Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates. A sandwich costs $2, and hot lunch costs $3.

This system of inequalities models the scenario:

2x + 3y ≤ 15
x + y ≥ 3

Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)

Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points)

Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)

The minimum value of f(8) - f(3) is 20.

The maximum value of f(8) - f(3) is 25.

In the question, we are given that, 4 ≤ f'(x) ≤ 5 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(8) - f(3).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [8, 3] with respect to dx, to get:

[tex]\int_{3}^{8}4dx \leq \int_{3}^{8}f'(x)dx \leq \int_{3}^{8}5dx\\\Rightarrow [4x]_{3}^{8} \leq [f(x)]_{3}^{8} \leq [5x]_{3}^{8}\\\Rightarrow 4*8 - 4*3 \leq f(8)-f(3) \leq 5*8 - 5*3\\\Rightarrow 20 \leq f(8) -f(3) \leq 25[/tex]

Thus, the minimum value of f(8) - f(3) is 20.

The maximum value of f(8) - f(3) is 25.

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Rewrite x − 2y = 16 in slope-intercept form as y = 1/2x - 8.

Slope (m) = 1/2

Y-intercept (b) = -8.

The slope-intercept equation helps us to easily identify the rate of change/slope (m) and the y-intercept (b) of an equation. It is given as y = mx + b.

Given, x − 2y = 16, in order to identify the slope (m) and y-intercept (b), rewrite the equation in slope-intercept form:

x − 2y = 16

-2y = - x + 16

Divide both sides by -2

-2y/-2 = -x/-2 + 16/-2

y = 1/2x - 8

As a function it would be written as y = 1/2x - 8.

Slope (m) = 1/2

Y-intercept (b) = -8.

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The area of each slice of the cake is 3π  square inches

The cake is 12 inches in diameter. The cake top is circular.

Therefore, the area of a circle is as follows;

area of a circle = πr²

where

Therefore,

r = diameter / 2

r = 12 / 2

r = 6 inches

Hence,

area of a circle = π × 6²

area of a circle = 36π

area of each sliced cake = 36π / 12  

area of each sliced cake = 3π  square inches

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Health insurance would be most helpful to Latoya.

Therefore, health insurance would be most helpful to Latoya.

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The number that could represent the number of students in class is = X + 2x

Let us take the number of boys to be = X

Then the number of girls is twice that of the boys. That is, y = 2x

Therefore the total number of students in the class z = X + 2x

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Answer:

x+40

Step-by-step explanation:

Let's say the the "number" is x.

"Forty more than a number" would be x+40

[tex]\Large\texttt{Answer}[/tex]

[tex]\bold{40+n}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ Letting n be the number

[tex]\bold n[/tex]

⇨ Add 40 to n (40 more)

[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)

Hope that helped

Answer: Choice D

Reason:

Add up the arc measures, then divide by 2

x = (32 + 54)/2

x = 86/2

x= 43 degrees

Answer:

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{6-3}{-4-2}=-\frac{1}{2}[/tex]

So, using the point (2,3), the equation is

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

Answer:

x = 5

Step-by-step explanation:

Ashley and Adam spent a total of 31 hours on their projects so: 3x+2+4x-6 = 31

3x+2+4x-6 = 31

7x-4 = 31

7x = 35

x = 5

Fraction of cake each children's  get 1/12.

fraction: In mathematics, a number that is stated as a quotient in which the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

Cake  available for Sharing = 1/6

The cake future divide into 1/2:

so,

= (1/6) x (1/2)

= 1/12

fraction of cake each children's  get 1/12.

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The solution of the given expression is:

(3*5)^6 = 11,390,625

Here we have an expression with an exponent, which is:

(3*5)^6

First, we can solve the thing inside the parenthesis is:

3*5 = 15

Replacing that we get:

(3*5)^6 = (15)^6

Now, the exponent 6 means that we need to multiply the number by itself 6 times, so we get:

(15)^6 = 15*15*15*15*15*15 = 11,390,625

Then we conclude that:

(3*5)^6 = 11,390,625

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Based on the given parameters, the value of the printer after 9 years is $3304

The given parameters about the exponential function are

Initial value, a = $7000

Depreciation rate, r = 8%

Time, t = 9

Exponential functions are different from linear functions, and they are calculated using the following exponential function

