Simplifying products and quotients of powers

7^2•7^8/7^4=7^a/7^4=7^b

A=
b=

Simplifying Products And Quotients Of Powers 7^27^8/7^4=7^a/7^4=7^bA= B=

Answers

Answer 1

Answer:

a=10

b=6

Step-by-step explanation:

add 2 to 8, to get a, then subtract 4 from 10 to get b

Answer 2

Answer:

10 and 6

Step-by-step explanation:

Simplifying Products And Quotients Of Powers 7^27^8/7^4=7^a/7^4=7^bA= B=

Related Questions

Brittany Monroe is a legal secretary. Her biweekly salary is $1,650.00 what is her annual salary?

Answers

Answer:

$42,900 a year

Step-by-step explanation:

so there are 26 bi-weeks in a year. (fun fact)

you take $1,650 and multiply that biweekly to get her annual salary.

1650*26=42,900

Need help with this math problem

Answers

Answer:

[tex]f(x)=-5x-3[/tex].

Step-by-step explanation:

From the given machine diagram it is clear that:

[tex]f(x)=-8[/tex] at [tex]x=1[/tex]

[tex]f(x)=-13[/tex] at [tex]x=2[/tex]

[tex]f(x)=-18[/tex] at [tex]x=3[/tex]

It is clear that the value of f(x) decreasing by 5 when the value of x is increasing by 1.

Since the function changing at a constant rate, therefore it represents a linear function.

If a linear function passing through two points, then the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The given linear function passes through (1,-8) and (2,-13), therefore the linear equation is

[tex]y-(-8)=\dfrac{-13-(-8)}{2-1}(x-1)[/tex]

[tex]y+8=\dfrac{-5}{1}(x-1)[/tex]

[tex]y+8=-5(x-1)[/tex]

[tex]y=-5x+5-8[/tex]

[tex]y=-5x-3[/tex]

So, the required function is [tex]f(x)=-5x-3[/tex].

256 divided by -16 with steps.

Answers

Answer:

256÷-16=16

Step-by-step explanation:

The complete expression is 256 divided by -16 is -16

How to determine the solution to the equation

From the question, we have the following parameters that can be used in our computation:

256 divided by -16 = what

When represented as an equation, we have

Result = 256 divided by -16

Make the result the subject of the formula

So, we have

Result = 256/-16

Rewrite as

Result = -256/16

Evaluate the quotient

Result = -16

Hence, the number is -16


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Determine if the set of vectors shown to the right is a basis for IR3 If the set of vectors is not a basis, determine whether it is linearly independent and whether the set 311-4 spans R 12 Which of the following describe the set?
A. The set is a basis for R3
B. The set is linearly independent.
C The set spans R3
D. None of the above

Answers

Answer:

The problem is clearly solved in the attachment

Help ASAP giving BRAINLIEST! Am i correct?

Answers

Answer:

You are correct

Step-by-step explanation:

x - 8 < 23

Add 8 to both sides

x - 8 + 8 < 23 + 8

Simplify

x < 31

Yes, you are correct.

The graph of a function is shown below.
D
Which statement best describes section D of the graph?
0 А.
linear and increasing
О В.
linear and decreasing
Ос.
nonlinear and increasing
OD
nonlinear and decreasing

Answers

Maybe the last option

Classify this triangle.


Acute scalene triangle
Obtuse isosceles triangle
Right isosceles triangle
Right scalene triangle

Answers

right scalene triangle

Answer: right isosceles

Step-by-step explanation:

the angle at the bottom is right therefore you need to figure out the lengths of the sides to conclude if it is isosceles or scalene. because two of the sides are the same length and the other is not it is isosceles

A fraction that is equivalent to 6/-5?

Answers

Answer:

12/-10

Step-by-step explanation:

Any multiple of a fraction is the equivalent of the original fraction, the only difference is that it wont be fully simplified. If we multiply the original fraction (6/-5) by 2, both the numerator and denominator, you will get 12/-10.

Answer:

12/-10

Step-by-step explanation:

6/-5

6×2= 12

-5×2=-10

12/-10

Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of 40.1 and standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude?

