Chris is buying supplies for a school fundraiser and has $56 to spend. He buys popcorn for $3 per bag and cotton candy for
$7 per bag. He needs at least 7 bags of popcorn.
Graph the boundary lines of the linear inequalities on the graph below.
Also, plot the points that are part of the solution set from the list below.

(3, 7), (2, 2), (8, 1), (10, 2), (5, 5)

The calculated value of the equation of the circle in standard form is: (x - 4)^2 + (y - 1)^2 = 9

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (4, 1) and the radius is 3.

So we can plug in these values to get:

(x - 4)^2 + (y - 1)^2 = 3^2

Simplifying and expanding, we get:

(x - 4)^2 + (y - 1)^2 = 9

So the equation of the circle in standard form is: (x - 4)^2 + (y - 1)^2 = 9

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To find the sale price, we need to apply the discount to the original price:

Discount = 30% = 0.30

Original price = $50

Discount amount = Discount x Original price

= 0.30 x $50

= $15

Sale price = Original price - Discount amount

= $50 - $15

= $35

Therefore, the sale price after a 30% discount on an original price of $50 is $35.

Answer:

$35

Step-by-step explanation:

70% of 50 is 35

Answer:

C and D

Step-by-step explanation:

The expressions that are equivalent to 5x are:

None of the other expressions listed are equivalent to 5x.

The tangent line and the radius are perpendicular. and the value of x is 8

The correct answer is B. The tangent line and the radius are perpendicular.

In a circle, the tangent line at a point on the circle is perpendicular to the radius drawn to that point. This is a fundamental property of circles.

The value of x is calculated as

9 * x = 12 * 6

So, we have

9x = 72

Divide

x = 8

Hence, the value of x is 8

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Based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

x = 8 and y = 4

Two triangles are said to be congruent if the three sides and three angles are equal in all directions.

Two right triangles are congruent to each other by the Hypotenuse-Length Congruence Theorem (HL) if the hypotenuse length and one leg of a right triangle are congruent to the hypotenuse length and leg of the other right triangle.

Thus, for both right triangles to be congruent, it means that their hypotenuse and one of their corresponding legs must be equal to each other.

Use this to create two equations and solve them to get the value of x and y.

Equal Hypotenuse:

    x + y = 3y

⇒ x +4 -4 = 3y -4

⇒ x = 3y -4              ------------------------ (1)

Equal legs:

x = y +4                    _______________ (2)

Find the value of y, by substituting x = (y + 4) into eqn. 1.

   y + 4 = 3y - 4

⇒ -2y = -8

⇒ y = 4

Find the value of x, by substituting y = 4 into eqn. 2.

   x = y + 4

⇒ x = 4 +4

⇒ x = 8

Therefore, based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are: x = 8 and y = 4.

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The probability that the website has fewer than 8 million visitors in a single day is 0.2061 or 20.61%.Hence, option C is correct.

The traffic to the web site of Made by Charmz, LLC which sells customized mugs, follows a normal distribution,

with a mean of 8.5 million visitors per day and a standard deviation of 610,000 visitors per day.

The problem asks us to find the probability that the website has fewer than 8 million visitors in a single day.

Therefore, we need to find P(X < 8 million).

Using the Z-score formula, we have;

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Where X = 8 million, μ = 8.5 million and σ = 610,000.

Substituting the given values in the formula, we get:

[tex]Z=\frac{8-8.5}{0.61}=-0.8197[/tex]

Using a standard normal table, the probability corresponding to Z-score = -0.8197 is 0.2061.

Therefore, the probability that the website has fewer than 8 million visitors in a single day is 0.2061 or 20.61%.Hence, option C is correct.

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The value of x from the given triangle is 55°.

What is an exterior angle?

The angle between any side of a shape and a line that extends from the next side is known as the exterior angle. the angle formed by a shape's side and a line that extends from another side.

Here, we have

Given: A side of the triangle below has been extended to form an exterior angle of 125°.

We have to find the value of x.

