Which of the following represents the value of x, the missing exponents needed to make the equation a true statement? Explain your reasoning.(Please answer! I need this ASAP)
Which of the following represents the value of x, the - 1


Answer 1

Answer:  x = 21



The exponent rules are

  • a^b * a^c = a^(b+c) .... lets call this rule 1
  • (a^b)/(a^c) = a^(b-c) .... lets call this rule 2
  • (a^b)^c = a^(b*c) ......... lets call this rule 3

The expression on the right hand side simplifies to c^(-1). We add the exponents to get this. So we're using rule 1 mentioned above.

We'll keep this in mind for later.


On the left hand side (c^5)^4 becomes c^(20) because we multiply the exponents (rule 3)

Then (c^20)/(c^x) becomes c^(20-x). We subtract exponents here (rule 2).


After using those exponent rules, the original equation turns into

c^(20-x) = c^(-1)

The bases are both c, so the exponents must be equal

20-x = -1

-x = -1-20

-x = -21

x = 21

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There are 5 times as many females as males on the maths course at university. What fractionof the course are male?
Give your answer in its simplest form




Step-by-step explanation:

Males = 1

Females = 5

Ration: 1:5

Male fraction = 1/6


Step-by-step explanation:

Let number of male = x

number of female = y

then according to given condition , we get ,

y =5*x


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A professor at a university wants to estimate the average number of hours of sleep the students get during exam week. The professor wants to find a sample mean that is within 4.266 hours of the true average for all college students at the university with 99% conconfidence. If the professor knows the standard deviation of the sleep times for all college students is 2.539, what sample size will need to be taken



The sample size is n = 2

Step-by-step explanation:

From the question we are told that

   The margin of error is  E =4.266

    The standard deviation is  \sigma = 2.539

From the question we are told the confidence level is  99% , hence the level of significance is    

      \alpha = (100 - 99 ) \%

=>   \alpha = 0.01

Generally from the normal distribution table the critical value  of  (\alpha )/(2) is  

   Z_{(\alpha )/(2) } =  2.58

Generally the sample size is mathematically represented as  

   n = [\frac{Z_{(\alpha )/(2) } *  \sigma }{E} ] ^2

=>  n = [(2.58  *  2.539  )/(4.266) ] ^2

=>  n = 2

The length of each side of a cube is increased by a factor of 4. What is the effect on the volume of the cube?



When dealing with VOLUME, an increase in a linear quantity, produces a third power result in the volume.

Increase the sides of a cube by 2 produces an 8 times effect in the volume.

Increasing each side of a cube by 4 produces a chnage of 4 * 4 * 4 or

64 times in the volume.

Step-by-step explanation:

Jessica is asked to solve this problem on her math quiz −29+14=? She remembered that she needed to watch for the signs on the numbers, but she is still confused on how the rules work for addition of integers. In complete sentences, explain to Jessica what rule she would use to solve this problem and how she can tell what the sign on her final answer should be in order to get the question correct on her quiz.



Step-by-step explanation:

-29 +14 =-15

The biggest number "29" has minus "-" in front, so in the final the sigh will be minus. The final sigh on the answer dibents on the biggest number.

If you have this exercise :

-14 +29 =15

The biggest number has "+" in front of it

Final answer:

To solve the problem −29+14, you subtract the smaller number from the larger number and give the answer the sign of the larger number, resulting in −15. The rules of addition for integers require attention to the sign and magnitude of the numbers involved.


Jessica, to solve the problem −29+14, we need to apply the rule for addition when dealing with integers that have different signs. Since −29 is negative and 14 is positive, you subtract the smaller number from the larger number and the answer will have the sign of the larger number. In this case, 29 is larger than 14, so we do 29 − 14, which equals 15. Because the larger number (29) was negative, the result will also be negative, so the final answer is −15.

Remember the rules of addition for different signs: when adding two numbers with opposite signs, the answer will have the sign of the larger absolute value. We subtract the smaller absolute value from the larger one to determine the numerical part of the answer. If you're ever unsure about the sign, just remember that the answer will take the sign of the number with the larger absolute value. This is also true when performing subtraction, except you change the sign of the number being subtracted first, then proceed with addition based on the rules for integers.

Jacqueline buys 2 fourths yard of green ribbon and 1 fourths yard of pink ribbon. How many yards of ribbon does she buy?




Step-by-step explanation:

Which represents 8(95) using the distributive property to simplify



8*90 + 8*9 = 760

Step-by-step explanation:

Because, 8(95) just means 8 times 95 so you just distribute 8 to 90 and 5.