Answers

Answer:

[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]

The degrees of freedom are

[tex]df=20+20-2=38[/tex]

And the p value is given by:

[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that  

[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]

And the statistic is given by this formula:

[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]

Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:

[tex]S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]

The system of hypothesis on this case are:

Null hypothesis: [tex]\mu_1 = \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]

We have the following data given:

[tex]n_1 =20[/tex] represent the sample size for group 1

[tex]n_2 =20[/tex] represent the sample size for group 2

[tex]\bar X_1 =43.5[/tex] represent the sample mean for the group 1

[tex]\bar X_2 =40.1[/tex] represent the sample mean for the group 2

[tex]s_1=4.1[/tex] represent the sample standard deviation for group 1

[tex]s_2=3.2[/tex] represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

[tex]\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525[/tex]

And the deviation would be just the square root of the variance:

[tex]S_p=3.678[/tex]

The statistic is givne by:

[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]

The degrees of freedom are

[tex]df=20+20-2=38[/tex]

And the p value is given by:

[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Using the t-distribution, as we have the standard deviation for the sample, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.

What are the hypothesis tested?

At the null hypothesis, it is tested if there is no difference, that is:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if there is a difference, that is:

[tex]H_a: \mu_1 - \mu_2 \neq 0[/tex]

What is the mean and the standard error of the distribution of differences?

For each sample, we have that they are given by

[tex]\mu_1 = 43.5, s_1 = \frac{4.1}{\sqrt{20}} = 0.9168[/tex]

[tex]\mu_2 = 40.2, s_2 = \frac{3.2}{\sqrt{20}} = 0.7155[/tex]

Hence, for the distribution of differences, the mean and the standard error are given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 43.5 - 40.2 = 3.3[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.9168^2 + 0.7155^2} = 1.163[/tex]

What is the test statistic?

It is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{3.3 - 0}{1.163}[/tex]

[tex]t = 2.84[/tex]

What is the decision?

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 20 + 20 - 2 = 38 df, the critical value is of [tex]|z^{\ast}| = 2.0244[/tex].

Since the absolute value of the test statistic is greater than the critical value, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.

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Please help ASAP! Will give BRAINLIEST! Please read the questionTHEN answer correctly! No guessing.

Answers

Answer:D

Step-by-step explanation:

(4/5)^0

4^0/5^0=1/1=1

What is the area of the triangle?
PLSSS help me

Answers

Answer:

The area of the triangle is [tex]A=6 \:units^2[/tex].

Step-by-step explanation:

The area A of a triangle is given by the formula [tex]A=\frac{1}{2} bh[/tex] where b is the base and h is the height of the triangle.

From the graph, we can see that the base is 3 units and the height is 4 units. Therefore, the area of the triangle is

[tex]A=\frac{1}{2} \cdot3\cdot 4=\frac{12}{2}=6 \:units^2[/tex]

A music professor offers his 40 students the option of coming to an additional rehearsal session the week before their juries (musical final exams.) In order to decide whether these extra sessions actually help students, he keeps track of who attends them and compares their jury scores to those of students who did not schedule extra sessions. This study is a(n): A) matched pairs design. B) randomized block design. C) nonrandomized experiment. D) observational study. E) completely randomized experiment.

Answers

Answer:

D. Observational Study

Explanation:

An observational  study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.  

This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study  is subject to bias because a positive or negative result might be because of other factors not related to the study.

Two terms of an arithmetic sequence are a12=70 and a30=124. Write an explicit rule for the nth term.

Answers

Answer:

Tn = 34-3n

Step-by-step explanation:

The formula for calculating the nth term of an arithmetic sequence is given as;

Tn = [tex]a+(n-1)d[/tex]

a is the first term

n is the number of terms

d is the common difference

If  two terms of an arithmetic sequence are a12=70 and a30=124 then;

T12 = a+(12-1)d = 70

T12 = a+11d = 70...(1)

T30 = a+(30-1)d = 124

T30 = a+29d = 124...(2)

Solving equation 1 and 2 simultaneously to get a and d;

Taking the difference of both equation we have;

29d - 11d = 124-70

18d = 54

d = 54/18

d = 3

Substituting d=3 into equation 1 to get the value of 'a' we have;

a+11(3) = 70

a+33=70

a = 70-33

a = 37

To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3

Tn = 37+(n-1)3

Tn = 37+3n-3

Tn = 34-3n

This gives the required nth term

Find two numbers for which the sum is 101 and the difference is 47

Answers

Answer:

74 and 27

Step-by-step explanation:

let x and y be the numbers

x + y =101........eqn 1

x - y = 47.......eqn 2

solve simultaneously

from equation 2, make x the subject

x= 47 + y........eqn 3

put eqn 3 into eqn 1

(47+y) + y = 101

47 + 2y = 101

       2y= 101 - 47

       2y=54

         y= 54/2

         y= 27

put y=27 into eqn 3

x = 47 + 27

x = 74

74 and 27

74+27=101
74–27=47

Plzzz mark as brainleast plzzz plzzz

how many tenths are in 4600​

Answers

Answer:

4600 tenths as a Fraction

Since 4600 tenths is 4600 over ten, 4600 tenths as a Fraction is 4600/10.

