We created this inequality to represent how Amy can meet her revenue goals:


-100x2 + 15,750x + 212,500 ≥ 243,600


In this activity, you’ll solve this inequality to find the minimum ticket price Amy should charge to meet her minimum revenue goal.


Part A

Set the inequality greater than or equal to 0.


Part B

Simplify the inequality by dividing by the GCF so the leading coefficient is positive.

Part C

Factor the left side of the inequality by grouping.

Part D

Solve the quadratic inequality. Remember to check any possible solutions for viability.

Part E

What is the minimum number of $2 increases that Amy needs to apply to the ticket price to reach her desired revenue?

Part F

What’s the minimum ticket price that Amy can charge and reach her goal? Recall that the ticket price is represented by 25 + 2x, where x represents the number of $2 increases.

Answer: $7

Step-by-step explanation:

R = Revenue = $160

$160 = 30A - 50

(+50) (+50)

210 = 30A

(÷30) (÷30)

$7 = A

Answer:

16 was overall loss

Step-by-step explanation:

8x2=16

Answer:

16 yards.

Step-by-step explanation:

If they lost 8 yards twice, you are multiplying 8 by 2.

8 · 2 = 16.

That is your answer.

Hope this helps.

The standard deviation the manufacturer must achieve to reduce the 36-month failure rate to only 10% is approximately 4 months, the correct option is (d) .

If manufacturer wants to reduce 36-month failure rate to only 10 percent , then

We need to find value of standard deviation that corresponds to a 36-month lifespan such that only 10% of machines fail before that time.

We can find this by finding the corresponding z-score that corresponds to a cumulative probability of 0.10.

We know , "z = (x - μ)/σ" ;

where:

⇒ x = 36 (desired lifespan)

⇒ μ = 42 (mean lifespan)

⇒ σ = standard deviation we want to find

⇒ z = z-score that corresponds to a cumulative probability of 0.10

Substituting the given values and solving for "σ", we get:

⇒ -1.28 = (36 - 42)/σ

⇒ σ = (42 - 36)/1.28

⇒ 4.69

So , the standard deviation is approximately 4 months.

Therefore, The correct option is (d) 4 months.

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The given question is incomplete , the complete question is

A manufacturer claims that lifespans for their copy maxhines (in months) can be described by a Normal model N(42,7).

The manufacturer wants to reduce the 36-month failure rate to only 10%. Assuming the mean lifespan will stay the same, what standard deviation must they achieve?

(a) 1 months

(b) 2 months

(c) 3 months

(d) 4 months.

Answer:

$200 + $10x = $375

Well we're going to round up to $380, cause their making money in increments of 10 rather than 5.

And based off that I'd subtract $375 from $200 (375 -200 = 180)

Then take that answer and divide it by 10. (180 / 10)

Jesse will need to wash at least 18 more cars in order to afford the bicycle

The set of all images of the elements in the domain of a function is called the "range" or "codomain" of the function.

The set of all images of the elements in the domain of a function is called the range. The domain of a function refers to the set of input values or independent variables that the function can accept. It represents the set of values for which the function is defined. On the other hand, the range of a function refers to the set of output values or dependent variables that the function can produce. It represents the set of values that the function can take on as the input values change. The range is determined by evaluating the function for all possible input values in the domain. Thus, it is essential to determine both the domain and range of a function to fully understand its behavior and properties.

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Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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Inequalities help us to compare two unequal expressions. The statements that are correct are B, D, and E.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The complete question is:

Which statements are true about the linear inequality y >3/4 x – 2? Check all that apply.

-The slope of the line is –2.

-The graph of y >3/4 x – 2 is a dashed line.

-The area below the line is shaded.

-One solution to the inequality is (0, 0).

-The graph intercepts the y-axis at (0, –2)

-The slope of the line is 3/4. Thus, the first statement is false.

-The graph of y >3/4 x – 2 is a dashed line. The given statement is true.

-The area below the line is shaded. The statement is false.

-One solution to the inequality is (0, 0). The given statement is true.

-The graph intercepts the y-axis at (0, –2) The statement is true.

Hence, the statements that are correct are B, D, and E.

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The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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Answer:

Yes or No: Yes

Explanation: It is a function because each input is paired with only one output, as shown in the table.

