Tony and Jacob are selling fruit for a school fundraiser. Customers can buy small boxes of grapefruit and large boxes of grapefruit. Tony sold 12 small boxes of grapefruit and 8 large boxes of grapefruit for a total of $276. Jacob sold 6 small boxes of grapefruit and 9 large boxes of grapefruit for a total of $228. find the cost each of one small box of grapefruit and one large box of grapefruit

The solution set of the inequality is x ≤ - 4. The graph of inequality is shown below and the points x = - 4, x = - 12, x = - 42 are part of the solution set.

In this question we must use algebraic axioms and theorems to solve an inequality and graph the solution set with the help of a graphing tool. Now we proceed to present the procedure to solve for x:

7 - 2 · x ≥ 15

7 - 15 ≥ 2 · x

2 · x ≤ - 8

x ≤ - 4

Now we present the graph of the inequality. The points x = - 4, x = - 12, x = - 42 are part of the solution set.

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Chris and Jim must replace a total quantity of 17 tyres.

In this problem we must use an inequality of the form f(x) ≥ a, where f(x) is the difference between the number of tyres replaced by Jim and the number of tyres replaced by Chris:

(25/20) · x - x ≥ 3

(5/20) · x ≥ 3

x ≥ 12

Then, the minimum number of tyres to be replaced is n = 15 + 12 = 17 tyres.  

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The value of the directrix is -5/4.

According to the statement

we have given that the equation of parabola is y2 = 5x. And we have to find that the which equation represents the directrix.

We know that the general equation of parabola is

(y - k)2 = 4a(x - h)  -(1)

and given parabola equation is

y2 = 5x.  -(2)

After comparing the both equations we get k=0 and h=0

And the formula to find the directrix is

x = h - a

Substitute the values of h and a in it then

x = 0-5/4

x = -5/4.

Here the directrix is -5/4.

So, The value of the directrix is -5/4.

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Answer:

6

Step-by-step explanation:

[tex]\frac{y}{2} =x^{2} -7[/tex]

[tex]\frac{a}{2} =2^{2} -7[/tex]

[tex]\frac{a}{2} =-3[/tex]

[tex]a=-6[/tex]

[tex]\frac{b}{2} =1^{2} -7[/tex]

[tex]\frac{b}{2} =-6[/tex]

[tex]b=-12[/tex]

From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.

[tex]-6=2m+b[/tex]        

[tex]-12=m+b[/tex]

[tex]-24=2m+2b[/tex]

[tex]18=-b[/tex]

[tex]b=-18[/tex]

[tex]-12=m-18[/tex]

[tex]m=6[/tex]

Therefore, the slope of line l is 6.

Answer:

slope = 6

Step-by-step explanation:

substitute the given points into the equation of the curve to find a and b

(2, a )

[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )

a = - 6

then point (2, a ) = (2, - 6 )

(1, b )

[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )

b = - 12

then point (1, b ) = (1, - 12 )

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )

m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6

Answer:

B

Step-by-step explanation:

the value of the x should be the same if we want to verify whether x+2 is a factor of f(x)

so if x=-2 ,f(-2) = 29

x+2=0 f(0) = 1

f(0) [tex]\neq[/tex] f(-2) ,so x+2 is not a factor

what it actually means it that if we move the graphic of f(x) to left along to x axis 2 units, the graphic of new one cannot coincide with the original one.

Answer:

B. [tex]2^{-14}*5^{10}[/tex].

Step-by-step explanation:

Use the power of a power property.

[tex](2^{-7}*5^{5} )^{2}[/tex]

Multiply all the exponents in the parenthesis by 2.

[tex](2^{-7}*5^{5} )^{2}=(2^{-14}*5^{10} )[/tex]

The answer is B. [tex]2^{-14}*5^{10}[/tex].

Hope this helps!

Answer:

52 degrees

Step-by-step explanation:

Really easy, i learned it this summer

1. 180-128=52

2. 3=52 cus  alternate interior angles

The true statements are:

If two planes are said to have intersect each other, the intersection will be regarded as a line.

Hence, looking at the image attached, you will see that Points C, D, and A are noncollinear and the line containing points F and G is on plane R.

Note that when a line and a plane are said to intersect each other , the intersection will be a single point, or say a line. So Points A, B, and D are on both planes.

Therefore, option 1, 2, 4 and 5 are correct.

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Answer: option 1 , 2 , 4 , 5

Step-by-step explanation: edge 2022

Applying multiplication of functions, the total number of seats in the auditorium is given by:

h(x) = 80x² + 560x.

They are multiplied applying the distributive property, that is, all the terms are multiplied and then the common terms are added.

In this problem, the functions are given as follows:

Then the multiplication is:

h(x) = f(x)g(x) = 80x(x + 7) = 80x² + 560x.

