20. A tank in the shape of a hemisphere has a diameter of
20 feet. If the liquid that fills the tank has a density of 60.3
pounds per cubic foot, what is the total weight of the liquid
in the tank, to the nearest full pound?

Answer:

Its A

Step-by-step explanation:

The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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The dimensions of the base are 180 feet in length and 165 feet in width.

The whole length of any closed shape's boundary is known as its perimeter. Let's use an illustration to try to comprehend this. You may have a sizable square-shaped farm, for instance. You now decide to fence your farm in order to protect it from stray animals. Finding the entire length of the farm's boundary is as simple as multiplying the length of one side of the farm by 4. There are a lot of situations like this when we can be applying the perimeter-finding notion without even realizing it.

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The maximum likelihood estimator for p is: X/N

Let X1, X2, ..., Xn be n independent Bernoulli trials with success probability p and let N be a known positive integer. The number of successes observed is denoted by X = X1 + X2 + ... + Xn, and we want to estimate p.

Suppose that N is known and only success probability p is unknown. Compute the method of moment estimator and the maximum likelihood estimator for p.

The sample mean is a method-of-moments estimator of the population mean. This is one way of defining the method of moments. In this particular case, the population mean is equal to p, which is what we want to estimate.

The sample mean is equal to X / N.

Therefore, the method of moments estimator for p is:X/N

Maximum likelihood estimator

The probability mass function of X is given by:

\(P(X = k) = C(N,k) * pk * (1 - p) {}^{(N-k)} \)

where C(N,k) is the binomial coefficient (N choose k).

The log-likelihood function is given by:

\(ln(L(p)) = ln[C(N,X) * px * (1 - p) {}^{(N-X} ]\)

where X is a constant. Taking the derivative of this function with respect to p and setting it equal to zero, we get:

p = X / N

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a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.

b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.

c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.

a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.

b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.

c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.

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Answer:

25 workmen

Step-by-step explanation:

C = work completion

Half the number of days

6/5 (= 12/10) the hrs/day

½ × 6/5 × C = ⅗C

C/(⅗C) = 5/3

5/3 × 15 = 25

Answer:

a, b, e,f

Step-by-step explanation:

i dont have one

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Given that x follows a binomial distribution with parameters n = 12 and p = 0.15, we can use the following formulas to find the expected value E(x) and variance Var(x):

E(x) = n * p

Var(x) = n * p * (1 - p)

Substituting n = 12 and p = 0.15, we get:

E(x) = 12 * 0.15 = 1.8

Var(x) = 12 * 0.15 * (1 - 0.15) = 1.53

Therefore, the expected value of x is E(x) = 1.8, and the variance of x is Var(x) = 1.53.

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Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol \(^nC_{r}\).

There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.

So the 3 software engineers =3! ways, 2 nurses =2! ways,

doctor =1! way , 2 technicians =2! ways.

We must determine how many different configurations are possible so that no two pieces of software may coexist.

In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.

\(We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.\)

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

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Answer:

Step-by-step explanation:

First you determine the variables x and y as:

x: the value for student tickets

y: the value for chaperone tickets.

Knowing that student tickets cost $ 2 more than companion tickets, it is represented by the equation:

x= y +2

On the other hand, there were 59 students and 6 companions. And the total cost of admission for the group was $ 508, that is to say that what all the students and the companions have paid adds up to $ 508. Expressed by an equation:

59x + 6y = 508

Then the system of equations to solve and thus obtain the price of a student ticket and the price of a companion ticket is:

\(\left \{ {{x=y+2} \atop {59x+6y=508}} \right.\)

Solving for x, the price of a student ticket:

Rearranging  the first equation,

y = x - 2

Replacing in the second equation and solving for x:

59*x + 6*(x -2)=508

59*x + 6*x -12=508

65*x -12=508

65*x= 508 +12

65*x= 520

\(x=\frac{520}{65}\)

x=8

The cost of a student ticket is 8$

The solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

To simplify the equation 3(x-6) - 1/2(8x+10) = -25, we can start by applying the distributive property and then combining like terms.

First, let's distribute the 3 and the -1/2 to the terms inside the parentheses:

3(x-6) - 1/2(8x+10) = 3x - 18 - (4x + 5)

Now, let's simplify further by combining like terms:

3x - 18 - 4x - 5 = -x - 23

So, the simplified equation is -x - 23 = -25.

To solve for x, we can isolate the variable by adding 23 to both sides of the equation:

-x - 23 + 23 = -25 + 23

This simplifies to:

-x = -2

Finally, we can solve for x by multiplying both sides of the equation by -1:

(-1)(-x) = (-1)(-2)

This gives us:

x = 2

Therefore, the solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

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Answer: B

Step by Step

5y + 6 = -3X

5y = -3X - 6

Y = -3/5X -6/5

Perpedicular is the flip of your slope so -3/5 becomes 5/3X

Step-by-step explanation:

1. us

p- parenthesis

e-exponents

m-multiplication

d-division

a -addition

s,-subtraction

ul

use that and go in order

The solution to the inequality 2|3x – 4| – 8 < 8 will be x < 4.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given inequality function is 2|3x – 4| – 8 < 8. The inequality will be solved as:-

2|3x – 4| – 8 < 8

6x - 8 - 8 < 8

6x - 16 < 8

6x < 24

x < 4

Therefore, the solution to the inequality 2|3x – 4| – 8 < 8 will be x < 4.

