Suppose that the functions p and q are defined as follows.
p(x)=x² +6
q (x)=√x+9
Find the following.
(pg) (7) =
(9 °p) (7) = [
X
0/0
5

Answer:

Formulas for a rectangular prism:

Volume of Rectangular Prism: V = lwh.

Surface Area of Rectangular Prism: S = 2(lw + lh + wh)

Space Diagonal of Rectangular Prism: (similar to the distance between 2 points) d = √(l2 + w2 + h2)

The inequalities to represent the situation is given as: x + y ≥ 36 and 2 x + 0.6 y < 40

The magnets are on sale for 60 cents each.

The key chains cost $2 each.

Katie must purchase at least 36 gifts but has to spend less than $40.

Now let x represent the amount of key chains.

Let y represent the amount of magnets.

So, the system of inequalities that form are:

x + y ≥ 36

and
2 x + 0.6 y < 40

Therefore, the inequalities to represent the situation is given as: x + y ≥ 36 and 2 x + 0.6 y < 40

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Answer:

Choice C

5x³ + 2x² - 4x  - 3

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

So simply add the two terms together

5x³ + 2x² -  7x + 4
                + 3x - 7
--------------------------
5x³ + 2x² - 4x  - 3

The required equation for the statement 'four executive integers whose sum is 30' is 4n + 6 = 30

In this question, we have been given a  statement 'four executive integers whose sum is 30'

we need to write an equation for above statement.

Let n, n + 1, n + 2, n + 3 be four consecutive integers.

The sum of these four consecutive integers is 30.

⇒ n + n + 1 + n + 2 + n + 3 = 30

⇒ (n + n + n + n) + (1 + 2 + 3) = 30

⇒ 4n + 6 = 30

which is a required equation.

Therefore, the required equation for the statement 'four executive integers whose sum is 30' is 4n + 6 = 30

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Answer: 120

Step-by-step explanation: Since the equation is asking for 24% percent of 500 we will have to solve by putting them both as fractions. 24 percent automatically means the denominator will be 100 so we have 24/100. 500 is the denominator since that's the base number we are trying to solve for 24% of 500. So we put x over 500. The equation will be:

24/100 x/500

We multiply diagonally so 24*500=12000.

We then divide 500 by 100 which equals 120.

The reason why we didn't multiply 100 and x is because we are trying to solve for x so we had to simplify each side until we got what x was equal to.

Answer:

She has 120 Red Marbles

Step-by-step explanation:

1% of 500= 5 so you can do 5x24 which would be 120.

I hope it helps you!

~XxBellsAloneXx~

Form given information, the probability of rain in Nevada, the probability that it will not rain is 0.7

The probability that if it does not rain, the school bus will be on time is 0.85

The probability that it will rain and the school bus will still be on time is 0.6

In this question, we have been given the probability of rain in Nevada is 0.3

If it rains, the probability of the school bus being late is 0.4

If it does not rain, the probability of the school bus being late is 0.15

We need to find the probability that

a) it will not rain

b) If it does not rain, the school bus bring on time

c) it will rain and the school bus will be on time

The probability that it will not rain in Nevada:

= 1 - probability of rain in Nevada

= 1 - 0.3

= 0.7

The probability that if it does not rain, the school bus will be on time is:

= 1 - probability of the school bus being late if it does not rain

= 1 - 0.15

= 0.85

The probability that it will rain and the school bus will still be on time is:

= 1 - probability of the school bus being late if it rains

= 1 - 0.4

= 0.6

Therefore, the probability of rain in Nevada, the probability that it will not rain is 0.7

The probability that if it does not rain, the school bus will be on time is 0.85

The probability that it will rain and the school bus will still be on time is 0.6

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Answer:

18

Step-by-step explanation:

u suck at life lololol

An arithmetic sequence is a sequence of numbers which will have a constant common difference throughout the sequence.