From the given figure, the exterior angle of the triangle is 125° and x is the exterior angle to that.

Now, 125°+x=180°

x=180°-125°

x=55°

Hence, the value of x from the given triangle is 55°.

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If repeats are forbidden, the provided letters u, v, w, x, y, and z can be used to create 8 lists of length 3, each of which has a w or u in the second entry.

We can apply the inclusion-exclusion concept to resolve this issue.

First, let's determine how many total lists of length three can be created using the provided letters without any limitations. There are six options for the first submission, five for the second (since it must be either w or u), and four for the third (since no characters can be repeated). Thus, there are a total of the following lists:

6 × 5 × 4 = 120

Next, let's count the number of lists of length 3 that do not have a w or u in the second entry. We have 6 choices for the first entry, 4 choices for the second entry (since we can't choose w or u), and 4 choices for the third entry (since we can't repeat any letters). Thus, the total number of such lists is:

6 × 4 × 4 = 96

Similarly, we can tally the number of lists of length 3 lacking a w or u in the first entry as well as the number of lists of length 3 lacking a w or u in either the first or second entry. Which are:

4 × 5 × 4 = 80 (no w or u in first entry)

4 × 4 × 4 = 64 (no w or u in first or second entry)

Finally, we can use the principle of inclusion-exclusion to count the number of lists that have a w or u in the second entry. This is:

120 - 96 - 80 + 64 = 8

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A deep appreciation for the natural world and a desire to contribute to advancing scientific knowledge is essential for pursuing a career in astronomy.

Astronomers require a combination of scientific attitudes to excel in their work. To begin with, they need to be curious and passionate about exploring the unknown universe. They should also have a strong sense of patience, persistence, and attention to detail, given that astronomical observations can take a long time to produce results. A capacity for critical thinking, creativity, and problem-solving is also crucial in analyzing and interpreting data, developing theories, and testing hypotheses. Additionally, astronomers must be skilled in communication, as they often collaborate with colleagues, present their findings to the scientific community and the public, and engage in public outreach and education efforts.

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The 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.

The following formula is used to calculate a confidence interval for the proportion of all American adults who support same-sex marriage

KI = p ± z*(√(p*(1-p)/n))

where:

p = percentage of respondents who support same-sex marriage

n = sample size (total number of respondents)

z = z-score for the desired confidence level

substitute all the values in the above formula,

CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/n))

To compute confidence intervals, we need to know the sample size (n). the sample size is large, so we can use the normal distribution.

the random sample size of 1000 is taken as no sample size is specified.

For n = 1000,

CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/1000))

= 0.517 ± 0.032

Therefore, the 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.

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Answer:

3`1

Step-by-step explanation:

Answer: 12 inches

Step-by-step explanation:

The 20 inches is the hypotenuse whereas 16 inches is the height of the triangle respectively.

So,

let keep the paper's length as x inches.

20² = 16² + x²

x² = 20² - 16²

x = [tex]\sqrt{20^{2}-16^{2} }[/tex]

x = 12

I am not sure if this is right because i have never done a sum in inches before but  I hope this helps sorry if it is not right.

The domain of a function refers to the set of all values of the independent variable (usually denoted by x) for which the function is defined.

For the function f(x) = 2, the expression is defined for all real values of x. Therefore, the domain of f(x) is all real numbers.

If the function was f(x) = 2 / (x - 9), then the expression is undefined for x = 9. Therefore, the domain of f(x) would be all real numbers except 9.

If the function was f(x) = 2 / (x - 3)(x + 3), then the expression is undefined for x = 3 and x = -3. Therefore, the domain of f(x) would be all real numbers except 3 and -3.

If the function was f(x) = sqrt(2x - 5), then the expression is only defined for values of x that make the argument of the square root non-negative. Therefore, the domain of f(x) would be all real numbers such that 2x - 5 >= 0, which simplifies to x >= 5/2.

Therefore, without more information about the function, it is impossible to determine its domain.