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piece of cake, it's $0.37

all you have to do is divide $5.92 by 16 to figure out price per pound.

\(\frac{5.92}{16}=0.37\)

to check your answer multiply 0.37 by 16 and you'll get 5.92

note: if you were to divide 16 by $5.92 (inverse operation) you would be solving for pounds per each dollar, and the question asks to find what she paid for each pound not how many pounds she bought for each dollar she spent; since you're trying to figure out a certain price so you also divide by a price. I hope this makes sense

Answer:

Step-by-step explanation:

the answer willbe 80

Answer:

Luna has half a cup (1/2) (0.5) left in her cup

Step-by-step explanation:

3/4+3/8=1.125 1.125-5/8 of a cup=0.5

L " (x - 1) dx integrals gives the volume of the solid generated by revolving R about the y-axis

The integration or antiderivative processes can be used to determine the curve's area under it. For this, we require the curve's equation (y = f(x)), the curve's axis boundary, and the curve's border limitations.

Let R be the area in the first quadrant enclosed by the hyperbolas xy = 1 and xy = 3, the lines y = x and y = 3x, and the lines xy = 1. The third quadrant is also constrained by those four curves, which we are ignoring. xy dA. = 1 v .

Let R be the region in the first quadrant bounded by the graph of y = Vx - 1. the x-axis, and the vertical line * = 10.

= L " (x - 1) dx integrals gives the volume of the solid generated by revolving R about the y-axis

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the function y = 5x^2+6x, we need to find dy/dt when x = -1 and dt/dx = 2. To find dy/dt.  which states that:

dy/dt = (dy/dx) * (dx/dt)We are given that dt/dy = -1/8.

dt/dx = 2. To find dy/dx, we differentiate

y = 5x^2+6x with respect to

x: dy/dx = 10x + 6

So when x = -1,

dy/dx = -4.Now we can find dy/dt by substituting the values of dy/dx and dt/dx in the above equation:

dy/dt = (dy/dx) *

(dx/dt) = (-4) * 2 = -8

We are given the function: y = 5x^2+6xWe need to find dy/dt when

x = -1 and dt/dx = 2.To find dy/dt, we use the chain rule of differentiation, which states that:

dy/dt = (dy/dx) * (dx/dt)We are given that

dt/dx = 2. To find dy/dx, we differentiate

y = 5x^2+6x with respect to x:

dy/dx = 10x + 6Now we can find dy/dt by substituting the values of dy/dx and dt/dx in the above equation: dy/dt = (dy/dx) * (dx/dt) = (-4) * 2 = -8

Therefore, dt/dy = -1/8.

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Answer:

4/7

Step-by-step explanation:

32:56

32÷2=16

56÷2=28

16:28

16÷2=8

28÷2=14

8:14

8÷2=4

14÷2=7

4:7

32:56 ~ 32/56

=4/7

The area in units of square meter is 2,090,318.4 sq cm,  under the given condition that  a house has a floor area of 2,250 square feet. So , the correct option from the following is  Option B.

To convert 2,250 square feet to square centimeters, we can use the conversion factor of 1 square foot = 929.0304 square centimeters⁵. Therefore,

2,250 sq ft = 2,250 x 929.0304 sq cm/ sq ft = 2,090,318.4 sq cm.

The area in units of square meter is 2,090,318.4 sq cm,  under the given condition that  a house has a floor area of 2,250 square feet. So , the correct option from the following is  Option B.

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Option A, p V q is the correct answer. We can also say it as p union q.

What do you mean by union in mathematics?

The set containing all the elements in a collection of sets is referred to as the union (denoted by ) in set theory. It is one of the fundamental operations that allows sets to be joined together and connected to one another. A union of zero (0) sets is referred to as a nullary union, because it is by definition equivalent to the empty set.

The diagram shown below represents two statements which are p and q.

Here in the diagram,

A covers the region in which only p is true.

B covers the region in which both p and q are true.

C covers the region in which only q is true.

The combine region of A, B, and C covers the region in which either p is true or q is true.

Therefore the region of A, B, and C is the union of p and q. It can be written as p v q or p ∪ q.

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According to the property of parallelogram, Angle ABC is right angle.

Given:In □ABCD is quadrilateral

AB=DC andAD=BC

To prove: Angle ABC is right angle

Proof: in △ABC and △ADC

AD=BC [Given]

AB=DC [Given]

AC=AC [Common side]

thus, By SSS property △ADC≅△ACB

∴∠DAC=∠DCA

∴AB∣∣DC

In△ABD and △DCB

DB=DB [Common side]

AD=BC [Given]

AB=DC [Given]

Thus, △ABD≅△DCB

AD∣∣BC

Since AB∣∣DC and AD∣∣BC, △ABCD is parallelogram

Therefore, Angle ABC is right angle.

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Answer:

x-3 is cancelled and just one remains in numerator.

Answer:

60%

Step-by-step explanation: