Solve: log2(3x 8) = 5 which is an equivalent equation? 25 = 3x 8 52 = 3x 8 25 = [log2(3x 8)]2 52 = [log2(3x 8)]5

Answer:

x = -11/2 , y = -1/6

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}-x-3y=6\\ 2x+3=-8\end{bmatrix}[/tex]

Solve:

[tex]\mathrm{Substitute\:}x=-\frac{11}{2}[/tex]

[tex]\begin{bmatrix}-\left(-\frac{11}{2}\right)-3y=6\end{bmatrix}[/tex]

[tex]Simplify[/tex]

[tex]\begin{bmatrix}\frac{11}{2}-3y=6\end{bmatrix}[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-\frac{11}{2},\:y=-\frac{1}{6}[/tex]

Hence, x = -11/2 , y = 1/6

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The area of a rectangle is l*w. We have the length as 4.5 in and we can find the width by doing 3+2+4.5 = 9.5 in.

Then, we multiply them. 4.5*9.5 = 42.75 inches²

Step-by-step explanation:

answer......

...........

Answer:

118,098

Step-by-step explanation:

Notice that each term is multiplied by 3, 2 x 3 is 6, 6 x 3 is 18... and so on.

so 54*3 = 162 and keep multiplying your answer by three until you have 11 times

The maximum and the least grossing movies are the combinations of movies A & B and movies C & D, respectively

The grossing amounts are given as:

The selection of two movies could be any of the following selections

Selection = AB, AC, AD, BC, BD, and CD

The gross of each selection is:

AB = $700 million + $680 million = $1.38 billion

AC = $700 million + $610 million = $1.31 billion

AB = $700 million + $420 million = $1.12 billion

BC = $680 million + $610 million = $1.29 billion

BD = $680 million + $420 million = $1.10 billion

CD = $610 million + $420 million = $1.03 billion

In the above computation, the maximum and the least gross amounts are:

AB = $1.38 billion

CD = $1.03 billion

Hence, the maximum and the least grossing movies are the combinations of movies A & B and movies C & D, respectively

Read more about combination at:

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Answer:

mean of A, C = 655

mean of B, C = 645

mean of C, D = 515

Step-by-step explanation:

you just take whatever the 2 numbers are (for A, B, C, D) and find the mean between them both,, also correct on edge

Answer:

(x-1)²=8.

Step-by-step explanation:

1) if the length before decreasing is 'x', then after decreasing it is x-1;

2) then the area is (x-1)²=8.

PS. the length before decreasing is 1+2√2.

the answer is "Using the trigonometric identity

sin²x + cos²x = 1 , then sin²x = 1 - cos²x

Consider the left side

sin²a - sin²b

= (1 - cos²a) - (1 - cos²b)

= 1 - cos²a - 1 + cos²b

= cos²b - cos²a

= right side , thus verified"

The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is 6 × 10–8.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

The sample-set S consists of all combinations of 6 distinct elements of the set of 50 elements, and;

[tex]\rm |S| =C(50, 6)=\dfrac{50!}{44!6!}[/tex]

The winning event E ⊆ S is just one winning combination, so that

|E| = 1.

Therefore, the probability of winning a lottery is;

[tex]\rm P(E)=\dfrac{|E|}{|S|}\\\\ P(E)=\dfrac{1}{\dfrac{50!}{44!6!}}\\\\\\ P(E)=\dfrac{44!6!}{50!}\\\\ P(E)= 6 \times 10 {-8}[/tex]

Hence, The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is 6 × 10–8.

Learn more about probability here;

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Answer:

y = -3x + 5

Step-by-step explanation:

y = mx + c

gradient = -3 = m

y-intercept = 5 = c

Step-by-step explanation:

answer is B

use unitary method to solve it

Answer:

each group would have cleaned for 3mins

it's would take 3mins before they both take a break

Step-by-step explanation:

band booster club

2 already done

7rows/min

leadership class

11 rows already done

4rows/min

11-2

=9

at 0min leadership class is ahead by 9

min=x

2+7x=11+4x

7x-4x=11-2

3x=9

x=3

after 3mins the leadership class and the club will have both done 23 rows

brailiest please

Answer:

313.6 sqft.

Step-by-step explanation

Decimal

First, convert the fractions into decimals to make it easier to multiply. 24 1/2 = 24.5. 12 4/5 = 12.8. 24.5*12.8 = 316.6.

