Solve for x. Write answers in decimal form. (8x)^4/3+44, №18010642, 16.03.2021 17:44

Mathematics

Solve for x. Write answers in decimal form. (8x)^4/3+44 = 300

Step-by-step answer

P Answered by Master

$8x \times 4 \3 = 6x + 44 = 300 \\ 6x = 300 - 44 = 256 \\ 6x= 256 = 44.2$

Mathematics

Evaluate the expression for the given values. (12x+5y)/3z, where x = 12, y = 6, and z = 4. (write answer in decimal form)

Step-by-step answer

P Answered by PhD

1

14.5

Step-by-step explanation:

12×12=144 5×6=30 144+30=174 3×4=12 174/12=14.5

Evaluate the expression for the given values. (12x+5y)/3z, where x = 12, y = 6, and z = 4. (write an

Mathematics

I just want someone to proof-read these so that I have a good understanding of what I am doing (leave feedback) Ok so these are the math questions I don t understand because they are trickily worded or just make no sense. E.) Explain how you could write 60,000,000 as the product of a number greater than or equal to 1 that is multiplied by a power of 10. I think the way to understand this is to focus just on how to understand it. This one is trickily worded so I m going to have to try to find the main idea of the question so that I can figure it

Step-by-step answer

P Answered by PhD

1

Yea it's good but make sure to check your answers to see if you did anything wrong.

Mathematics

1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the number 30. a. 1, 2, 3, 5, 6, 10, 15, 30 b. 2, 3, 4, 10, 20, 30, 40 c. 1, 2, 4, 5, 10, 15, 30 d. 1, 2, 4, 5, 8, 10, 20, 40 3. find the prime factorization of the number 168. a. 24 x 3 x 7 b. 23 x 3 x 7 c. 24 x 33 x 13 d. 23 x 33 x 7 4. find the gcf of the numbers 140 and 180. a. 20 b. 90 c. 30 d. 10 5. the weights of 3 bags containing footballs are 15 oz, 30 oz, and 60 oz. the greatest common factor of 15, 30, and 60 gives the weight of each ball

Step-by-step answer

P Answered by PhD

64

QUESTION 1

We want to find the digit that should fill the blank space to make

3,71-

divisible by 9.

If a number is divisible by 9 then the sum of the digits should be a multiple of 9.

The sum of the given digits is,

3 + 7 + 1 = 11

Since

11 + 7 = 18

which is a multiple of 9.

This means that

3,717

is divisible by 9.

The correct answer is B

QUESTION 2

The factors of the number 30 are all the numbers that divides 30 exactly without a remainder.

These numbers are ;

1,2,3,5,6,10,15,30

The correct answer is A.

QUESTION 3.

We want to find the prime factorization of the number 168.

The prime numbers that are factors of 168 are

$2,3 \: and \: 7$

We can write 168 as the product of these three prime numbers to obtain,

$168={2}^{3}\times 3\times7$

We can also use the factor tree as shown in the attachment to write the prime factorization of 168 as

$168 ={2}^{3}\times 3\times7$

The correct answer is B.

QUESTION 4.

We want to find the greatest common factor of

$140\:\:and\:\:180$

We need to express each of these numbers as a product of prime factors.

The prime factorization of 140 is

$140={2}^{2}\times 5\times7.$

The prime factorization of 180 is

$180={2}^{2} \times{3}^{2}\times5.$

The greatest common factor is the product of the least degree of each common factor.

$GCF={2}^{2}\times5$

GCF=20

The correct answer is A.

QUESTION 5.

We want to find the greatest common factor of

$15,30\: and\:60.$

We need to first find the prime factorization of each number.

The prime factorization of 15 is

$15=3\times5.$

The prime factorization of 30 is

$30=2\times 3\times 5.$

The prime factorization of 60 is

$60={2}^{2}\times3 \times5$

The greatest common factor of these three numbers is the product of the factors with the least degree that is common to them.

$GCF=3 \times5$

GCF=15

The correct answer is C.

QUESTION 6

We want to determine which of the given fractions is equivalent to

$\frac{3}{8}.$

We must therefore simplify each option,

$A.\: \: \frac{15}{32}=\frac{15}{32}$

$B.\:\:\frac{12}{32}=\frac{4\times 3}{4\times8}=\frac{3}{8}$

$C.\:\:\:\:\frac{12}{24}=\frac{12\times1}{12\times 2}=\frac{1}{2}$

$D.\:\:\frac{9}{32}=\frac{9}{32}$

The simplification shows that

$\frac{12}{32}\equiv \frac{3}{8}$

The correct answer is B.