Answer:

12a^3 +2a^2+23a+18

Step-by-step explanation:

We can conclude that 10% of the football players complete their degree in five years.

How to investigate the university's claim?

To investigate the university's claim, we can set up a hypothesis test.

Null hypothesis: The proportion of football players who complete their degree in five years is 0.9.

Alternative hypothesis: The proportion of football players who complete their degree in five years is less than 0.9.

We can use a one-tailed binomial test to test this hypothesis. The test statistic is the number of football players who received their degree in our sample of 20. Under the null hypothesis, this follows a binomial distribution with n=20 and p=0.9.

We can calculate the probability of observing 14 or fewer football players receiving their degree if the true proportion is 0.9:

P(X ≤ 14) = Σ P(X = i) for i = 0 to 14

= binom.cdf(14, n=20, p=0.9)

≈ 0.001

This means that the probability of observing 14 or fewer football players receiving their degree in a random sample of 20, if the true proportion is 0.9, is only 0.001.

If we use a significance level of 0.05, this means we reject the null hypothesis if the p-value is less than 0.05. Since our p-value is much smaller than 0.05, we can reject the null hypothesis and conclude that the proportion of football players who complete their degree in five years is less than 0.9.

Therefore, based on the given sample, we cannot conclude that 90% of the football players complete their degree in five years.

So, we can conclude that 10% of the football players complete their degree in five years.

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We can conclude that 10% of the football players complete their degree in five years.

To investigate the university's claim, we can set up a hypothesis test.

Null hypothesis: The proportion of football players who complete their degree in five years is 0.9.

Alternative hypothesis: The proportion of football players who complete their degree in five years is less than 0.9.

We can use a one-tailed binomial test to test this hypothesis. The test statistic is the number of football players who received their degree in our sample of 20. Under the null hypothesis, this follows a binomial distribution with n=20 and p=0.9.

We can calculate the probability of observing 14 or fewer football players receiving their degree if the true proportion is 0.9:

P(X ≤ 14) = Σ P(X = i) for i = 0 to 14

= binom.cdf(14, n=20, p=0.9)

≈ 0.001

This means that the probability of observing 14 or fewer football players receiving their degree in a random sample of 20, if the true proportion is 0.9, is only 0.001.

If we use a significance level of 0.05, this means we reject the null hypothesis if the p-value is less than 0.05. Since our p-value is much smaller than 0.05, we can reject the null hypothesis and conclude that the proportion of football players who complete their degree in five years is less than 0.9.

Therefore, based on the given sample, we cannot conclude that 90% of the football players complete their degree in five years.

So, we can conclude that 10% of the football players complete their degree in five years.

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Point E: (7, 3), Point F: (1, 3), Point G: (1, -2) and Point H: (7, -2) are the coordinates of each point.

To translate a point in the (x, y) coordinate plane, we add the translation distances to the x-coordinate and the y-coordinate of the point.

For each point in the quadrilateral EFGH, we can apply this translation as follows:

Point E: (4, 5) + (3, -2) = (7, 3)

Point F: (-2, 5) + (3, -2) = (1, 3)

Point G: (-2, 0) + (3, -2) = (1, -2)

Point H: (4, 0) + (3, -2) = (7, -2)

Therefore, after the translation of 3 units right and 2 units down, the coordinates of the points in quadrilateral EFGH are:

Point E: (7, 3)

Point F: (1, 3)

Point G: (1, -2)

Point H: (7, -2)

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With little knowledge of the square shape, we know that the area of the shaded region is (B) x² - 2y².

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

As we previously stated, a square is nothing more than a rectangle with equally long neighboring sides.

The area of a rectangle is therefore expressed as Area = Length Breadth.

So, according to the given figure:
The area of the shaded region would be:

x² - y²

But as we know that 2 triangles make up 1 small square, so the formula can be molded as:

x² - 2y²

Therefore, with little knowledge of the square shape, we know that the area of the shaded region is (B) x² - 2y².

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The area of the rectangle is [tex]$\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$[/tex] square units. Thus, the answer is option D: 10 square units.

