A=7x
2
−3x+10
B=−4x
2
+6x−4
​

A-B=A−B=

If  certain refrigerator requires 170 watts of electricity when it is running. It typically runs about 20 minutes per hour. The amount it cost to run this refrigerator for one year if the cost per kWh is $0.11 is:  $53.856.

Given:

Electricity watts = 170 watts

Minutes run = 20 minutes

Cost per KWh =$0.11

Hence,

170 watts = 1.7×10^-1

20 min = 1/3 h

Now let calculate the cost of running the refrigerator for one year  

1.7×10^-1 × 1/3 × 24 ×360 × $0.11

= $53.856

Therefore If  certain refrigerator requires 170 watts of electricity when it is running. It typically runs about 20 minutes per hour. The amount it cost to run this refrigerator for one year if the cost per kWh is $0.11 is:  $53.856.

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Answer:

6

Step-by-step explanation:

You have to divide 24 by four.

Applying the quotient rule, the derivative of the function is given by:

[tex]f^{\prime}(x) = \frac{3(3x - 6)^2(3(2x - 2) - 2(3x - 6))}{(2x - 2)^4}[/tex]

Suppose a quotient function defined as follows:

f(x) = g(x)/h(x).

The derivative of the function is defined according to the following rule:

f'(x) = [g'(x)h(x) - h'(x)g(x)]/(h(x))²

For this problem, the function is given by:

f(x) = (3x-6)³ /(2x-2)³.

Hence the parameters are:

Applying the power rule and the chain rule, the derivatives of the functions are:

Hence the derivative of the function is:

[tex]f^{\prime}(x) = \frac{9(3x - 6)^2(2x - 2)^3 - 6(2x - 2)^2(3x - 6)^3}{(2x - 2)^6}[/tex]

[tex]f^{\prime}(x) = \frac{3(3x - 6)^2(2x - 2)^2(3(2x - 2) - 2(3x - 6))}{(2x - 2)^6}[/tex]

[tex]f^{\prime}(x) = \frac{3(3x - 6)^2(3(2x - 2) - 2(3x - 6))}{(2x - 2)^4}[/tex]

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You need to make 3 batches if you want to get 6 dozen cookies.

Here we know that you need to make a total of 6 dozen cookies, and we know that each batch you make gives 2 dozen.

Then if you make b batches, the number of dozens of cookies that you get is given by the linear equation:

d = 2*b

So, if you want to get 6 dozens, you need to replace d by 6, we will get:

6 = 2*b

Solving that for b, we get:

6/2  =b = 3

You need to make 3 batches if you want to get 6 dozen cookies.

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A stem and leaf plot is a table used to display data. The 'stem' is shown on the left side of the table and shows the first digit or digits of data values. The 'leaf' is shown on the right side of the table and shows the last digit of the data value.

A stem and leaf plot displays numerical data by splitting each data point into a "leaf" (usually the last digit) and a "stem" (the leading digit or digits).

Split each data point into a stem and a leaf. The stem is everything before the final digit, and the leaf is the final digit. Write the stems in a vertical column and don't skip stems just because they don't have any data.

2

3

4

5

4

5

our stems are the 10 digit data.

2 ! 0 ,1, 2

3! 3, 4,

4! 4 , 5 , 9

5 ! 0

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If the scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score needed to be in the top 7% is calculated to be 85.404.

This type of problem can be categorized as a normal distribution problem and can be solved with the help of z-score.

If we consider Z = standard score,

μ = mean

σ = standard deviation

Then the z-score to figure out the lowest score to be in the top 7% is given as,

Z = x - μ / σ

If the p-value is known, the z-score can be found with the help of the standard table.

As the minimum score to be in the top 7% is to be determined, p-value = 0.07

The z-score that corresponds to the p-value of 0.07 is 1.476 in the standard table.

Hence,

1.476 = x - 76.4 ÷ 6.1

1.476 × 6.1 = x - 76.4

1.476 × 6.1 + 76.4 = x

9.004 + 76.4 = x

x = 85.404

Therefore, 85.404 is the minimum score that is needed to be in the top 7%.