Step-by-step explanation:

100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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Answer:

\(5\)

Step-by-step explanation:

Segments are named by their endpoints. Therefore, segment PQ will have endpoints P and Q. The length of the segment is equal to the distance between these points.

To find the distance between P and Q given their coordinates, use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Let:

\(P(-2, 7)\implies (x_1, y_1),\\Q(1, 3)\implies (x_2, y_2)\)

The distance between these points is equal to:

\(d=\sqrt{(1-(-2))^2+(3-7)^2},\\d=\sqrt{3^2+(-4)^2},\\d=\sqrt{9+16},\\d=\sqrt{25},\\d=\boxed{5}\)

Answer:

\(5\)

Step-by-step explanation:

This problem gives one the following points on a line: (\(P(-2,7)\)), and (\(Q(1,3)\)). The problem asks one to find the distance between the two points. The formula to find the distance between two points on a coordinate point is the following,

\(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Substitute the given values in and solve for the distance;

\(D=\sqrt{(-2)-(1))^2+((7)-(3))^2}\)

Simplify,

\(D=\sqrt{(-2)-(1))^2+((7)-(3))^2}\\\\D=\sqrt{(-3)^2+(4)^2}\\\\D=\sqrt{9+16}\\\\D=\sqrt{25}\\\\D = 5\)

According to the USA Today "Snapshot," 3% of Americans surveyed lie frequently. This means that out of a large sample of Americans, 3% of them admit to lying frequently. In your survey of 500 college students, you found that 20 of them lie frequently.

To compute the probability of at least 20 lying frequently in a random sample of 500 college students, assuming the true percentage is 3%, we can use a binomial distribution.
The formula for the probability of x successes in n trials with probability p of success is P(x) = (nCx)(p^x)((1-p)^(n-x)), where nCx represents the number of combinations of n things taken x at a time.

Using this formula, the probability of at least 20 college students lying frequently in a random sample of 500 college students is approximately 0.00002, or 0.002%. This is an extremely low probability, indicating that the results of your survey are unlikely to have occurred by chance alone.

However, this does not necessarily mean that the USA Today "Snapshot" is contradictory. It is possible that the true percentage of Americans who lie frequently is different from the percentage of college students who lie frequently. Additionally, the sample size and composition of your survey may not be representative of the entire population of college students. Therefore, while the results of your survey suggest that the true percentage of college students who lie frequently may be higher than 3%, it does not necessarily contradict the USA Today "Snapshot."
According to a USA Today "Snapshot," 3% of Americans surveyed lie frequently. We need to compute the probability that in a random sample of 500 college students, at least 20 lie frequently, assuming the true percentage is 3%. To do this, we can use the binomial probability formula:

P(x >= 20) = 1 - P(x <= 19)

Here, n = 500 (sample size), p = 0.03 (true percentage), and x represents the number of students who lie frequently.

Step 1:

Calculate the cumulative probability P(x <= 19):
We can use a cumulative binomial probability table or a calculator with a binomial cumulative distribution function (CDF). Using the CDF, we get:

P(x <= 19) = binomcdf(500, 0.03, 19) ≈ 0.964

Step 2:

Calculate the probability P(x >= 20):
P(x >= 20) = 1 - P(x <= 19) = 1 - 0.964 = 0.036

The probability that at least 20 out of 500 college students lie frequently is 0.036 or 3.6%. This result is slightly higher than the USA Today Snapshot's 3% figure.

However, this difference does not necessarily contradict the USA Today Snapshot. The slight discrepancy could be due to various factors, such as sample variation, differences in the population of college students compared to the general American population, or other sampling biases. The probability we calculated (3.6%) is still reasonably close to the 3% figure from the USA Today Snapshot, so it is not a strong contradiction.

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The length of BC in this problem is given as follows:

BC = 3.6.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The similar triangles for this problem are given as follows:

ABC and ADE.

Hence the proportional relationship for the side lengths is given as follows:

3/5 = BC/6.

Applying cross multiplication, the length BC is given as follows:

BC = 6 x 3/5

BC = 3.6.

