work out the size of angle x.

A sample is one that is representative of the population, selected at random, and large enough to provide accurate data.

A sample is a smaller group that is representative of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.

For example, if a researcher is studying the impact of inflation on US families. It is not feasible to reach the whole of the families in the US. So, the researcher would use a representative group of US families. This is known as a sample.

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The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

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Answer:

Soda tax — Should people have to pay an extra tax on soda or junk food?

Your conversation should include the following:

A total of at least five entries for each side (10 entries total—two to three sentences each)

Accurate facts used to support both perspectives

At least two properly cited sources used for research

Step-by-step explanation:

The value of cos Θ /2 and tan Θ /2 can be found to be:

We are given that  90° < Θ < 180°,  which means that theta would be in the second quadrant.

We can therefore use half - angle formulas to find cos Θ /2 and tan Θ /2.

To find cos Θ /2, we have:

cos(Θ/2) = ±√((1 + cos(Θ))/2)

cos(Θ/2) = ±√((1 - √(4/13))/2)

cos(Θ/2) = √((1 - √(4/13))/2)

To find tan Θ /2, we have:

tan(Θ/2) = ±√((1 - cos(Θ))/(1 + cos(Θ)))

tan(Θ/2) = ±√((1 + √(4/13))/(1 - √(4/13)))

tan(Θ/2) = √((1 + √(4/13))/(1 - √(4/13)))

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The full question is:

Suppose that tan Θ = - 3/2 and 90 °< Θ < 180 °.

Find the exact values of cos Θ /2 and tan Θ /2

Answer:

It should be something like that :

we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

To compute n, we can use the formula:
n = ((zα/2)^2 * 2p*(1-p*)) / (ε^2)
Where zα/2 is the z-score associated with a confidence level of 1-α, p* is the probability of success for a binomial distribution, and ε is the margin of error.
Since we are given that the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 is at least 0.80, we can set α = 0.20 to find the corresponding z-score of 1.28.
Using p* = 1/2 as an upper bound for both P1 and P2, we can calculate the margin of error as:
ε = zα/2 * sqrt((p*(1-p*)) / n)
Plugging in the values, we get:
0.05 = 1.28 * sqrt((0.25) / n)
Solving for n, we get:
n = 501.76
Therefore, we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

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Alice says that the volume of the rectangular prism is greater than two times the volume of the triangular crystal.

The above statement is true.

The prism on the right is a rigid body whose two faces (called bases) are polygons. The bases of the regular prisms have the same size and shape and are parallel to each other. The remaining faces are rectangles perpendicular to the base.

The volume of a prism is defined as the amount of space the prism occupies. A prism is a solid three-dimensional shape with two equal sides and another side similar to a parallelogram. The units of volume of a prism are cubic meters, cubic centimeters, cubic inches, or cubic feet.

Rectangular Prism:

The volume of a rectangular prism is defined as the space occupied inside the rectangular prism. A rectangular prism is a polyhedron with two pairs of congruent and parallel bases. It has 6 faces (all rectangular), 12 sides and 8 vertices. Since a rectangular prism is a three-dimensional shape (three-dimensional shape), the unit of volume of a rectangular prism is cm3, m3, etc. In mathematics, a polyhedron with all these properties is called a cuboid.

According to the Question:

Given that:

Length = 26 millimeter

Width = 8.5 millimeter

Height = 07 millimeter.

Now,

Area of Rectangle = Length × Width

                              =  26 × 8.5 millimeter

                              = 221 millimeter square.

Now,

Volume of rectangular Prism = Area of rectangle × height

                                                =  221 × 07

                                                = 1547 cubic millimeter.

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Answer:

hope this helps

Step-by-step explanation:

6.1 represent the lbs that a child gains every x years

10 represents the starting weight of a newborn

The volume of a cylinder is equal to the area of the base times the height. The area of the base is pi * r^2, where r is the radius. In this case, the radius is 5 meters, so the area of the base is pi * 5^2 = 25pi. The height is 15 meters, so the volume of the cylinder is 25pi * 15 = 375pi cubic meters.

