The cost to rent a moving truck is a flat fee of $25 plus $0.60 per mile. The equation c = 25 + 0.6m models the cost, c, in dollars for the number of miles, m, traveled in the truck. Identify the independent and dependent variables. The is the independent variable. The is the dependent variable.

Answer:

2

Step-by-step explanation:

1 + 1 = 2

Answer:

1 + 1

= 2

1+1

= THIS THING

Answer:

Step-by-step explanation:

4x+5x=27

9x=27

x=27/9

x=3

4x3=12

5x3=15

The total number of cats were 12.

Based on the ratio of dogs to cats in the shelter, we know that out of 27 animals, there are 12 cats.

The ratio of cats to dogs is 4:5 which means that there are 5 dogs for every 4 cats.

This means that out of 9 animals, 4 would be cats and 5 would be dogs. If there was 27 animals therefore:

= 4 / 9 x 27

= 108 / 9

= 12 cats

In conclusion, there are 12 cats.

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Answer:

0.9940

Step-by-step explanation:

P(at least 1) = 1 − P(zero)

P(at least 1) = 1 − (1 − 0.64)⁵

P(at least 1) = 1 − (0.36)⁵

P(at least 1) = 0.9940

The probability that at least one of them has been vaccinated is 0.9939.

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure. It helps to check the probability of getting “x” successes in “n” independent trials of a binomial experiment.

For the given situation,

Number of people vaccinated = 64% = 0.64

The formula of binomial distribution is

[tex]P(x:n,p) = nC_{x} p^x (1-p)^{n-x}[/tex]

Here x is the number of successes, x ≤ 1

n is the number of trials, n = 5

p is the probability of a success on a single trial, p = 0.64 and

where, [tex]nC_{x}=\frac{n!}{x!(n-x)!}[/tex]

The probability is [tex]P(X \leq 1)=1-P(X=0)[/tex]

[tex]P(X=0)= 5C_{0} (0.64)^{0} (1-0.64)^{5-0}[/tex]

⇒ [tex]P(X=0)= 1(1) (0.36)^{5}[/tex]

⇒ [tex]P(X=0)= 0.0060[/tex]

Thus, [tex]P(X \leq 1)=1-P(X=0)\\[/tex]

⇒ [tex]P(X \leq 1)=1-0.0060[/tex]

⇒ [tex]P(X \leq 1)=0.9939[/tex]

Hence we can conclude that the probability that at least one of them has been vaccinated is 0.9939.

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Answer:

[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]

[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]

And we can find the probability with this difference:

[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] n = 171[/tex] represent the sample size

[tex]p =0.39[/tex] the proportion of interest

We want to find the following probability:

[tex] P( 0.21 < \hat p < 0.32)[/tex]

We can use the normal approximation for this case since np >10 and n (1-p) >10

For this case we know that the distribution for the sample proportion is given by:

[tex]\hat p \sim N( p , \sqrt{\frac{p (1-p)}{n}} )[/tex]

And we can use the following parameters:

[tex] \mu_{\hat p}= 0.39[/tex]

[tex] \sigma_{\hat p} =\sqrt{\frac{0.39*(1-0.39)}{171}}= 0.0373[/tex]

And we can apply the z score formula given by:

[tex] z = \frac{p \\mu_{\hat p}}{\sigma_{\hat p}}[/tex]

And using this formula we got:

[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]

[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]

And we can find the probability with this difference:

[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]

Answer:

The Pythagorean Theorum

Step-by-step explanation:

you can literally search it and see that it is right!

Answer:

x = 3

Step-by-step explanation:

9x = 27

Divide both sides by 9,

x = 27/9 which on factorization of the numerator is written as

x = 9 x 3/9 = 3

Calculation 2: Exponent Or Index Method

9x = 27

Since 9 = 3² and 27 = 3³, the given equation takes the form

3² x = 3³

This gives

x = 3³ ÷ 3² = 3³­­­­­¯² [using the formula a^m ÷ a^n = a^(m-n)]

= 3¹ = 3 (since the first power of a number is the number itself)

9 x 1 = 9

9 x 2 = 16

9 x 4 = 36

We stop here because we have already got the answer 27, the right-side of the equality, when 9 is multiplied by 3 . So,

x = 3

hope this helped!

Answer:

x=150 because these are supplementary angles

Answer:

C............PAC-MAN

Step-by-step explanation:

Answer:

a) The size of each of the two samples(equal), n = 518

b) Sample size, n = 439

Step-by-step explanation:

For clarity and easiness of expression, the complete solution to this question is handwritten and attached as files. Check the attached files below for the explanations.

Answer:

2 x [tex]\pi[/tex] x 10.7 = 67.2

Step-by-step explanation:

Step-by-step explanation:

c=2πr

c=2×π×10.7m

c=67.2m

so about 67

Answer:

Step-by-step explanation:

Given data  

Current in cord is  I  = 8 a m p

Power of iron is   P = 1200 W

Voltage converted is  

V = 120 V

The power can be expressed as

[tex]P=IV=\\I=\frac{P}{V}[/tex]

Substitute the given value in above we get,

I = [tex]\frac{1200}{120}= 10amps[/tex]

Thus, the current use by iron is  

10 A

Answer:

6/x^2

Step-by-step explanation:

6x^-2

6*x^-2

6*(1/x^2)

6/x^2

Answer:

George is 43.20 ft East of his starting point.

Step-by-step explanation:

Let Paula's speed be x ft/s

George's speed = 9 ft/s

Note that speed = (distance)/(time)

Distance = (speed) × (time)

George takes 50 s to run a lap of the track at a speed of y ft/s

Meaning that the length of the circular track = y × 50 = 50y ft

George and Paula meet 14 seconds after the start of the run.

Distance covered by George in 14 seconds = 9 × 14 = 126 ft

Distance covered by Paula in 14 seconds = y × 14 = 14y ft

But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track

That is,

126 + 14y = 50y

50y - 14y = 126

36y = 126

y = (126/36) = 3.5 ft/s.

Hence, Paula's speed = 3.5 ft/s

Length of the circular track = 50y = 50 × 3.5 = 175 ft

So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of

9 × 240 = 2160 ft.

2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.

Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft

So, 60 ft along a circular track subtends an angle θ at the centre of the circle.

Length of an arc = (θ/360°) × 2πr

2πr = total length of the circular track = 175

r = (175/2π) = 27.85 ft

Length of an arc = (θ/360) × 2πr

60 = (θ/360°) × 175

(θ/360°) = (60/175) = 0.343

θ = 0.343 × 360° = 123.45°

The image of this incomplete lap is shown in the attached image,

The distance of George from his starting point along the centre of the circular track = (r + a)

But, a can be obtained using trigonometric relations.

Cos 56.55° = (a/r) = (a/27.85)

a = 27.85 cos 56.55° = 15.35 ft

r + a = 27.85 + 15.35 = 43.20 ft.

Hence, George is 43.20 ft East of his starting point.

Hope this Helps!!!

Answer: 4

Step-by-step explanation:

in order to divide one fraction by another, you must multiply by the reciprocal(the reverse of a certain fraction). the reciprocal of 1/6 is 6/1. so:

[tex]\frac{2}{3} / \frac{1}{6}[/tex] =           multiply by the reciprocal of 1/6

[tex]\frac{2}{3} * \frac{6}{1}[/tex] =         cross out

[tex]\frac{2}{1} * \frac{2}{1}[/tex] =         multiply

[tex]\frac{4}{1}[/tex] =               simplify

4

Answer:

4

Step-by-step explanation:

(2/3)/(1/6)

Eleminate the denominator by multiplying numerator and denominator with whatever is the reciprocal of the denominator. In this case the denominator is 1/6 so the reciprocal is 6/1 or "just" 6.

So, multiply numerator and denominator by 6. The next three (bold) steps, have been written down for explanatory purposes only, and normally are not nessasary.

(2/3)*6 / (1/6)*6

(2/3)*6 / (6/6)

(2/3)*6 / 1

(2/3)*6

12/3

4

Answer:

737.97  acres

Step-by-step explanation:

Given

Approximately 83% of a large western state  land is federally owned.

Total land in percentage will be 100%

% of land not federally owned = Total land in percentage  - % of land  federally owned = 100% - 83% = 17%

Thus, percentage of land not federally owned = 17% of total land

Also given "A large western state consist of 4341 million acres of land"

Therefore,

number of acres that are not federally owned = 17% of total western state land

number of acres that are not federally owned =  17/100 * 4341 = 737.97

Thus,  737.97  acres  of western state  land are not federally owned.

Answer:

Part 1.

Juice = 8 L.

Lemonade = 32 L.

Part 2.

20 L punch Josie can make.

Part 3.

New ratio juice : lemonade = 2 : 9

Step-by-step explanation:

Part 1.

1+4 = 5 parts altogether, 1 parts for juice and 4 parts for lemonade.

40 : 5 = 8 L is 1 part.

Juice - 1 part - 8 L.

Lemonade - 4 parts - 4*8 = 32 L.

Part 2.

1 parts of juice needs 4 parts of lemonade

4 L of juice     needs  x L of lemonade

1 : 4 = 4 : x

x = 4*4/1 = 16 L lemonade

4+ 16 = 20 L punch Josie can make

Part 3.

It was 4 L of juice and 16 L of lemonade.

After 2 L lemonade was added, we have 4 L of juice and (16+2) = 18 L of lemonade.

