what is the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet?

Answer:

7.2

Step-by-step explanation:

3/5 * 12

The standard deviation of the sampling distribution of pCheck to see if the 10% condition is 0.44.

If a large candy machine has 45% orange candies, and an SRS of 25 candies is taken from it, then the 10% condition can be checked to see if it is met. To do this, it is necessary to calculate the sample proportion p. To calculate p, the number of orange candies in the sample (let's call it x) is divided by the total number of candies in the sample (25). Thus, p = x/25. The 10% condition is met if the value of p is less than or equal to 0.1 (10%).

Since the value of p is unknown, the number of orange candies in the sample must first be determined. To find this number, the proportion of orange candies in the entire candy machine must be used. The proportion of orange candies is 45%, or 0.45.

This means that for every 100 candies in the candy machine, 45 are orange. Since there are 25 candies in the sample, 0.45*25 = 11.25 orange candies are expected in the sample. Since this is a sample proportion, the exact value of x must be rounded to the nearest whole number. This gives a value of 11 orange candies in the sample.

Now that the value of x is known, the value of p can be calculated. This gives p = 11/25 = 0.44.

Since 0.44 is greater than 0.1 (10%), the 10% condition is not met in this case.

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The value of c that satisfies the equation  \(\sum_{n=1}^{\infty} e^{nc}=10\)  is approximately -0.0451.

What is a equation?

An equation is a mathematical statement that asserts the equality of two expressions.

To find the value of c such that the infinite series \(\sum_{n=1}^{\infty} e^{nc}\) is equal to 10, we can use the formula for the sum of an infinite geometric series with \(a = e^c\).

The formula for the sum of an infinite geometric series is given by:

S = a / (1 - r),

where S is the sum of the series, a is the first term, and r is the common ratio.

In this case, \(a = e^c\) and the common ratio \(r = e^c\).

We can rewrite the equation as:

\(10 = e^c / (1 - e^c)\)

Next, let's solve for c:

\(10(1 - e^c) = e^c\)

\(10 - 10e^c = e^c\)

\(10 = 11e^c\)

\(e^c = 10 / 11\)

Taking the natural logarithm (ln) of both sides:

\(c = ln(10 / 11)\)

Using a calculator, we can find the approximate value of c:

c ≈ -0.0451.

Therefore, the value of c that satisfies the equation  \(\sum_{n=1}^{\infty} e^{nc}=10\)  is approximately -0.0451.

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To find the angle of least nonnegative measure that is coterminal with θ = -570°, we can add or subtract multiples of 360° until we get an angle between 0° and 360°.

We can start by adding 360° to -570°:

-570° + 360° = -210°

This is still negative, so we can add another 360°:

-210° + 360° = 150°

This is between 0° and 360°, so the angle of least nonnegative measure that is coterminal with θ = -570° is 150°. Therefore, 0c is 150°.

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The values of the t statistic that are statistically significant at the α=0.005 level are t < -2.977 or t > 2.977.

To determine the values of the t statistic that are statistically significant at the α=0.005 level, we need to find the critical values of the t-distribution with 14 degrees of freedom (df = n - 1 = 15 - 1 = 14).

Using a t-table or a calculator, we can find that the critical values for a two-tailed test with α=0.005 are -2.977 and 2.977. This means that any t statistic less than -2.977 or greater than 2.977 would be considered statistically significant at the α=0.005 level.

In other words, if the calculated t statistic falls within the range of -2.977 to 2.977, we would fail to reject the null hypothesis (H0: μ=10) and conclude that there is not enough evidence to suggest that the population mean is different from 10. However, if the calculated t statistic falls outside of this range, we would reject the null hypothesis and conclude that there is evidence to suggest that the population mean is different from 10.

So, the values of the t statistic that are statistically significant at the α=0.005 level are t < -2.977 or t > 2.977.

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K = 10^(2.5186) = 330.93

The given sequence is not an arithmetic or geometric sequence since there is no common difference or ratio between the terms. However, we can observe that the sequence alternates between positive and negative values and that the absolute value of the terms is increasing as we move through the sequence.

