Average Allowance
Amount Frequency
$20
$15
$10
$5
11 P What is the
mode of this
data on
allowance
amounts?
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MH MH
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Answer:

13:

x= 86°

14:

x= 30°

16:

x= 59°

Answer:

See attached graphs Graph1, Graph2 and Graph3 and detailed explanation below

Step-by-step explanation:

The process for plotting and shading are essentially the same but with different inequalities

To plot any line

To determine area to shade

Choose a point on either side of the line from the graph. See if the corresponding (x,y) values satisfy the inequality. If they do, then that's the area to shade. If not, shade the other area

1. Inequality y > -3x - 2

The line equation is y = -3x -2

Let's choose x = 0. Then y = -3(0) -2 = -2. So one point is (0, -2)

Choose another value for x, say x = 1

y = -3(1) - 2 = -3-2 = -5. So another point is (1,-5).

Draw a straight line through both points (see attached Graph1)

Determining area to shade

Choose a point on the graph on one side of the line. Let's choose (1,2). So x = 1 and y = 2. Does this satisfy the inequality y = -3x -2? Let's see

Is 2 > -3(1) - 2 ?

2 > -3-2 ?

2 > -5 ? YES since a positive number is greater than a negative number. So the area containing (1,2) should be shaded as shown in Graph 1

2. Inequality 4x + 5y ≤ 20

Line equation is  4x + 5y =20

Convert to a function of x as follows

Choose two values of x and find corresponding y values to get the coordinates of two points

Plug x = 0 into line equation ==> y = 4- 4x/5

==> y = 4 - 4(0)/5 = 4

==> (0, 4) is one point

Choose another value of x, say 5(this is a convenient value since we are dividing by 5)

==> y = 4- 4(5)/5 = 4-4 = 0

==> (5, 0) is another point

Draw straight line through (0,4) and (5,0)

To determine area to shade let's choose a point on the graph. (0,0) is a convenient point.  Do the values of x=0 and y=0 satisfy the inequality
4x + 5y ≤ 20?

Plugging in x = 0 and y = 0 gives us

4(0) + 5(0) = 0 and 0 is indeed ≤ 20

So the inequality is satisfied at (0,0)

Shade the region on the side of the line where (0,0) is (see Graph2)

3. Inequality y > -4

The line equation is y = -4

Since this equation does not involve x, the line plot will be a horizontal line at y = -4 for all x values

Simply draw a horizontal line which crosses the y axis at y = -4

To determine which area to shade, choose a point. Use (0,0)

Does y = 0 satisfy the inequality y > -4?

0 > -4 so indeed the point (0,0) satisfies the inequality. Just shade the area on the side of the line which contains (0,0). This will be the region above the line y = -4 See Graph3

Hope that helps :)

Domain = ∈ [2, ∞]

Range = ∈ [0, ∞]

Graph [tex]\sqrt{x - 2 [-10, 10, -5, 5]}[/tex]

Just outline the function.

The typical root operation is:

[tex]y = a * \sqrt{(x - h)} + k[/tex]

where x - h ≥ 0

The value within the root sign of a square root function CANNOT be < 0

∴ x - h ≥ 0

∴ x ≥ 2

Therefore, Domain = ∈ [2, ∞]

Regarding range, the function we were provided doesn't have a K value.

As a result, the range spans from 0 to infinity.

Therefore, Range = ∈ [0, ∞]

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The least cost per unit of peanut butter is $0.095 for 20 ounces for ​$1.90 therefore option (B) will be correct.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variable called division.

Given the four options of jars;

1) 16 ounces for ​$1.70

Cost per ounces = 1.70/16 = $0.10625

2) 20 ounces for ​$1.90

Cost per ounces = 1.90/20 = $0.095

3) 26 ounces for ​$3.33

Cost per ounce = 3.33/26 = $0.128

The least cost per ounce is $0.095 for 20 ounces for ​$1.90.

Hence "The least cost per unit of peanut butter is $0.095 for 20 ounces for ​$1.90".

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Answer:

B & C

Step-by-step explanation:

a rate has to have an incline or decline. A&D are set amounts.

-[tex]\sqrt{3}[/tex] is the exponent of the power function.

The power function is generally just f(x) = c x^p for some constant c and some real number exponent p. (It can only be defined for positive values ​​of x.) For example, the square root function f(x) = √x is a power function with p = 1/2.

In this case, N=kA‾‾√3 , -[tex]\sqrt{3}[/tex] is the exponent of this function.

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent or power n, and pronounced as "b to the n".

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The exponent of the power function is 1/2.

How often we are multiplying a number by itself is indicated by its exponent. To multiply 3 four times, for instance, we get 34. It is 3333 in its enlarged form. A number's power is another name for an exponent. It may take the form of an integer, a fraction, a negative integer, or a decimal.

