On a​ map, 1 inch equals 15 miles. If two cities are 5 inches apart on the​ map, how far are they actually​ apart?

Answer:

0.333...

Step-by-step explanation:

since it's forever repeating it still counts as rational

Answer:

$5.30 is the answer

Step-by-step explanation:

since there are 12 muffins in a dozen muffins and 6 is half of twelve you multiply $2.65 by 2

Answer:

$5.30

Step-by-step explanation:

6 muffins is 2.65, a dozen is 12, 12 is double 6, 2.65 doubled is 5.30!

Answer:

C)  x = -1, y = 2

Step-by-step explanation:

Given system of linear equations:

\(\begin{cases}2x + 5y = 8\\4x + 3y = 2\end{cases}\)

Multiply the first equation by -2:

\(\implies -2 \cdot 2x -2 \cdot 5y=-2 \cdot 8\)

\(\implies -4x-10y=-16\)

Add this to the second equation to eliminate x:

\(\begin{array}{crcrcr}& 4x & + & 3y & = & 2\\+&(-4x & - &10y&=&-16\\\cline{2-6}&&-&7y&=&-14\end{array}\)

Solve for y:

\(\implies -7y=-14\)

\(\implies \dfrac{-7y}{-7}=\dfrac{-14}{-7}\)

\(\implies y=2\)

Substitute the found value of y into one of the equations and solve for x:

\(\implies 2x+5(2)=8\)

\(\implies 2x+10=8\)

\(\implies 2x=-2\)

\(\implies x=-1\)

Therefore the solution to the given system of linear equations is:

Answer:

c

Step-by-step explanation:

just trust me

Answer:

The population is 34,000. The sample is 2,000

Step-by-step explanation:

Population in statistics can be explained as the group or set of all elements which are of particular interest to a researcher or a study. In the scenario above, the research interest concerns customers who pay with a debit card, whose number amounts to 34,000, this value refers to the population. The sample is referred to as the subset of the population or larger sample, the sample from the study corresponds to number of debit card users who were selected at random to participate in the survey. This value is 2000.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

Think about the function y = f. (x). The range of the function is the range of all the y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see whether it is positive, negative, or equal to other values.

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Answer:

its 16

Step-by-step explanation:

8 /x = 10/20

20 * 8 =160

10 * x =10x

10x = 160

x=16

Answer:

(-4,2)

Step-by-step explanation:

See attachment

Answer:

A. 5

Explanation:

Given the points (-1,2) and (2,6):

To find the distance between the points, we use the distance formula:

The distance between the given points is 5 units.

Answer:

C

Step-by-step explanation:

it's c because this is a false statement, which means that the original statement is also a false one

so it doesn't have any answer

Answer:

The cost of the chocolate bar is $0.54. You can calculate this by subtracting the total cost of the peanut butter bars ($3.50) from the total cost of the 5 peanut butter bars and 6 chocolate bars ($6.40), resulting in $2.90 for the cost of the chocolate bars, which is then divided by 6 to get $0.54.

By using a fraction we can calculate 3/4 cups serving of 8/9 cups of yogurt. The answer is 3.56 times.

A fraction is a component of a whole. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in both the denominator and numerator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To determine how many 3/4 cups servings are in 8/9 cups of yogurt, we need to divide the amount of yogurt by the amount in one serving.

First, we need to convert 8/9 cup to a fraction with a denominator of 3:

8/9 cup = (8/9) ÷ (1/3) = 8/9 x 3/1 = 24/9 cup

Next, we can divide the total amount of yogurt by the amount in one serving:

24/9 cup ÷ 3/4 cup/serving = (24/9) ÷ (3/4) = 24/9 x 4/3 = 96/27 = 3.56

Therefore, there are approximately 3.56 servings of 3/4 cups in 8/9 cups of yogurt. Since we can't have a fraction of a serving, we can say that there are 3 servings of 3/4 cups in 8/9 cups of yogurt.

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Hello!

\(\large\boxed{z = -3}\)

1/2z + 6 = 3/2(z + 6)

Distribute the coefficient outside of the parenthesis:

1/2z + 6 = 3/2(z) + 3/2(6)

1/2z + 6 = 3/2z + 9

Subtract 1/2z from both sides:

6 = 2/2z + 9

Subtract 9 from both sides. Simplify 2/2z into z:

6 - 9 = z + 9 - 9

-3 = z

Both of the triangles are RIGHT triangles. y X(0,13) Y(0,7) Z(0,3) (0,0) J.  the length of vertical segment XY is 6.

Generally, A part of a line that is totally vertical is referred to as a vertical line segment. This means that the two vertices that make up the segment's ends have the same x- and y-coordinates but different z-coordinates than one another.

