A square has approximately 300 square feet . The length of each side of the square is between which two whole numbers?

For the distance of 5 miles covered in 4 hours, we can write the unit rate as {r] = 1.25 miles/hour.

The rate at which one value changes with respect to per unit change in the other value is called the unit rate. Mathematically -

{ r } = y/x                                                          .... Eq { 1 }

Given is the distance of 5 miles covered in 4 hours.

We can write the unit rate as -

{r} = 5/4

{r} = 1.25 miles/hour

Therefore, for the distance of 5 miles covered in 4 hours, we can write the unit rate as {r] = 1.25 miles/hour.

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The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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Grant should pay approximately $211.96 today for the annual membership, considering an interest rate of 10% and the option to pay in 12 monthly installments of $55 each.

To determine how much Grant should pay today for the annual membership, we need to calculate the present value of the 12 monthly payments of $55 each, considering an interest rate of 10%.

The present value (PV) can be calculated using the formula:

PV = C * (1 - (1 + r)^(-n)) / r

Where:

C = the monthly payment amount ($55)

r = the monthly interest rate (10% / 12 = 0.00833)

n = the number of payments (12)

Plugging in the values into the formula, we can calculate the present value:

PV = 55 * (1 - (1 + 0.00833)^(-12)) / 0.00833

PV ≈ 55 * (1 - 0.6806) / 0.00833

PV ≈ 55 * 0.3194 / 0.00833

PV ≈ 211.96

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Answer:

n >= 1

Step-by-step explanation:

2(7n - 1) >= 3(5 - n)

use the distributive property

14n - 2 >= 15 - 3n

     +2       +2      

14n >= 17 - 3n

+3n          +3n

17n >= 17

n >= 1

Plz mark as brainliest if this helped! Have a nice day!!!

-Lil_G

Step-by-step explanation:

\(2(7n - 1) \geqslant 3(5 - n) \\ 14n - 2 \geqslant 15 - 3n \\ 14n + 3n \geqslant 17 \\ 17n \geqslant 17 \\ n \geqslant 1 \\ thank \: you\)

Answer:

-1

Step-by-step explanation:

Answer:

8 times

Step-by-step explanation:

Volume of sphere 4/3 *pi*r^3

Let small sphere radius r1=r

So radius of large sphere R= 2r (given)

Put all valves in sphere formula and calculate

Small sphere vol v1 = 4/3*pi*r^3......... Let assume eq 1

Large sphere vol= 4/3*pi*(2r)^3

= 4/3*pi* 8r^3

Or = 8v1

substitute 4/3*pi*r^3 value from eq1

Answer:

8

Step-by-step explanation:

Given the ratio of the radii = a : b, then

ratio of volume = a³ : b³

Here the ratio of radii = 1 : 2 , thus

ratio of volume = 1³ : 2³ = 1 : 8

That is the volume of the larger sphere is 8 times the volume of smaller sphere.

Answer: (x+5)(2x+10)

Step-by-step explanation: Hope you find it helpful, I am in the rush so can't give you a full explanation on paper yet!

Answer:

here you go. hope this helps!

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

One general method for determining all the factors of a counting number is by using the prime factorization method.

Here are the steps:

1. Start with the smallest prime number, 2, and divide the number by 2.

2. If the number is divisible by 2, write down 2 as a factor and divide the number by 2 to get a new number.

3. If the new number is still divisible by 2, repeat the process. If not, move on to the next smallest prime number, 3.

4. Continue this process with each prime number until you have fully factored in the original number.

Let's illustrate this method with the number 150:

1. 150 ÷ 2 = 75. So, 2 is a factor and our new number is 75.

2. 75 is not divisible by 2, so we move on to the next smallest prime number, 3.

3. 75 ÷ 3 = 25. So, 3 is a factor and our new number is 25.

4. 25 is not divisible by 3, so we move on to the next smallest prime number, 5.

5. 25 ÷ 5 = 5. So, 5 is a factor and our new number is 5.

6. 5 ÷ 5 = 1. So, 5 is a factor and our new number is 1.

We have now fully factored 150 into its prime factors: 2, 3, 5, and 5. To find all the factors of 150, we can multiply these prime factors in different combinations:

1 × 150 = 150
2 × 75 = 150
3 × 50 = 150
5 × 30 = 150
6 × 25 = 150
10 × 15 = 150

So, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

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Answer:

47

Step-by-step explanation:

1 ) Simplify 6×3  to  18.

52+18÷9−7

2) Simplify 18÷9  to 2.

52+2-7

3) Simplify  52+2 to 54.

54-7

4) Simplify.

47

Therefor, the answer is, 47.

The vertex angle is defined as the angle opposite the base. It can be calculated by formula, 180° - 2B = A where, B=base angle and A=vertex angle.

The two sides of an isosceles triangle are congruent, which means they are the same length. The third side of an isosceles triangle is larger than the other two and is known as the base.

