What is the first step in isolating the variable in this equation?
(½)p + 75 = 100
A)
Subtract 75 from both sides.
B)
Subtract ½ from both sides.
C)
Divide both sides by 75.
D)
Divide both sides by ½.

Answer:

a. reflection across the y-axis

Answer:

d) 280

Step-by-step explanation:

40320/3=6720

8720/24=280

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%

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:

the ladle should scoop out 56 scoops to empty the bucket because if one scoop equals 1/14, there are 14 scoops per liter, and 4 liters, so 4 times 14 equals 56

The ladle should scoop out 56 scoops to empty the bucket

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity

Given,

A bucket holds 4 liters of water.

If a ladle can scoop out 14 of a liter We need to find how many scoops will it take to empty the bucket

We know that one scoop equals 1/14 liters

1 scoop=1/14 litres

1 litre=14 scoops

As there are 4 litres

We have to multiply 14 with four to find the number of scoops to take to make the bucket empty.

14×4

56

Hence, the ladle should scoop out 56 scoops to empty the bucket

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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

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Answer:

16 yards

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

F. 2x⁵y² - 6x⁴y³

That is the answer.

By means of distribution.

Answer:

16

Step-by-step explanation:

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

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:

[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]

Answer:

1600

Step-by-step explanation:

it is already rounded

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]

After going through the statement in the question, the number of each colored ornament Nick have is 3.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.

Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

There are three colors.

We can infer that there are 3 ornaments of each color because there are 6 ornaments for each of the other two colors.

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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 answer is C -1-2 to the equation

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.

I think its 1

Step-by-step explanation:

if it ain't my bad

Answer:

(5, -11)

Step-by-step explanation:

We know that (8, -5) is 6 units above and 3 units to the right of point P. Knowing this, let's work backwards by starting from (8,-5) and counting 6 units down and 3 units to the left on the graph.

If you counted correctly, this should place you at the (5, -11). (You can also check your work by counting 6 units up and 3 units to the right from (5, -11) and seeing if you end up at (8, -5).)

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.

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°.

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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