Pi is approximately equal to 3.14, so the volume of the cylinder is approximately equal to 375 * 3.14 = 1177.5 cubic meters.

To the nearest tenth, the volume of the cylinder is 1178 cubic meters.

Here are the steps in more detail:

- Find the area of the base: pi * r^2 = pi * 5^2 = 25pi

- Multiply the area of the base by the height: 25pi * 15 = 375pi

- Approximate pi to 3.14: 375pi * 3.14 = 1177.5

- Round to the nearest tenth: 1177.5 rounded to the nearest tenth is 1178

The volume of the cylinder is 1178.6 m³.

We know that,

the volume of a cylinder = π×r²×h

where r is the radius of the base of the cylinder,

and, h is the height of the cylinder.

Now, according to the question,

the radius of the base of the cylinder = 5m,

the height of the cylinder is 15 m

Putting the value of base and height in the above formula for the volume of the cylinder, we get,

the volume of the cylinder = π × r²×h

                                               = 22/7 × 5² × 15

                                               = 1178.6

Hence, the volume of the cylinder is 1178.6 m³.

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The complete question is -

Find the volume of the cylinder. Round your answer to the nearest tenth.

The radius of the cylinder is 5 meters and its height is 15 meters.

The volume of the cylinder is about ? cubic meters.

Answer:

$126

Step-by-step explanation:

The plot of land is worth $18,000 and the tax on the land is $0.70 per $100. You would divide 18000 by 100 which is 180. Then you would multiply 180*0.70 which is $126.

Step-by-step explanation:

Here, given that;

The total value of land us $18000.00

tax per $100.00 is $0.70

now,

$100.00 taxes $0.70

$18000.00 taxes ($18000.00÷100)/$0.70 (as in question given that the tax is charged in each $100)

= $126.

is the required tax amount.

Hope it helps..

Answer:

option a. similar;AA similarity; triangle plm

The correct Numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.

The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:

9 x 4 + (3 − 2)

To solve this expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Evaluate the subtraction inside the parentheses:

3 − 2 = 1

Step 2: Rewrite the expression with the simplified value:

9 x 4 + 1

Step 3: Perform the multiplication:

9 x 4 = 36

Step 4: Add the products:

36 + 1 = 37

Therefore, the correct numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.

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Answer:

3\(\sqrt{11}\) + 2\(\sqrt{11}\) = 5\(\sqrt{11}\)

Step-by-step explanation:

\(\sqrt{99}\) = \(\sqrt{(9)(11) }\) = 3 \(\sqrt{11}\)    (separate perfect squares using factoring)

\(\sqrt{44}\) = \(\sqrt{(4)(11)}\) = 2 \(\sqrt{11}\)

3 \(\sqrt{11}\) + 2 \(\sqrt{11}\) = 5 \(\sqrt{11}\)   (add like terms. Think of the \(\sqrt{11}\) like x's.)

                                        (Just add the coefficients)  

Answer:

5\(\sqrt{11}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b\) = \(\sqrt{ab}\)

Simplifying the radicals

\(\sqrt{99}\)

= \(\sqrt{9(11)}\)

= \(\sqrt{9}\) × \(\sqrt{11}\)

= 3\(\sqrt{11}\)

-----------------------

\(\sqrt{44}\)

= \(\sqrt{4(11)}\)

= \(\sqrt{4}\) × \(\sqrt{11}\)

= 2\(\sqrt{11}\)

Then

\(\sqrt{99}\) + \(\sqrt{44}\)

= 3\(\sqrt{11}\) + 2\(\sqrt{11}\)

= 5\(\sqrt{11}\)

with a = 5 and b = 11

Answer:

  443,232,000 lb

Step-by-step explanation:

You want the weight in pounds of a pyramid 180 yd square and 90 yd high made of material weighing 456 lb/cubic yard.