A = a *(1 - r)^t

To calculate the value in nine years, we have:

Substitute the known values in the above equation

A = 7000 * (1 - 8%)^9

Express 8% as decimal

A = 7000 * (1 - 0.08)^9

Evaluate the difference

A = 7000 * (0.92)^9

Evaluate the exponent

A = 7000 * 0.472

Evaluate the product

A = 3304

Hence, the value of the printer after 9 years is $3304

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Answer: 5040

Step-by-step explanation

We need to find how much it will depreciate each year based of of original cost.
8% of 7000
turn the percent into a decimal
.08
multiple .08 by the 7000
.08 * 7000 = 560

The printer depreciates 560 each year , to find the total for 9 years multiply by 9

560*9 =5040

Answer:

Answer:

  48 minutes

Step-by-step explanation:

The rate of filling from both pipes is the sum of the rates in units of tanks per hour. We want the time for 2/3 of a tank.

The sum of the filling rates is ...

  rate A + rate B = (1/3) tank/hour + (1/2) tank/hour = 5/6 tank/hour

The time to fill a tank or part thereof will be the number of tanks divided by the rate in tanks per hour:

  time = (2/3 tank)/(5/6 tank/hour) = ((4/6)/(5/6)) hour = 4/5 hour

There are 60 minutes in an hour, so the fill time is ...

  (4/5 hour)×(60 min/hour) = 48 min

It will take 48 minutes for both pipes to fill 2/3 of the tank.

Answer:

mint ----> 6

strawberry ----> 105

chocolate -----> 16

Step-by-step explanation:

90° ------> 12

so , 15° -----> 2

mint ---> 45° --> 15°× 3 ---> 2×3 --> 6

strawberry ---> 14 ---> 2×7 ---> 15° × 7 -->105°

chocolate ---> 120° ---> 8×15° --> 8×2 ---> 16

Yes, the pie chart and table show some information about the children's favorite ice cream flavors.

The pie chart shows that the most popular flavor is chocolate, with 30% of the children choosing it. Vanilla is the second most popular flavor, with 25% of the children choosing it. Strawberry is the third most popular flavor, with 20% of the children choosing it. The other flavors are less popular, with each receiving less than 10% of the votes.

The table shows the number of children who chose each flavor. There were 15 children who chose chocolate, 12 children who chose vanilla, 10 children who chose strawberry, 4 children who chose mint, 3 children who chose cookies and cream, and 2 children who chose coffee.

The pie chart and table together provide a good overview of the children's favorite ice cream flavors. Chocolate is the clear favorite, followed by vanilla and strawberry. The other flavors are less popular, but they still have some fans.

Here is a table that summarizes the information from the pie chart and table:

Flavor Number of Children Percentage

Chocolate 15 30%

Vanilla 12 25%

Strawberry 10 20%

Mint 4 10%

Cookies and cream 3 7.5%

Coffee 2 5%

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Answer:

Wouldn't she have had 5 cats before? Adding 2 other cats would make it 7, which fits the "more than 5 cats" requirement.

Answer:

66/65.

Step-by-step explanation:

22/5 / 13/3

Invert the divisor and multiply.

---> 22/5 * 3/13

= 66/ 65

Answer: Step 1

Step-by-step explanation: The order of operations states that multiplication must be done before addition. However, in step 1, 3x3-2 turns into 3x1 which is wrong. It should be 9-2 because you need to do the multiplication first.

The hypothesis is given as

H0:  μd< 0

H1: μd > 0

The null hypothesis is given as

H0:  μd< 0

H1: μd > 0

SWe have to find the value of s

we would use this formula s = sqrt [ (Σ(di - d)^2 / (n - 1) ]

This gives us  3.454

Next we have to determine the standard error

s / √(n)

3.454/2.8284

= 1.22

Degree of freedom = 8 - 1

= 7

t = (x1 - x2) - D / S.E

=  1.025

Find t critical at 0.10

= 1.895

P-value = 0.1697

d. Given that p value is greater thatn 0.1 we fail to reject the null hypothesis.

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Answer:

0

Step-by-step explanation:

A 0 horas, la temperature era 9.

The answer is 4x + 5y.

Here, what needs to be done is to combine like terms.

