce the value 7/5. So this option is not correct.

c. 1/5, 2/5, 3/5

= 1/5 + 2/5 + 3/5

= (1 + 2 + 3)/5

= 6/5

It can't produce the value 7/5. So this option is not correct.

d. 1/5, 4/5, 2/5

= 1/5 + 4/5 + 2/5

= (1 + 4 + 2)/5

= 7/5

It produces the value 7/5. So this option is correct.

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The complete question is:

Darin wrote 1 2/5 as a sum of three fractions. What fractions might Darin have used?

a. 1/5, 2/5, 2/5

b. 3/5, 3/5, 3/5

c. 1/5, 2/5, 3/5

d. 1/5, 4/5, 2/5

Answer:

x = 17

Step-by-step explanation:

          x² + 9 = 298

Subtract 9 from both sides,

         x² + 9 - 9 = 298 - 9

                 x²    = 289

Prime factorize 289,

                 x²   = 17*17

Take square root,

                \(\sf \sqrt{x^2}= \sqrt{17*17}\)

                    x = 17

Trevor is shopping at Game Stop with a gift card, so he can spend, at most, $200. New video games cost $60 and used video games cost $25. If he buys one new video game, the maximum amount of used video games he can buy is 7.

The reason behind this is that Trevor has $200 gift card and he wants to buy one new video game that cost him $60. So the total amount he has spent on a new video game is $60 and now he has $140 left to spend on used video games.He can purchase the used video games for $25 each and the total cost must be less than or equal to $140 so that he doesn't exceed his budget. To find out the maximum number of used games he can buy, divide the remaining budget by the cost of the used games. The calculation is:140/25 = 5.6The calculation shows that Trevor can buy at least 5 used video games. However, the total cost of 5 used video games is $125, which is less than the remaining amount of $140 left on the gift card. Therefore, Trevor can buy at least 5 used video games plus one new video game that he has already purchased.Total used video games he can buy = 5 used video gamesSo, he can buy 5 used video games and 1 new video game. Therefore, Trevor can buy a total of 6 video games from Game Stop.

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The volume of the cone with a height of 9 inches and a diameter of 14 inches is 147π cubic inches. So, the correct answer is D).

To calculate the volume of a cone, we use the formula

V = (1/3)πr²h

where "r" is the radius of the base and "h" is the height of the cone.

In this problem, we are given the diameter of the base, which is 14 inches. To find the radius, we divide the diameter by 2

r = 14/2 = 7 inches

We are also given the height, which is 9 inches.

Now we can substitute these values into the formula

V = (1/3)π(7²)(9)

V = (1/3)π(49)(9)

V = (1/3)(441π)

V = 147π

So the volume of the cone is 147π cubic inches.

So the answer is option (D) 147π.

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You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

A. Anticlines Is the answer hope it is helpful

In hypothesis tests about the population correlation coefficient, the alternative hypothesis of not equal to zero is used when testing whether two variables are correlated or not.

The population correlation coefficient, denoted by ρ (rho), measures the strength and direction of the linear relationship between two variables in a population. If the null hypothesis is that the population correlation coefficient is zero (ρ = 0), then the alternative hypothesis of not equal to zero (ρ ≠ 0) implies that there is some non-zero correlation between the variables. In other words, the null hypothesis assumes that there is no linear relationship between the variables, while the alternative hypothesis allows for the possibility of a positive or negative linear relationship.

To test this hypothesis, a sample of data is collected, and the sample correlation coefficient, denoted by r, is calculated. If the sample correlation coefficient is sufficiently different from zero, then we can reject the null hypothesis in favor of the alternative hypothesis and conclude that there is evidence of a non-zero correlation between the variables. The level of significance and the sample size play important roles in determining the statistical significance of the correlation coefficient.

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Answer:

30:5 > Simplifies to 6:1 > 6/7 men or 1/7 females.

Answer:

6x + 12y

Step-by-step explanation:

Using distributive property means multiplying the number outside of the parentheses to each individual number within the parentheses:

3 × 2x = 6x

3 × 4y = 12y

Since there is an addition sign within the parentheses, we add these two numbers together. However, they are not like terms so their sum cannot actually be calculated

6x + 12y

Tom pays $23.54 for the shirt, and his cousin pays $18.72 for the shirt.

Since $1.54 is greater than $0.72, Tom spent more on tax compared to his cousin.

a. To calculate how much Tom and his cousin pay for the shirts, we need to add the sales tax to the base price of each shirt.