A fractional exponent is one where the exponent of a number is a fraction. Parts of fractional exponents include square roots, cube roots, and nth roots. Square root of the base is a number having a power of half.

Hence we get the exponent of the function as 1/2.

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The statement that best describes the expression p-1(x) is (c) the amount for x grams

The equation of the function is given as

P(n) = 0.2n + 5.3

(a) which statement best describes (p^-1) (x)?

The function is given as

P(n) = 0.2n + 5.3

This means that the inverse of the function is represented as p-1(n)

Hence, the statement that best describes the expression p-1(x) is (c) the amount for x grams

(b) The function p^-1 (x)

We have

P(n) = 0.2n + 5.3

Rewrite as

y= 0.2x + 5.3

Swap x and y

x = 0.2y + 5.3

Make y the subject

y = 5x - 26.5

Express as inverse function

p^-1(x) = 5x - 26.5

(c) The value of p^-1 (6.6)

We have

p^-1(x) = 5x - 26.5

This gives

p^-1(6.6) = 5 x 6.6 - 26.5

Evaluate

p^-1(6.6) = 6.5

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Answer:50.63

Step-by-step explanation: line them up on top of each other and multiply 9 by all them and if its over 10 put the 2nd digit the the next number.

Answer:

45/8

Step-by-step explanation:

Answer:

Either 40 or 80, depending on whether you worded the question correctly or not.

Step-by-step explanation:

If you mean he has gone 80 miles:

velocity is distance per time, so 80miles/2hours = 40 miles/hour

If you mean he is going 80mph, then the answer is in the question, 80 miles/hour and the distance he has traveled is in miles, therefore you need to multiply by hours, i.e., 80*2=160 miles.

The surface area covered by the rectangular cookie crumble topping is of 35.1 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

For this problem, the bottom is not covered, hence the surface area will be of:

S = 2(hw + lh) + lw.

The dimensions are given as follows:

l = 4.45, w = 4.06, h = 1.

Hence the surface area is:

S = 2(4.06 x 1 + 4.45 x 1) + 4.45 x 4.06 = 35.1 m².

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The approximate rate of change of the function is 224.95

The rate of change of the given function is expressed according to the equation below;

f'(x) = f(b)- f(a)/b-a

Given the interval [-4, 3]

a = -4

b = 3

f(a) = 9(-4)⁴ + 7/(-4)²

f(-4) = 2304+ 7/16

f(-4) = 2304.4375

f(b) = 9(3)⁴ + 7/(3)²

f(3) = 729 + 7/9

f(3) = 729.7778

Substitute to have:

f'(x) = 729.7778-2304.4375/3+4

f'(x) = 1574.65/7

f'(x) = 224.95

Hence the approximate rate of change of the function is 224.95

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Answer:

The answer is 28.26 square feet.

Step-by-step explanation:

The area of a circle is [tex]\pi r^{2}[/tex], so if the radius is 36, [tex]\pi *36^{2}[/tex] is equal to about 4071.5. The formula for converting square inches to square feet is to divide by 144, and [tex]\frac{4071.5}{144}[/tex] is around 28.26.

The distance between the two points is 8.6 units

The points are given as

(4, 9) and (9, 2)

The distance between the two points is then calculated as

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(4 - 9)^2 + (9 - 2)^2

Evaluate the sum of exponents

So, we have

d = √74

Evaluate the exponents

So, we have

d = 8.6

Hence, the distance between the two points is 8.6 units

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Answer: To the nearest thousand.

Step-by-step explanation:

   First, we will round 126,945 to the requested place values;

(it says ten thousand once, so I'm going to include hundred thousand)

hundred thousand ➜ 126,945 ➜ 100,000

ten thousand ➜ 126,945 ➜ 130,000

thousand ➜ 126,945 ➜ 127,000

   Next, we will subtract these values from 126,945, and see which absolute value is the smallest.

hundred thousand ➜ 126,945 - | 100,000 | = 26,945

ten thousand ➜ 126,945 - | 130,000 | = 3,050

thousand ➜ 126,945 - | 127,000 | = 55

   The rounded amount that is closest to the actual attendance is thousand.

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Step-by-step explanation:

y-intersec is (0,y)

sub x=0 in 3x-2y=15

3*0-2y=15

0-2y=15

y=-15/2

Answer:

[tex]x = 28[/tex]

[tex]2x { } ^{2} - 5x - 6 = 0[/tex]

The representation of x^pi in base e is e^xln3.

An exponential function is a the kind of mathematical function that involves exponents.

       f (x) = aˣ

where x is a variable and an is a constant known as the function's base.

        f (x) = eˣ

When the exponent in this component increases by one, the function's value increases by a factor of e.