QUESTION 7.

We want to express

$\frac{10}{22}$

in the simplest form.

We just have to cancel out common factors as follows.

$\frac{10}{22}=\frac{2\times5}{2 \times11}$

This simplifies to,

$\frac{10}{22}=\frac{5}{11}$

The correct answer is C.

QUESTION 8.

We were given that Justin visited of the states.

The question requires that we express as a fraction of 50.

This will give us

$\frac{25}{50}=\frac{25\times1}{25\times2}$

We must cancel out the common factors to have our fraction in the simplest form.

$\frac{25}{50}=\frac{1}{2}$

The correct answer is C.

QUESTION 9.

We want to write

$2\frac{5}{8}$

as an improper fraction.

We need to multiply the 2 by the denominator which is 8 and add the product to 5 and then express the result over 8.

This gives us,

$2 \frac{5}{8}=\frac{2\times8+5}{8}$

this implies that,

$2\frac{5}{8}=\frac{16+5}{8}$

$2\frac{5}{8}=\frac{21}{8}$

Sarah needed

$\frac{21}{8}\:\:yards$

The correct answer is D.

QUESTION 10

See attachment

QUESTION 11

We wan to write

$3\: and\:\:\frac{7}{8}$

as an improper fraction.

This implies that,

$3+\frac{7}{8}=3\frac{7}{8}$

To write this as a mixed number, we have,

$3\frac{7}{8}=\frac{3\times8+7}{8}$

This implies that,

$3\frac{7}{8}=\frac{24+7}{8}$

This gives

$3\frac{7}{8}=\frac{31}{8}$

The correct answer is B.

QUESTION 12

We want to find the LCM of and using prime factorization.

The prime factorization of 30 is $30=2\times 3\times 5$

The prime factorization of 46 is $40=2\times 23$ .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times \times3 5\times 23$

LCM=690

The correct answer is D.

QUESTION 13

We want to find the least common multiple of 3,6 and 7.

The prime factorization of is .

The prime factorization of 6 is $6=2\times 3$ .

The prime factorization of 7 is .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times3 \times7$

LCM=42 .

The LCM is 42, therefore 42 days will pass before all three bikes will at the park on the same day again.

The correct answer is B.

See attachment for continuation.

1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the

Mathematics

I just want someone to proof-read these so that I have a good understanding of what I am doing (leave feedback) Ok so these are the math questions I don t understand because they are trickily worded or just make no sense. E.) Explain how you could write 60,000,000 as the product of a number greater than or equal to 1 that is multiplied by a power of 10. I think the way to understand this is to focus just on how to understand it. This one is trickily worded so I m going to have to try to find the main idea of the question so that I can figure it

Step-by-step answer

P Answered by PhD

1

Yea it's good but make sure to check your answers to see if you did anything wrong.

Mathematics

1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the number 30. a. 1, 2, 3, 5, 6, 10, 15, 30 b. 2, 3, 4, 10, 20, 30, 40 c. 1, 2, 4, 5, 10, 15, 30 d. 1, 2, 4, 5, 8, 10, 20, 40 3. find the prime factorization of the number 168. a. 24 x 3 x 7 b. 23 x 3 x 7 c. 24 x 33 x 13 d. 23 x 33 x 7 4. find the gcf of the numbers 140 and 180. a. 20 b. 90 c. 30 d. 10 5. the weights of 3 bags containing footballs are 15 oz, 30 oz, and 60 oz. the greatest common factor of 15, 30, and 60 gives the weight of each ball

Step-by-step answer

P Answered by PhD

64

QUESTION 1

We want to find the digit that should fill the blank space to make

3,71-

divisible by 9.

If a number is divisible by 9 then the sum of the digits should be a multiple of 9.

The sum of the given digits is,

3 + 7 + 1 = 11

Since

11 + 7 = 18

which is a multiple of 9.

This means that

3,717

is divisible by 9.

The correct answer is B

QUESTION 2

The factors of the number 30 are all the numbers that divides 30 exactly without a remainder.

These numbers are ;

1,2,3,5,6,10,15,30

The correct answer is A.

QUESTION 3.

We want to find the prime factorization of the number 168.

