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The volume of the spherical boulder is approximately 71.21 cubic feet.

To find the volume of a spherical boulder, we can use the formula for the volume of a sphere:

V = (4/3)πr³

where V is the volume and r is the radius of the sphere.

We are given that the diameter of the boulder is 10 feet, so the radius is half of that, or:

r = 10/2 = 5 feet

We are also given that the boulder weighs almost 6 tons. To convert this weight to pounds, we can multiply by 2000 (since 1 ton is equal to 2000 pounds):

6 tons * 2000 pounds/ton = 12,000 pounds

The weight of the boulder is related to its volume through its density. The density of a boulder will depend on its composition, but we can make an estimate based on common rock types. For example, granite has a density of about 2.7 grams per cubic centimeter, or 2.7 metric tons per cubic meter (since 1 metric ton is equal to 1000 kilograms). A boulder made of granite would therefore weigh about 2.7 times its volume in cubic meters.

Assuming the boulder is made of granite, we can find its volume by setting its weight equal to its volume times its density:

12,000 pounds = V * 2.7 metric tons/m³

To convert pounds to metric tons, we can divide by 2204.62 (since 1 metric ton is equal to 2204.62 pounds):

12,000 pounds / 2204.62 pounds/metric ton = 5.44 metric tons

Substituting this into the equation above, we get:

5.44 metric tons = V * 2.7 metric tons/m³

Dividing both sides by 2.7, we get:

V = 5.44 metric tons / 2.7 metric tons/m³ = 2.0148 m³

To convert this volume to cubic feet, we can use the conversion factor 1 cubic meter = 35.3147 cubic feet:

V = 2.0148 m³ * 35.3147 ft³/m³ = 71.21 ft³

Therefore, the volume of the spherical boulder is approximately 71.21 cubic feet.

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Answer:

40000

Step-by-step explanation:

To find 4 percent of a number, multiply the number by 0.04. In this instance, 0.04 x 1000000 = 40000. Therefore, 4 percent of 1000000 is equal to 40000.

The perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6) is given as follows:

31.04 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The vertices of the polygon in this problem are given as follows:

D(-4, 5), E(-4, -6) and F(3, -6).

Hence the side lengths are given as follows:

Hence the perimeter of the polygon is given as follows:

11 + 13.04 + 7 = 31.04 units.

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We can estimate that 84 eighth graders in the school spend 2 hours each night on homework.We can use the proportion of students in the sample who spend 2 hours each night on homework to estimate the number of students in the school who spend the same amount of time on homework.

We are given that a random sample of 50 eighth-grade students was taken, and 15 of them spent 2 hours each night on homework. Therefore, the proportion of students in the sample who spend 2 hours each night on homework is:

15/50 = 0.3

We can use this proportion to estimate the number of eighth graders in the school who spend 2 hours each night on homework. If we assume that the sample is representative of the larger population, we can multiply the proportion by the total number of eighth graders in the school:

0.3 x 280 = 84

Therefore, we can estimate that 84 eighth graders in the school spend 2 hours each night on homework. It's important to note that this is just an estimate and the actual number may differ due to sampling variability.

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Step-by-step explanation:

Use the distance formula  ( a modified Pyhtagorean theorem)

d^2 = (x1-x2)^2 + ( y1-y2)^2

d^2 = ( -6 - -9)^2 + ( -1 - -6)^2

d^2 = ( 3^2)  + ( 5^2)

d^2 = 34

d = sqrt (34 ) =~ 5.8 units  

The only difference for these devices in 3701 is that the jk-FF (or jk-latch) has an additional control input, which is the clock (CK). The CK input is used to enable and disable the device so that the inputs, j and k, do not always affect the output (Q) of the device.

The SR-FF (or SR-latch) has two inputs, S and R, which directly affect the output, Q. When S=1, the output is set to 1, and when R=1, the output is reset to 0.

On the other hand, the jk-FF (or jk-latch) has three inputs, J, K and CK. When CK is 0, the device is disabled and the outputs remain the same. When CK is 1, the J and K inputs can be used to either set (J=1, K=0) or reset (J=0, K=1) the output, Q.

In summary, the j and k in the jk-FF (or jk-latch) are similar to the s and r in the SR-FF (or SR-latch).

So, the only difference is the addition of a clock (CK) input in the jk-FF (or jk-latch). This clock (CK) input enables and disables the device, which allows the inputs, j and k, to affect the output (Q) of the device.

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The best applicant to fill the only position available based on the test score is Vincent as he scored highest. The method for determining which applicant performed the best on the aptitude test is to use z-scores, which are measurements of how far from the mean a test score falls in standard deviation units.