The length of vertical segment XY can be found by subtracting the y-coordinate of point X from the y-coordinate of point Y.

In this case, the y-coordinate of point X is 13 and the y-coordinate of point Y is 7, so the length of vertical segment XY is

13 - 7 = 6.

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The definite integral ∫(0 to 2) f(x)√(16 - x^4) dx, using u-substitution (u = x^2), simplifies to ∫(0 to 4) f(√u)√(16 - u^2) (1/2) du. The specific value of the integral depends on the function f(x) provided.

To solve the integral ∫(0 to 2) f(x)√(16 - x^4) dx using u-substitution, we begin by letting u = x^2. This choice of substitution allows us to simplify the expression and integrate with respect to u instead of x.

First, we need to find the differential du in terms of dx. Differentiating u = x^2 with respect to x, we have du = 2x dx.

Next, we substitute u and du into the integral. The limits of integration will also change accordingly. When x = 0, u = (0)^2 = 0, and when x = 2, u = (2)^2 = 4. The new integral becomes ∫(0 to 4) f(x)√(16 - x^4) dx = ∫(0 to 4) f(√u)√(16 - u^2) (1/2) du.

Now, we can evaluate the integral with respect to u, and then substitute back u = \(x^{2}\) to obtain the final result.

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Answer:

37%

Step-by-step explanation:

10 + 10 + 17 = 37 with pets

20 + 29 + 14 = 63 with no pets

63 + 37 = 100 students regarding pets or no pets

37/100 = percentage of students with pets

37/100 = 0.37 = 37%

Hope This Helps! •v•

Answer:

36

Step-by-step explanation:

so basically thats the answer

To show that two sides of one triangle are proportional to two corresponding sides of another triangle, with the included corresponding angles being congruent, you can use the Side-Side-Side (SSS) similarity criterion.

The SSS similarity criterion states that if the corresponding sides of two triangles are proportional and their corresponding angles are congruent, then the triangles are similar.
To prove this, follow these steps:

1. Given two triangles, let's call them triangle ABC and triangle DEF.
2. Identify two corresponding sides in each triangle that you want to show are proportional. Let's say AB and DE.
3. Also, identify the corresponding included angles, which are the angles formed by the corresponding sides. Let's say angle BAC and angle EDF.
4. Using the given information, state that AB/DE = BC/EF.
5. Now, prove that angle BAC = angle EDF. You can do this by showing that the two angles have the same measure or that they are congruent.
6. Once you have established that AB/DE = BC/EF and angle BAC = angle EDF, you can conclude that triangle ABC is similar to triangle DEF using the SSS similarity criterion.
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A differential equation with some initial conditions is used to solve an initial value problem.

The required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.

Let the given equation be \($y^{1/2} dy\ dx y^{3/2} = 1\), y(0) = 9

\($(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1\) …..(1)

Divide the given equation (1)  by \($\sqrt{ y} $\)  giving

\($y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$\), which is in Bernoulli's form.

Put \($u=y^{(1+1 / 2)}=y^{(3 / 2)}$\)

Then \($(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$\).

Multiply (2) by \($\sqrt{ } y$\) and we get

\(y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1\)

(2/3) \(u^{\prime}+u=1$\) or \($u^{\prime}+(3 / 2) y=3 / 2$\),

which is a first order linear equation with an integrating factor

exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is

\(u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$\)  or

\(\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}\)

To obtain the particular solution satisfying y(0) = 4,

put x = 0, y = 4, then

8 = (9/4) + c

c = (23/4)

Hence, the required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

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Answer:

2500 pieces of blank paper measuring 8 inches by 10 inches would need to be taped together.

Step-by-step explanation:

To determine how many 8-inch by 10-inch pieces of paper are needed to fit the enlarged map, we need to calculate the dimensions of the enlarged map.

The original map had a scale of 1 inch = 50 miles. Since the map was 8 inches by 10 inches, the actual area it represented was:

8 inches x 50 miles/inch = 400 miles (width)

10 inches x 50 miles/inch = 500 miles (height)

Now, we have a new scale of 2 inches = 25 miles. To find the dimensions of the enlarged map, we can use the ratio of the scales:

2 inches / 1 inch = 25 miles / x miles

Cross-multiplying, we get:

2x = 1 inch x 25 miles

2x = 25 miles

x = 25 miles / 2

x = 12.5 miles

So, the enlarged map will represent an area of 400 miles (width) by 500 miles (height), using the new scale of 2 inches = 25 miles.

