1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
WITCHER [35]
3 years ago
9

Is 7 to the 8th power times 7 equivalent to 7 to the the third power times 7 to third power equivalent?

Mathematics
1 answer:
Akimi4 [234]3 years ago
8 0

Answer:

They are not equivalent.

Step-by-step explanation:

Before we solve the question, we need to know that from the laws of indices:

A^x x A^y = A^(x+y).

7 to the power of 8th power means 7^8

7^8 times 7 means 7^8 x 7. From the laws of indices we have 7^8 x 7 = 7^9.

7 to the power of 3rd power means 7^3

7^3 times 7 to the power of 3rd power means 7^3 x 7^3. From the laws of indices we have 7^3 x 7^3 = 7^6.

Obviously, 7^9 ≠ 7^3 therefore, they are not equivalent.

You might be interested in
Y intercept of this graph​
Aleksandr [31]

Answer:

The y intercept is - 2

Step-by-step explanation:

Because in the y axis the line crosses - 2

8 0
3 years ago
A regular work week is 40 hours. Overtime pay is time and one-half. Isabel drives a truck for $8.75 an hour. If she worked 48 ho
Harlamova29_29 [7]
For 40 hours it would be $350

And since it is only half pay for overtime then she would only make $35 in eight hours


So altogether she would make $385 this week
8 0
2 years ago
Find the solution to the following system using substitution or elimination:​
raketka [301]

Answer:

B) (3,1)

Step-by-step explanation:

y = -2x + 7

y = 3x - 8

3x - 8 = -2x + 7

combine like terms:

5x = 15

divide both sides of the equation by 5:

x = 3

y = 3(3) - 8 = 1

4 0
3 years ago
Plssss help (the answer choices are the same for all)
Lilit [14]
1) x < 8/3
2) x > -9
3) Infinite Solutions
4) No Solution

Please correct me if I’m wrong. Hope this helps!
3 0
2 years ago
According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For
SpyIntel [72]

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.71

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here n = 16, we want P(X \geq 13). So

P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591

P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835

P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273

P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042

P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now n = 160. So

\mu = E(X) = np = 160*0.71 = 113.6

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74

Using continuity correction, this is P(X \geq 110 - 0.5) = P(X \geq 109.5), which is 1 subtracted by the pvalue of Z when X = 109.5. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{109.5 - 113.6}{5.74}

Z = -0.71

Z = -0.71 has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

3 0
3 years ago
Other questions:
  • Em um campeonato de vôlei, o time Maravilha obteve 6 vitórias, 4 empates e 2 derrotas nas 12 partidas disputadas. De quantas man
    13·1 answer
  • You are fixing the roof of your house when a hammer breaks loose and slides down. the roof makes an angle of 65
    6·1 answer
  • Tell whether 24 is a factor or multiple of the number 6
    12·1 answer
  • Which is equivalent to 3^4
    13·1 answer
  • Amanda exercised for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40
    8·1 answer
  • Find the volume of a triangular prism with the following dimensions. Round to the nearest whole number.
    10·2 answers
  • Find a number that is 15 more than 4 times its opposite
    6·1 answer
  • Tom has three times as many pencils as pens but has a total of de 100 writing utensils. How many pencils and pens does toms have
    8·1 answer
  • In a class of 20 students, 9 are female and 15 have an A in the class. There are 2 students who are male and do not have an A in
    12·1 answer
  • PLEASE SOMEONE HELP ME
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!