The volume of the pyramid is given by the formula ...

  V = 1/3s²h . . . . . . . . where s is the side length and h is the height

  V = 1/3(180 yd)²(90 yd) = 972000 yd³

At a weight of 456 pounds per cubic yard, the weight of the pyramid is estimated to be ...

  (456 lb/yd³)×(972,000 yd³) = 443,232,000 lb

The pyramid weighs about 443,232,000 pounds.

__

Additional comment

At 456 lb per cubic yard, the stone is less dense than most wood and will float high in water.

i didn’t realize u were chill like that

Answer:

the answer is C

Step-by-step explanation:

Step-by-step explanation:

If x = 6 and y = 4. Substitute x and y in the expression.

4x+y

4(6)+(4)

24+4

28

2y²

2(6)²

2(36)

72

( x - y )²

(6+4)²

(10)²

100

Answer:

3-5x

Step-by-step explanation:

Answer:

Direction: Opens Up

Vertex:

(

4

,

−

18

)

(4,-18)

Focus:

(

4

,

−

71

4

)

(4,-714)

Axis of Symmetry:

x

=

4

x=4

Directrix:

y

=

−

73

4

y=-734

Select a few

x

x values, and plug them into the equation to find the corresponding

y

y values. The

x

x values should be selected around the vertex.x

y

2

−

14

3

−

17

4

−

18

5

−

17

6

−

14

xy2-143-174-185-176-14

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex:

(

4

,

−

18

)

(4,-18)

Focus:

(

4

,

−

71

4

)

(4,-714)

Axis of Symmetry:

x

=

4

x=4

Directrix:

y

=

−

73

4

y=-734

x

y

2

−

14

3

−

17

4

−

18

5

−

17

6

−

14

xy2-143-174-185-176-14

image of graph

Using inequality, the number of weeks he will be able to purchase his guitar is after 14 weeks.

He has 62$ and wants a new guitar. He will need at least $200 plus 7% sales tax.

Therefore,

let calculate the sale tax

sale tax = 7% of 200 = 7 / 100 ×200 = 14 dollars

Langston makes $22 dollars a week but always puts half into savings for college, Therefore, he only save 11 dollars for purchase of his guitar.

Hence, the number of weeks he will save to be able to purchase the guitar can be computed as follows;

amount + sales tax = 200 + 14 = 214

Using inequality

62 +  11x ≥ 214

11x ≥ 214 - 62

11x ≥ 152

x ≥ 152 / 11

x ≥ 13.8181818182

x ≥ 13

He will be able to purchase his guitar after 14 weeks.  

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Answer:

7776 outcomes

Step-by-step explanation:

To get the total number of outcomes we multiply the total number of possibilities for each roll. Since there are 5 rolls, the total number of outcomes will be:

6 x 6 x 6 x 6 x 6 = 7776 outcomes

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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The probability is the area under the normal distribution curve between -2 and 2 standard deviations.

To calculate the probability that the sample mean would differ from the population mean by less than 2 or more standard deviations, we need to use the concept of the standard error and the normal distribution.

Given:

Mean diameter of the current steel bolts = 145 meters

Standard deviation (σ) of the current steel bolts (population) = 40.56 meters

Desired difference from the population mean = 2 standard deviations

Step 1: Calculate the standard error (SE):

The standard error (SE) is calculated as σ / sqrt(n), where σ is the population standard deviation and n is the sample size.

Since the sample size (n) is not given, we'll assume a large enough sample size such that the central limit theorem applies. In such cases, we can use a sample size of at least 30 to approximate the standard error.

Step 2: Calculate the z-score:

The z-score represents the number of standard deviations a value is from the mean. In this case, we want to calculate the probability of the sample mean differing from the population mean by less than 2 standard deviations.