For Tom:

Base price of the shirt = $22.00

Sales tax = 7% of $22.00 = $22.00 * 0.07 = $1.54

Total amount paid by Tom = Base price + Sales tax = $22.00 + $1.54 = $23.54

For his cousin:

Base price of the shirt = $18.00

Sales tax = 4% of $18.00 = $18.00 * 0.04 = $0.72

Total amount paid by his cousin = Base price + Sales tax = $18.00 + $0.72 = $18.72

Therefore, Tom pays $23.54 for the shirt, and his cousin pays $18.72 for the shirt.

b. To determine who spent more on tax, we compare the amount of sales tax paid by Tom and his cousin.

Tom paid $1.54 in sales tax, while his cousin paid $0.72 in sales tax.

Since $1.54 is greater than $0.72, Tom spent more on tax compared to his cousin.

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Answer:

since the decay rate constant of0.0 250 min.

hence the time required for the sample to decay to one forth of it's initial value is

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a)Given differential equation is:d²y/dt² + 6 dy/dt +9y = cos t Where y(0)=1 and y′(0)=2.Let’s take the Laplace transform of both sides of the equation:d²y/dt² + 6 dy/dt +9y = cos tLaplace transform of the above equation is:L{d²y/dt²}+6L{dy/dt}+9L{y}=L{cos t} Where L{y}= Y(s), L{dy/dt}= sY(s)-y(0) and L{d²y/dt²}= s²Y(s) -sy(0)-y'(0) Laplace transform of the given function cos(t) is given by:L{cos t} = s/(s² + 1)

Therefore, the Laplace transform of the given differential equation is:s²Y(s)-sy(0)-y'(0)+6(sY(s)-y(0))+9Y(s)=s/(s²+1)Substituting y(0)=1, y′(0)=2, and solving for Y(s), we get:Y(s) = (s+1)/(s²+4s+8)(b)We have, Y(s) = (s+1)/(s²+4s+8)Let’s factorize the denominator of the above equation by completing the square:s²+4s+8 = (s+2)²+4Therefore,Y(s) = (s+1)/( (s+2)²+4)Let's first use a table of Laplace transforms and take the inverse Laplace transform of Y(s), we get:y(t) = e^{-2t} (cos2t - sin2t) + e^{-2t} + (1/2)cos(t)Therefore, the functions of time that will appear in the solution are e^{-2t}, cos2t, sin2t and cos(t).

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Answer:

v=0

Step-by-step explanation:

I think you mean 7(2+5v)=2v+14.

14+35v=2v+14 distribute

33v=0  Subtract 2v and 14

v=0 divide by 33 on both sides

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Patsy left home at 0730hrs to go Carol's house. She walked for 1hr^(40)mins then she stopped at the shop for 35 mins. She walked for a further 1hr^(20)mins. Therefore, Patsy arrived at Carol's house at 1125hrs.

The total time Patsy spent walking to the time she spent at the shop. Then, we can add this total time to the time she left home (0730hrs) to find the time she arrived at Carol's house.

Here are the steps: Convert 1hr^(40)mins to minutes: 1 hour = 60 minutes, so 1hr^(40)mins = 60 + 40 = 100 minutes.

Convert 1hr^(20)mins to minutes: 1 hour = 60 minutes, so 1hr^(20)mins = 60 + 20 = 80 minutes.

Add the walking time to the time spent at the shop: 100 + 35 + 80 = 215 minutes.

Convert 215 minutes to hours and minutes: 215 minutes = 3 hours and 35 minutes.

Add the time spent to the time Patsy left home: 0730hrs + 3 hours 35 minutes = 1125hrs

Therefore, Patsy arrived at Carol's house at 1125hrs.

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Answer: N=-4

Step-by-step explanation:

STEP

1

:

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  -4n - 9  =   -1 • (4n + 9)

Equation at the end of step

2

:

 -3 • (4n + 9) -  21  = 0

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  -12n - 48  =   -12 • (n + 4)

Equation at the end of step

4

:

 -12 • (n + 4)  = 0

STEP

5

:

Equations which are never true:

5.1      Solve :    -12   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2      Solve  :    n+4 = 0

Subtract  4  from both sides of the equation :

                     n = -4

One solution was found :

n = -4

Answer:

The answer is Negative Four -4

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Plug in x = 1 into the function expression. You should get  f(xx) = 4

Plug in x = 2 and you will get f(x) = 13

So the function value has increased from 4 at x = 1 to 13 at x = 2

or, just plot it and see it visually

The area of the sector is A = π cm² and amplitude is a = 0.75 cm

Given data ,

The area of a sector is given by the formula:

A = (1/2) x r² x θ

where r is the radius of the sector and θ is the central angle in radians.

On simplifying , we get

A = π cm²

r = 1.5 cm

Substituting these values into the formula, we get:

π = (1/2) x (1.5)² x θ

π = (3/4) x θ

Solving for θ, we get:

θ = (4/3) x π

The amplitude of the sector is half of the radius, so:

amplitude = (1/2) x 1.5 cm = 0.75 cm

Hence , the amplitude of the sector is 0.75 cm

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