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Answer:

The answer is b

Step-by-step explanation:

:)

Answer:

[tex]\dfrac{5}{2}\pi[/tex]

Step-by-step explanation:

Rotation about the y-axis

[tex]\textsf{Volume}=\displaystyle \int^b_a \pi x^2\:\text{d}y[/tex]

where:

Given function of y:  [tex]y = 3x^2[/tex]

Rewrite the given function as a function of y:

[tex]\implies x^2=\dfrac{1}{3}y[/tex]

Substitute the values into the formula:

[tex]\implies \displaystyle \int^4_1 \dfrac{1}{3}\pi y\:\:\text{d}y[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ay^n\:\text{d}y=a \int y^n \:\text{d}y$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $y^n$}\\\\$\displaystyle \int y^n\:\text{d}y=\dfrac{y^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Take out the constant and integrate:

[tex]\begin{aligned}\implies \dfrac{1}{3}\pi\displaystyle \int^4_1 y\:\:\text{d}y & = \dfrac{1}{3}\pi \left[\dfrac{1}{2}y^2\right]^4_1\\\\& =\dfrac{1}{3}\pi \left[\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1)^2\right]\\\\&=\dfrac{1}{3}\pi\left[8-\dfrac{1}{2}\right]\\\\&=\dfrac{5}{2}\pi \end{aligned}[/tex]

Therefore, the exact value of the volume of revolution is:

[tex]\dfrac{5}{2}\pi[/tex]

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Answer:

[tex]T_{23}=-153[/tex]

Step-by-step explanation:

[tex]T_{23}=a+(n-1)d\\[/tex]

[tex]=a+(23-1)d=a+22d[/tex]

Now [tex]a=-21[/tex] and

[tex]d=-27-(-21)\\=-6[/tex]

So [tex]T_{23}==21+((22)6\times-1)[/tex]

[tex]=-153[/tex]

The perimeter of the mat is 4m and the area of the mat is [tex]m^{2}[/tex].

The complete length of a square's boundary is referred to as its perimeter. To get the perimeter of a square, we must add all of its sides.

Perimeter of square = sum of the length  of all 4 sides.

In the question side of the mat is m.

Perimeter of the mat = m + m + m + m

                                   = 4m.

Therefore, the perimeter of the mat is 4m.
What is the area of the square?

The total number of unit squares in a square's shape is used to calculate its area.

Area = (Side x Side)

Since, side of the mat is m.

Area of the mat = m x m

                           = [tex]m^{2}[/tex]

Therefore, the area of the mat is [tex]m^{2}[/tex].

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Answer:

C. Radius or diameter must be known.

Step-by-step explanation:

The radius or diameter must be known so you can use the formula.

Hope this helps!

Answer: 14.353 or 18.647

Step-by-step explanation:

Hi.

Subtracting:

16.5 - 2.147 = 14.353

Adding:

16.5 + 2.147 = 18.647

The cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add  [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from  [tex]C_{i}[/tex]-1 to  [tex]c_{n}+1[/tex] and from  [tex]c_{n}+1[/tex] to  [tex]C_{i}[/tex]. Place  [tex]c_{n}+1[/tex] between  [tex]C_{i}[/tex]−1 and  [tex]C_{i}[/tex] to get the desired path.

Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n. By generalizing this in form of a principle which we would use to prove any mathematical statement is 'Principle of Mathematical Induction'.

The question says that between any two cities X and Y, either there’s an

one-way road from X to Y or from Y to X, but not both. Then show that

there is a path from some city A which visits all the cities exactly once.

This problem is very similar to the Football league problem #7 in Homework 1. This problem can be modeled as a directed graph in which cities

are represented as vertices and there’s an edge from vertices X to Y if

there’s a road from cities X to Y. And then, our goal is to find a path

in this graph which visits every vertex in the graph.

The rest of the solution is very similar to the argument in Problem 7 of

homework 1. We use induction of number of cities, say n.

As a base case, if n = 2, there are only two cities X and Y and the path

is simply the edge between X and Y.

For induction hypothesis, assume that the statement is true for any set

of n cities. That is’ for any set of n cities, we can find a path which visits

all the cities exactly once.

Let’s prove the statement for n + 1 cities. Leave out n + 1 th city (say,

[tex]c_{n}+1[/tex]) and for the remaining n cities, by induction hypothesis, we can find a path which visits all these n cities exactly once. Let us label the cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add  [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from  [tex]C_{i}[/tex]-1 to  [tex]c_{n}+1[/tex] and from  [tex]c_{n}+1[/tex] to  [tex]C_{i}[/tex]. Place  [tex]c_{n}+1[/tex] between  [tex]C_{i}[/tex]−1 and  [tex]C_{i}[/tex] to get the desired path.

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Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is (72.37, 81.63).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are given as follows:

[tex]\overline{x} = 77, \sigma = 12.2, n = 46[/tex]

Hence the lower and upper bound of the interval are given, respectively, by:

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Answer:

the 50th percentile = 66

The 25th percentile = 35

The 75th percentile = 85

Step-by-step explanation:

 We have 11 numbers ,so we are dealing with an odd set of values.

