Suppose that the functions and are defined as follows. p(x)=-x and q(x)=2x^2-2
find the following (q°p)(2)=
and (p°q)(2)=

Answer:

24/5

Step-by-step explanation:

[tex]\frac{6}{1}*\frac{4}{5} = \frac{24}{5}[/tex]

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Multiply, and simplify your answer, and write it as a mixed number,

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Write the first fraction as 6/1 and multiply it times 4/5.

[tex]\bf{\dfrac{6}{1}\times\dfrac{4}{5}=\dfrac{6\times4}{1\times5}}=\dfrac{24}{5}}[/tex] | Have you noticed that we multiply the numerators together, and we do the exact same thing with the denominators?

[tex]\bf{4\dfrac{4}{5}}[/tex]

[tex]\cline{1-3}[/tex]

[tex]\bf{Result:}[/tex]

                 [tex]\bf{=4\dfrac{4}{5}}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]

The  production department factory overhead rates for Cut and sew department is 89 and Pattern is 67.

a. Pattern Department            

Factory overhead rate=Total Overhead Cost/Direct Labor Hours

Factory overhead rate= 140,700/2700

Factory overhead rate=67

Cut and sew Department

Factory overhead rate=231,400/2600

Factory overhead rate=89

b.  Factory overhead per unit

Pattern Department:      

Small glove=.04 x 67

Small glove=2.68    

Medium glove= .05 x 67

Medium glove=3.35

Large glove= .06 x 67

Large glove=4.02

Cut and sew Department:      

Small glove=.07 x 89

Small glove=6.23    

Medium glove=.09 x 89

Medium glove=8.01  

Large glove=.11 x 89

Large glove=9.79

Therefore the  production department factory overhead rates for Cut and sew department is 89 and Pattern is 67.

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The complete question is:

Handy Leather, Inc., produces three sizes of sports gloves: small,

medium, and large. A glove pattern is first stenciled onto leather in the Pattern Department. The stenciled patterns are then sent to the Cut and Sew Department, where the glove is cut and sewed together. Handy Leather uses the multiple production department factory overhead rate method of allocating factory overhead costs. Its factory overhead costs were budgeted as follows:

Pattern department Overhead                $140,700

Cut and sew Department overhead        $231,400

Total    $372100

Direct labor labor estimated for each department was as follows:

Pattern   Dept. -                       2100 direct labor hours

Cut and Sew Department      2600

Total                                          4700 direct labor hours

Direct labor hours are used to allocate the production department overhead to the products. The direct labor hours per unit for each product for each production department were obtained from the engineering records as follows:

Production Departments        Small Glove    Medium Glove          Large Glove

Pattern dept. 0.04         0.05                          0.06

cut and sew dept.                             0.07                 0.09                          0.11

direct labor hours per unit               0.11                   0.14                          0.17

If required, round all per unit answers to the nearest cent.

a. Determine the two production department factory overhead rates.

Cut and sew department and Pattern

b. Use the two production department factory overhead rates to determine the factory overhead per unit for each product.

small glove, medium glove and large glove

Answer:

20

Step-by-step explanation:

To find x, note that:

Therefore,

(2x + 20)° = 60°

Removing bracket.

2x + 20 = 60

collecting like term.

2x = 60 - 20

2x = 40

dividing bothsides by 2

2x/2 = 40/2

x = 20

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

How do I solve for X?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Angles [tex]\bf{60^\circ}[/tex] and [tex]\bf{2x+20}[/tex] are vertical angles. They are congruent, or equal.

Thus,

[tex]\bf{2x+20=60}[/tex] | subtract 20

[tex]\bf{2x=40}[/tex] | divide the equation by 2

[tex]\bf{x=20}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

          [tex]\bf{=x=20}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]

Answer:

4n - 10

Step-by-step explanation:

Jay: n tickets

Pillar: 3n tickets

Jay + Pillar = n + 3n = 4n tickets

Now, Jay and Pillar together sold 10 more tickets than Amie, which means, in reverse, Amie sold 10 less tickets than Jay and Pillar together, so the expression for the number of tickets sold by amie would be:

4n-10 (4n is the number of tickets Jay and Pillar sold together, 10 is the difference between them and Amie).

The chi-squared test statistic will be 3.11. The test statistic is contrasted with a predicted value based on the Chi-square distribution.

Finding the squared difference between the actual and anticipated data values, then dividing that difference by the expected data values, constitutes the test statistic.

The formula for the chi-squared test statistic is;

[tex]\sum \frac{(O_i-E_i)^2}{E_i } \\\\[/tex]

Where,

[tex]\rm O_i[/tex] is the observed value

[tex]\rm E_i[/tex] is the expected value

The chi-square test statics is;

[tex]\rm( \frac{18-18}{18} )^2 +( \frac{14-18}{18} )^2 + (\frac{24-18}{18} )^2+( \frac{16-18}{18} )^2 \\\\ 0+ \frac{16}{18}+ \frac{36}{18} +\frac{4}{18}\\\\ \frac{56}{18} \\\\ 3.11[/tex]

Hence, the chi-squared test statistic will be 3.11.

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Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

What does the problem want:

 ⇒use the substitution method

      ⇒ to solve the problem

Let's substitute y's value from the second equation to our first equation

  [tex]2x-y=8\\y=x-3\\\\\rm \hookrightarrow 2x-(x-3)=8\\\rm \hookrightarrow 2x-x+3=8\\\rm \hookrightarrow x=8-3=5[/tex]

Now substitute the x's value into the first equation

[tex]y=x-3\\x=5\\\\\rm \hookrightarrow y=(5) - 3 =2[/tex]

The solution is (5,2)

Answer: (5,2) or (B)

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The integer form is + 40.

The integer form is - 25

An integer is a whole number from the set of negative, non-negative, and positive numbers.

Therefore, integers can be written without fractional components.

Hence, integers may include negative or positive numbers . Examples are -1, 2, 5, -8, 9 and many more.

A deposit of 40 dollars means gain. Therefore, the integer form is + 40.

A loss of 25 pounds mean loss. Therefore, the integer form is - 25

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Answer: 23

Step-by-step explanation:

The first term is 0.5 and the common difference is 0.4.

Using the sum of an arithmetic series formula,

[tex]S_{10}=\frac{10}{2}[2(0.5)+(10-1)(0.4)]=\boxed{23}[/tex]

The missing numbers are 13 and 50

Given the numbers;

1, 2, 3, 7, -, 24, -.

Find the numbers by preceding numbers together, thus;

1 + 1 =2

1 + 2 = 3

1 + 2 + 3 = 7

1 + 2 + 3 + 7 = 13

1 + 2 + 3 + 7 + 13 + 24 = 50

Thus, the missing numbers are 13 and 50

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Answer:

X=-8

Step-by-step explanation:

A number x is multiplied by 4, added to 3, and then divided by x+2, leaving us with 7/2. Or, as an equation:

[tex] \frac{4x + 3}{x + 2} = \frac{7}{2} [/tex]

Now, let's cross multiply:

[tex]2(4x + 3) = 7(x + 2)[/tex]

[tex]8x + 6 = 7x + 14[/tex]

And solve:

[tex]x + 6 = 14[/tex]

[tex]x = - 8[/tex]

Answer:

√-1

Step-by-step explanation:

The imaginary number i is defined as √(-1)

NOTE : i² = -1

Answer:

The correct answer: a line

See the graph in the attached image.

Given that, 567 teams participate in a football tournament, If each team plays against every other team only once, number of matches played in total is 160461.

To determine the total number of matches played, we apply Combination.

ⁿCr = n! / r!( n-r )!

Given that;

We substitute

[tex]^nC_r = \frac{n!}{r!(n-r)!} \\\\^nC_r = \frac{567!}{2!(567-2)!} \\\\^nC_r = \frac{567!}{2!(565)!}\\\\^nC_r = \frac{567 * 566 * 565!}{2!(565)!} \\\\Cancel-common - factor: 565!\\\\^nC_r = \frac{567 * 566 }{2!} \\\\^nC_r = \frac{567 * 566 }{2*1}\\\\^nC_r = \frac{ 320922 }{2} \\\\^nC_r = 160461[/tex]

Given that, 567 teams participate in a football tournament, If each team plays against every other team only once, number of matches played in total is 160461.

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Answer:

p = 9

Explanation:

There is no remainder when a polynomial is completely divided by divisor.

Here:

Set to zero:

Insert into equation.

f(6) = 0

(6)³ - 13(6)² + 6p(6) - 72 = 0

216 - 468 + 36p - 72 = 0

-324 + 36p = 0

36p = 324

p = 324/36

p = 9

After 24 hours, 35.4% of the initial dosage remains on the body.

The exponential decay is written as:

[tex]f(x) = A*e^{-k*x}[/tex]

Where A is the initial value, in this case 2.8mg.

k is the constant of decay, given by the logarithm of 2 over the half life, in this case, is:

[tex]k = ln(2)/16h[/tex]

Replacing all that in the above formula, and evaluating in x = 24 hours we get:

[tex]f(24h) = 2.8mg*e^{-24h*ln(2)/16h} = 0.9899 mg[/tex]

The percentage of the initial dosage that remains is:

[tex]P = \frac{0.9899mg}{2.8mg}*100\% = 35.4\%[/tex]

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The best measurement for the angle is less than 90°. The correct option is a. less than 90°

From the question, we are to determine which of the given options is the best measurement for the angle

In the given diagram, we can observe that the angle is an acute angle. Thus, the measure of the angle will be lesser than 90°.

Hence, the best measurement for the angle is less than 90°. The correct option is a. less than 90°.

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The GDP and the years illustrated will be:

It should be noted that the gross domestic product simply means the monetary value of the overall economic activity in a country.

The gross domestic product and their corresponding years have been given.

The business cycle that was illustrated showed that there was a gradual expansion before getting to the peak where recession sets in

Also, the short run Philips curve is illustrated as there's a trade off between inflation and unemployment.

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Answer:

hope they do help. in case of any questions feel free to ask.

Answer:

This is the graph of y = 0.4x

Answer:

67.

Step-by-step explanation:

n - m = 66

The 66 includes the number m+1   up to and including n (buy not m).

So the number of integers is 66 +1 = 67

Putting different values in the variable could give the total money spend.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Marcy had $10.00 to spend at the state fair. She spent all of it on the ride tickets.

The rides cost either $0.50, $1.00, or $1.25 each.

The equation form;

0.50x + 1.00y + 1.25z = 10

Putting different values in the variable could give the total money spend.

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The parallel lines cuts the sides in equal proportion to give NP = 0.8

The given diagram consists of a line parallel to one of the sides of the triangle.

According to the triangle proportionality theorem, the parallel line, NQ, proportionally divides the sides MR and MP, such that:

NQ || PR

By triangle proportionality theorem;

[tex]\mathbf{ \frac{ MN }{ NP} } = \frac{ MQ }{ QR } [/tex]

Which gives;

[tex] \mathbf{ \frac{ 5 }{ NP} } = \frac{ 8}{ 2 } [/tex]

2×5 = 8 × NP

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The value of x in the proportion is x = 39/8

The proportion is given as:

3/8 =x/13

Cross multiply

8 * x = 3 * 13

Evaluate

8x = 39

Divide by 8

x = 39/8

Hence, the value of x in the proportion is x = 39/8

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Answer:

Step-by-step explanation:

Attached is graphed piecewise function.

Take note, if the inequality is a less than or equal to or (more than or equal to), the dots will be solid, otherwise it will be hollow.

Since this is a piecewise function, here is one question you might want to ask yourself:

Does the limit exist when x approaches 4?

Answer:

y = 2x + 3

Step-by-step explanation:

Hello!

Solve for y by isolating the variable.

The solution is y = 2x + 3.

To Calculate :-

Solution :-

⇒ -20x + 10y = 30

☆ Transposing (-20x) to R.H.S. sign would be changed to positive.

⇒ 10y = 30 + 20x

⇒ y = 30 + 20x / 10

⇒ y = 10 (3 + 2x) / 10

☆ Cancelling 10,

⇒ y = 3 + 2x / 1

⇒ y = 2x + 3

Answer:

23

Step-by-step explanation:

the answer is the y intercept of the equation

Answer:

23m, at t=2s

Step-by-step explanation:

Putting the physics part aside, you can rewrite the height function as

[tex]h(t)= 23 - 5(t-2)^2[/tex]. Now you have a fixed value, 23, and you're subtracting to it a quantity that, being a square, is at least zero. The maximum value of that sum you have when you're not subtracting anything, that is 23. That happens when [tex]5(t-2)^2 = 0 \rightarrow t=2[/tex]

Alternatively, if you know how to determine the velocity from that kind of motion, you can find out the speed, and the highest altitude you reach when the speed is zero, which leads to a bunch of calculation for the same result.

Let, the points be A (8, −4) and B (1, −5). The slope of line AB exists 1/7.

Utilize the slope formula to estimate the slope of a line provided the coordinates of two points on the line.

The slope formula exists [tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex], or the difference in the y values over the difference in the x values. The coordinates of the first point symbolize [tex]$x_{1}[/tex]and [tex]$y_{1}[/tex]. The coordinates of the second points exist [tex]$x_{2} , y_{2} .[/tex]

The slope of the line exists the ratio of the rise to the run, or rise separated by the run.

[tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex]

The Line, AB contains points A (8, −4) and B (1, −5).

Substitute the value of points in the equation then we get

[tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex]

m = (-5-(-4))/(1 - 8)

Simplifying the above equation, we get

m = (-5+4)/(1 - 8)

m = (-1)/(-7)

m = 1/7

Therefore, the slope of line AB exists 1/7.

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The inventory account expected to have by December 31 is more than $5800. Option C

The formula for end inventory is given as ;

Ending inventory = Beginning inventory + net purchases –sales

Beginning inventory = $5800

Net purchases = $65000

Sales = $112000

Put into the formula

Ending inventory = $ [tex]5800 + 65000 - 112000[/tex]

Add first,

Ending inventory = $ [tex]70800 - 112000[/tex]

Ending inventory = $ -41, 200

Thus, the inventory account expected to have by December 31 is more than $5800. Option C

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