Divide. Write your answer as a fraction or a mixed number in simplest form.

4\frac{2}{9} ÷ 1\frac{1}{3}

The graph of the exponential function f(x) = 5(2)ˣ is as shown in the attached file.

We want to draw the graph of the exponential function;

f(x) = 5(2)ˣ

At input of x = 0, we have;

f(x) = 5(2)⁰ = 5

At input of x = 1, we have;

f(x) = 5(2)¹ = 10

At x = -1, we have;

f(x) = 5(2)⁻¹ = 2.5

At x = -2, we have;

f(x) = 5(2)⁻² = 1.25

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Answer:

28.5 ft²

Step-by-step explanation:

shaded area = area of triangle minus area of rectangle

shaded area = (1/2)bh - LW

base of triangle = 5 ft + 4 ft = 9 ft

height of triangle = 3 ft + 6 ft = 9 ft

shaded area = (1/2)(9 ft)(9 ft) - (4 ft)(3 ft)

shaded area = 40.5 ft² - 12 ft²

shaded area = 28.5 ft²

Answer:

[tex]140in {}^{3} [/tex]

Step-by-step explanation:

Substituting values of B and h into the Formular.

[tex]v = \frac{bh}{3} \\ v = \frac{15 \times 28}{3} = 140in {}^{3} [/tex]

the PERT weighted average is 9 days

PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.

The formula for finding the PERT weighted average is given as;

PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6

We have;

Substitute the values into the formula

PERT weighted average  = [tex]\frac{6 + 4(8) + 16 }{6}[/tex]

PERT weighted average  = [tex]\frac{54}{6}[/tex]

PERT weighted average  = 9 days

Thus, the PERT weighted average is 9 days

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Percentage for lakeside is 38%

Percentage for Jungle is 26%

Percentage for Desert is 18%

Percentage for Coast is 12%

Percentage for Prairie is 6%

To determine the percentage, divide the given value by the total number and multiply by 100

Total  = 24000

Percentage for lakeside = [tex]\frac{9120}{24000}[/tex] × 100

% of lakeside = [tex]0. 38[/tex] × 100 = 38%

Percentage for Jungle = [tex]\frac{6240}{24000}[/tex] × 100

% of Jungle = [tex]0. 26[/tex] × 100 = 26%

Percentage for Desert = [tex]\frac{4320}{24000}[/tex] × 100

% of Desert = [tex]0. 18[/tex] × 100 = 18%

Percentage for Coast = [tex]\frac{2880}{24000}[/tex] × 100

% of coast = [tex]0. 12[/tex] × 100 = 12%

Percentage for Prairie = [tex]\frac{1440}{24000}[/tex] × 100

% of Prairie = [tex]0. 06[/tex] × 100 = 6%

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The data is significant at a significance level of 0.01 indicating that the average mass of apples in a farmer's orchard differs from 100g to a level of 0.01. Option C is correct.

Given as the farmer states that the average mass of an apple grown in his orchard is 100g, he measures the mass of 150 apples grown in his orchard and finds that the average mass per apple is 98g and the results are calculated as statistically significant at the 0.01 level.

The null hypothesis is:

H₀ = 100

Because of the farmer's claim.

The alternative hypothesis is:

H₁ ≠ 100

The alternative hypothesis tests the farmer's claim at a level of significance. Results are calculated as statistically significant at the 0.01 level.

This means that at the 0.01 level, the null hypothesis is rejected, i.e. H the average mass of the farmer's orchard differs from 100. Since it is significant at the 0.01 level, it will be significant at the 0.05, 0.1 and increasing levels.

Thus, at the significance level of 0.01, the average mass of apples grown in the farmer's orchard differs by 100 g. The correct answer is therefore given by option C.