We can express this pattern using an exponential function of the form a(n) = (-1)^(n+1)*b, where b is the absolute value of the first term. Substituting the values from the sequence, we get:

a(1) = (-1)^(1+1)*18 = 18

a(2) = (-1)^(2+1)*12 = -12

a(3) = (-1)^(3+1)*8 = 8

Therefore, the formula for the nth term of the given sequence is:

a(n) = (-1)^(n+1)*18*(3/2)^(n-1)

To find the value of K, we need to solve the equation 2.5186 = log(K) for K. Taking the antilogarithm of both sides, we get:

K = 10^(2.5186) = 330.93

Rounding this to the nearest integer, we get:

K ≈ 331.

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Answer:

The answer is c. 81.76%

Answer:

-7, -1

This should be correct

Answer:

1,008 square yards

Step-by-step explanation:

21 yards long X 48 feet wide = 1,008 square yards

hope it helps!

The measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.

Angles are bisected if they are divided into two equal parts.

If the angle BC bisects <ABC, hence <ABD and <DBC are equal, hence;

2(11x + 23) = <ABC

Given the following parameters

<ABC = 25x + 34

2(11x + 23) = 25x + 34

Expand

22x +46 = 25x + 34

22x-25x = 34 - 46

-3x = -12

x = 4

Determine the measure of the angles

<ABD = 11x + 23 = <DBC
<ABD = 11(4) + 23

<ABD = 44 + 23

<ABD = 67 degrees

<ABC = 2(67)

<ABC = 134 degrees

Hence the measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.

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Answer:

in an arithmetic series, an = a0+ (n-1) *d

that means the nth term is equal to the first term plus n-1 times the common difference.

if she shifted all of her money market investments to cash, she might have done that because there is: no withdrawal fee on a low-risk account.

A part of the economy that offers short-term funds is the money market. The money market specialises in short-term loans, typically with terms of a year or less.

The money market emerged as a segment of the financial market for assets used in short-term borrowing, lending, buying, and selling with original maturities of one year or less as short-term securities turned into a commodity. Money market trading is done over the counter and is wholesale.

The majority of Western nations use a variety of money market instruments, including federal funds, short-term mortgage- and asset-backed securities, commercial paper, banker's acceptances, deposits, certificates of deposit, bills of exchange, and treasury bills.

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Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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Tyler will have ridden the bus 135 days once school is out for summer.

If Tyler rides the bus home from school 3 days every week, and there are 45 weeks in the school year, we can calculate the total number of bus-riding days by multiplying the number of days per week by the number of weeks:

If Tyler rides the bus home from school 3 days every week and the school year lasts for 45 weeks, the total number of days he will have ridden the bus can be calculated by multiplying the number of days per week (3) by the number of weeks (45). Therefore, Tyler will have ridden the bus for a total of 135 days once school is out for summer.

3 days/week * 45 weeks = 135 days

Therefore, Tyler will have ridden the bus 135 days once school is out for summer.

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Answer:

=£5898.38

Step-by-step explanation:

5000×1.07×1.05^(2)

=£5898.38

Answer:

116.663333333 repeating

Step-by-step explanation:

do 349.99 divided by 3

The area of the circle with a radius of 4 ft is approximately 50.24 square feet. This means that if we were to draw a circle with a radius of 4 ft on a flat surface, it would cover an area of approximately 50.24 square feet.

The area of a circle is defined as the amount of space enclosed by its circumference. It can be found using the formula A = πr^2, where A is the area, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14.

In this case, we are given that the radius of the circle is 4 ft. By substituting this value into the formula, we get:

A = π(4)^2

A = 16π square feet

Now, to find an approximate value for the area, we can use the approximation π ≈ 3.14. Substituting this in, we get:

A ≈ 16 × 3.14

A ≈ 50.24 square feet

Therefore, the area of the circle with a radius of 4 ft is approximately 50.24 square feet. This means that if we were to draw a circle with a radius of 4 ft on a flat surface, it would cover an area of approximately 50.24 square feet.

It's worth noting that the units of the area are always squared, i.e., square feet in this case. This is because the area is a measure of the two-dimensional space enclosed by the circle, and hence has units of length squared.

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We want to see which expression does not belong, the one that has a difference with the others is the third one, so that is the one that does not belong.

