solve this equation 4log√x - log 3x =log x^2​

Answer:

The inverse is 1/64 x^2 = y   x ≥ 0

Step-by-step explanation:

f(x) = 8 sqrt(x)

y = 8 sqrt(x)

Exchange x and y

x = 8 sqrt (y)

Solve for y

Divide each side by 8

1/8 x = sqrt(y)

Square each side

(1/8 x)^2 = (sqrt(y))^2

1/64 x^2 = y

The inverse is 1/64 x^2 = y   x ≥ 0

since x ≥0 in the original function

Answer:

[tex]\Huge \boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

[tex]f(x)=8\sqrt{x}[/tex]

[tex]\sf Replace \ with \ y.[/tex]

[tex]y=8\sqrt{x}[/tex]

[tex]\sf Switch \ the \ variables.[/tex]

[tex]x= 8\sqrt{y}[/tex]

[tex]\sf Divide \ both \ sides \ of \ the \ equation \ by \ 8.[/tex]

[tex]\displaystyle \frac{x}{8} =\sqrt{y}[/tex]

[tex]\sf Square \ both \ sides \ of \ the \ equation.[/tex]

[tex]\displaystyle (\frac{x}{8} )^2 =y[/tex]

[tex]\displaystyle \frac{x^2 }{64} =y[/tex]

[tex]\displaystyle f^{-1}(x)=\frac{1}{64} x^2[/tex]

Answer:

D

Step-by-step explanation:

So we have the expression:

[tex]-4-(-7)[/tex]

First, simplify. Two negatives make a positive. Therefore, the -(-7) turns into +7:

[tex]-4-(-7)\\=-4+7[/tex]

When adding on the number line, we move to the right.

Therefore, the correct interpretation is the value 7 digits to the right of -4.

D is the correct answer.

Answer:

D.  the number that is 7 to the right of -4 on the number line

Step-by-step explanation:

interpret -4 - (-7)

=  -4 +7

therefore

the number that is 7 to the right of -4 on the number line

so its D.

Answer:

800= about 1.76 lbs

700= about 1.54 lbs

(there are about 453.5 grams in a pound

Step-by-step explanation:

Answer:

800 grams = 1.76  pounds

700 grams =  1.54  pounds

Step-by-step explanation:

i googled it

Answer:

Stratified Random sampling.

Step-by-step explanation:

As per the scenario, It is stratified random sampling as it divides students into strata which represent Sophomores, Juniors, and Seniors.

Simple random samples of the given sizes of the proportional to the size of the stratum which is to be taken from every stratum that is to be about 10 percent of students from every class that is selected here.

Hence, according to the given situation, the correct answer is a random stratified sampling.

Answer:

144 ways

Step-by-step explanation:

Number of paintings = 7

Renaissance = 4

Baroque = 3

We are hanging from left to right and we will first hang Renaissance painting before baroque painting.

For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24

For baroque we have 3! Ways of doing so. 3x2x1 = 6

We have 4!ways x 3!ways

= (4x3x2x1) * (3x2x1) ways

= 144 ways

Therefore we have 144 ways to hang the painting.

Answer:

Since the calculated value of t= 2.249 does not  falls in the rejection region we therefore accept  the null hypothesis at 5 % significance level . On the basis of this we conclude that the  bonus plan has not  increased sales significantly.

Step-by-step explanation:

The null and alternative hypotheses as

H0: μd=0    Ha: μd≠0

Significance level is set at ∝= 0.05

n= 6

degrees of freedom = df = 6-1 = 5

The critical region is t  ( base alpha by 2 with df=5) ≥ ± 2.571

The test statistic under H0 is

t = d/ sd/ √n

Which has t distribution with n-1 degrees of freedom

Sales                                      Difference

Person      After      Before   d = after - before      d²

1                   94          90                4                      16

2                  82          84               -2                       4

3                  90          84               6                       36

4                  76           70               6                       36

5                  79           80               -1                        1

6                  85          80                 5                       25  

∑                                                       18                   118

d`= ∑d/n= 18/6= 3

sd²= 1/6( 118- 18²/6) = 1/6 ( 118 - 54) = 10.67

sd= 3.266

t= 3/ 3.266/ √6

t= 2.249

Since the calculated value of t= 2.249 does not  falls in the rejection region we therefore accept  the null hypothesis at 5 % significance level . On the basis of this we conclude that the  bonus plan has not  increased sales significantly.