Since the test is not on the same scale, it is impossible to compare raw test scores. What are Z-scores?A z-score, also known as a standard score, is a score that indicates the number of standard deviations from the mean a raw score is. In other words, a z-score tells you how far from the mean the score is in terms of standard deviations.

In other words, we can use the following formula to calculate the z-score for each person's test result.$$Z = \frac {x - \mu}{\sigma}$$where x is the test score, μ is the test mean, and σ is the standard deviation.The Z-scores for each of the candidates based on their test results are as follows: Demetria:$$Z = \frac {85.1 - 61.1}{12} = 2.00$$,Vincent:$$Z = \frac {299.2 - 264}{22} = 1.6$$,Tobias:$$Z = \frac {7.26 - 7.1}{0.4} = 0.4$$. From the calculations, Vincent has the highest z-score, indicating that he outperformed the other candidates. The candidate with the highest z-score is the best performer, thus Vincent is the best candidate for the job.

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The equation change of volume of a sphere Rohana uses to solve for this value in cubic feet is V = (4/3)π(10)³ which gives the value 4,188.79 cubic feet.

The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is a constant value approximately equal to 3.14159.

In this problem, the radius of the sphere is given as 10 feet. So, we can substitute this value into the formula to get the volume of the sphere as:

V = (4/3)π(10)³

Simplifying the right side, we get:

V = (4/3) × π × (1000)

V = (4/3) × 3.14159 × 1000

V = 4.18879 × 1000

V = 4,188.79 cubic feet

Therefore, the volume of the sphere with a radius of 10 feet is 4,188.79 cubic feet.

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The prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.

Prοbability is a measure οf the likelihοοd οf an event οccurring, expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, and a prοbability οf 1 means the event is certain.

Out οf the tοtal number οf teams that wοn their first game, 12 are frοm the AFC and 6 are frοm the NFC. Out οf the tοtal number οf teams that lοst their first game, 4 are frοm the AFC and 10 are frοm the NFC.

Therefοre, the tοtal number οf AFC teams is 12 + 4 = 16, and the tοtal number οf NFC teams is 6 + 10 = 16.

If we randοmly select a team that wοn their first game, the prοbability that the team is frοm the AFC is:

P(AFC) = number οf AFC teams / tοtal number οf teams

= 16 / (16 + 16)

= 1/2

The prοbability that the team selected wοn their first game and is frοm the AFC is:

P(wοn first game AND AFC) = number οf AFC teams that wοn first game / tοtal number οf teams that wοn first game

= 12 / (12 + 6)

= 12/18

= 2/3

Therefοre, the prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.

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Answer:

slope is -2/3, and the y intercept is 1.

Step-by-step explanation:

Using y=Mx+b (slope intercept form), where M=slope, and B = Y intercept , you can find which valurs are which.

After deducting a commission of 1.5%, Brian will receive 155.71 pounds in exchange for R2100.

To find out how many pounds Brian will get, we first need to calculate the amount of commission he will pay. The commission is 1.5% of R2100, which is equal to 0.015 x R2100 = R31.50.

The amount of money he will actually receive in pounds is the remaining R2100 minus the commission, which is R2068.50. To convert this to pounds, we multiply by the exchange rate of R1 = 0.075199 pound:

2068.50 x 0.075199 = 155.706675 pounds

Therefore, Brian will get 155.71 pounds for R2100 after paying the agent commission.

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The calculated equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.

The equation of a line that is parallel to y = -2x + 4 will have the same slope as -2 since parallel lines have the same slope.

Therefore, we need to look for an equation that has a slope of -2.

(a) 1/2x + y = 1 has a slope of -1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.

(b) -2x + y = 8 has a slope of 2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.

(c) -2x - y = 3 can be rearranged to y = -2x - 3, which has a slope of -2, so it is parallel to y = -2x + 4.

(d) -1/2x + y = 5 has a slope of 1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.

Therefore, the equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.

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By dividing the diameter by 2, one may get the radius of the cone's base:[tex]r = d/2 = 11.9/2 = 5.95 ft[/tex] The volume of a cone is calculated as follows: V = (1/3)πr^2h Inputting the values provided yields.

[tex]V = (1/3)π(5.95^2)(35) (3.5) V equals 138.2 cubic feet[/tex]. Using tenths of a cubic foot increments, we obtain: V ≈ 138.2 ft^3 Hence, the right circular cone has a volume of around 138.2 cubic feet. some further data on the volume of the cone. The formula: can also be used to express a cone's volume in terms of its height and slant height. V is equal to (1/3)r2h plus (1/3)r2(h2 + r2). where the square root symbol is represented by. Since we already know the height and radius, we can use the Pythagorean theorem to get the slant height.

