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Simplify: [3(2a)^3/2]^2

A: 34^4√2a^9

B: 72a^3

C: 216a^3

D: 24a^3​

Given:

15. [tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex]

17. [tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex]

19. [tex]2^{\log_2100}[/tex]

To find:

The values of the given logarithms by using the properties of logarithms.

Solution:

15. We have,

[tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex]

Using property of logarithms, we get

[tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)=1[/tex]         [tex][\because \log_aa=1][/tex]

Therefore, the value of [tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex] is 1.

17. We have,

[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex]

Using properties of logarithms, we get

[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-\log_{\frac{3}{4}}\left(\dfrac{3}{4}\right)[/tex]                    [tex][\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}][/tex]

[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-1[/tex]                 [tex][\because \log_aa=1][/tex]

Therefore, the value of [tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex] is -1.

19. We have,

[tex]2^{\log_2100}[/tex]

Using property of logarithms, we get

[tex]2^{\log_2100}=100[/tex]          [tex][\because a^{\log_ax}=x][/tex]

Therefore, the value of [tex]2^{\log_2100}[/tex] is 100.

Answer:

so the total is 20 and its at ten so

10/20=5/10=1/2

so 50 percent

plzzz brainlest

Answer:

4

Step-by-step explanation:

x²+8x+11=0

x²+8x+(+4)²-(+4)²+11=0

Answer:

16

Step-by-step explanation:

x2+8x=  −11−11

28​=4→(4)2=16

x2+8x+16=x2+8x+16=  −11+16−11+16

(x+4)2=  55

16

Answer:

$27.2

Step-by-step explanation:

680x0.04=. 27.2

She made $27.2 last week

Answer:

(6,3,0)

Step-by-step explanation:

Given,

x -  y + 0z  =  3

6x -  0y - 2z = 36

0x + 6y + 2z = 18

You have the following augmented matrix:

(1) 1     -1     0      3

(2) 6    0   -2      36

(3) 0    6    2       18

Let's (3) add to (2) and divide by 6

(1)  1    -1    0       3

(2) 1     1    0       9

(3) 0    6   2       18

Now, let's (2) add  to (1) and divide by 2

(1)  1   0    0     6

(2) 1    1    0     9

(3) 0   6   2     18

Let's (3) ÷ 2

(1)  1    0   0     6

(2) 1    1   0      9

(3) 0   3   1      9  

Let's (1) subtract from (2)

(1)  1   0   0     6

(2) 0   1   0     3

(3) 0   3   1     9

Finally, let's (2) multiply by 3 and subtract from (3)

(1)  1   0   0     6

(2) 0   1   0     3

(3) 0   0   1     0

Thus,

x = 6, y = 3 and z = 0

The answer is (6, 3, 0)

We have to verify the answer

6 - 3 = 3  ⇒⇒ 3 = 3

6*6 - 5*0 = 36   ⇒⇒ 36 = 36

6*3 + 2*0 = 18    ⇒⇒ 18 = 18  

Answer:

x *2 + (28-x)*4 = 100

Step-by-step explanation:

Given

Total number of questions in the paper = 28

Out of these 28 questions let us say that x number of questions are of 2 points and 28-x questions are of 4 points.

Also, the complete test is of 100 marks

Thus, the linear equation representing the

x *2 + (28-x)*4 = 100

Answer:

=14.2

Step-by-step explanation:

a^2 + b^2 = c^2

21 ^2 + x ^2 = 35^2

= 28

28 + 4 = 32

The side with 21 then becomes the new x

x/a =

=14.2

The height of the house that can be ladder reached now will be 14.18 feet.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

A 35-foot ladder is set against the side of the house so it reaches up 21 feet.

Then the base length will be

  35² = 21² + b²

1225 = 441 + b²

   b² = 784

     b = 28 feet

If the ladder is at its base and pulls it 4 feet farther from the house.

Then the height of the house that can be ladder reach now will be

  35² = 32² + h²

1225 = 1024+ h²

   h² = 201

     h = 14.18 feet

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ2

Step-by-step explanation:

20 ml is your answer

i hope it helps u

Answer:

If I'm reading it correctly the answer should be 20.

To get that answer all you do is 4x5.

Answer:

[tex] \frac{16}{33} [/tex]

Step-by-step explanation:

[tex]x = 0.48... \\ 100 \times x = 0.48 \times 100 \\ 100x - x = 48.48.. - 0.48 \\ 99x = 48 \\ \frac{99x}{99} = \frac{48}{99} \\ x = \frac{16}{33} [/tex]

Answer:

the second green shape because the first one is a rectangle which has 2 equal sides

Answer:

the third orange one

Step-by-step explanation:

i have the same question and these 2 show up as answers on both so it has to be this one

Answer:

9

Step-by-step explanation:

f(x) = x − 7 and g(x) = x^2

g(f(4))

First find f(4)

f(4) = 4-7 = -3

Then put this result in g(x)

g(-3) = (-3) ^2 = 9

g(f(4) = 9

g(f(4)) =9.