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Answer:

(18, 25 )

Step-by-step explanation:

The translation rule

(x, y ) → (x + 3, y - 7 )

means add 3 to the original x- coordinate and subtract 7 from the original y- coordinate, then

(15, 32 ) → (15 + 3, 32 - 7 ) → (18, 25 )

Answer:

-18 + x = 11

x = 29

Step-by-step explanation:

To solve this, you can use the formula of a + b = c

\(-18 + x = 11\\-18 = 18\\11 + 18 = 29\\x = 29\)

Answer:

29

Step-by-step explanation:

Your equation can be -18+x=11. Since we don't know the number, we can use x. We are trying to find out a number that when it's added to -18, the answer will be 11.

Now, we solve the equation:

-18+x=11

x=11+18

x=29. Answer

To check this answer:

we can use our equation and substitute 29 for x.

-18+x=11

-18+(29)=11

11=11.

They are equal. Therfore, the answer is correct.

Answer:

2 metres per 1 hour

12 metres per 6 hours

30 minutes to glide 1 metre.

Step-by-step explanation:

1. To find the average speed, simply divide the distance covered by the amount of time taken, like so:

4 metres / 2 hours = 2 metres per 1 hour

2. To find how many metres the snail will glide in 6 hours, multiply the 2 metres per 1 hour by 6, like so:

6(2 metres per 1 hour) = 12 metres per 6 hours

3. Because we know that 2 metres take 1 hour to glide over, if we divide 2 in half, we get 1, so we can also divide 1 hour in half to get 30 minutes. Therefore, it takes 30 minutes to glide 1 metre.

Hope this helps :)

Answer:

328

Step-by-step explanation:

\(\frac{a}{1-r}\) is the equation for the sum of an infinite geometric series, where \(a\) is the first term of the infinite geometric series, and r is the common ratio between the terms. Here, we can find the common ratio between any consecutive terms. \(\frac{209.92}{262.4} = \frac{4}{5}\)

Therefore, \(\frac{a}{1-\frac{4}{5}} = 1640\).

This simplifies to \(5a = 1640\)

Therefore, \(a = 328\)

Jill earned $207 last week for picking 370 containers.

According to the information given, Jill picks corn and is paid at a piecework rate.

She receives 55 cents per container for the first 300 containers picked, and then she receives 60 cents per container for every container picked beyond 300.

Last week, Jill picked 370 containers. To calculate how much she earned, we can break it down into two parts:

the first 300 containers and the remaining 70 containers.

For the first 300 containers, Jill earns 55 cents per container. So, the amount she earned for the first 300 containers is:

300 containers x $0.55/container = $165

For the remaining 70 containers, Jill earns 60 cents per container. So, the amount she earned for the remaining 70 containers is:

70 containers x $0.60/container = $42

To find out the total amount Jill earned, we add the amounts she earned for the first 300 containers and the remaining 70 containers:

$165 + $42 = $207

Therefore, Jill earned $207 last week for picking 370 containers.

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Answer:

b

Step-by-step explanation:

In order to check if the new industrial product is profitable, we need to determine if the mean of the advance orders (4 units) is greater than or equal to the required number of units per customer (4.2 units).

Industrial products are physical goods or services produced by industries. These products are used in the production of other goods or services.

We can use a one-sample t-test to determine if the difference in means is statistically significant at the 1% level. The null hypothesis for this test is that the mean of the sample is equal to the required number of units per customer (4.2 units).

The one-sample t-test yields a p-value of 0.73, which is greater than the 1% level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the sample is not significantly different from the required number of units per customer. As such, the new industrial product is likely to be profitable.

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The series diverges according to the integral test.

To determine whether the series ∑(n=1 to infinity) (n-7) converges or diverges, we can use the integral test. The integral test states that if the series ∑(n=1 to infinity) a_n converges or diverges, where a_n is a positive, continuous, and decreasing function, then it is equivalent to the convergence or divergence of the integral ∫(1 to infinity) f(x) dx, where f(x) is the continuous and positive function that represents a_n.

In this case, we have the series ∑(n=1 to infinity) (n-7). To apply the integral test, we need to find the corresponding function f(x). We can see that (n-7) represents the value of the series at the nth term, so we can write it as a_n = n - 7.

Now, we need to find the function f(x) such that f(x) represents a_n = n - 7. Since a_n = n - 7, we can rewrite it as n = a_n + 7. We replace n with x in the equation to find f(x): x = a_n + 7. Solving for a_n, we get a_n = x - 7.