The first term of the sequence is given as a₁ = 12 and

The common difference of the sequence is given as d = -2

We need to find the first four terms of the arithmetic sequence

So, the formula to find the first four terms of an arithmetic sequence is

a, a+d , a+2d, a +3d...

where   a = 12

            d = -2

Then, the arithmetic sequence of the first four-term is

= 12,12 + (-2) , 12 + 2(-2) , 12 + 3 (-2)

= 12 , 12-2 , 12 -4 , 12 - 6

= 12 , 10 , 8 , 6

So the arithmetic sequence of the first four-term is

12,10,8,6.

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Answer: 3998 cents, or $39.98

Step-by-step explanation: Hope it helps!

Answer:

(a) $878.24

(b) $848.30

(c) Amy would pay less for the golf clubs if she gets them directly from the distributor

Step-by-step explanation:

Part (a)

The wholesale price is $499. When the pro shop gets them from the distributor, it has to pay a mark-up of 10%. 10% expressed as decimal is 10/100 = 0.10

10% of 499 = 0.10 x 499 = 49.90

So total cost including markup for the pro shop is 499 + 49.90 = $548.90

We can compute this directly without computing mark-up cost using the formula

Cost = 499(1+0.10) = 499 x 1.1 = 548.90

The pro shop puts a mark up of 60% which in decimal is 60/100 = 0.6 on the above cost

So the price Amy pays = 548.90(1+0.6) = 548.90 (1.6) = $874.28

Part (b)

Wholesale price = $499

If Amy purchases directly from distributor there is a 70% markup on the wholesale price. 70% = 70/100 = 0.7

So the price Amy would have to pay = 499(1+0.7) = 499 x 1.7 = $848.30

Part (c)

Since the cost of purchasing directly from distributor is less than the cost of purchasing from pro shop the answer is

Amy would pay less for the golf clubs if she gets them directly from the distributor

Answer:

A line is connected set of points that extends forever in both directions.

A line segment is a part of line with two end points.

A ray is a part of straight line that extends only in one direction from a fixed point.

Using proportions, the total percentage of the athletes who do not enjoy cycling is: 24.5%.

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, the proportions of people who do not like cycling are:

Hence the total proportion is:

0.3 x 0.45 + 0.2 x 0.55 = 0.245.

Multiplying by 100% to convert from proportion to percentage, 24.5% of the athletes who do not enjoy cycling.

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Answer:

Step-by-step explanation:

The image of the point (-1,-4) after a rotation of 90 counterclockwise about the origin is (4,-1)

What is coordinate system?

A coordinate system can be defined as the method used to  identifying the location of a point graphically. Most of the coordinate systems use two numbers generally x and y to define a  coordinate and to identify location of any point. The center of graph or system is known as origin and generally pointed as zero (0).

The 2 coordinates is generally written as x and y. There are generally 4 quadrants in 2d coordinate system. These are :

Now in the given question the point is (-1,-4)

i.e. the point lie in 4th quadrant (-x,-y)

If the point is rotated 90 degree counterclockwise then the point becomes (y , -x)

Thus, point (-1,-4) becomes (4,-1)

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The predicted area of the circle is 49.67 cm²

Given the expression that represents the least regression line as shown below:

log(Area) = 0.490 + 2.004log(time)

Given that the time after the stone is dropped is 4 seconds, the equivalent area is expressed as:

log(Area) = 0.490 + 2.004log(4)

log(Area) = 0.490 + 8.016

log(Area) = 1.6965cm

Area = 10^1.696

Area= 49.67 cm²

Hence the predicted area of the circle is 49.67 cm²

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Explanation:

1/4 = 0.25

0.25*360 = 90

90 white beans, 360-90 = 270 black beans

The ratio of white to black is 90:270 which fully simplifies to 1:3 after dividing both parts by the GCF 90.

So matrix which show equation 4x+2y=4 is  [tex]\left[\begin{array}{ccc}4&2&4\\12&-1&26\end{array}\right][/tex] .