4600 tenths as a Decimal

If you divide 4600 by ten you get 4600 tenths as a decimal which is 460.00.

4600 tenths as a Percent

To get 4600 tenths as a Percent, you multiply the decimal with 100 to get the answer of 46000 percent.

4600 tenths of a dollar

First we divide a dollar into ten parts where each part is 10 cents. Then we multiply 10 cents with 4600 and get 46000 cents or 460 dollars and 0 cents.

Step-by-step explanation:

Hope this helped!

Stay safe!!!

Answer:

Step-by-step explanation:

To answer this, multiply 4600 by 10:  46000.  There are 46000 tenths in 4600.

Equations
What is the solution of the system of linear equations?
-3x + 4y = -18
2x - y = 7

(-2,-3)
(-2,3)
(2, -3)
(2, 3)​

Answers

Answer:

Step-by-step explanation:

-3x + 4y = -18

8x - 4y =   28

5x = 10

x = 2

4 - y = 7

-y = 3

y = -3

(2, -3)

The solution of the system of linear equations given is (2,-3), the correct option is C.

What is System of Linear Equation?

The system of linear equation is set of equations which have a common solution.

The equations are

-3x+4y = -18

2x-y =7

The linear equations can be solved using substitution method

y = 2x -7 from equation 2 will be substituted in equation 1

-3x +4 ( 2x -7) = -18

-3x +8x -28 = -18

5x = 10

x = 2

y = 2 * 2 -7 = -3

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Which figure below has point symmetry

Answers

Answer:

Figure D

Step-by-step explanation:

Point Symmetry is when every part has a matching part: the same distance from the central point. but in the opposite direction. Hope this helps! :)

A footbridge has a span of 54 feet. A sign is
to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge?

Answers

Answer:

27

Step-by-step explanation:

Because if it is halfway, that means

halfway=1/2

1/2=1/2 of 54

54/2 or 1/2 of 54=27

PLS MARK ME BRAINLIEST I NEED IT PLEASE

The center of the sign will be 27 feet apart from both ends of the bridge.

Given that,
A footbridge has a span of 54 feet. A sign is to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge is to be determined.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,

Since the bridge is 54 feet long,
Now at the center of the bridge, a sign is placed,
So the distance of sign from both ends is equal to half of the total length of the bridge. i.e.
= 54 / 2
= 27

Thus, the center of the sign will be 27 feet apart from both ends of the bridge.

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A number pattern starts with 10 and follows the rule "multiply by 3." What is true
about all of the numbers in this pattern?

Answers

i think the answer is they are all divisible by 3

Which value has an absolute deviation of 5 from the mean of this data set?
26, 12, 35, 28, 14
A 28
B. 35
C. 26
D. 14

Answers

Answer: 28

Step-by-step explanation: see prev. explanation

The absolute deviation of 5 from the mean of this data set is 28.

What is absolute deviation?

Absolute deviation is "the distance between each data point to the mean".

According to the question,

The data set is 26, 12, 35, 28, 14

Average of the data set = [tex]\frac{sum of the data value }{Total number of observation}[/tex]

= [tex]\frac{26+12+35+28+14}{5}[/tex]

= [tex]\frac{115}{5}[/tex]

= 23.

Thus, the average of the data set is 23.

In order to find absolute deviation of 5 subtract each data point from the mean.

26 - 23 = |3| = 3

12 - 23  = |-11| = 11

35 - 23 = |12| = 12

28 - 23 = |5| =  5

14 - 23  = |-9| = 9.

Hence, the absolute deviation of 5 is from the mean of the data set is 28.

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What is the number of possible permutations of 5 objects taken 2 at a time? A. 10 B. 20 C. 60 D. 120

Answers

Answer:

B. 20

Step-by-step explanation:

5P2 is equal to 20 using the permutation formula.