Also ,we notice that the numbers are already in order.

then

the 50th percentile of the set  27, 34, 35, 48, 48, 66, 75, 85, 85, 96, 99

is the 6 number in the list [ 6 = (11+1)/2 ]

Which is 66.

The 25th percentile (the median) of the set 27, 34, 35, 48, 48

is the 3rd number [ 3 = (5+1/)2 ]

Which is 35.

The 75th percentile (the median) of the set 75, 85, 85, 96, 99

is the 3rd number [ 3 = (5+1/)2 ]

Which is 85.

Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.

A linear function is modeled by:

y = mx + b

In which:

The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:

w = 32 - 0.05n

The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.

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Answer:

.05 liters

Step-by-step explanation:

The method that was used to arrive at the approximate population probability is called; a reasonable statistical generalization

Statistical generalization is a concept that involves inferring the results from a sample and applying it to a population. Carrying out this means that the sample must be selected randomly and be representative of the population.

Now, in this case, we see that the sample gave a probability of 68% to represent those were in favor of legalizing recreational marijuana use.

Now, since the conclusion was approximated to 70% to reflect the probability of the population then we can say that a reasonable statistical generalization was utilized.

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The values of 'j' are -11,5.

What is a Quadratic Equation?

Here, the given equation is (2x+7)(x-5) = - 43 + jx

On simplifying the equation we get,

[tex]2x^{2} -10x+7x-35=-43+jx\\2x^{2} -3x-35+43-jx=0\\2x^{2} -3x-jx+8=0\\2x^{2} -(3+j)x+8=0.....(1)\\[/tex]

By comparing the given equation with the standard form of the quadratic equation we get,

a = 2

b = - (3 + j)

c = 8

Therefore,

[tex](-(3+j))^{2} -4\times2\times8=0\\(3+j)^{2} -64=0\\(3+j)^{2} =64\\[/tex]

Take the square root of both sides,

[tex]\sqrt{(3+j)^{2} }=\sqrt{64} \\[/tex]

3 + j = ±8

Therefore,

3 + j = 8

j = 8 - 3        

j = 5

or

3 + j = -8

j = -8 - 3

j = -11

Hence, the possible values of 'j' are -11,5.

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The sequence of transformation will be;

Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.

We want to find the transformation that maps Quadrilateral ABCD onto Quadrilateral A'B'C'D'.

Looking at the given image, the sequence of transformation will be;

Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.

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Answer:

this graph has an x-intercept values of -1 and 2

Answer:

1.11

Step-by-step explanation:

The inference that can be made from the dot plot is the range of each round is the same.

A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.

Range is the difference between the largest number and smallest number.

Range of round 1 = 8 - 5 = 3

Range of round 2 = 9 - 6 = 3

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For the males' data, we can logically deduce the following data elements:

Mathematically, the male IQR can be calculated by using this formula:

IQR = Q₃ - Q₁

IQR = 14 - 2

Male IQR = 12.

Next, we would find the difference between the median values:

Note: The median of male's data is equal to 10 while median of female's data is equal to 18.

Difference, d = 18 - 10

Difference, d = 8.

The male's data has an outlier probably due to sampling technique used while the female's data doesn't have an outlier. Thus, the median would be a better measure of center for the male's data and the mean being a better measure of center for the female's data.

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Answer: s

Step-by-step explanation:

The probability of rolling an odd number is 9/19.

According to the statement

Total number of possible outcomes = 38

Odd numbered of outcomes = 18

Now we find the probability

Probability = possible outcomes / total outcomes

Probability = 18/38

Probability = 9/19

So, The probability of rolling an odd number is 9/19.

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The extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.

In the question, we are given a graph showing the bird population of a large lake and are asked the reason for the extreme drop between November and December most likely represent.

Birds migrate in order to shift from low-resource regions to high-resource areas or vice versa. The two main items sought after are food and places to build nests.

Thus, the fall in the graph for the number of birds between November and December represents the migration pattern of birds, in search of new resources.

Hence, the extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.

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Answer: A reflection of the migratory nature of the birds at the lake.

Answer:

Answer:The chocolate are 0.0042 lighter than the stated on the label

Mike brought $15 and Hallie brought $45 to the movie

There are many ways to define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

The value of the variable that makes the equation a true statement is the solution to the equation.

We have to find how much money Mike and Hallie brought to the movie.

Let the money Brought by Mike be $ m and by Hallie be $ h.

Mike and hallie are going to a movie. together they bring $60 in cash

m + h = $ 60.............(1)

Hallie brings three times as much cash as mike does

h = 3 m.......... (2)

Pur the value of h from equation (2) in equation (1)

m + 3 m = $ 60

4 m = $ 60

m = $ 60/4

m = $ 15

put this value of m in equation (2)

h = 3(15)

h = $ 45

Hence we created a system of equations that models the information given in this problem and Mike brought $15 and Hallie brought $45 to the movie

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