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Answer:

Θ ≈ 58°

Step-by-step explanation:

using the Cosine Rule in the triangle

cosΘ = [tex]\frac{80^2+60^2-70^2}{2(80)(60)}[/tex] = [tex]\frac{64000+3600-4900}{9600}[/tex] = [tex]\frac{5100}{9600}[/tex] = [tex]\frac{51}{96}[/tex] , then

Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{51}{96}[/tex] ) ≈ 58° ( to the nearest degree )

See

The point D is

3 units left from origin

1 units up from origin

The point is

Direct variation

Multiply k=2

Option A

Based on the given inequality; x < 9 or x ≥ 14, the possible values of x are $8 and $14

x < 9 or x ≥ 14

From the options

All values less than 9 are

$8

All values greater than or equal to 14 are

$14

Therefore, based on the options given, the possible values of x are $8 and $14

Complete question:

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15

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[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8 < 3x+1 < 13 }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8+-1 < 3x+1+-1 < 13+-1 \ (Add \ -1 \ to \ all \ parts) }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{-9}{3} < \frac{3x}{3} < \frac{12}{3} \ (Divide \ all \ parts \ by \ 3) }} \end{gathered}$}[/tex]

[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-3 < x < 4 }} \end{gathered}$} }}[/tex]

The value of a + b + c based on the product formula is 8.

From the information given, the product of the proper divisor is illustrated.

Based on the information, the addition of the symbols will be:

= a + b + c

= 3 + 3 + 2

= 8

In conclusion, the correct option is 8.

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We cannot reject the null hypothesis as the p value is less than 0.01.

From the information given, Luiza wants to go on a popular talent TV show and in order to be accepted, her audition must get at least 60% positive votes from the people in the crowd.

The observed outcome also has a probability less than 1% under the tested hypothesis. Based on the information, the test statistic will be - 1.58.

After this, this will be checked under the standard normal distribution table where the p value will be 0.0571.

Based on this information, we cannot reject the null hypothesis as the p value is less than 0.01.

In conclusion, the correct option is that we cannot reject the hypothesis.

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Answer:

Yes,

Common ratio = 5.

Step-by-step explanation:

If its geometric it will have a common ratio.

5/1 = 5

25/5 = 5

125/25 = 5

So its geometric with commo ratio 5.

The display that would best show the measures of variation of the given prices is; B: Box and Whisker Plot

We are given the prices of Phone chargers in a store as;

$19, $18, $15, $17, $19, $12, $19, and $15.

Now, since we want to determine the display that would best show the measures of variation, the best display would be a box and whisker plot. This is because Box and Whisker plots are a great chart to use when showing the distribution of data points across a selected measure. These  box and whisker plots display ranges within variables measured.

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Answer:

(x + 3)^2 + (y - 2)^2 = 25 .

Step-by-step explanation:

The center is at (-3, 2) and the radius is 5.

General form is

(x - h)^2 + (y - k)^2 = r^2

So here we have:

(x  - (-3)^2 + (y - 2)^2 = 5^2

(x + 3)^2 + (y - 2)^2 = 25

The translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

The translation rule is given as:

T–4, 6(x, y)

This can be rewritten as

T(x- 4, y + 6)

The above represents a translation 4 units left and 6 units up

Hence, the translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

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Answer: [tex]y=-2x+6[/tex]

Step-by-step explanation:

The slope of line l is

[tex]\frac{5-1}{0-2}=-2[/tex]

Since parallel lines have the same slope, the slope of the line we need to find is -2.

Substituting into point-slope form,

[tex]y=-2(x-3)\\\\y=-2x+6[/tex]

The steps that can be used to increase the ball is:

Scale factor = [tex]\frac{Scale diagram}{Original}[/tex]

This refers to the measure for similar figures that is used to show the scale through which a figure is bigger or smaller than another.

Hence, we can see that from the given image, one can increase the size of the ball by making use of the scale factor which measures the scale diagram and then divides it from the original and this would retain the dimension but would make it larger.

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1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)

2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)

3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)

4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)

Answer:

x/8 gallons.

Step-by-step explanation:

The 8 containers have the larger capacity as the 2 totals are x and the other containers are 16 in total.

Capacity of each of the large containers = x/8 gallons.