The prime numbers that are factors of 168 are

$2,3 \: and \: 7$

We can write 168 as the product of these three prime numbers to obtain,

$168={2}^{3}\times 3\times7$

We can also use the factor tree as shown in the attachment to write the prime factorization of 168 as

$168 ={2}^{3}\times 3\times7$

The correct answer is B.

QUESTION 4.

We want to find the greatest common factor of

$140\:\:and\:\:180$

We need to express each of these numbers as a product of prime factors.

The prime factorization of 140 is

$140={2}^{2}\times 5\times7.$

The prime factorization of 180 is

$180={2}^{2} \times{3}^{2}\times5.$

The greatest common factor is the product of the least degree of each common factor.

$GCF={2}^{2}\times5$

GCF=20

The correct answer is A.

QUESTION 5.

We want to find the greatest common factor of

$15,30\: and\:60.$

We need to first find the prime factorization of each number.

The prime factorization of 15 is

$15=3\times5.$

The prime factorization of 30 is

$30=2\times 3\times 5.$

The prime factorization of 60 is

$60={2}^{2}\times3 \times5$

The greatest common factor of these three numbers is the product of the factors with the least degree that is common to them.

$GCF=3 \times5$

GCF=15

The correct answer is C.

QUESTION 6

We want to determine which of the given fractions is equivalent to

$\frac{3}{8}.$

We must therefore simplify each option,

$A.\: \: \frac{15}{32}=\frac{15}{32}$

$B.\:\:\frac{12}{32}=\frac{4\times 3}{4\times8}=\frac{3}{8}$

$C.\:\:\:\:\frac{12}{24}=\frac{12\times1}{12\times 2}=\frac{1}{2}$

$D.\:\:\frac{9}{32}=\frac{9}{32}$

The simplification shows that

$\frac{12}{32}\equiv \frac{3}{8}$

The correct answer is B.

QUESTION 7.

We want to express

$\frac{10}{22}$

in the simplest form.

We just have to cancel out common factors as follows.

$\frac{10}{22}=\frac{2\times5}{2 \times11}$

This simplifies to,

$\frac{10}{22}=\frac{5}{11}$

The correct answer is C.

QUESTION 8.

We were given that Justin visited of the states.

The question requires that we express as a fraction of 50.

This will give us

$\frac{25}{50}=\frac{25\times1}{25\times2}$

We must cancel out the common factors to have our fraction in the simplest form.

$\frac{25}{50}=\frac{1}{2}$

The correct answer is C.

QUESTION 9.

We want to write

$2\frac{5}{8}$

as an improper fraction.

We need to multiply the 2 by the denominator which is 8 and add the product to 5 and then express the result over 8.

This gives us,

$2 \frac{5}{8}=\frac{2\times8+5}{8}$

this implies that,

$2\frac{5}{8}=\frac{16+5}{8}$

$2\frac{5}{8}=\frac{21}{8}$

Sarah needed

$\frac{21}{8}\:\:yards$

The correct answer is D.

QUESTION 10

See attachment

QUESTION 11

We wan to write

$3\: and\:\:\frac{7}{8}$

as an improper fraction.

This implies that,

$3+\frac{7}{8}=3\frac{7}{8}$

To write this as a mixed number, we have,

$3\frac{7}{8}=\frac{3\times8+7}{8}$

This implies that,

$3\frac{7}{8}=\frac{24+7}{8}$

This gives

$3\frac{7}{8}=\frac{31}{8}$

The correct answer is B.

QUESTION 12

We want to find the LCM of and using prime factorization.

The prime factorization of 30 is $30=2\times 3\times 5$

The prime factorization of 46 is $40=2\times 23$ .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times \times3 5\times 23$

LCM=690

The correct answer is D.

QUESTION 13

We want to find the least common multiple of 3,6 and 7.

The prime factorization of is .

The prime factorization of 6 is $6=2\times 3$ .

The prime factorization of 7 is .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times3 \times7$

LCM=42 .

The LCM is 42, therefore 42 days will pass before all three bikes will at the park on the same day again.

The correct answer is B.

See attachment for continuation.