Fraction

First, make the fractions into improper fractions. 24 1/2 = 49/2. = 12 4/5 = 64/5. 49/2*64/5 = 313 3/5 = 313 6/10 = 313.6.

Answer:

6 in

Step-by-step explanation:

4×12×w=288

48×w=288

/48. /48

w=6

Finding perimeter is simple. All you do is add up all of the side lengths, and bada bing bada boom, you got the perimeter.

Answer:

21

Step-by-step explanation:

Answer:

296, 288, 280, 240

Step-by-step explanation:

y = -8x + 296 is a linear equation by which you're plugging the x values of 0,1,2,7 into it to get a y value.

y = 296 when x = 0,

y = 288 when x = 1,

y = 280 when x = 2,

y = 240 when x = 7.

Cheers!

it is just still 5 I believe :P hope this helps

Answer:

24.75

Step-by-step explanation:

keychain=$6.75

t.shirt=X

according to question

X+6.75=31.50

X=24.75

The basic formula for a circle is (x - h)^2 + (y - k)^2 = r^2, where the center is (h, k) and the radius is found by taking the square root.

h = 4

k = -2

Center: (4, -2)

square root of 9 = 3

Radius: 3

Correct Answer: C

Hope this helps!

Answer:

standard form:   y = x² - 2x - 8

vertex form:  y = (x − 1)² - 9

factorized form:  y = (x + 2)(x - 4)

Step-by-step explanation:

From inspection of the graph:

Standard quadratic form:   y = ax² + b x + c

Vertex form of a quadratic equation:   y = a(x − h)² + k

If a > 0 then the parabola opens upwards

If a < 0 then the parabola opens downwards

(h, k) is the vertex

c is the y-intercept

Inputting the vertex into the vertex form gives:

y = a(x − 1)² - 9

  = a(x² - 2x + 1) - 9

  = ax² - 2ax - 8

Using the x-intercepts to create a quadratic equation:

y = a(x + 2)(x - 4)

  = a(x² - 2x - 8)

  = ax² - 2ax - 8a

Comparing the y-intercepts:

-8 = -8a  ⇒  a = 1

Therefore,   y = x² - 2x - 8

Answer:

Step-by-step explanation:

The length of LM is 24√(3)

the short leg is 24

the hypotenuse is 24*2 = 48

The answer is A

difference means to subtract

while product means to multiply!

(i hope this helps!)

Answer: 4 1/2 hours

Step-by-step explanation:

if it takes luke 3 hours to drive 150 miles that means in 6 hours he would have driven 300 miles.

he drives 50 miles per hour

so 250 miles is 4 1/2

Answer:

25%

Step-by-step explanation:

First, divide 91 by 364

91/364 = 0.25

Multiply this answer by 100

0.25 × 100 = 25%

This gives you what percent of 364 that 91 is

So it is a 25% decrease

<-------------------288km---------->

x=48 km 5x=240km

⊙__________⊙___________⊙

jonesville smitville cityville

6x=288

x=48

=48km

Answer:

-9 is the answer for 3^-2

Answer:

see attached

Step-by-step explanation:

(i) F' shown in red = Rotation 180° about point (2, 1)

(ii) F'' show in blue = Reflection of F' in x-axis

The valid conclusions for the manager based on the considered test is given by: Option

One sample z-test is performed if the sample size is large enough (n  > 30) and we want to know if the sample comes from the specific population.

For this case, we're specified that:

Forming hypotheses:

where [tex]\mu_0[/tex] is the hypothesized population mean of the money his customer spends in his store.

The z-test statistic we get is:

[tex]z = \dfrac{\overline{x} - \mu_0}{\sigma/\sqrt{n}} = \dfrac{160 - 150}{30.20/\sqrt{40}} \approx 2.094[/tex]

The test is single tailed, (right tailed).

The critical value of z at level of significance 0.025 is 1.96

Since we've got 2.904 > 1.96, so we reject the null hypothesis.

(as for right tailed test, we reject null hypothesis if the test statistic is > critical value).

Thus, we accept the alternate hypothesis that customer spends more in his store than the national average.

Learn more about one-sample z-test here:

https://brainly.com/question/21477856

Answer:

A

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Median from 24 to 28

Median from 28 to 34

Interquartile range