Here you need to remember the rules:

\(a^x*a^y = a^{x + y}\\\\(a^x)^y = a^{x*y}\\\\\frac{a^x}{a^y} = a^{x - y}\)

Now we can use these to rewrite the given expressions as:

\(\frac{2^8}{2^5} = 2^{8 - 5} = 2^3 = 8\)

\((\frac{3}{4} )^{-5}*(\frac{3}{4})^8 = (\frac{3}{4})^{-5 + 8}= (\frac{3}{4} )^3\)

\((4^{-5})^8 = 4^{-5*8} = 4^{-40}\)

\(\frac{10^8}{5^5} = \frac{2^8*5^8}{5^5} = (2^8)*(5^{8-5}) = 2^8*5^3\)

So you can see that in the first, second, and fourth expressions we have positive exponents and there always appears the exponent 3, while on the third one that does not happen, so the one that does not belong is the third expression.

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Answer:

We can start solving the problem by using algebra. Let x be the number of points scored by each girl, and y be the number of points scored by each boy. Then, based on the information given in the problem, we have the following equations:

x + y = 27 (the total number of points scored by the team)

3x - 2y = 15 (the difference between the number of points scored by the 3 girls and the 2 boys)

To solve for x and y, we can use the second equation to eliminate one of the variables. Multiplying both sides of the second equation by 2, we get:

6x - 4y = 30

Now we can substitute this into the first equation:

6x - 4y + y = 27

6x = 27 + 4y

x = (27 + 4y)/6

Now we can substitute this back into the second equation:

3((27 + 4y)/6) - 2y = 15

27 + 2y - 2y = 15

27 = 15

This is a contradiction, so the given information is insufficient to find the number of points scored by each girl and each boy.

Step-by-step explanation:

Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.

According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:

7s + 11t = 125 ---(1)

On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:

14s + 8t = 180 ---(2)

We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.

Multiplying equation (1) by 8 and equation (2) by 11, we get:

56s + 88t = 1000 ---(3)

154s + 88t = 1980 ---(4)

Subtracting equation (3) from equation (4) eliminates 't':

(154s + 88t) - (56s + 88t) = 1980 - 1000

98s = 980

s = 980 / 98

s = 10

Substituting the value of 's' back into equation (1), we can solve for 't':

7s + 11t = 125

7(10) + 11t = 125

70 + 11t = 125

11t = 125 - 70

11t = 55

t = 55 / 11

t = 5

Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Formula for a circle with center (h,k) and radius r    is

(x-h)^2 + (y-k)^2   =  r^2

   so for the given info   center is     3, -4     and    r = sqrt (36) = 6  

The integral of e from -5 to 5 is equal to zero.

The integral from -5 to 5 of e dx can be written as:

∫₋₅⁵ e dx

To evaluate this integral, we can use the fundamental theorem of calculus, which states that the definite integral of a function can be evaluated by finding its antiderivative and evaluating it at the limits of integration. In other words, we need to find the antiderivative of the function e and evaluate it at 5 and -5.

The antiderivative of e is itself, so we have:

∫₋₅⁵ e dx = e|(-5 to 5)

Now, we can evaluate e at the limits of integration:

e|(-5 to 5) = e(5) - e(-5)

Since e is a constant, we have:

e|(-5 to 5) = e - e

Therefore, the integral from -5 to 5 of e dx is equal to zero.

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Complete Question:

Evaluate the integral: integral from -5 to 5 edx

The approximate volume of the sphere is 6.01 ft³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the surface area of the sphere is 16 square feet.

First, we determine the radius r:

Surface area = 4πr²

Hence

16 = 4πr²

Dividing both sides by 4π, we get:

r² = 16/4πr

r = √( 16/4πr )

r = 1.128 ft

Plugging in the value of r that we just found, we get:

Volume =  (4/3)πr³

Volume =  (4/3) × 3.14 × (1.128 ft)³

Volume =  6.01 ft³

Therefore, teh volume is 6.01 ft³.

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Answer:

The area of an equilateral triangle is:

\(A=144\sqrt{3}\) cm²      

Hence, the left bottom option i.e. \(144\sqrt{3}\) cm² is the correct option.

Step-by-step explanation:

We know that the perimeter of a triangle is just the sum of its three sides.

Given that the perimeter of an equilateral triangle is 72cm.

i.e. \(P = 72\) cm

Important Tip:

Let 'a' be the length of an individual side of an equilateral triangle.