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The symbolic notation are;

a. Atlanta is the capital of Georgia, or there are 3 feet in a yard.

2. ⇒ p ∧ q

b. Atlanta is the capital of Georgia and there are not 3 feet in a yard.

6. ⇒ p ∨ ~ q

c. Atlanta is not the capital of Georgia, or there are 3 feet in a yard.

5. ⇒ ~ p ∧ q

d. Atlanta is the capital of Georgia, and there are 3 feet in a yard.

1. ⇒ p ∨ q

What is Symbolic notation?

Symbolic notation is a way of representing the counting numbers by writing a simple symbol.

Now,

For the false statement we use the symbol ( ~ ).

If in the statement the word ''or'' is present then we use the symbol ''∧'' and for the word ''and'' we use the symbol ''∨''.

Hence,

For the statement;

a. Atlanta is the capital of Georgia, or there are 3 feet in a yard.

Both are truth and with the word ''or'', then the symbolic notation,

⇒ p ∧ q

For the statement;

b. Atlanta is the capital of Georgia and there are not 3 feet in a yard.

One statement is truth and second is false , then the symbolic notation,

⇒ p ∨ ~ q

For the statement;

c. Atlanta is not the capital of Georgia, or there are 3 feet in a yard.

First statement is false and second is truth , then the symbolic notation,

⇒ ~ p ∧ q

For the statement;

d. Atlanta is the capital of Georgia, and there are 3 feet in a yard.

Both are truth and with the word ''and'', then the symbolic notation,

⇒ p ∨ q

So, The symbolic notation are;

a. Atlanta is the capital of Georgia, or there are 3 feet in a yard.

2. ⇒ p ∧ q

b. Atlanta is the capital of Georgia and there are not 3 feet in a yard.

6. ⇒ p ∨ ~ q

c. Atlanta is not the capital of Georgia, or there are 3 feet in a yard.

5. ⇒ ~ p ∧ q

d. Atlanta is the capital of Georgia, and there are 3 feet in a yard.

1. ⇒ p ∨ q

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The percent increase and decrease between the given starting and ending quantities above are as follows:

In Mathematics, there are two main types of percentage and these include the following:

Mathematically, percentage increase can be calculated by using this formula:

Percentage increase/decrease = [Final value - Initial value]/Initial value × 100

Substituting the given parameters into the formula, we have;

Percentage increase = [10 - 3]/3 × 100

Percentage increase = 7/3 × 100

Percentage increase = 233.3%.

Percentage increase = [20 - 9]/9 × 100

Percentage increase = 11/9 × 100

Percentage increase = 122.2%.

Percentage decrease = [100 - 85]/9 × 100

Percentage decrease = 15/85 × 100

Percentage decrease = 17.7%.

Percentage decrease = [45 - 20]/20 × 100

Percentage decrease = 25/20 × 100

Percentage decrease = 125%.

Percentage increase = 30/30 × 100

Percentage increase = 100%.

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Answer:

x = -4,-2

Step-by-step explanation:

x² + 6x + 8 = 0

Factor the equation

(x+4)(x+2) =0

Using the zero product property

x+4 =0   x+2 =0

x=-4  x=-2

x = -4,-2

Answer:

[tex] \sf \: x = - 2 \: \: or \: \: - 4[/tex]

Step-by-step explanation:

[tex] \sf {x}^{2} + 6x + 8 = 0[/tex]

Factorise.

[tex] \sf {x}^{2} + 6x + 8 = 0 \\ \sf {x}^{2} + 4x + 2x + 8 = 0[/tex]

[tex] \sf x(x + 4) + 2(x + 4) = 0 \\ \sf(x + 2)(x + 4) = 0[/tex]

Use the zero product property.