Given that we have an equation that is 4x+2y=4

So equation is a statement that the values of two mathematical expressions are equal (indicated by the sign =).

So in order to write this equation in matrix form we have to write it into augmented matrix

So augmented matrix is a matrix whose elements are the coefficients of a set of simultaneous linear equations with the constant terms of the equations entered in an added column.

Therefore the matrix will be:

[tex]\left[\begin{array}{ccc}4&2&4\\12&-1&26\end{array}\right][/tex]    .

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Answer: You Can Search In Internet

Step-by-step explanation: There IS All Step By Step Explanation There Thank You!

h = 9.3 - V/πr² is an equivalent expression to V = πr²(9.3 - h) for cylindrical grain cilo.

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Finding an object's volume can help us figure out how much of it will be needed to fill it, such as how much water will be needed to fill a bottle, aquarium, or water tank.

It is shown that Volume V = πr²(9.3 - h)

Lets divide both sides with πr²

V/πr² = πr²(9.3 - h)/πr²

         = 9.3 - h

Now, subtract 9.3 from both sides

V/πr²- 9.3  = 9.3 - h - 9.3

                 = -h

Now multiply both sides with -1

-1(V/πr²- 9.3) = -1(-h)

-V/πr² + 9.3 = h

⇒ h = 9.3 - V/πr²

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Answer:

4.5 gallons of gas

Step-by-step explanation:

180 ÷ 40= 4.5

Answer:

4.5 gallons

Step-by-step explanation:

Proportions:

40 miles ⇒ 1 gallon

180 miles ⇒ D gallons

D = 180miles * 1 gallon / 40 miles

D = 4.5 Gallons

Answer:

I can answer this is you provide a picture of the graph

Step-by-step explanation

The initial value of the graph is normally the y intercept of the graph. If you provide the graph linked to this question, I could answer it for you.

Answer:

10

Step-by-step explanation:

If Werner Company produces and sells disposable foil baking pans to retailers for $2.25 per pan, and the variable cost per pan are [Direct materials $0.24, Direct labor 0.60, Variable factory overhead 0.73, Variable selling expense 0.17] while, fixed manufacturing cost totals $115,117 per year and Administrative cost (all fixed) totals $15,698, then:

1. 256,000 Pans must be sold for Werner to break even.

2. The unit variable cost is $1.74, and the unit variable manufacturing cost is $1.57.

3. 266400 pans must be sold for Werner to earn an operating income of $5,049.

4. A sales revenue of $599,400 must Werner have to earn operating income of $5,049.

First, we have to calculate the number of pans that must be sold for Werner to break even.

Given, Fixed manufacturing costs $115,117

And, Fixed administrative costs $15698

Therefore, Total fixed costs $[tex](115,117+15,698)=130,815[/tex]

Also given, Selling price per unit $2.25

And, total Variable costs per unit $[tex](0.24+0.60+0.73+0.17)=1.74[/tex]

Contribution margin per unit = $[tex](2.25-1.74)=0.51[/tex]

[Since, contribution margin is the difference of the selling price and the variable costs]

Now, formula to calculate Break-even units goes as

(Total fixed costs / unit contribution margin).

Therefore, Break-even units in our case = [tex]\frac{130,815}{0.51}=256,000[/tex] units.

Secondly, we are required to calculate the unit variable cost and the unit variable manufacturing cost.

The unit variable cost is already calculated to be $1.74.

And, the unit variable manufacturing cost is the sum of all the variable costs excluding the variable selling expense, i.e., [tex](1.74-0.17)=1.57[/tex].

Thirdly, we will have to calculate the number of pans must be sold for Werner to earn an operating income of $5,049.

Already calculated, Total fixed costs are $130,815 and Contribution margin per unit $0.51.

Given, target operating income is $5049.