Junior bought a bag of mixed fruit snacks. The flavors in the bag are 4 strawberry, 3 cherry, and 5 grape. If he chooses one fruit snack at random, what it the probability of the first one being grape?

Answers

Answer:I believe it would be 5/12

Step-by-step explanation:

You add all of them up then since it's 5 grapes and in total there is 12 fruit snacks. It should be 5 grapes of 12 fruit snacks in the bag.

Sara goes on a slingshot ride in an amusement park. She is strapped into a spherical ball that has a radius of centimeters. What is the volume of air in the spherical ball? Use this formula: , where r is the sphere’s radius.
A.

B.

C.

D.

Answers

Answer:

A. 4×π×3²×[tex]10^{6}[/tex]

Step-by-step explanation:

r = 3×10² = 3×100 = 300

[tex]\frac{4}{3}[/tex]×π×300³=

[tex]\frac{4}{3}[/tex]×π×27,000,000=

[tex]\frac{108,000,000}{3}[/tex]×π=

36,000,000π

Answers solved:

A. 36,000,000π

B. 108,000,000π

C. 3,600,000π

D. 32,400,000π

The solution is Option A.

The volume of the air in the spherical ball is given by the equation

V = 4π ( 3 )² ( 10 )⁶ cm³

What is a Sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the volume of the sphere be represented as V

Now , the radius of the spherical ball be r

The value of r = 3 ( 10 )² cm

So , the volume of the spherical ball = ( 4/3 ) πr³

Substituting the values in the equation , we get

Volume of the spherical ball V = ( 4/3 ) x π x [ 3 ( 10 )² ]³

On simplifying the equation , we get

Volume of the spherical ball V = ( 4/3 ) x π x ( 3 )³ ( 10 )⁶

Volume of the spherical ball V = 4 x π x ( 3 )² ( 10 )⁶

Therefore , the value of V is 4π ( 3 )² ( 10 )⁶

Hence , the volume of the spherical ball is 4π ( 3 )² ( 10 )⁶

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6
An ordinary fair dice is thrown once.
(a) On the probability scale mark with a cross (X) the probability ti
the dice lands on an even number.
1
2
(b) Write down the probability that the dice lands on a number les
than 3.​

Answers

Answer:

(a) 1/2(b) 1/3

Step-by-step explanation:

(a) 3 of the 6 numbers on the die are even, so the probability that one of them will show is 3/6 = 1/2.

__

(b) 2 of the 6 numbers on the die are less than 3, so the probability that one of them will show is 2/6 = 1/3.

Apply the distributive property to factor out the greatest common factor of all three terms. Explanation: 9-12x+6y what is the answer??

Answers

Answer: [tex]3(3-4x+2y)[/tex]

Step-by-step explanation:

[tex]9-12x+6y[/tex]

[tex]3(3-4x+2y)[/tex]

A movie membership costs $10 a month plus an additional $5 for each movie purchased. If you have only budgeted to spend a maximum of $25 this month, how many movies can you purchase?

Answers

Answer:

3

Step-by-step explanation:

25-10/3=3

Answer:

3 movies

Step-by-step explanation:

You can pay for 3 movies because

5*3=15 and you have to pay for the membership which is 10 so

10+15=25

What is the measure of angle A?

Answers

Answer:

A = 19.47

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hypotenuse

sin A = 2/6

Take the inverse sin of each side

sin ^-1 ( sin A) = sin ^-1 (2/6)

A =19.47122063

To the nearest hundredth

A = 19.47

Graph the circle (x-3)^2+(y-7)^2=4

Answers

The equation is in the form of the equation of the circle. x^2+y^2=r^2. This equation is for the centre, (0,0).

x-3 and y-7 represents the shift in the centre of the circle in the respective axis. Therefore the centre is (3,7). r=2. d=4. So this circle’s centre is at (3,7) with radius 2.

Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.

Answers

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

B because first you need to read the problem and understand the information.

what is the best college to go to?

Answers

It is different for everyone especially what you want to do in the future. What do you want to major in?

Answer:

The the best college to go to is the one where you feel comfortable.

Step-by-step explanation:

It is so important to understand the sence of what is actually "the best" college to go to.

You can look at that from a viriety of perspectives, and it is debatable to just go for the college which holds the highest rank on some site.

There are a lot of factors to consider, and what is generally considered the best college does not necassarilly the right one for you.

Ask your loved ones for advice and if you can take a look at yourvtop thee collages.

The the best college to go to is the one where you feel comfortable.

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