[tex] \sf \: x + 2 = 0 \\ \sf \: x = 0 - 2 \\ \sf x = - 2[/tex]

Or

[tex] \sf \: x +4 = 0 \\ \sf \: x = 0 - 4 \\ \sf \: x = - 4[/tex]

Therefore,

[tex] \sf \: x = - 2 \: or \: \: - 4[/tex]

Answer:

explain why a mission statement should not include monetary amount numbers percentages ratios or objectives

By respecting the given ratio:

1) 10 of blue paint and 15 of yellow.

2) 4 of blue paint and 6 of yellow.

3) 2 cans of blue paint and 3 of yellow.

We know that on day 1 he uses:

On day 2 he uses:

Adding that we get:

He initially has 20 cans of yellow, so he has left:

20 - 15 = 5 cans of yellow.

He initially has 14 cans of blue, so now he has:

14 - 10 = 4

4 cans of blue paint.

The original ratio is:

6 yellow to 4 blue.

The quotient gives: 6/4 = 3/2

So if she has 5 cans of yellow paint and 4 cans of blue paint, the maximum amount that he can use that respects that ratio is 3 cans of yellow paint and 2 cans of blue paint.

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Answer:

  12 5/6 inches

Step-by-step explanation:

You want to find the value of L when S=12 1/2, using the formula S = 3L -26.

You can substitute for S in the formula before or after you solve for L. Here, we'll solve for L first:

  S +26 = 3L . . . . add 26 to both sides

  (S +26)/3 = L . . . . divide both sides by 3

Substituting 12 1/2 for S, this becomes ...

  L = (12 1/2 +26)/3 = (38 1/2)/3 = (77/2)/3 = 77/6 = 12 5/6

A man's foot is 12 5/6 inches long if he wears a size 12 1/2 shoe.

Answer:

the length of his foot in inches is 12

Answer:

b

Step-by-step explanation:

the 2 legs of the triangle are congruent, thus the triangle is isosceles with the 2 base angles congruent , then

3x = 60 ( divide both sides by 3 )

x = 20

Answer: b

Step-by-step explanation: the 2 legs of the triangle are congruent, thus the triangle is isosceles with the 2 base angles congruent , then

3x = 60 ( divide both sides by 3 )

x = 20

Answer:

2400+56=2456 OR

2500-44=2456

Answer:

Step-by-step explanation:

614x4=2,456

Answer:

530-450=80

Answer = 80 feet

The constant of proportionality between y and x in the graph is 1.

From given graph we can see that

When x=2 then y=2

When x=4 then y=4

When x=6 then y=6

when x=10  then  y= 10

It means when x increases then y also increases .

It is in direct proportion.

Direct proportion:y/x=k.

Where k=Proportionality constant

Using the formula

y/x=10/10=2/2=1

Hence, the value of proportionality constant=1

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Using proportions, Mrs. Terry total medical expenses are of $2,526.4.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, her expenses are divided as follows:

Hence her total medical expenses are given as follows:

2500 + 0.2 x 132 = $2,526.4.

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4(X-3)+14=7X-3(X+7)

or, 4X-16+14=7X-3X

or, 4X-7X+3X=(-21)+16-14

or, 0= -19

Hence, the answer is wrong but the process is right.

The least amount of money she needs to deposit to avoid a fee is;  $16.62

We are given;

Amount Keisha has in her checking account = $585.43

Minimum balance to be maintained = $300

Check written = $302.05

Now, if x represents the variable, that would be used for the least amount of money she needs to deposit to avoid a fee, then the inequality is;  $585.43 - $302.05 + x ≥ $300

$283.38 + x ≥ $300

Subtract 283.38 from both sides to get;

x ≥ $16.62

Thus, the least amount of money she needs to deposit to avoid a fee is;  $16.62

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Jerry spend $240 on clothes for school and jerry received $60

Jerry needs clothes for school

He buys 2 pair of jeans for $17. each =2*17=34

He buys a pair of shoes for $125.00.

He also needs a pack of socks. They are $12.

he also needs 3 shirts, They are on sale for $23 each = 3*23=69

then we have to find how much does he spend?