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After considering and calculating, the modulus of z is r = [tex]2^{1/32}[/tex] and the argument of z is θ = 5π/32.

To solve this equation, we can first express −1−i in polar form as:

−1−i = √2cis(3π/4)

where cis(θ) = cos(θ) + i sin(θ) is the polar form of a complex number.

Now, we can express z in polar form as:

z = r cis(θ)

where r is the modulus of z and θ is its argument. Substituting this into the equation z¹⁶ = √2cis(3π/4), we get:

r¹⁶ cis(16θ) = √2cis(3π/4)

Taking the modulus of both sides, we get:

r¹⁶ = √2

Taking the argument of both sides, we get:

16θ = 3π/4 + 2kπ or 16θ = -3π/4 + 2kπ

where k is an integer. Solving for θ in the range 0 < θ < 2π, we find that the second smallest positive solution is:

θ = (3π/4 + 2π)/16 = 5π/32

Therefore, the value of z is:

z = r cis(θ) = [tex]\sqrt{2}^{1/16}[/tex] cis(5π/32)

We can simplify this as:

z = [tex]2^{1/32}[/tex]cis(5π/32)

So, the modulus of z is:

r = [tex]2^{1/32}[/tex]

And the argument of z is:

θ = 5π/32

Therefore, the answer is:

z = [tex]2^{1/32}[/tex]  cis(5π/32)

So, the modulus of z is r = [tex]2^{1/32}[/tex] and the argument of z is θ = 5π/32.

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The revenue for a company's product is the amount of money the company earns from selling the product. R(x) = 0.36x^3 + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.

R(x) = 0.36x^3 + 824x

The revenue for a company's product is the amount of money the company earns from selling the product. To find the revenue function for a company, we can use the demand and price functions given. The demand function tells us how much of the product customers are willing to buy at a certain cost, while the price function tells us how much the company can charge for the product. R(x) = 0.36x^3 + 824x + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.

At x = 10,

R(10) = 0.36(10^3) + 824(10) + 824

R(10) = 3600 + 8240 + 824

R(10) = 17,664

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The perimeter of the square garden is 100 feet.

To find the perimeter of the square garden, first we need to determine the length of one side of the square. The given

information states that the hose, which lies along one diagonal of the garden, has a length of 25√2 feet.

Recall that the diagonal of a square divides it into two congruent right triangles, with the diagonal being the

hypotenuse.

Use the Pythagorean theorem to find the side length of the square. Let 'a' represent the side length of the square.

Then, we have:

a² + a² = (25√2)²

Simplify the equation:

2a² = 625 × 2

Divide both sides by 2:

a² = 625

Find the square root of both sides:

a = 25

Now that we know the side length of the square garden is 25 feet, we can calculate the perimeter.

The perimeter of a square is given by the formula:

Perimeter = 4 × side length

Substitute the side length:

Perimeter = 4 × 25

Calculate the perimeter:

Perimeter = 100

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Answer:3/2

Step-by-step explanation:

[tex]\frac{9}{6} = \frac{\frac{9}{3} }{\frac{6}{3} }=\frac{3}{2}[/tex]

a. The probability of getting exactly 1 girl in 8 births is given as follows: 0.0313 = 3.13%.

b. The probability of getting 1 or fewer girls in 8 births is given as follows: 0.0352 = 3.52%.

c. The relevant probability for significantly low is given as follows: B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.

d. The correct option regarding whether the probability is significantly low is: D. Yes, since the appropriate probability is less than 0.05, it is a significantly low number.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

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

The parameters are listed as follows:

The relevant probabilities for this problem are given as follows:

Hence the probability of 1 or fewer, used to verify if the event is significantly low, is:

P(X <= 1) = P(X = 0) + P(X = 1)

P(X <= 1) = 0.0352.

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Answer:

B. 1/2 multiplied by 1/2

Step-by-step explanation:

To find the probability, you would multiply. If you did not know this, you could solve each answer choice to find which one equals 1/4 since the problem already said the probability of flipping two heads is 1/4.

A. 1/2 - 1/2 = 0

B. 1/2 x 1/2 = 1/4

C. 1/2 / 1/2 = 1

D. 1/2 +1/2 = 1

Time 20 contestants and average their times is the best option to find a reasonable estimate for the amount of time it takes to run the obstacle course. Thus, option D is the correct answer.

A good estimate is an approximation amount of value that is based on analytical reasoning and data available. That estimation must be within a valid margin of error. It is not expected to be accurate, but it is expected to deliver a fair view of the value being estimated.