Every triangle has three angles that add up to a total of 180°. The base angles are the two angles located along the base of isosceles triangles. In isosceles triangles, the base angles are always congruent, or equal.

The vertex angle is defined as the angle opposite the base. The vertex angle is always greater than the sum of the two base angles. The vertex angle is always calculated by subtracting the base angles from 180°, using the general formula: 180° - 2B = A, where B represents the base angle and A represents the vertex angle.

Thus, vertex angle is defined as the angle opposite the base.

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The average deviation of predicted DVD sales from the actual is 12.2279 million dollars. F-critical value is 4.0785>4.0785 we can reject the null hypothesis. The 95% confidence interval is (17.1536, 25.1554). The 95% prediction interval for the given value of x is (-3.8623, 46.1713).

Estimate the level of DVD sales for movies, by using the amount of annual revenue  generated by the box office gross

We randomly selected a sample of 43 movies for the same year.

Excel  α = 0.05,  r^2 = 0.5123

=51.23%

51.23% of the DVD sales variation is explained by annual revenue.

SY.X = 12.2279.

Therefore, the average deviation of predicted DVD sales from the actual is 12.2279 million dollars.

b. The hypothesis being tested is:

Null Hypothesis, H0: β1 = 0

Alternative Hypothesis, H1: β1 ≠ 0

The test statistic, F = (6439.6133/1)/((12570.025 - 6439.6133)/(42 - 1)) = 43.07

The F-critical value is 4.0785.

Since 43.07 > 4.0785, we can reject the null hypothesis.

Therefore, we can conclude that there is a linear relationship between the revenues of DVD sales and the box-office gross.

c. y = bo + b1*x

y = 4.8445 + 0.1631*x

Put x = 100

y = 4.8445 + 0.1631*100 = 21.1545

The 95% confidence interval for the given value of x is:

= y ± t*s*\(\sqrt{0.026249}\)

= 21.1545 ± 2.020*12.2279*\(\sqrt{0.026249}\)

= (17.1536, 25.1554)

d.  The 95% prediction interval for the given value of x is:

= y ± t×s×\(\sqrt{}\)1 + hin [The t-value is calculated using =TINV(0.05,42-1) in Excel]

= 21.1545 ± 2.020*12.2279*\(\sqrt{1 + 0.026249}\)

= (-3.8623, 46.1713)

Therefore, the value is (-3.8623, 46.1713).

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To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

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Answer:

Step-by-step explanation:

The mean score for the test is 80.

We have,

To find the mean score for the test, we can use the relationship between the mean, the standard deviation, and the z-score.

The formula for the z-score is:

z = (x - μ) / σ

Where:

z is the z-score,

x is the given score,

μ is the mean, and

σ is the standard deviation.

In this case, we know that Cathy's score (x) is 74 and it is 1 standard deviation below the mean (z = -1).

The standard deviation (σ) is given as 6.

Plugging these values into the z-score formula, we can solve for the mean (μ):

-1 = (74 - μ) / 6

Multiplying both sides by 6:

-6 = 74 - μ

Rearranging the equation:

μ = 74 + 6

μ = 80

Thus,

The mean score for the test is 80.

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The t-statistic is 1.07 and the degrees of freedom is 19.

To calculate the t-statistic and degrees of freedom with the given information, we use the formula:

t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the given values, we get:

t = (62 - 60) / sqrt(2.45^2/10 + 3.16^2/10) = 1.07

The degrees of freedom for the t-distribution can be calculated using the formula:

df = (s1^2/n1 + s2^2/n2)^2 / [(s1^2/n1)^2 / (n1 - 1) + (s2^2/n2)^2 / (n2 - 1)]

Substituting the given values, we get:

df = (2.45^2/10 + 3.16^2/10)^2 / [(2.45^2/10)^2 / 9 + (3.16^2/10)^2 / 9] = 18.84

Rounding to the nearest whole number, the degrees of freedom is 19.

Therefore, the t-statistic is 1.07 and the degrees of freedom is 19.

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Answer:

\(\frac{8}{27}\)

Step-by-step explanation:

\(\frac{9}{4} ^{-\frac{3}{2} }\)

reciprocate to remove the minus sign

\(\frac{4}{9} ^{\frac{3}{2} }\)

take square root to remove the 2

\(\sqrt({\frac{4}{9}) ^{3} }\)

\((\frac{2}{3} )^{3}\)

\(\frac{8}{27}\)

hope this helped :)

Step-by-step explanation:

To find the velocity of the particle, we need to take the derivative of the position vector with respect to time.

r(θ) = (a + b * cos(θ)) * i + (b * sin(θ)) * j

d/dt[r(θ)] = d/dt[(a + b * cos(θ)) * i + (b * sin(θ)) * j]

d/dt[r(θ)] = (-b * sin(θ)) * i + (b * cos(θ)) * j

So, the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

Answer:

Step-by-step explanation:

the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

Answer:

9 and 6

Step-by-step explanation:

You see, 9x2=18 and 6x3=18

By simple algebra, Jane is 57 9/20 inches taller.