To determine how many 8-inch by 10-inch pieces of paper are needed, we divide the dimensions of the enlarged map by the dimensions of each piece of paper:

Number of paper pieces needed = (400 miles / 8 inches) x (500 miles / 10 inches)

Number of paper pieces needed = 50 x 50

Number of paper pieces needed = 2500

Therefore, to fit the entire enlarged map, approximately 2500 pieces of blank paper measuring 8 inches by 10 inches would need to be taped together.

Answer:

rectangle only has 4 sides , a rectangular prism has 6 sides

The probability that the sample mean is between 190 lbs and 205 lbs is approximately 0.9617.

The sample mean to lie within 2.83 lbs of the population mean with probability 68%, or in other words, we expect the sample mean to be between 197.17 lbs and 202.83 lbs with probability 68%.

The sample mean weight of 50 baby elephants is a normally distributed variable with a mean of 200 lbs and a standard deviation of \(20/\sqrt{(50)} lbs = 2.83 lbs\)(by the central limit theorem).

The standard normal distribution to calculate the probability that the sample mean is between 190 lbs and 205 lbs:

z1 = (190 - 200) / 2.83 = -3.53

\(z2 = (205 - 200) / 2.83 = 1.77\)

\(P(-3.53 < Z < 1.77) = P(Z < 1.77) - P(Z < -3.53)\)

= 0.9619 - 0.0002

= 0.9617

The interval within which we expect the sample mean to lie within probability 68%, we need to find the values of x that satisfy the following equation:

\(P(\mu - x < X < \mu + x) = 0.68\)

X is the sample mean weight and \(\mu = 200\) lbs.

Using the formula for the standard error of the mean, we can rewrite this equation as:

\(P(-x / (20 / \sqrt{(50)}) < Z < x / (20 / \sqrt{(50)})) = 0.68\)

Z is a standard normal variable.

From the standard normal distribution table, we find that the 68% probability interval is from -1 to 1.

Therefore, we can solve for x as follows:

\(x / (20 / \sqrt{(50)}) = 1\)

\(x = 20 / \sqrt{(50)}\)

\(x \approx 2.83\)

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The required integral is:\(∫0π​sinmπxsinnπxdx={0,,​m=nm=n​∫−ππ​sinnxsinnxdx={0,​m=n​\)

Given the integral:

∫0π​sinmπxsinnπxdx={0,,​m=nm=n

​∫−ππ​sinnxsinnxdx={0,​m=n

​We need to prove the integral equal to zero for all m and n.

For m ≠ n:

∫0π​sinmπxsinnπxdx

Now use trigonometric identity:

sinA sinB = (1/2)[cos(A-B)-cos(A+B)]

Substituting A= mπx and B = nπx, we have:

∫0π​sin(mπx)sin(nπx)dx= (1/2)

∫0π​cos[(m-n)πx]dx= 0

because cos[(m-n)πx] is an odd function and the limits of integration are symmetric about the origin.

For m = n: ∫-ππ​sinn2x dx

Here, we use the identity:

cos2x= 2cos^2 x -1

⇒cos^2 x= (1/2)(1+cos2x)

Substituting this value in the integral, we get:

∫-ππ​(1/2)(1-cos2x)n dx= (1/2)

∫-ππ​(1-cos2x)n dx

Expanding the binomial:

∫-ππ​1 - ncos2x + ... dx= π- n

∫-ππ​cos2x dx= π

if n is odd, and 0 if n is even.

Hence, the required integral is:∫0π​sinmπxsinnπxdx={0,,​m=nm=n​∫−ππ​sinnxsinnxdx={0,​m=n​.

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Answer/Explanation

x    y

-1    -3

0     0

y- intercept (0,0)

slope: 3

Answer:

21x+6

Step-by-step explanation:

The  null and alternative hypothesis test the economist's claim is-

H₀: u = 863 ,H₁: u < 863

What is hypothesis test?

A applied math hypothesis test may be a technique of applied math abstract thought accustomed decide whether or not the info at hand sufficiently support a selected hypothesis. Hypothesis testing permits us to create probabilistic statements regarding population parameters.

Main body:

Let ц =average calories of virginia school lunches

The average calories in the school lunch is 863

Here the economists claims that after the testing period ends, the average caloric content in the lunches were dropped

The null hypothesis is H₀ц = 863

Means H₀ ;The average caloric content in the school lunch is 863

The alternative hypothesis is H₁ц <863

Hence , H₁; the average caloric content in the lunches was dropped.

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Answer:

40 feet

Step-by-step explanation:

-10 -30

12+0.2x=−25−0.7x

Stay Safe!!

Answer:

I got $0.42

Step-by-step explanation:

Answer:

(5,0)

Step-by-step explanation:

Answer: (5,x) or (5,0)