The length of an individual side of an equilateral triangle will be:

\(\:a\:=\:\frac{P}{3}\:\)

 \(a=\:\frac{72}{3}\)         ∵ The perimeter \(P = 72\)

 \(a= 24\) cm

Thus,

The length of an individual side of an equilateral triangle: a = 24 cm

The area of an equilateral triangle can be determined using the formula

\(A=\frac{\sqrt{3}}{4}a^2\)

where 'a' is the length of an individual side

now substitute a = 24 cm in the formula

\(A=\frac{\sqrt{3}}{4}\left(24\right)^2\)

\(A=\frac{\sqrt{3}}{4}\left(576\right)\)                ∵ 24² = 576

\(A=144\sqrt{3}\)  cm²           ∵ \(\:\frac{576}{4}=144\)

Therefore, the area of an equilateral triangle is:

\(A=144\sqrt{3}\) cm²      

Hence, the left bottom option i.e. \(144\sqrt{3}\) cm² is the correct option.

Answer:

2x+3

Step-by-step explanation:

2x+3=Alan's Weight

2x= Dylan's weight times two

+3= the plus three more pounds

Which then equals Alan's weight.

The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will  lighter, not darker.

The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.

Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.

After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.

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Yes, snow and "cold" weather are independent events. The probability of snow and a "cold" day is 15.

Based on the given probabilities, we can determine if snow and "cold" weather are independent events. Independent events occur when the probability of both events happening together is equal to the product of their individual probabilities.

P(snow) = 0.30

P(cold) = 0.50

P(snow and cold) = 0.15

If snow and cold are independent, then P(snow and cold) = P(snow) * P(cold).

0.15 = 0.30 * 0.50

0.15 = 0.15

Since both sides of the equation are equal, snow and "cold" weather are independent events.

Your answer: b. yes

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Answer:

  A. see instructions below

  B. w = 3

Step-by-step explanation:

A. Apparently, your (machine instructions, algebra) are ...

  (multiply by 5, 5w)

  (subtract 6, 5w-6)

  (divide by 3, (5w-6)/3)

  (add 2, (5w-6)/3 +2)

  (output the number, 5)

__

B. Working backward, we want to undo each instruction.

  (subtract 2, 5-2 = 3)

  (multiply by 3, 3·3 = 9)

  (add 6, 9+6 = 15)

  (divide by 5, 15/5 = 3)

  (input the number, 3)

The equation (5w-6)/3 +2 = 5 has the solution w = 3.

The per minute charge is $0.21 and charge for mentioned ride is $9.68.

Firstly forming the two equations based on mentioned information. Let the amount charged per minutes be x and amount charge per mile be y.

Equation for Ariel :

2 + 14x + 10y = 16.94 - Equation 1

Equation for Victoria :

2 + 10x + 6y = 11.30 - Equation 2

Simplifying Equation 1

14x + 10y = 14.94

Dividing by 2

7x + 5y = 7.47 - Equation 3

Simplifying equation 2

10x + 6y = 9.30

Dividing by 2

5x + 3y = 4.65 - Equation 4

Multiplying equation 3 with 3 and equation 4 with 5. Subtracting the resultant equation

21x + 15y = 22.41

-25x + 15y = 23.25

-4x = -0.84

x = 0.21

The charge per minute is $0.21.

Keep the value of x in equation 3 to calculate y

7×0.21 + 5y = 7.47

1.47 + 5y = 7.47

5y = 6

y = 6/5

y = 1.2

So, the charge per mile is $1.2

Charge for 8 minutes and 5 miles is -

Charge = 2 + 0.21×8 + 1.2×5

Charge = 2 + 1.68 + 6

Charge = $9.68

Thus, the charge per minute is $0.21 and charge for mentioned duration is $9.68.

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The integral of 37/(\(x(lnx)^p\)) converges for p > 1, as the denominator becomes increasingly smaller as x approaches infinity.

The integral of the function \(37/(x(lnx)^p)\) can be calculated to determine whether it converges or diverges. The integral converges if the limit of the integral is finite. This means that the integral can be defined for any real value of x, from 0 to infinity. The value of p must be greater than 1 in order for the integral to converge smaller as x approaches infinity .This is due to the fact that the denominator of the function,\(x(lnx)^p\), will become increasingly smaller as x approaches infinity. Therefore, the integral of the function \(37/(x(lnx)^p)\)converges for values of p greater than 1.

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