Mathematics

Exponential growth/decay function hint/tip: remember, the basic general exponential function form is: y = abx in detail, b is written as (1-r) where r is the rate of growth or decay, so our detailed formula is: y = a(1-r)x always work with the rate as a decimal number, not as percentage. if the rate is given as percent (%), you will need to divide it by 100 to have the decimal form. the value of a car is $21,500. it loses 12% of its value every year. (a) write a function that represents the value y (in dollars) of the car after x years. (b) use

Step-by-step answer

P Answered by PhD

1

(a) Write a function that represents the value and (in dollars) of the car after x years.
For this case what we should do is write the equation of exponential type.
We have then:
y = A (b) ^ x
Substituting the values:
y = 21500 (0.88) ^ x

y = 21500 (0.88) ^ x

(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
We use the function found in part (a) and evaluate for x = 6.
We have then:
y = 21500 (0.88) ^ 6
y = 9985 $

the value of the car after 6 years is:
y = 9985 $

Mathematics

Exponential growth/decay function hint/tip: remember, the basic general exponential function form is: y = abx in detail, b is written as (1-r) where r is the rate of growth or decay, so our detailed formula is: y = a(1-r)x always work with the rate as a decimal number, not as percentage. if the rate is given as percent (%), you will need to divide it by 100 to have the decimal form. the value of a car is $21,500. it loses 12% of its value every year. (a) write a function that represents the value y (in dollars) of the car after x years. (b) use

Step-by-step answer

P Answered by PhD

1

(a) Write a function that represents the value and (in dollars) of the car after x years.
For this case what we should do is write the equation of exponential type.
We have then:
y = A (b) ^ x
Substituting the values:
y = 21500 (0.88) ^ x

y = 21500 (0.88) ^ x

(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
We use the function found in part (a) and evaluate for x = 6.
We have then:
y = 21500 (0.88) ^ 6
y = 9985 $

the value of the car after 6 years is:
y = 9985 $

Mathematics

Astore employee performs most of the daily unit counts, but the owner personally recorded that there were 61 units remaining after 3 days and 33 units remaining after 13 days. use these two data points to determine the equation for the line of best fit for the store s inventory. write the answer in decimal form. y=__x+__

Step-by-step answer

P Answered by PhD

25

(3,61),(13,33)
slope = (33 - 61) / (13 - 3) = -28/10 = - 14/5 = -2.8

y = mx + b
slope(m) = -2.8
use either of ur points(3,61)...x = 3 and y = 61
now sub into the formula and find b, the y int
61 = -2.8(3) + b
61 = -8.4 + b
61 + 8.4 = b
69.4 = b
so ur equation is : y = -2.8x + 69.4

Mathematics

A farmer uses x lb of fertilizer per acre at a cost of 1.4 per pound, leading to a revenue of R = 700 – 400e -x/100 dollars per acre. (a) How many pounds of fertilizer should be applied per acre to maximize profit? Write you answer in decimal form rounding to three decimal places Number pounds per acre. (b) What is the maximum profit on a 200 acre farm? $ Number

Step-by-step answer

P Answered by PhD

The cost can be written as:

C(x) = $1.4*x

The revenue can be written as:

R(x) = $700 - $400*e^(-x/100)

And as you know, the profit is written as the difference between the revenue and the cost:

P(x) = R(x) - C(x)

P(x) = $700 - $400*e^(-x/100) - $1.4*x

Now we want to maximize this, then we must look at the zeros in the derivate of P(x)

dP/dx = P'(x) = (-1/100)*$400*e^(-x/100) - $1.4

The maximum will be when P'(x) = 0.

we can solve:

0 = (-1/100)*$400*e^(-x/100) - $1.4

$1.4 = (-1/100)*$400*e^(-x/100)

(-100)*$1.4 = $400*e^(-x/100)

$140 = $400*e^(-x/100)

($140/$400) = e^(-x/100)

0.35 = e^(-x/100)

Now we can apply the Ln() in both sides and get:

ln(0.35) = ln(e^(-x/100) ) = -x/100

-ln(0.35)*100 = x = 104.98

You should apply 104.90 pounds of fertilizer.

b) The profit per acre, is:

P(x) = $700 - $400*e^(-x/100) - $1.4*x

Then if you have 200 acres, the profit will be:

200*P(x) = 200*($700 - $400*e^(-x/100) - $1.4*x)

and the maximum profit is whit x = 104.98 pounds, then:

200*P(104.98) = 200*($700 - $400*e^(-104.98/100) - $1.4*104.98) = $82,604.98

Solve for x. Write answers in decimal form.

(8x)^4/3+44 = 300

Step-by-step answer

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