If he gives the cashier  $300 bills, how much change receive?

now the Total amount jerry spent on clothes is

34+125+12+69 = 240dollar

Hence Jerry pay $240 to the cashier but jerry pay $300 to the cashier so jerry received $300- $240 = $ 60

therefore Jerry spend $240 on clothes for school

and jerry received $60

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   The simplification of the given expression can be expressed as: 8√2m⁷n⁹

Simplification is defined as a final operation that shows the result of a reduction of a number or set without altering its value.

 In other words, when we simplify we express the same value in a shorter or summarized form.

  The algebraic expression that we must simplify to its minimum expression is:

4√32 m⁷n⁹,  we can see that it is an expression that has two variables

we reduce the value of the square root

√32 = √4x4x2 = √4²x2 = 4√2

4(4√2)m⁷n⁹  Variables are irreducible

8√2m⁷n⁹

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The exponential function that models exponential growth is y = 5(3)ˣ.

The example of an exponential function that models exponential decay is y = 2(0.8)ˣ

Exponential growth is the process by which quantity increases over time. It happens whenever the instantaneous rate of change of a volume with respect to time has been proportional to the volume itself.

Consider exponential function; y = a(b)ˣ.

For the exponential growth a > 0 and b > 0.

Suppose a = 5 and b = 3.

Then, the function will become after substituting the both values.

y = 5(3)ˣ which is the exponential growth of the exponential function.

According to the law, exponential decay would be the decrease in a quantity (1) where is the exponential function and the initial value, for a parameter as well as constant (known as the decay constant).

Now, as per the question.

For the exponential decay a > 0 only.

Consider exponential function; y = a(b)ˣ.

Let, a = 2 and b = 0.8.

Then,

y = 2(0.8)ˣ

Therefore, the exponential function in the form of exponential decay is y = 2(0.8)ˣ.

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All the zeros of each function y=3x³-7x²-14 x+24 are

X₁ = -2, X₂≈ 1.33333, X₃ = 3

Polynomial roots are the answers to any polynomial for which we need to determine the value of the unknowable variable. Knowing the roots will allow us to evaluate the polynomial's value to zero. A polynomial of degree "n" in variable x is an expression with the following formula: anxn + an-1xn-1 +...... + a1x + a0.

The greatest power of a variable in a polynomial is referred to as the polynomial's degree.

A monomial is a polynomial with a single term. A monomial is referred to as a polynomial of zero degrees if it simply has a constant term.

According to the given data,

y=3x³-7x² -14x + 24

Substitute y = 0

0=3x³-7x²- 14x + 24

Move the expression to the left

0-3x³+7x² +14x-24=0

Remove 0

Rewrite

- 3(x³+8) +7x(x+2)=0

Factor the expression

-3(x+2) x(x²-2x + 4) +7x(x+2)=0

Remove the parentheses

-(x+2)x(3x²-6x+12-7x) = 0

Collect like terms

-(x+2)x (3x²-13x+12) 13x+12=0

Rewrite the expression

(x+2)x(3x-4)x(x-3)=0

Separate into possible cases

x+2=0

3x-4=0

X 3=0

Solve the equations

x = -2

X=4/3

X = 3

The equation has 3 solutions

Solution

X₁ = -2  , X₂=4/3 , X₃ = 3

Alternative Form

X₁ = -2, X₂= 1.33333, x₃ = 3

Hence ,all the zeros of each function y=3x³-7x²-14 x+24 are

X₁ = -2, X₂≈ 1.33333, X₃ = 3

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Answer:

D. y = 8x

Step-by-step explanation:

[tex]\mathrm{y(out put) = x(in put) \times 8}[/tex]

The equivalent expression is z raised to the fourteenth power over y raised to the fourteenth power. Option D

Algebraic expressions are defined as expressions composed of variables, terms, constants, coefficients and factors.

They are also made up of arithmetic operations like;

Note that equivalent expressions are expression with the same solution but different arrangement of values.