4 L juice : 18 L lemonade = 4/2 L juice : 18/2 L lemonade =

= 2 L juice: 9L lemonade

New ratio juice : lemonade = 2 : 9

Step-by-step explanation:

work is shown and pictured

The discriminant of quadratic equation is,

⇒ D = 0

What is Quadratic equation?

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:  ax² + bx + c = 0

We have to given that;

Quadratic equation is,

⇒ - 3 = x² + 4x + 1

Now, We can write as;

⇒ x² + 4x + 1 + 3 = 0

⇒ x² + 4x + 4 = 0

Hence, Discriminant of quadratic equation is,

⇒ D = b² - 4ac

⇒ D = (4)² - 4×1×4

⇒ D = 16 - 16

⇒ D = 0

Thus, The discriminant of quadratic equation is,

⇒ D = 0

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Answer:

a) The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79

b) $0.57

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96*\frac{1.86}{\sqrt{41}} = 0.57[/tex]

So the answer for b) is $0.57.

The lower end of the interval is the sample mean subtracted by M. So it is 12.22 - 0.57 = $11.65

The upper end of the interval is the sample mean added to M. So it is 12.22 + 0.57 = $12.79

The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79

Answer:

(x-2)(x-2)

Step-by-step explanation:

You should be trying to find two numbers that add to make the coefficient of x (in this case, -4), and two numbers that multiply to make the constant term (in this case, +4). The two numbers that work for both of those criteria are -2 and -2.

-2 x -2 = +4 (satisfies the constant term)

-2 + -2 = -4 (satisfies the coefficient of x)

Answer:

The bottom left table

Step-by-step explanation:

the same x value cannot have different y values

Answer:

B. The radius

Step-by-step explanation:

The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle so we need to know the radius for it

Answer:

3

Step-by-step explanation:

27^1/3 = cuberoot(27) = 3

Answer:

The correct answer is letter c. Josh had 24 games and Peter had 32 by the end of the week.

Step-by-step explanation:

We know that Josh has a total of 32 games, while that value is 133% as many as Peter's, therefore the number of games Peter had at the beginning of the week is:

[tex]josh = \frac{133}{100}*peter\\peter = \frac{josh}{1.33}\\peter = \frac{32}{1.33}\\peter = 24.06[/tex]

At the beginning of the week Peter had 24 games. At the end of the week Josh gave Peter 25% of his games, therefore Peter's total is:

[tex]peter = 24 + 0.25*josh\\peter = 24 + 0.25*32\\peter = 24 + 8 = 32[/tex]

While Josh had:

[tex]josh = 32 - 8 = 24[/tex]

The correct answer is letter c.

[tex] \purple \bold{a^2 - b^2} [/tex]

Step-by-step explanation:

X+4 is prime. X2-9can be factored using the [tex] \purple \bold{a^2 - b^2} [/tex] formula

[tex] x^2 - 9\\

=x^2 - 3^2 \\

= (x+3)(x-3)[/tex]

Answer: difference-of-squares

next one is (x+3)(x-3)(x+4)

Step-by-step explanation:

just took it on ed genuity :)

If the area of ΔBAC = 24 in², the area of ΔEDF is 6 in².

If two triangles' angles are congruent and their corresponding sides are proportionate, they are considered similar. To put it another way, similar triangles are the same in shape but not necessarily in size. If ΔPQR and ΔMNO are two similar triangles, then we can write it as ΔPQR ∼ ΔMNO.

The square of the ratio of any pair of their respective sides is equal to the ratio of the areas of two similar triangles.

Since ΔBAC ∼ ΔEDF, we can use the above statement to find the area of ΔEDF. Let the area of ΔEDF be x in². Given that length of EF and BC is 2 in and 4 in respectively.

So, we have to solve this equation,

24/x = 4²/2²

Now, 24/x = 16/4

i.e. 24/x = 4

i.e. 4x = 24

i.e. x = 24/4 = 6

Therefore the area of ΔEDF is 6 in².

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Answer:

4 sqrt(6)

Step-by-step explanation:

sqrt(96)

We know sqrt(ab) =sqrt(a) sqrt(b)

sqrt(16*6)

sqrt(16) sqrt(6)

4 sqrt(6)

Answer:Please include images of the graphs!

Step-by-step explanation:

Look at each graph given. Ensure that there is a line, and that you can locate two points on the line given.

Use the following equation to get the slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Note that you can obtain the numbers for the equation by getting two points on the number line. Plug in the numbers by variables:

(x₁ , y₁) & (x₂ , y₂)

In this equation, make sure that the slope (m) will equal 1/4 (given).

The full equation that you will use is:

1/4 =  (y₂ - y₁)/(x₂ - x₁)

Find the graph that will satisfy this equation.

Answer:

D

Step-by-step explanation:

It's a football ....=> So ... A sphere !!