Answer:

a = -1

Step-by-step explanation:

1. Subtract [tex]\frac{2}{3}[/tex] from both sides.

[tex]6a=-\frac{16}{3} - \frac{2}{3}[/tex]

2. Solve the side after the equal sign.

[tex]6a=-6[/tex]

3. Divide 6 from both sides.

[tex]a=-1[/tex]

4. Hope this helped!

[tex]:)[/tex]

Answer:

x-3

Step-by-step explanation:

Laura's age goes first. You don't know what it is, so you have to leave it as x. You know Jeri is 3 years younger, so you subtract from x.

The probability that the call center will get fewer calls than 440 is 0.26115.

Given mean of 4900 and standard deviation of 700.

We have to calculate the probability that the call center will get fewer than 4400 calls.

Probability lies between 0 and 1.

μ=4900

σ=700

We can  apply z as well as t statistics because the sample size is not given.

We are applying z statistics.

P(X<4400)=0.5-P(4400<X<4900)

z=X-μ/σ

where μ= mean

σ=standard deviation

z=4400-4900/700

=-500/700

=-0.71

p value of -0.71 is 0.23885.

So the p value of calls less than 4400 is 0.5-0.23885=0.26115.

Hence the probability that the call center will get calls less than 440 is 0.26115.

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New mean is 2.53% larger than the original mean.

What is mean?

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

We can find the percentage larger is the mean of the new list in comparison with the original as shown below:

Given, set of number 55, 70, 81, 83, 88, 91

Median= (81+83)/2

= 164/2

= 82

Mean = (55+70+81+83+88+91)/6

= 468/6

= 78

New value which is added = 82*1.12

= 91.84

New Mean = (55+70+81+83+88+91+91.84)/7

= 559.84/7

= 79.97

Increase in mean = 79.97-78

=1.97

increase percentage (1.97/78) *100

= 2.53%

Hence, new mean is 2.53% larger than the original mean.

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Answer:

Bet $100 and remove all non-face cards.

Step-by-step explanation:

Each option may be answered on the basis of the ratio of face cards to non-face cards, which we'll say is R.

a. removing all of the black cards  No.  The vale of R does not change.  R is the same for both black and red cards, so removing one color does not change R.

b. removing all non-face cards  Yes.  The only cards left are face cards.  The odds of drawing 2 face cards in a row from this modified deck is 100%

c. removing all kings  No.  Face cards are being removed and will thus lower the probability of picking one.

d. removing all of the red cards  No.  Same reasoning as in (a.).

A journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant

From the question, we have the following highlights:

From the graph attached to the question, we can see that the graph that shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013 is a linear graph

This is so because the points on the graph are connected by a straight line.

Linear graphs have constant rate

Hence, a journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant

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Complete question

The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013. The owner of the sugar mill said in an interview that the production increased at an exponential rate since the inauguration. What would a journalist say about this piece of information after analyzing the data?

The measure of angle C is obtained as 35 degrees

Give that;

b^2 = a^2 + c^2 - 2ac Cos B

a = 29

c = 24

B = 101 degrees

b^2 = (29)^2 + (24)^2 - [2 * 29 * 24 cos 101]

b^2 = 841 + 576 + 266

b = 41 cm

Now;

b/sinB = c/sinC

bsinC = csinB

sinC = csinB/b

sinC =  24 * sin 101/41

C = sin-1(24 * sin 101/41)

C = 35 degrees

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The measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

A triangle with two sides and angles of equal length and degrees is an isosceles triangle.

Acute Triangle:-

A triangle whose all angels are greater than and less than 90° i.e., all angels are acute is called an acute triangle.

Therefore, all the three angles are less than 90 degrees and two angles are equal.

If one angle is 36 degrees, the other two angles will be 72 degrees each.

If the two angles are 36 degrees each, the last angle will be 108 degrees. 108 degrees is greater than 90 degrees..

Therefore, the angles will be 36°, 36° and 72°.

Hence, the measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

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