What is area of rectangle?

The area of a rectangle is the measure of the region enclosed by its sides, and is calculated by multiplying the length and the width of the rectangle. The unit of area is typically expressed in square units, such as square meters (m²) or square feet (ft²).

The area of rectangle can be calculated using the distance formula to find the length and width of the rectangle, and then multiplying them. Let A(2,1), B(1,3), C(5,5), and D(6,3) be the coordinates of the rectangle's vertices.

The distance between A and B is [tex]\sqrt{(1-2)^2 + (3-1)^2} = \sqrt{1+4} = \sqrt{5}$.[/tex]

The distance between B and C is [tex]\sqrt{(5-1)^2 + (5-3)^2} = \sqrt{16+4} = \sqrt{20}$.[/tex]

So, the length of the rectangle is [tex]\sqrt{20}$ units.[/tex]

The distance between A and D is [tex]\sqrt{(6-2)^2 + (3-1)^2} = \sqrt{16+4} = \sqrt{20}$.[/tex]

The distance between C and D is [tex]\sqrt{(6-5)^2 + (3-5)^2} = \sqrt{1+4} = \sqrt{5}$.[/tex]

Therefore, the width of the rectangle is [tex]\sqrt{5}$ units.[/tex]

Hence, the area of the rectangle is [tex]$\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$[/tex] square units. Thus, the answer is option D: 10 square units.

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In 1960, the percentage of black students attending integrated schools in the South was approximately 2%.

Brown v Board of Education was a landmark decision in 1954 that declared segregation in public schools unconstitutional. However, it took several years for this decision to be implemented in Southern states, and in 1960, only 2% of black students in the South attended integrated schools. This highlights the resistance to desegregation in Southern states and the slow pace of change. It also underscores the ongoing struggles for civil rights and the continued efforts to address systemic racism in education and other aspects of American society.

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Thus, the two factors of quadratic expressions found after factorization are 2 and 3.

Factorization is the technique of expressing a given statement as the product between two or more components. The sum of the greatest common factors of the integer coefficients and the same letters with the smallest powers yields the greatest common factor for two or more monomials.

Given quadratic expressions:

=  x² - 5x + 6

To factorize the expression, find the factors of 6 such that on addition it becomes -5.

= x² - 3x - 2x + 6

Taking x common from first two terms and -2 from last two terms.

= x(x -3) -2(x - 3)

Taking (x - 3) common.

= (x - 3)(x - 2)

x -3 = 0

x = 3

and, x - 2 = 0

x = 2

Thus, the two factors of quadratic expressions found after factorization are 2 and 3.

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Complete question:

Factorize quadratic expressions:  x² - 5x + 6

Step-by-step explanation:

Perhaps you entered your question incorrectly

maybe you meant

x^2 -x + 6     THIS factors to

(x-3)(x+2)     <=====if you multiply this out, you will see = x^2 -x+6

Are you familiar with the Quadratic Formula ?

   for this Quadrtatic     a = 1      b = -1      c = 6

    if you plug these numbers into the Quadratic Formula you get the roots:

            x = 3   and x = -2

       then you know the quadratic is   (x-3)(x+2)

Answer:The surface area of rectangular prism is 166 m².

Step-by-step explanation:

Given that,

length l= 4 m

Width b= 5 m

Height h=7 m

Using the formula of surface area of rectangular prism

We substitute the value into formula

Hence, The surface area of rectangular prism is 166 m².

After solving (d + 3)(d² - 4d + 1) by using the FOIL method we get d³ - d² - 11d + 3.

The foil method is a strategy for organising your memory of the steps

needed to multiply two binomials. First, outer, inner, and last are the

letters that make up the acronym F-O-I-L.