Answer:

Step-by-step explanation:

[tex]44.64+ 43.45+42.79+42.28\\\\= \frac{44.64+ 43.45+42.79+42.28}{4} \\\\\\= \frac{173.16}{4} \\\\= 43.29\\[/tex]

Answer:

-2/12, -0.1, 1/9

Step-by-step explanation:

Answer:

Least to greatest: -2/12 , -0.1 , 1/9

Greatest to least: 1/9, -0.1, -2/12

Step-by-step explanation:

Change all of the numbers so that they are either fractions or decimals. Usually it is easier to change all the numbers to decimal.

Divide:

1/9 = ~0.111 (rounded)

-0.1 = -0.1

-2/12 = - ~0.167 (rounded)

Put the numbers in number order:

-~0.167 , -0.1 , ~0.111

-2/12 , -0.1 , 1/9

~

Answer:

64 70 74 80 92

Answer = 74

Step-by-step explanation:

The median is when you have an order of numbers in ascending order (smallest to largest) then you find the middle number

Hope this helps :)

If anything is incorrect then please comment and I shall change the answer to the correct one

Median for the given data 70, 64, 80, 74,92 is equals to 74.

"Median is defined as the central value of the given data after arranging them into ascending or descending order."

According to the question,

Given data for pulse rates = 70, 64, 80, 74,92

Arrange the data in ascending order we get,

64, 70 , 74, 80, 92

Number of pulse rate reading is 5 , which is an odd number.

Therefore, median is the central value.

Median for the given data = 74

Hence, median for the given data 70, 64, 80, 74,92 is equals to 74.

Learn more about median here

https://brainly.com/question/21396105

#SPJ2

Answer:

The correct option is  A

Step-by-step explanation:

From the question we are told that

    The  population is  [tex]\mu = 6.6[/tex]

     The level of significance is [tex]\alpha = 5\% = 0.05[/tex]

      The sample data is  9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds

The Null hypothesis is [tex]H_o : \mu = 6.6[/tex]

 The Alternative hypothesis is  [tex]H_a : \mu > 6.6[/tex]

The critical value of the level of significance obtained from the normal distribution table is

                       [tex]Z_{\alpha } = Z_{0.05 } = 1.645[/tex]

Generally the sample mean is mathematically evaluated as

      [tex]\=x = \frac{\sum x_i }{n}[/tex]

substituting values

      [tex]\=x = \frac{9.0 + 7.3 + 6.0+ 8.8+ 6.8+ 8.4+6.6 }{7}[/tex]

      [tex]\=x = 7.5571[/tex]

The standard deviation is mathematically evaluated as

           [tex]\sigma = \sqrt{\frac{\sum [ x - \= x ]}{n} }[/tex]

substituting values

          [tex]\sigma = \sqrt{\frac{ [ 9.0-7.5571]^2 + [7.3 -7.5571]^2 + [6.0-7.5571]^2 + [8.8- 7.5571]^2 + [6.8- 7.5571]^2 + [8.4 - 7.5571]^2+ [6.6- 7.5571]^2 }{7} }[/tex][tex]\sigma = 1.1774[/tex]

Generally the test statistic is mathematically evaluated as

            [tex]t = \frac{\= x - \mu } { \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

           [tex]t = \frac{7.5571 - 6.6 } { \frac{1.1774 }{\sqrt{7} } }[/tex]

            [tex]t = 1.4274[/tex]

Looking at the value of  t and  [tex]Z_{\alpha }[/tex]   we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis

  What this implies is that there is no sufficient evidence to state that the sample data show as significant increase in the average birth rate

The conclusion is that the mean is  [tex]\mu = 6.6 \ lb[/tex]

Answer:

y+6=-1/2(x-3)

Step-by-step explanation:

Point slope form: y-y1=m(x-x1)

Given that:

m=-1/2 and point (3, -6), you just add these numbers into the equation, and this gives:

y+6=-1/2(x-3)

Hope this helped!