The area of  the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.

For given question,

We need to find the area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2]

The region bounded by given curves is as shown below.

The area of this region would be,

[tex]\Rightarrow A=\int\limits^\frac{1}{2} _0 {y-\frac{4}{\sqrt{1-x^{2}}}} \, dx \\\\\Rightarrow A=\int\limits^\frac{1}{2} _0 {4e^{-x}-\frac{4}{\sqrt{1-x^{2}}}} \, dx[/tex]

Now we evaluate above integral.

[tex]\Rightarrow A=4\int\limits^\frac{1}{2} _0 {e^{-x}-\frac{1}{\sqrt{1-x^{2}}}} \, dx\\\\\Rightarrow A=4[\int\limits^\frac{1}{2} _0 {e^{-x}}\,dx -\int\limits^\frac{1}{2} _0{\frac{1}{\sqrt{1-x^{2}}}} \, dx]\\\\\Rightarrow A=4([e^{-x}]_0^{\frac{1}{2} } -[sin^{-1}(x)]_0^{\frac{1}{2} })\\[/tex]

[tex]\Rightarrow A=4([1-\frac{1}{\sqrt{e} } ] -[\frac{\pi}{6} ])\\\\\Rightarrow A=4(1-\frac{1}{\sqrt{e} } -\frac{\pi}{6} )\\\\\Rightarrow A=|4~\times (-0.13013)|\\\\\Rightarrow A=0.521[/tex]

Therefore, the area of  the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.

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Answer:

8/11

Step-by-step explanation:

In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:

P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.

The limit does not exist.

In order for such a limit to occur, the fraction [tex]\frac{x^{2} }{x^{2} +y^{2} }[/tex] must be comparable to the same value [tex]L[/tex], regardless of the way we take to get there [tex](0,0)[/tex].

Try approaching [tex](0,0)[/tex] along the x-axis.

This means setting [tex]y=0[/tex] and finding the limit [tex]lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].

We obtain:

[tex]lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1[/tex]

Now evaluate approaching [tex](0,0)[/tex] along the y-axis.

This means setting [tex]x=0[/tex] and finding the limit [tex]lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].

[tex]lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0[/tex]

Approaching the origin via these two methods results in distinct limits.

[tex]lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex] ≠ [tex]lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }[/tex]

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

[tex]lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }[/tex]

Answer:

A perfect cube monomial must have three identical root , such that the product of the roots equal the perfect square monomial . The coefficient of the monomial must be divisible by 3 . Any monomial can be a perfect cube root .

Step-by-step explanation:

1.)1000=10 cube

2.) 729=9 cube

3.) 512=8 cube

4.) 343=7 cube

5.) 216=6 cube

6.) 125=5 cube

7.) 64=4 cube

8.) 27=3 cube

9.) 8=2cube

10.) 1=1 cube

1/2

Step-by-step explanation:

All outcomes of a single die= 6

Events less than 4 =3

probability=3/6

=1/2

The value of expression 9/9/3-6/10-6/10 is 9/5.

Given an expression 9/9/3-6/10-6/10.

We are required to simplify the expression 9/9/3-6/0-6/10.

Expression is combination of numbers,fraction, coefficients, determinants,indeterminants, symbols.It is mostly not found in equal to form. It also includes algebraic operations also.

Expressions: 9/9/3-6/10-6/10

This is present in fraction which is combination of two numbers one is numerator and denominator. The numbers above division sign are known as numerator and the numbers below division sign are known as denominator.

Invert the fraction which is given in denominator.

=(9*3)/9-6/10-6/10

=27/9-6/10-6/10

Taking LCM now.

=(270-54-54)/90

=(270-108)/90

=162/90

=9/5

Hence the value of expression 9/9/3-6/10-6/10 is 9/5.

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Using a quadratic regression equation, it is found that the prediction of y when x = 6 is of -154.70.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to  be inserted into the calculator are given as follows:

(-1, -2.75), (0, 2.15), (1, -1.60), (2, -13.85), (3, -34.55).

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = -4.721428571x² + 1.482857143x + 3.201428571

Hence, when x = 6, the prediction is:

y = -4.721428571 x 6² + 1.482857143 x 6 + 3.201428571

y = -154.70

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