To solve the given expression using the FOIL method, you have to follow the below steps:

F: Multiply the First terms (d x d²)

O: Multiply the Outer terms (d x -4d)

I: Multiply the Inner terms (3 x d²) and

L: Multiply the Last terms (3 x 1)

Finally, combine the like terms to get the answer

(d + 3)(d² - 4d + 1)= d(d² - 4d + 1) + 3(d² - 4d + 1)

                           = d³ - 4d² + d + 3d² - 12d + 3

                           = d³ - d² - 11d + 3

Thus, (d + 3)(d² - 4d + 1) equals d³ - d² - 11d + 3.

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Answer:

I think second one is the answer

Step-by-step explanation:

if a number is raised to a negative power u put 1 as the numerator and the number with a positive power and for p3 it stays the same

Answer:

[tex]\frac{p^3}{n^6}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

[tex]n^{-6}[/tex] p³

= [tex]\frac{1}{n^{6} }[/tex] × p³

= [tex]\frac{p^3}{n^6}[/tex] ( with positive exponents )

Answer:

B) 4 cubes

Step-by-step explanation:

V = s³

[tex] s = \sqrt[3]{V} [/tex]

[tex] s = \sqrt[3]{64} [/tex]

[tex] s = 4 [/tex]

Option D is incorrect because it gives a value that is not consistent with the scatter plot and the line of fit. The correct answer is: The y-intercept is 40.98. The machine starts with 40.98 ounces of diet soda.

In the context of a graph, the y-intercept is the point where a straight line or curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero. Mathematically, it is the value of y when x = 0 in the equation of the line or curve. The y-intercept is also known as the initial value or starting point of the graph. It is often denoted as (0, b), where b is the y-coordinate of the intercept point.

The y-intercept of the line of fit represents the starting point of the relationship between the two variables, in this case, the amount of diet soda in the machine and the time after the machine is filled. Therefore, the y-intercept value of 40.98 means that the machine starts with 40.98 ounces of diet soda when it is filled.

Option A is incorrect because the y-intercept is a starting value, and it does not represent a rate of change.

Option B is also incorrect because it suggests that the machine loses 4.8 fluid ounces of diet soda every hour, which is not what the y-intercept represents.

Option D is incorrect because it gives a value that is not consistent with the scatter plot and the line of fit.

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The cost of making a 5-minute international call using the given international calling plan is $2.25.

To calculate the cost of making a 5-minute call using unitary method, we need to determine the cost per minute of the call, and then multiply it by the number of minutes.

Given that the international calling plan charges 45 cents per minute or fraction of a minute, we can say that the cost per minute is 45 cents.

Using the unitary method, we can determine the cost of 1 minute of the call as follows

1 minute = 45 cents

5 minutes = 5 x 45 cents = 225 cents

= $2.25

Therefore, the cost of making a 5-minute call is $2.25

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Open circle and move to the left.

Answer:

angleC = 35°

Step-by-step explanation:

Because AC is the diameter of the circle, angle B = 90°

Then we can use the idea that there are 180° in a triangle to find angle C.

55 + 90 + c = 180

145 + c = 180

c = 35

The measure of angleC = 35°

To fill up the blanks such that each rectangle has the same area, we could assign the following numbers:

1. First two upper boxes in the first rectangle 2 and 4. The side box, 3.

2. For the two upper boxes in the second rectangle, we could assign the numbers, 10 and 8.

To find the area of a rectangle, you should multiply the length of the rectangle by its width. So, for the first rectangle, the sum of the length will be 6 and this will be multiplied by the width, which is 3.

Also, for the second rectangle, we could sum up the length to be 10 + 8 which is 18. If multiplied by 1, the result of the area will be 18.

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The rate that would result in a single investment doubling in 3 years with annual compound interest can be calculated using the rule of 72.

The rule of 72 states that if you divide 72 by the annual interest rate (as a percentage), you get the approximate number of years it takes for an investment to double in value.

So, to find the annual interest rate that would result in a single investment doubling in 3 years, we need to solve the equation: 72 / r = 3 where the r is the annual interest rate (as a percentage).

Simplifying the equation, we get:

r = 24

Therefore, the annual interest rate that would result in a single investment doubling in 3 years is 24%.

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