Have a nice day!

Answer:

Hey there!

True. You use individuals rules, pieces of evidence, and experimentally found ideas that can be combined to form a general mathematical statement.

Let me know if this helps :)

Answer:

AE = 7.5

Step-by-step explanation:

Since <BAC = [tex]90^{0}[/tex], then;

<BAD = <DAE = <CAE = [tex]30^{0}[/tex] (complementary angles)

From ΔABC, applying the Pythagoras theorem to determine the length of side AC;

[tex]/BC/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/AB/^{2}[/tex]

[tex]/10/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/5/^{2}[/tex]

100 = [tex]/AC/^{2}[/tex] + 25

[tex]/AC/^{2}[/tex] = 100 - 25

[tex]/AC/^{2}[/tex] = 75

AC = [tex]\sqrt{75}[/tex]

Applying trigonometric function to ΔCAE,

Cos [tex]30^{0}[/tex] = [tex]\frac{AE}{\sqrt{75} }[/tex]

AE = [tex]\sqrt{75}[/tex] × Cos [tex]30^{0}[/tex]

    = 7.5

Therefore, AE = 7.5

Answer:

(0,9.8) and (10, 1.2)

Step-by-step explanation:

These are the only points that are the best fit for the garph correlation.

Answer:

(0, 9.8) and (10, 1.2)

Step-by-step explanation:

:) hope this helped

Answer:

B. y = –2.9x + 13.5

Step-by-step explanation:

You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is

y = a + bx, where a is the y intercept and b is the slope.

To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.

x    y    xy    x²  

1  .  11 = 11 → x² = 1² = 1

2 .  8 = 16 → x² = 2² = 4

3 .  4 = 12 → x² = 3² = 9

4 .  1 = 4 → x² = 4² = 16

5 .  0 = 0 → x² = 5² = 25

Total x = 1 + 2 + 3 + 4 + 5 = 15

Total y = 11 + 8 + 4+ 1 + 0 = 24

Sum of xy = 11 + 16 + 12 + 4 + 0 = 43

Sum of x² =  1 + 4 + 9 + 16 + 25 = 55

n = 5

So b =  5 (43) - (15) . (24) / 5 (55) - 15² = -2.9

a =  y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5

Question options :

A. There is sufficient evidence to reject the claim

u < 99.

B. There is sufficient evidence to support the claim

u < 99.

C. There is not sufficient evidence to reject the claim

u < 99.

D. There is not sufficient evidence to support the claim

u< 99.

Answer:

B. There is sufficient evidence to support the claim

u < 99.

Step-by-step explanation:

We construct the n*ll and alternative hypotheses to support our claim

The n*ll hypothesis :H0

The alternative hypothesis : Ha

N*ll hypothesis =H0: u=99

Alternative hypothesis =Ha: u<99

So if n*ll hypothesis (H0) u=99 is rejected, then we accept the alternative hypothesis that u<99

we can therefore have sufficient evidence to support our claim that u<99

Answer:

7+sqrt(37)

Step-by-step explanation:

7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)

Answer:

C. $37.76

Step-by-step explanation:

30% of $49.95

=30/100×49.95

=$14.99

selling price = 49.95 -14.99

= $34.96

8% sales tax included

=8/100×34.96

=$2.80

new price= 34.96+2.80

=$37.76

Answer:

a) P [ X < 24 mm ] = 0,3015          or     P [ X < 24 mm ] =  30,15 %

b) P [ X > 32 mm ]  = 0,1251          or        P [ X > 32 mm ]  = 12,51 %

c) P [  25 < X < 30 ] = 0,4964      or     P [  25 < X < 30 ] = 49,64 %

d) z(s) = 0,84

Step-by-step explanation:

