16.03.2021

Solve for x. Write answers in decimal form.

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

. 0

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Mathematics
Step-by-step answer
P Answered by Master

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

Mathematics
Step-by-step answer
P Answered by PhD

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
Step-by-step answer
P Answered by PhD

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 25 of the50 states.

The question requires that we express 25 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 30 and 46 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 3 is 3.


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


The prime factorization of 7 is 7.


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
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
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
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
Step-by-step answer
P Answered by PhD

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 25 of the50 states.

The question requires that we express 25 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 30 and 46 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 3 is 3.


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


The prime factorization of 7 is 7.


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
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
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
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
Step-by-step answer
P Answered by PhD
(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
Step-by-step answer
P Answered by PhD
(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
Step-by-step answer
P Answered by PhD
(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
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

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