From the information given, we have that;

Substitute into the expression;

{y^-2 × z³/z^-4 × y^5 }^-2

Following the law of indices, we have

{y^-2 -5 z^3-(-4) }^-2

{y^-7 z^7}^-2

y^-14 z^14

z^14/y^14

Thus, the equivalent expression is z raised to the fourteenth power over y raised to the fourteenth power. Option D

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The Cost of the juice per gallon is the $9.

According to the statement, We have to find that the cost of the juice.

So, For this purpose, we know that the

A cost function may be a mathematical formula wont to used to chart how production expenses will change at different output levels.

From the given information:

The price of eight 4.23 ounce juice boxes is $2.39. we should always know that: 1 Gallon = 128 Ounces and 1 juice boxes = 4.23 ounce

So, juice boxes per gallon = 128/4.23 = 30.26

But the worth of 8 juice boxes is $2.39

The value of 1 gallon = (30.26/8) * 2.39 = 9.04

Then,

the price per gallon of the juice = $9

So, The Cost of the juice per gallon is the $9.

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y -coordinate of the vertex of the parabola y=-3(x-4)²+5 is -5.

A parabola is an approximately U-shaped, mirror-symmetrical planar curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola may be described using a point and a line.

Given,

y=-3(x-4)²+5

⇒ y = - 3x² - 48 + 24x + 5

⇒ y =  - 3x² + 24x - 43

⇒ a = -3, b = 24, c = -43

⇒ x = -b/2a

⇒ x = -24 /- 6 = 4

⇒ y = - 48 + 96 - 43

⇒  y = - 5

⇒ x= 4, y = -5

⇒ The coordinates of vertex will be - (4,-5)

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Answer:

163 degrees

Step-by-step explanation:

163 degrees is equal to y

Z = x

The measure of angle y is 163° and the measure of angle x and z is 17 degrees.

Given that:

Two lines are intersected with each other.

It is required to find the measure of angles x, y, and z.

The angles formed on the opposite side of the intersecting line are called vertical angles.

Also, by the Vertical Angles Theorem, the vertical angles formed are always equal.

Here, y is vertical to the given measure of 163°.

So, y = 163°.

Now, x and y are the angles formed along a line.

So, they are linear pair of angles.

Linear pair of angles are supplementary.

So, x + y = 180

x = 180 - 163

  = 17°

Also, x and z are vertical angles.

So, z = 17°

Hence, x = 17°, y = 163°, and z = 17°.

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1. (a) The answer to the given part is 12.56

(b)the answer to the given part 50.24

(c) the answer to the given part153.86

2. (a)the answer to the given part ₋1

(b)the answer to the given part 2

(c) the answer to the given part4

3. (a)the answer to the given part 12

(b) the answer to the given part5

(c) the answer to the given part1

Given,

1. A(r) = πr²

a. A(2) = π(2)²

= π4

= 3.14 ₓ 4

= 12.56

b. A(4)

A(r) = πr²

= π(4)²

= π16

= 50.24

c. A(7)

A(r) = πr²

= π(7)²

=  π(49)

= 153.86

2. s(t) = t² ₋ 2t ₊ 1

a. S(0) = 0² ₋ 2(0) ₋ 1

= ₋1

b. S(3) = 3² ₋ 2(3) ₋ 1

= 9 ₋ 6 ₋ 1

= 2

c. S(₋1) = (₋1)² ₋ 2(₋1) ₊ 1

= 1 ₊ 2 ₊ 1

= 4

3. (a) f(₋3) which means x ≤ ₋1

therefore, f(₋3) = 4 ₋ 3x

= 4 ₋ 3(₋3)

= 4 ₊ 9

= 12

(b) f(0) which means ₋1<x<1

therefore, value of f(0) = 5.

(c) f(2) which means x≥ 1

therefore, value of f(2) = x² ₋ 3

= 2² ₋ 3

= 4 ₋ 3

= 1

hence, we get the desired results.

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