Normal Distribution    N (  μ₀  ;   σ )   is  N ( 26,5 ; 4,8 )

a) P [ X < 24 mm ] = ( X - μ₀ ) / σ

P [ X < 24 mm ] = (24 - 26,5)/ 4,8 = - 0,5208 ≈ - 0,52

P [ X < 24 mm ] = - 0,52  

And from z-table we find area for z score

P [ X < 24 mm ] = 0,3015          or     P [ X < 24 mm ] =  30,15 %

b)P [ X > 32 mm ]  =  1  - P [ X < 32 mm ]

P [ X < 32 mm ]  = ( 32 - 26,5 ) / 4,8

P [ X < 32 mm ]  = 5,5/4,8  =  1,1458 ≈ 1,15

P [ X < 32 mm ]  = 1,15

And from z-table  we get

P [ X < 32 mm ]  = 0,8749

Then:

P [ X > 32 mm ]  =  1  -  0,8749

P [ X > 32 mm ]  = 0,1251          or        P [ X > 32 mm ]  = 12,51 %

c) P [  25 < X < 30 ] = P [ X < 30 ] - P [ X < 25 ]

P [ X < 30 ]  = 30 - 26,5 / 4,8   =  0,73

From  z-table    P [ X < 30 ]  =  0,7673

P [ X < 25 ] = 25 - 26,5 / 4,8  = - 0,3125  ≈  - 0,31

From z-table  P [ X < 25 ] =  0,2709

Then

P [  25 < X < 30 ] =  0,7673 -  0,2709

P [  25 < X < 30 ] = 0,4964      or     P [  25 < X < 30 ] = 49,64 %

d) If  20 %

z- score for 20% is from z-table

z(s) = 0,84

Answer: The triangles are not congruent

==========================================

Explanation:

For triangle DEF, the missing angle D is

D+E+F = 180

D+80+60 = 180

D+140 = 180

D = 180-140

D = 40

While the missing angle K in triangle JKL is

J+K+L = 180

80+K+50 = 180

K+130 = 180

K = 180-130

K = 50

---------------------

The three angles for triangle DEF are

The three angles for triangle JKL are

We don't have all the angles matching up. We need to have the same three numbers (the order doesn't matter) show up for both triangles in order for the triangles to be congruent. This is because congruent triangles have congruent corresponding angles.

The only pair that matches is E = 80 and J = 80, but everything else is different. So there is no way the triangles are congruent.

Notice how triangle JKL has two congruent base angles (K = 50 and L = 50), so this triangle is isosceles. Triangle DEF is not isosceles as we have three different angles, so this triangle is scalene.

No, that is not a function.

To be a function, each different input (x) needs a different output (y)

In the given function there are two -3’s as inputs and they have different y values, so it can’t be a function.

Answer: no

Step-by-step explanation: To determine if a relation is a function, take a look at the x–coordinate of each ordered pair. If the x–coordinate is different in each ordered pair, then the relation is a function.

Note that the only exception to this would be that if the x-coordinate pairs up with the same y-coordinate in a relation more than once, it's still classified ad a function.

Ask yourself, do any of the ordered pairs

in this relation have the same x-coordinate?

Well by looking at this relation, we can see that two

of the ordered pairs have the same x-coordinate.

In this case, the x-coordinate of 3 appears twice.

So no, this relation is not a function.

Answer:

The total   profit is [tex]p = 17x + 2124[/tex]

Step-by-step explanation:

From the question we are told that

   The profit made on each mp3 is  k  =  $35

    The profit made on each mp3 is  y =  $18

     The total amount sold is   n  =  118

 Now given that the amount of mp3 sold is x then the amount of  DVD sold is mathematically evaluated as

                      [tex]n - x[/tex]

Now the profit made on the x number of mp3 sold is  

                      [tex]x * 35 = 3x[/tex]

And the the profit made from the n-x number of  DVD  sold is  18 (n-x ) =  18 - 18x