Now we have the function f(x) = x - 7. We can integrate this function to determine the convergence or divergence of the series:

∫(1 to infinity) (x - 7) dx.

Evaluating this integral, we get:

∫(1 to infinity)\((x - 7) dx = [x^2/2 - 7x]\)evaluated from 1 to infinity.

Taking the limit as x approaches infinity, we have:

lim\((x→∞) [x^2/2 - 7x] - [1^2/2 - 7(1)]\)

= lim(x→∞)\([x^2/2 - 7x - 1/2 + 7]\)

= lim(x→∞)\([x^2/2 - 7x - 6.5].\)

As x approaches infinity, the dominant term is\(x^2/2. \\\)Therefore, the limit becomes:

lim(x→∞)\(x^2/2.\)

Since this limit is divergent (approaches positive infinity), the integral ∫(1 to infinity) (x - 7) dx diverges.

By the integral test, we can conclude that the series ∑(n=1 to infinity) (n-7) also diverges.

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Answer:

6 x 3= 18

162/18=9

Each student sells 9 balloons.

Step-by-step explanation:

Answer:

9 balloons sold per student

Step-by-step explanation:

6 total groups 3 per group

6*3=18

18 students selling balloons

162/18=9

9 balloons sold per student

Answer:

Find K between M(1, -3) and N(4, 6) such that the

ratio of MK to KN is 1:2.

Step-by-step explanation:

Find K between M(1, -3) and N(4, 6) such that the

ratio of MK to KN is 1:2.

The coordinates of point K are (2, 0).

Given that there are three points M, K and N, such that M = (1, -3) and N = (4, 6) and the ratio of MK to KN is 1:2.

We need to find the coordinates of point K.

To find point K between M(1, -3) and N(4, 6) such that the ratio of MK to KN is 1:2, we can use the concept of section formula.

Let's assume the coordinates of point K are (x, y).

The section formula states that if a point K divides a line segment MN in the ratio m:n, then the coordinates of K are given by:

x = (n·x₁ + m·x₂) / (m + n)

y = (n·y₁ + m·y₂) / (m + n)

where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.

In this case, the ratio of MK to KN is 1:2, so m = 1 and n = 2.

Substituting the coordinates of M(1, -3) and N(4, 6) into the formula:

x = (2·1 + 1·4) / (1 + 2)

= (2 + 4) / 3

= 6 / 3 = 2

y = (2·(-3) + 1·6) / (1 + 2)

= (-6 + 6) / 3

= 0 / 3

= 0

So, the coordinates of point K are (2, 0).

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Answer:

b

Step-by-step explanation:

b

The constant of proportionality in the equation {y = x/9} is equivalent to (1/9).

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is the linear equation as follows -

y = x/9

This is the equation of a straight line, which is -

y = mx + c

{m} is slope and is also called the constant of proportionality.

We can write -

y = (1/9)x + 0

So, the constant of proportionality is equivalent to (1/9).

Therefore, the constant of proportionality in the equation {y = x/9} is equivalent to (1/9).

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Answer:

y = -2x + 9

Step-by-step explanation:

1) Use the equation y = mx + c (m being gradient and c being y-intercept)

2) Substitute all the values to get 7 = -2(1) + c

3) Solve to get c:

4) Final answer: y = -2x + 9

Answer: Line AB

Hope this helps

According to scientists with the USGS Cascades Volcanic Observatory, a lahar could take four hours to reach Puyallup but less than an hour to reach Orting.

The Washington Emergency Management Division has issued a survey to Pierce County residents to learn more about lahars, which are volcanic mudflows that contain a mixture of water and volcanic debris such as boulders. The survey is scheduled to close on Friday.

Hazard maps show that if Mount Rainier erupts, lahar could travel through river valleys as far as Puyallup, Tacoma, and Randle.

Some areas would have more time than others to evacuate. According to the US Geological Survey, previous Mount Rainier lahars travelled at 45-50 miles per hour.

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Answer:

C. y=x

Step-by-step explanation:

If you use a graphing calculator and plot the points (-3,5) & (5,-3) and then graph y=x you can see it is the line of reflection.

Also when reflecting over the line y=x, we switch our x and y.