a
100 cm²
b
9 cm²
c
225 cm²
d
28.26 cm²

F. 2x⁵y² - 6x⁴y³

That is the answer.

By means of distribution.

Answer:

16 yards

Step-by-step explanation:

I hope this helps!

Answer:

16

Step-by-step explanation:

becasue from -21 to -5 it's 16 units (-21 - -5= 16).

Answer:

d) 280

Step-by-step explanation:

40320/3=6720

8720/24=280

Answer:

a. reflection across the y-axis

Answer:

[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

Given;

Sin θ = 3/4

To calculated Cos θ;

make a sketch of right-angled triangle with following sides;

opposite side = 3

hypotenuse side = 4

then, the adjacent  side will be calculated from Pythagoras theorem;

let the adjacent side = b

b² = 4² - 3²

b² = 16 - 9

b² = 7

b = √7

Therefore, Cos θ is now calculated as;

Cos θ = adjacent / hypotenuse

Cos θ = √7/4

[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]

Therefore, [tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]

Complete Question

The daily output at a plant manufacturing chairs is  approximated by the function

[tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] chairs

where L is the size of the labor force measured in hundreds

of worker-hours and K is the daily capital investment in  thousands of dollars. If the plant manager has a daily budget  of $13,000 and the average wage of an employee is $9.00  per hour, what combination of worker-hours (to the nearest  hundred) and capital expenditures (to the nearest thousand)  will yield maximum daily production?

a)200 worker-hours and $9000 in capital expenditure

b)1100 worker-hours and $3000 in capital expenditure

c)500 worker-hours and $8000 in capital expenditure

d)900 worker-hours and $5000 in capital expenditure

e)600 worker-hours and $6000 in capital expenditure

f)300 worker-hours and $10,000 in capital expenditure

Answer:

d)900 worker-hours and $5000 in capital expenditure

Step-by-step explanation:

From the question we are told that

Daily output at a plant manufacturing chairs is  approximated by the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]

Daily budget  of $13,000

Average wage of an employee is $9.00  per hour

a) Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to for (a)

Mathematically solving with L=200 K=9000

[tex]f(L=200,K=9000) = (45\sqrt[3]{9000})200^3^/^5[/tex]

[tex]f(L=200,K=9000) = 45*20.8*24[/tex]

[tex]f(L=200,K=9000) = 22464[/tex]

b)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to for (b)

Mathematically solving with L=1100 K=3000

[tex]f(L=1100,K=3000) = (45\sqrt[3]{3000})1100^3^/^5[/tex]

[tex]f(L=1100,K=3000) = 45*14.4*66.8[/tex]

[tex]f(L=1100,K=3000) = 43286.4[/tex]

c)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to find (c)

Mathematically solving with L=500 K=8000

[tex]f(L=500,K=8000) = (45*\sqrt[3]{8000})*500^3^/^5[/tex]

[tex]f(L=500,K=8000) = 45*20*41.63[/tex]

[tex]f(L=500,K=8000) =37467[/tex]

d)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to find (d)

Mathematically solving with L=900 K=5000

[tex]f(L=900,K=5000) = (45*\sqrt[3]{5000})*900^3^/^5[/tex]

[tex]f(L=900,K=5000) = 45*17.09*59.2[/tex]

[tex]f(L=900,K=5000) =45577.88[/tex]

e)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to find (e)

Mathematically solving with L=600 K=6000

[tex]f(L=600,K=6000) = (45\sqrt[3]{6000})600^3^/^5[/tex]

[tex]f(L=600,K=6000) = 45*18.17*46.4[/tex]

[tex]f(L=600,K=6000) =37974[/tex]

f)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to find (e)

Mathematically solving with L=600 K=6000

[tex]f(L=300,K=10,000) = (45*\sqrt[3]{10,000})*300^3^/^5[/tex]

[tex]f(L=300,K=10,000) = 45*21.5*30.6[/tex]

[tex]f(L=300,K=10,000) = 29704.2[/tex]

Therefore the function f shows maximum at L=900 K=5000

Giving the correct answer to be

d)900 worker-hours and $5000 in capital expenditure

Answer:

Step-by-step explanation:

Answer:

You need to multiply the exponents, then you can multiply the two factors.