 So the total profit made last week from the sales of both mp3 and DVD  is  

                   [tex]p = 35x + 18n - 18x[/tex]

                    [tex]p = 17x + 18(118)[/tex]

                    [tex]p = 17x + 2124[/tex]

Answer:

The Width = 28 inches

The Height = 21 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3

Using Pythagoras Theorem

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 35²

We are given ratio: 4:3 as aspect ratio

Width = 4x

Height = 3x

(4x)² +(3x)² = 35²

= 16x² + 9x² = 35²

25x² = 1225

x² = 1225/25

x² = 49

x = √49

x = 7

Hence, for the 35 inch tv set

The Width = 4x

= 4 × 7

= 28 inches.

The Height = 3x

= 3 × 7

= 21 inches

Answer:

32449.3

Step-by-step explanation:

use the formula A = P(1+r / 100)^t

20000 × (1+ (8.4 / 100))^6

=32449.3

Answer:

[tex]Probability = \frac{1}{3}[/tex]

Step-by-step explanation:

Given

[tex]Set:\ \{1, 2, 3, \ldots, 24\}[/tex]

[tex]n(Set) = 24[/tex]

Required

Determine the probability of selecting a factor of 4!

First, we have to calculate 4!

[tex]4! = 4 * 3 * 2 * 1[/tex]

[tex]4! = 24[/tex]

Then, we list set of all factors of 24

[tex]Factors:\ \{1, 2, 3, 4, 6, 8, 12, 24\}[/tex]

[tex]n(Factors) = 8[/tex]

The probability of selecting a factor if 24 is calculated as:

[tex]Probability = \frac{n(Factor)}{n(Set)}[/tex]

Substitute values for n(Set) and n(Factors)

[tex]Probability = \frac{8}{24}[/tex]

Simplify to lowest term

[tex]Probability = \frac{1}{3}[/tex]

Answer:

The 95% CI is   [tex]2.108 < \mu < 2.892[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean [tex]\mu = 2.5[/tex]

    The standard deviation is  [tex]\sigma = 0.8[/tex]

Given that the confidence level is  95% then the level of confidence is mathematically evaluated as

          [tex]\alpha = 100 - 95[/tex]

   =>  [tex]\alpha = 5\%[/tex]

  =>    [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

here we would assume that the sample size is  n =  16 since the person that posted the question did not include the sample size

  So    

               [tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]

               [tex]E = 0.392[/tex]

The  95% CI is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

              [tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]

substituting values

              [tex]2.108 < \mu < 2.892[/tex]

Answer:

p + q = -3

Step-by-step explanation:

First we need to take the original equation, and factor it to a form that's easier to get two binomial factors from (i.e., let's get a quadratic):

x^3 + px^2 + qx + 1

= x (x^2 + px + q) + 1

Now that we have factored out the x, we have a quadratic trinomial which we know can be broken down into two linear binomials.  The problem gives us two linear binomials, so let's take a look.

(x - 2) (x + 1) = (x^2 + px + q)

x^2 - 2x + x -2 = x^2 + px + q

Now let's solve.

x^2 - x - 2 = x^2 + px + q

-x - 2 = px + q

From here, we can easily see that p = -1 (the coefficient of x) and q = -2.

Hence, p + q = -1 + -2 = -3.

Cheers.

Answer:

16x^2 - 64

Step-by-step explanation:

(4x − 8)(4x + 8)

We recognize that this is the difference of squares

(a-b) (a+b) = a^2 - b^2

                 =(4x)^2 - 8^2

                 =16x^2 - 64

Answer:

To find the x-intercept, substitute in  0  for y and solve for x.

To find the y-intercept, substitute in  0 for x  and solve for y.

x-intercept(s):  

(−6,0)

y-intercept(s):  

(0,3)

So I would say -6 and 0 and 2 are in domain

Answer:

-6, 0 ,2 are in the domain

Step-by-step explanation:

The domain is what values that x can take

There are no restrictions on the values that x can take

All real numbers are in the domain

-6, 0 ,2 are in the domain