Answer:

Solution given;

(x) = x − 7 and g(x) = x2 .

now

g(f(4))=g(4-7)=g(-3)=(-3)²=9

Answer:

i think its like this:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

[tex]\frac{2}{3} (x + 2) - \frac{1}{3} (x - 2)[/tex]

First, multiply [tex]\frac{2}{3}[/tex] to [tex](x + 2)[/tex] , then [tex]\frac{1}{3}[/tex] to [tex](x - 2)[/tex], after you have done that, you would get an equation looking like this[tex]\\[/tex]:

[tex]\frac{2}{3} x + \frac{4}{3} - \frac{1}{3}x - \frac{2}{3}[/tex]

Next, add and/or subtract the fractions with the variables together and the ones without together, and that is how you get to your final answer

[tex]\frac{1}{3}x + \frac{2}{3}[/tex]

Answer:

20 people

Step-by-step explanation:

At the movie theater, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer.

On Monday, 3,000 customers came to the theater.

To find the number of people who got both free items, we will calculate the Least Common Multiple (LCM) of 30 and 75.

LCM of 30, 75

= 5 × 3 × 5 × 2

= 150

Each 150th customer will receive both free items.

Total number of people who receive both free items = 3000 ÷ 150

                                                                                      = 20 people

On Monday 20 people will receive both free items.

Answer:

you need to zoom in i cant see plz :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

compare the numbers

Answer:

(1,0)

Step-by-step explanation:

The zero of the function is where it crosses the x axis ( where y=0)

x=1 where y=0

(1,0)

Answer:

p-value of 0.1357 > 0.1, which means that we do not reject the null hypothesis, that is, there is not sufficient evidence to conclude that the population mean is above 85.

Step-by-step explanation:

Decision:

If the p-value is greater than the significance level, we accept the null hypothesis. Otherwise, we reject the null hypothesis.

In this question:

Null hypothesis:

μ = 85

Alternate hypothesis:

a: μ > 85

SPSS reports a two-tailed p-value of 0.2714.

We are testing if the mean is greater than a value, which is a one-tailed test, so the p-value is of 0.2714/2 = 0.1357

Decision:

p-value of 0.1357 > 0.1, which means that we do not reject the null hypothesis, that is, there is not sufficient evidence to conclude that the population mean is above 85.

Answer:

What product

Step-by-step explanation:

Answer:

The other point lies on the graph is (0, - 8).

Step-by-step explanation:

Point (3, - 4) lies on the graph [tex]y = (x -5)^2 + K[/tex]

So, put x = 3 and y = - 4 in the equation.

[tex]- 4 = ( 3 -5)^2 + K\\\\- 4 = 4 + K \\\\K= - 8[/tex]

So, the equation of graph is

[tex]y = (x - 5)^2 -8[/tex]

Let x = 5 lies on the graph so

[tex]y = (5 -5)^2 -8 \\\\y = -8[/tex]

So, the other point lies on the graph is (0, - 8).

Answer:

The cosine of ∠V is of 0.74.

Step-by-step explanation:

Relations in a right triangle:

The cosine of an angle is given by the length of the adjacent side divided by the length of the hypotenuse.

XW = 65, WV = 97, and VX = 72.

[tex]\sqrt{65^2+72^2} = 97[/tex], and thus, this is a right triangle.

What is the value of the cosine of ∠V to the nearest hundredth?

The hypotenuse is the largest side, that is, WV = 97.

The adjacent side of angle V is VX = 72. So

[tex]\cos{B} = \frac{72}{97} = 0.74[/tex]

The cosine of ∠V is of 0.74.

Answer:

-415 meters

Step-by-step explanation:

As it was already -300 and it decended even more

so:

-300-`115=-415

Answer:

The answer is A, -415 meters.

Step-by-step explanation:

All right, so the key words we need here are -300, descends, and 115.

Descends means go lower, or in this case, subtract.

We are already at -300 and we descend 115, so we are going to subtract.

Subtracting a number is the same as adding the negative of that number.

-300 + -115 = -415

The answer is A, -415 meters.

Hope this helps, please mark brainliest if possible. :)

Answer:

11 pounds

Step-by-step explanation:

You would do 88 divided by 8 to get 11

Answer:

its 4/2 or simplified to 2/1

Step-by-step explanation:

mark me brainliest pls

Answer:

106

Step-by-step explanation:    ts 6 9 21  30

After Monday

    102 + Tuesday + Wednesday + Thursday + Friday         After

    102 +       1        +        1             +        1        +      1       =       106

Answer:

The probability that the mean salary offer is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean salary for the population, [tex]\sigma[/tex] is the standard deviation for the population and n is the size of the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Z-score with the Central Limit Theorem:

Z-is given by:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

What is the probability that the mean salary offer for these students is X or less?

The probability that the mean salary offer is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean salary for the population, [tex]\sigma[/tex] is the standard deviation for the population and n is the size of the sample.

Answer:

$16.40

Step-by-step explanation:

Answer:

98.40

Step-by-step explanation:

First find the tip

82* 20%

82* .20

16.40

Add the tip to the cost of the mean

82+16.40

98.40