Correct answer of the equation:

2^4 x 2^5, multiply exponents

16 x 32, multiply

= 512

Step-by-step explanation:

For every topping, you can either "take-it or leave-it" for your burger. This means there are 2 options for every topping.

Hence number of possible burgers = 2⁸ = 256.

Answer:

4

Step-by-step explanation

Stefan can buy 4 apple with $6 because the apples are $1.50 each

Answer:

option C

Step-by-step explanation:

[tex]3x^2+2x-1\\\\=(3x+a)(x+b)\\\\(3b+a)=2\\\\ab=-1[/tex]

and here we think of b=1 and a=-1

so we have

[tex](3x-1)(x+1)[/tex]

Answer:

Length=25m

Parameter=100m

5 round cost RS 12500

Step-by-step explanation:

The area of a square

=x²

According to the question the equation is

x²=625

x=√625

x=25

The parameter is

25×4

100 meter

So

1 meter costs 25

100 " " 25×100

2500

1 round = 100 meter

So

5 round cost 2500×5

12500

Answer:

The answer is "[tex]d \neq 3c,[/tex]f and g are arbitrary".

Step-by-step explanation:

The matrix of the device is increased  

[tex]\left[\begin{array}{ccc}1&3&f\\ c&d&g\\ \end{array}\right][/tex]

Reduce the echelon row matrix  

[tex]\left[\begin{array}{ccc}1&3&f\\ c&d&g\\ \end{array}\right] \\\\R_1 \leftrightarrow R_2 \\\\\frac{R_2 -1}{C R_1 \to R_2} \sim \left[\begin{array}{ccc} c&d&g\\ 0 & \frac{3c-d}{c}& \frac{cf-g}{c}\\ \end{array}\right][/tex]

Therefore, if 3c[tex]\neq[/tex] 0 is d [tex]\neq[/tex]  3c, the device is valid.  Therefore d [tex]\neq[/tex] are arbitrary 3c, g and f.

The values of the coefficients c and d are 1 and 3, respectively

The system of equations are given as:

[tex]x_1 + 3x_2 = f[/tex]

[tex]cx_1 + dx_2 = g[/tex]

From the question, we understand that the system of equations is consistent.

Assume that the system of equations is also dependent, then it means that:

[tex]c =1[/tex]

[tex]d =3[/tex]

[tex]g =f[/tex]

Hence, the values of the coefficients c and d are 1 and 3, respectively

Read more about systems of equations at:

https://brainly.com/question/13729904

Answer:

140

Step-by-step explanation:

115+165+140+90=510

180*4=720 (sum of interior angles of hexagon)

115+165+140+90+x+2x=720

why 2x because i kept ANGLE DEF as x and ANGLE CDE is twice so 2x

510+2x+x=720

3x=210

x=210/3

x=70

ANGLE DEF IS 70

so  because ANGLE CDE IS TWICE ANGLE DEF thus 70*2=140

ANGLE CDE =140

The angle CDE is 140°.

A hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles.

According to the given problem,

We know,

Sum of the interior angles of a polygon is,

Sum = 180° (n - 2) where n is the number of sides,

Here n = 6 , then

Sum = 180° × 4 = 720°

Let ∠ DEF be x  

Therefore ∠ CDE = 2x,

Sum the interior angles,

⇒ 160 + 90 + 145 + 115 + 2x + x = 720

⇒ 510 + 3x = 720 ( subtracting 510 from both sides )

⇒ 3x = 210 ( dividing both sides by 3 )

⇒ x = 70

∠ CDE = 2x

           = 2 × 70

           = 140°

Hence, we can conclude, in the hexagon, the angle CDE is 140°.