If one object or person's height exceeds that of another, the taller object or person is said to exist. There is a two-object or two-person limit. Taller is a relative term. For instance: Hoppy stands at 7 feet.

You can begin this issue by first figuring out Dwight's height. At 54 3/4 inches, he would be 1 1/2 inches taller than Chloe:

54 3/4 plus 1 1/2 equals 55 + (3/4 + 1/2) equals 55 + (3/4 + 2/4) equals 55 + 5/4 equals 56 1/4 inches.

Dwight stands at 56 1/4 inches.

Dwight is 1 1/5 inches shorter than Jane, so

56 1/4 plus 1 1/5 is 57 plus (1/4 plus 1/5) is 57 plus (5/20 plus 4/20) is 57 plus 9/20 is 57 9/20 inches.

Jane stands at 57 9/20 inches.

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The probability that a player will toss the die at least 2 times before blue lands faceup is 15/28.

The geometric distribution, which is a probability distribution that models the number of trials needed to achieve the first success in a sequence of Bernoulli trials, where each trial has a constant probability of success.

In this case, the Bernoulli trial is whether the die lands on blue, and the geometric distribution models the number of tosses needed to achieve the first blue face.

To find the probability that a player will toss the die at least 2 times before blue lands faceup, we need to find the probability of getting either a red or a yellow face on the first toss, and then either a blue face or another red/yellow face on the second toss.

The probability of getting a red or yellow face on the first toss is:

P(Red or Yellow) = 3/8 + 3/8 = 6/8 = 3/4

If the first toss is a red or yellow face,

then the probability of getting a blue face on the second toss is:

P(Blue on 2nd toss | Red or Yellow on 1st toss) = 2/7

So, the probability of getting blue on the second toss given the first toss is red or yellow is 2/7.

Therefore, the probability of not getting a blue face on the second toss given the first toss is red or yellow is 1-2/7=5/7.

Putting it all together, the probability of tossing the die at least 2 times before blue lands faceup is:

P(at least 2 tosses)

= P(Red or Yellow on 1st toss) × P(Not Blue on 2nd toss given Red or Yellow on 1st toss)

= (3/4) × (5/7)

= 15/28

Therefore,

The probability that a player will toss the die at least 2 times before blue lands faceup is 15/28.

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Answer:

Step-by-step explanation:

a + 9 = 15

a = 15 - 9

a = 6

c + 9 = 16

     c = 16 - 9

     c = 7

d = c + 9

   = 7 + 9

  = 16

e = d + 15

  = 16 + 15

e = 31

P(selecting a boy) = total boy /total pupils = 16/31

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Answer:

Below

Step-by-step explanation:

Here are three methods:

  Graphing the equations  (intersection of the graphs is solution)

  Substitution method

   Elimination method

Check the picture below.

\(\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ c = \sqrt{10^2+7^2~-~2(10)(7)\cos(108^o)} \implies c = \sqrt{ 149 - 140 \cos(108^o) } \\\\\\ c\approx \sqrt{149-(-43.262379)}\implies c\approx \sqrt{192.262379}\implies \boxed{c\approx 14}\)

Answer:

1/64 or 0.01563

Step-by-step explanation:

1/4*1/4*1/4=1/64

Answer:

3n+m+2p

Step-by-step explanation:

group all like terms and solve.

so,

4n-n = 3n

-m + 2m = m

3p - p = 2p

Then, group them together: 3n+m+2p

in the case when the process is not centered, the process is not capable of meeting design specifications.

To determine if the process is capable of meeting design specifications, we need to compare the process capability index (Cpk) to the specified tolerance.

Cpk is calculated as the minimum of two values: Cpk = (USL - μ) / (3 * σ) and Cpk = (μ - LSL) / (3 * σ), where USL is the upper specification limit, LSL is the lower specification limit, μ is the process mean, and σ is the process standard deviation.

Given that the process is centered with a standard deviation of 0.10 ounces and the specified tolerance is ±0.35 ounces:

a) Process is centered (μ = 12 ounces):

LSL = 12 - 0.35 = 11.65 ounces

USL = 12 + 0.35 = 12.35 ounces

Cpk = min((12.35 - 12) / (3 * 0.10), (12 - 11.65) / (3 * 0.10))

   = min(1.17, 1.17)

   = 1.17

Since Cpk > 1, the process is capable of meeting design specifications.

b) Process is not centered (μ = 11.75 ounces):

LSL = 12 - 0.35 = 11.65 ounces

USL = 12 + 0.35 = 12.35 ounces

Cpk = min((12.35 - 11.75) / (3 * 0.10), (11.75 - 11.65) / (3 * 0.10))

   = min(1.83, 0.33)

   = 0.33

Since Cpk < 1, the process is not capable of meeting design specifications when the average net weight of the cans is 11.75 ounces.

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