When the exponent is reduced by one, the value of the function is reduced by the same factor (it is divided by e ).

        f ( x ) = 10ˣ

Now, for the given function.

3x=e^ln3^x

= e^xln3

Therefore, the base e representation of the expression is e^xln3.

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[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad B(\stackrel{x_2}{10}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{7}{10}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{10}-\stackrel{x_1}{(-3)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{(-8)})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 13 ~~,~~ 13 \right)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left( \stackrel{x_1}{-3}~~+~~\frac{7}{10}(13)~~,~~\stackrel{y_1}{-8}~~+~~\frac{7}{10}(13) \right)\implies \left(-3+\cfrac{91}{10}~~,~~-8+\cfrac{91}{10} \right) \\\\\\ \left( \cfrac{-30+91}{10}~~,~~\cfrac{-80+91}{10} \right)\implies \left(\cfrac{61}{10}~~,~~\cfrac{11}{10} \right)\implies \left(6\frac{1}{10} ~~,~~1\frac{1}{10} \right)[/tex]

No student took both calculus and physics out of the 30 students.

Given that, total number of students are 30. Out of which 18 took calculus and 12 took physics. Then, we have to calculate how many took both calculus and physics. So, by using venn diagram we have,

Total number of students = 30

Students who took calculus = P(A) = 18

Students who took physics = P(B) = 12

Students who took both calculus and physics = P(A∩B) = x

Students who took only physics = P(B)-x = (12-x)

Students who took only calculus = P(A)-x = (18-x)

From venn diagram, we get

(18-x)+x+(12-x) = 30

18-x+x+12-x = 30

⇒ x = 0

∴ P(A∩B) = 0

Therefore, No student took both physics and calculus.

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We need to know about roots of a quadratic equation to solve the problem. The quadratic equation is [tex]x^{2} -3x-40=0[/tex]

Quadratic equation is an equation with the highest degree of the variable being 2. A quadratic equation has two roots. The two roots can be real and different or real and equal or imaginary. The roots of a quadratic equation can be found using factorization method. The roots of a quadratic equation can be used to find the quadratic equation itself. Here in this question we have two points (-5,0) and (8,0). These points lie on the x-axis hence we can say that they are the two roots of the equation and the quadratic equation is in terms of x since it cuts the x-axis. Hence we can say that the two roots of the equation are -5 and 8.

For a quadratic equation [tex]ax^{2} +bx+c=0[/tex] let us say that the roots are α and β

α+β=-b/a

αβ=c/a

Here α and β are -5 and 8

-5+8=-b/a ⇒b/a=-3

c/a=-5 x 8=-40

The quadratic equation is given by [tex]x^{2} +\frac{b}{a} x+\frac{c}{a} =0[/tex] which is [tex]x^{2} -3x-40=0[/tex]

Therefore we found the quadratic equation using the two points given, the equation is [tex]x^{2} -3x-40=0[/tex]

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Answer:

Can you please send the picture of the graph

Step-by-step explanation:

Answer:c

Step-by-step explanation:

c

The simplified expression of 4y - 4(-2z + 6y) - 2z is -20y  + 6z

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

4y - 4(-2z + 6y) - 2z

Open the bracket

4y - 4(-2z + 6y) - 2z = 4y + 8z - 24y - 2z

Collect the like terms

4y - 4(-2z + 6y) - 2z = 4y - 24y  + 8z - 2z

Evaluate the like terms

4y - 4(-2z + 6y) - 2z = -20y  + 6z

Hence, the simplified expression of 4y - 4(-2z + 6y) - 2z is -20y  + 6z

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The total price that Cheyenne must pay if he gets his haircut and beard shaved $60.89

A sales tax is one that applies to the purchase of goods and services for consumers and to the sale of goods and services for businesses. It's a type of consumption tax, meaning it taxes people for spending money.

The formula for calculating the sales tax on a good or service is: selling price x sales tax rate, and when calculating the total cost of a purchase, the formula is:

total sale amount = selling price + sales tax.

Given that

spot cost = $20

shave cost =  $25

state sales tax = 8.25%

tips = 25%.

find out  the total price that Cheyenne pay.

total selling price = spot + shave cost

total selling price = $20 + $25

total selling price = $45

we know that

sales tax = selling price x sales tax rate

sales tax = $45 x 8.25%

sales tax = $45 x 8.25 / 100

sales tax = $3.7125.

Cost with sales tax = $45 + $3.7125

Cost with sales tax = $48.7125

Tip is calculated on total bill

Tip Total: $ 12.18

Total (Bill + Tip): $ 60.89

hence , total amount of $ 60.89 is that Cheyenne must pay if he gets his haircut and beard shaved with the bill and tip.

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