Now, formula to calculate Desired Units to earn profit goes as

(Total fixed cost + Target operating income)/(Contribution margin),

i.e., in our case, [tex]\frac{130815+5049}{0.51} = \frac{135864}{0.51}=266400[/tex] unit pans must be sold for Werner to earn an operating income of $5,049.

Lastly, We need to calculate the sales revenue must Werner have to earn operating income of $5,049.

Since, [Sales revenue = (Desired units * selling price)]

And desired units = 266400, while Selling price per unit, given as $2.25.

Therefore, Sales revenue = [tex](266,400*2.25)=599,400[/tex].

That is, a sales revenue of $599,400 must Werner have to earn operating income of $5,049.

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Answer:

interior angle is 70 so go answer my question pls

The amount a person would have to deposit today to be able to take out 500$ a year for ten year from an amount earning 9% i

The formula for calculating amount is expressed as:

Amount = Principal + Interest

Determine the interest

Interest = 500*0.09 * 10

Interest = 5 * 90

Interest = $450

Principal= $500 - $450

Principal = $50

Hence the amount a person would have to deposit today to be able to take out 500$ a year for ten year from an amount earning 9% is $50

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The number of voters who are registered democrats according to the description in the task content is; 2,250.

In order words, the total number of registered voters as democrats from the above is 2,250

It follows from the task content that the number of voters who are registered democrats be determined.

On this note, since 3/8 of the total 6000 voters are registered democrats;

However, the number of registered democrats is;

(3/8) × 6000

= 2,250.

Ultimately, the total number of voters who are registered democrats from the above is; 2,250.

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The number of different ways to plan his trip is 240240

The given parameters are

Places, n = 14

Stops, r = 5

From the question, we understand that the places are in specific order

This represents permutation

So, the number of different ways to plan his trip is

Ways = [tex]^nP_r[/tex]

This gives

Ways = [tex]^{14}P_5[/tex]

Apply the permutation formula

Ways = 14!/9!

Evaluate

Ways = 240240

Hence, the number of different ways to plan his trip is  240240

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The perimeter of the shape is determined as 19.91 units and the area is 20.87 sq. units.

The perimeter of an object or a shape is the distance around the edge of the shape.

Length of AB = √[(6 - 3)² + (5 - 5)²] = 3 units

Length of AC = √[(4 - 3)² + (-1 - 5)²]  = 6.1 units

Length BD = √[(6 - 1)² + (5 - -1)²] = 7.81 units

Length CD = √[(1 - 4)² + (-1 - -1)²]  = 3 units

Perimeter of the shape ABCD = 3 units + 6.1 units + 7.81 units + 3 units = 19.91 units.

The formula for area of a trapezoid will be used to determine the area of the shape as shown below;

A  = ¹/₂(6.1 + 7.81) x 3

A = 20.87 sq. units

Thus, the perimeter of the shape is determined as 19.91 units and the area is 20.87 sq. units.

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After plotting the line of the best fit, the estimated values of a and b are

(30,1.15) and the equation is M = 30L ₊ 1.15

Given, the values of L and M are plotted on the graph.

Then the line of best fit is created on the graph.

A line that most accurately depicts the relationship between data points on a scatter plot is called the line of best fit.

When data points appear to be in a straight line, the line of greatest fit is a straight line.

Therefore, we get the point on the line as (30,1.15)

The equation representing the relation:

M = aL + b

(a,b) from the graph is (30,1.15)

substitute the estimated the values,

M = 30L + 1.15

Hence the required values are estimated and plotted on the graph.

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the function as 17 / 2 = C t for the data given.

Credits we have = 60

credits needed to graduate = 128

Credits in 1 semester = 8

Let the number of semesters be t

Number of credits = C

So, we get the function as:

128 = 60 + 8 C t

128 - 60 = 8 C t

68 = 8 C t

17 / 2 = C t

Therefore, we get that, the function as 17 / 2 = C t for the data given.

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