The z-score is calculated as (x - μ) / SE, where x is the desired difference (2 standard deviations) and μ is the population mean.

Step 3: Find the probability:

We can use the z-score to find the probability using a standard normal distribution table or a statistical software.

The probability is the area under the normal distribution curve between -2 and 2 standard deviations.

Please note that if the sample size is small (less than 30) or the population distribution is not approximately normal, a different approach may be required, such as using the t-distribution instead of the normal distribution.

Perform the calculations using the provided values and substitute the appropriate values into the equations to determine the probability that the sample mean would differ from the population mean by less than 2 standard deviations.

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Answer:

by calculating per capita income

Answer:

20 hours later.

Step-by-step explanation:

If all three buses leave at the same time, they will arrive back in the park in 20 hours. If we want them to arrive at the exact same time, we need to find the least common multiple of all the numbers because the time it takes to get back into the park are different and without using least common multiple they would all arrive at different times. So, the least common multiple is 20 becuase they all have 20 as a multiple. In 20 hours all of the buses will arive back in the park at the same time.

Hope this helps

:)

Answer:

12,000m

Step-by-step explanation:

distance=speed×time

1500×8=12000m

Answer:

12,000

Step-by-step explanation:

1500m\s

8s

1500×8

= 12,000

We are asked to determine the angle "x" that will produce arclength of 6 inches in a circle with a radius of 4 inches. To do that we will use the following formula:

Where:

Now, we solve for the angle by dividing both sides by "r":

Now, we plug in the values:

Now, we solve the operations:

Therefore, the angle is 1.5 radians.

Answer:

10

Step-by-step explanation:

This is an arithmetic sequence.  The common difference is -6, and the first term is 52.

a = 52 − 6(n − 1)

When n = 8:

a = 52 − 6(8 − 1)

a = 52 − 42

a = 10

To determine when the rate of change of population is fastest, we need to analyze the behavior of the derivative dP/dt. Since the population is at its carrying capacity when P = 75, the rate of change of population is fastest when P is farthest from its carrying capacity. In this case, it would be at the lowest population value, which is P = 0.

The differential equation given is:

dP/dt = 2(1 - P/150)P

To find the carrying capacity, we need to determine the equilibrium point of the population, where the rate of change is zero (i.e., dP/dt = 0).

Setting dP/dt = 0 in the differential equation:

0 = 2(1 - P/150)P

Simplifying:

0 = 2P - \(2P^2\)/150

0 = P - \(P^2\)/75

Rearranging:

\(P^2\)/75 - P = 0

Factoring out P:

P(P/75 - 1) = 0

This equation is satisfied when either P = 0 or P/75 - 1 = 0.

For P = 0, the population is at its lowest and there is no growth.

For P/75 - 1 = 0, solving for P:

P/75 = 1

P = 75

So, the carrying capacity of the population, in this case, is 75.

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find the carrying capacity of differential equation: dP/dt= 2(1-P/150)P Suppose p(t) represents population of species x at time t years. what would be the population when the rate of change of population is fastest?

Answer:

width = 9/2 inches, length = 18 inches

Step-by-step explanation:

Step-by-step explanation:

l = length

w = width

l×w = 81 in²

l = 2w + 9

we can use the identity of the second equation in the first equation :

(2w + 9)×w = 81

2w² + 9w = 81

2w² + 9w - 81 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = w

a = 2

b = 9

c = -81

w = (-9 ± sqrt(9² - 4×2×-81))/(2×2) =

= (-9 ± sqrt(81 + 648))/4 =

= (-9 ± sqrt(729))/4 = (-9 ± 27)/4

w1 = (-9 + 27)/4 = 18/4 = 9/2 in

w2 = (-9 - 27)/4 = -36/4 = -9

a negative solution for a side length does not make any sense, so, width = 9/2 in is the only valid solution.

l = 2w + 9 = 2×9/2 + 9 = 9+9 = 18 in

so, the last answer option is correct.