Learn more about hexagon here:

https://brainly.com/question/2001860

#SPJ2

Answer:

9r3

Step-by-step explanation:

93-10=83-10=73-10=63-10=53-10=43-10=33-10=23-10=13-10=3

so 93÷10=9 remainder of 3

Answer:

Step-by-step explanation:

the range is the out put of the function.. what can y be.. in other words

so it's all real numbers...  :)

Answer:I got $21.76

Step-by-step explanation:

;-;

Answer:

15/8

5/8 ÷ 1/3

[Reciprocate the second fraction] =>

5/8 × 3/1

=>15/8

Answer:

1.875

as a fraction 15/8

Or

1 and 7/8

Siri told me.

Answer:

the value is

Step-by-step explanation:

=3(5.10+2)

=3(7.1)

=21.3

Answer:

3(5. 10+2)

Step-by-step explanation:

3(5.12)

3(60)

180

Answer:

the answer is C -1-2 to the equation

Answer:

[tex]\boxed{\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}}[/tex]

Step-by-step explanation:

Given equation to us is :-

[tex]\implies y = 6 - 4x [/tex]

So , here we can put different values of x in order to get different values of y .

Initial table given to us is ,

[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & & & 2&&-6 \\\cline{1-6}\end{tabular}[/tex]

Put x = (-1) :-

[tex]\implies y = 6 - 4x \\\\\implies y = 6 -4(-1) \\\\\implies y = 6 + 4 \\\\\red{\bf\implies y = 10} [/tex]

Put x = 0 :-

[tex]\implies y = 6 - 4x \\\\\implies y = 6-4(0) \\\\\implies y = 6 - 0 \\\\\pink{\bf\implies y = 6 }[/tex]

Put x = 2 :-

[tex]\implies y = 6-4x \\\\\implies y = 6 - 4(2) \\\\\implies y = 6 - 8 \\\\\blue{\bf\implies y = (-2)} [/tex]

Hence the final table would be :-

[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}[/tex]

Answer:

Interest earned = $3546.50

Option B is correct option.

Step-by-step explanation:

Time t = 20 years

Principal Amount P =$3815.24

Interest r = 3.3% or 0.033

Compounded quarterly n = 4

We need to find How much interest has Lucas earned?

First we need to find the future value in the account after 20 years

The formula used to find future value A is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Putting values of t, r , n and P to find A i.e future value

[tex]A=P(1+\frac{r}{n})^{nt}\\A=3815.24(1+\frac{0.033}{4})^{20*4} \\Simplifying:\\A=3815.24(1+0.00825)^{20*4} \\A=3815.24(1.00825)^{80}\\A=3815.24(1.929)\\A= 7361.74[/tex]

Now finding interest amount by subtracting the initial deposit from the future value

Interest earned = Future Value (A)- Initial Deposit (P)

Interest earned = 7,361.74 - 3815.24

Interest earned = 3546.50

So, Lucas have earned interest = $3546.50

Option B is correct option.

Complete question is;

Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened at the bank. Determine whether each statement below is true. Select True or False for each statement.

V(0) = 2 means that the value of the bank account when it is opened is $2000

V(5) = 2.2 means that 2.2 years after the bank account is opened, its value is $5000

V(10) – V(5) = 0.4 means that the bank account grows by $400 between 5 and 10 years after its opening

Answer:

Statement 1: True

Statement 2: False

Statement 3: False

Step-by-step explanation:

We are told that the function V(t) represents the value of a bank account, in thousands of dollars, t years after the account is opened at the bank.

This means that if V(10) = 50, it means that the bank account is valued after 10 years is $50,000

From this little explanation, it's clear that only statement 1 is correct.

Answer:

32%

The probability according to these results is 32% because 25 people ordered a cold drink. 8 of those were smalls. 8 divided by 25 is 0.32 which is the percentage of a 100% chance aka 32%