The official time for 20 contestants is a large sample size which is enough to provide a reasonable estimate of the meantime for all 200 contestants. The actual can average the times for the 20 contestants to calculate the average time for the whole group.

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a) The probability is $\frac{65}{357}$.

b)  The probability is $\frac{781}{1000}$.

c)  The probability is $\frac{58}{195}$.

d) The probability is $\frac{65}{357}$.

e) We can construct a probability tree for these probabilities. Below is the probability tree:probability tree for airlines. Therefore, the above figure is the probability tree for airlines.

The probability that a randomly selected flight was Delta and was late is $\frac{65}{357}$.Therefore, the probability is $\frac{65}{357}$.

The probability that a randomly selected flight was United or was on-time is $\frac{781}{1000}$.Therefore, the probability is $\frac{781}{1000}$.

Given the flight was late, the probability that it was from American is $\frac{58}{195}$.Therefore, the probability is $\frac{58}{195}$.

Given the flight was from Delta, the probability that it was late is $\frac{65}{357}$.Therefore, the probability is $\frac{65}{357}$.

We can construct a probability tree for these probabilities. Below is the probability tree:probability tree for airlines. Therefore, the above figure is the probability tree for airlines.

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Answer:

forgot how to do this

Step-by-step explanation:

150√374 283727273737272727272

Answer:

A)  £20
B)  £180

Step-by-step explanation:

The original price is £200. The price was reduced by 10% so the sale price is 90% of the original price.

A)  Price Reduction = 200 * 0.1 = £20

B)  Sale Price = Original Price - Price Reduction = 200 - 20 = £180
                          Original Price * Percent Paid = 200 * 0.9 = £180

The length of side AB in the right triangle ABC is approximately 3.21 units.

To find the length of side AB in the right triangle ABC, we can use trigonometric ratios.

Given:

Angle BAC = 40 degrees

Side AC = 5 units

Let's use the trigonometric ratio for the sine of angle BAC:

sin(BAC) = opposite/hypotenuse

sin(40°) = AB/AC

Rearranging the equation to solve for AB, we have:

AB = AC * sin(BAC)

Substituting the given values, we get:

AB = 5 * sin(40°)

Using a calculator to evaluate sin(40°), we find:

AB = 5 * 0.6428

≈ 3.21

Therefore, the length of side AB in the right triangle ABC is approximately 3.21 units.

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The number of negative real zeros of f is either 3 or 0.

Using Descartes's Rule of Signs, the possible numbers of positive and negative zeros of the function f(x) = 6x3 + 7x2 + x + 5 can be determined. The number of variations in sign in f(x) is 3. This means that the number of positive real zeros of f is either 3 or 0. The number of variations in sign in f(-x) is 3. This means that the number of negative real zeros of f is either 3 or 0.

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Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:

-17/4 * 5/5 = -85/20, 32/5 * 4/4 = 128/20, -85/20 - 128/20 = -213/20

A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers. The depiction of fractions appears easier than when decimal values are used.

A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To simplify:

-4 and 1/4 - 6 and 2/5

For the two mixed integers, we must identify a common denominator. The least frequent multiple of 4 and 5 is 20 since their prime components are 2 and 5. Both mixed numbers can be transformed into improper fractions with a denominator of 20 as follows:

-4 and 1/4 = -17/4

6 and 2/5 = 32/5

Now we can subtract these fractions:

-17/4 - 32/5

We must locate a common denominator in order to subtract fractions. Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:

-17/4 * 5/5 = -85/20

32/5 * 4/4 = 128/20

We can now take the two fractions apart:

-85/20 - 128/20 = -213/20

Therefore, -4 and 1/4 - 6 and 2/5 simplify to -213/20.

So, the answer is negative 213 over 20.

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The value of the tip she left is $42.53.

Sales tax is a compulsory amount levied by the government on the sales price of a good or service. Sales price increase the cost of a good or service.

The first step is to determine the total bill after the sales tax has been included.

Total bill after sales tax = (1 + percent sales tax/100) x total bill

(1 + 7/100) x $265

(1 + 0.07) x $265

1.07 x $265

= $283.55

Now, multiply the total bill after sales tax by the percentage value of the tip.

Value of the tip = 15% x $283.55

0.15 x $283.55 = $42.53

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The true statement about the function is (a) It is an exponential function because the y-values increase by an equal factor over equal intervals of x-values

From the question, we have the following parameters that can be used in our computation:

The table of values

In this table, each y-value is obtained by multiplying the previous y-value by 4.

This means that the function has a constant ratio or factor between each x- and y-value.

Such a pattern is typical of exponential functions, where equal intervals of x-values produce increasing or decreasing ratios of y-values.

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