The diameter of a cone's circular base is 8 inches. The height of the cone is 10 inches.

What is the volume of the cone?

Use π≈3.14.

Therefore, the probability that half of the six employees score more than 85 and half less is 0.5469.

To find the probability that half of the employees score more than 85 and half less, we can use the binomial distribution.

Let X be the number of employees who score more than 85 out of the 6 employees. Then, X follows a binomial distribution with n=6 and p=0.5 (since we want half of the employees to score more than 85).

To get half the employees to score more than 85, we need X to be either 2 or 3 (since there are only 6 employees). Thus, we want to find the probability P(X=2 or X=3).

Using the binomial probability formula, we get:

P(X=2 or X=3) = P(X=2) + P(X=3)

= (6 choose 2)(0.5)^6 + (6 choose 3)(0.5)^6

= 0.2344 + 0.3125

= 0.5469

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Answer:

hope it helps

Step-by-step explanation:

23 is the right answer

Answer:

ans 37

Step-by-step explanation:

substract 61 - 24

Answer:

You go to Target. You buy a box of mints for $2.25. You also want to buy some packs of Goldfish for snacks. They each cost $1.50. You have $12.75 to spend. How many packs of Goldfish can you buy along with the box of mints?

The evaluate value of a definite integral \( I = \int_{0}^{1} ( 2x + x^{\frac{1}{3}}) dx\) is equals to the \( \frac{ 7}{4} \) .

An important factor in mathematics is the sum over a period of the area under the graph of a function or a new function whose result is the original function that is called integral. Two types of integral definite or indefinite. When limits of integral is known, it is called definite integral. We have a definite integral, \( I = \int_{0}^{1} ( 2x + x^{\frac{1}{3}}) dx\)

We have to evaluate this integral value.

Using linear property of an integral,

\( = \int_{0}^{1} 2x dx + \int_{0}^{1} x^{\frac{1}{3}} dx\)

Using the rule of integration, \(=[\frac{ 2x²}{2}]_{0}^{1} + \frac{x^{\frac{1}{3} + 1}}{ \frac{1}{3} + 1}]_{0}^{1}\)

\( = [\frac{ 2× 1²}{2}] + \frac{1^{\frac{4}{3}}}{ \frac{4}{3}}]\)

\( = (\frac{ 3}{4}] + 1 )\)

\( = \frac{ 7}{4} \)

Hence, required value is \( \frac{ 7}{4} \) .

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Complete question:

Evaluate the integral \( I = \int_{0}^{1} ( 2x + x^{\frac{1}{3}}) dx\).

\(\huge \sf༆ Answer ༄\)

As we know, Circumference of the circle can be expressed as :

\( \large \boxed{ \: \: \: \: \: \sf2\pi r \: \: \: \: \: }\)

where, r is the radius of the circle, now equate the expression with the given Circumference to find the Radius.

Therefore, it's radius is 2 feet.

Now, let's calculate its area using the formula ~

\( \large \boxed{ \: \: \: \: \: \: \sf \pi {r}^{2} \: \: \: \: \: \: }\)

plug the value of r (radius) as 2.

Area of circle is 12.96 ft²

Answer:

loss =Rs 56

Step-by-step explanation:

loss =cp-sp

Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.

We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.

The null hypothesis is that the population proportion is equal to 11.3%:

H0: p = 0.113

The alternative hypothesis is that the population proportion is greater than 11.3%:

Ha: p > 0.113

The sample proportion is P = 58/400

= 0.145

The standard error of the sample proportion is:

SE = √(p*(1-p)/n)

= √(0.113*(1-0.113)/400)

= 0.0197

The test statistic is:

z = (P - p) / SE

= (0.145 - 0.113) / 0.0197

= 1.6244

The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:

p-value = P(Z > 1.6244)

= 0.0515 (using a standard normal distribution table)

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The triangles formed by the path of the ball and the wall in the given diagram are similar triangles.

The point on the wall she should aim is; A. 7.8 feet away from point B

The possible diagram in the question is attached

Let x represent the distance from point B where the ball lands.

ΔCDE is similar to ΔABE, by Angle-Angle similarity postulate.

By trigonometric ratio, the tangent of the angles ∠CDE and ∠BAE are;

\(tan(\angle CDE) = \mathbf{\dfrac{20 - x}{25}}\)

\(tan(\angle BAE) = \mathbf{ \dfrac{x}{16}}\)

tan(∠CDE) = tan(∠BAE)

Therefore;

\(\dfrac{20 - x}{25} = \dfrac{x}{16}\)

Which gives;

16 × (20 - x) = 25·x

320 = 41·x

x = 320 ÷ 41 ≈ 7.8

The point on the wall she should aim if she's standing at point A is therefore;

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The solution of the given initial-value problem is: `x(t) = e^(2t) - 2e^t`

Given the differential equation is: `(d^2x)/(dt^2) - 3(dx)/(dt) - 2x = 0`

The given initial value is: `x(0) = -1` and

`(dx)/(dt)|_(t=0) = -3`

To solve the given initial-value problem, we assume that the solution is of the form

`x(t) = e^(rt)`

Such that the auxiliary equation can be written as:

`r^2 - 3r - 2 = 0`

By solving the quadratic equation, we get the roots as:

`r = 2, 1`

Therefore, the general solution of the given differential equation is:

`x(t) = c_1e^(2t) + c_2e^t`

Now, applying the initial condition `x(0) = -1`, we get:

`-1 = c_1 + c_2`....(1)

Also, applying the initial condition `(dx)/(dt)|_(t=0) = -3`,

we get:

`(dx)/(dt)|_(t=0) = 2c_1 + c_2 = -3`....(2)

Solving equations (1) and (2), we get: `c_1 = 1` and `c_2 = -2`

Therefore, the solution of the given initial-value problem is:

`x(t) = e^(2t) - 2e^t`.

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Answer:

4

Step-by-step explanation:

firstly you separate y

y=-x-1

which means that the slope is equal to -1

then you flip the slope so -1 over -1 which is equal 1

The equivalent expression of (a⁻⁷ . b⁻²)⁻⁹ is a⁶³b¹⁸

using the law of indices,

\((a^{x}) ^{y} = a^{x X y} =a^{xy}\)

Therefore, we multiply the inner exponent by the outer exponent.

(a⁻⁷ . b⁻²)⁻⁹ = a⁻⁷ ˣ ⁻⁹ b⁻² ˣ ⁻ ⁹

a⁻⁷ ˣ ⁻⁹ b⁻² ˣ ⁻ ⁹ = a⁶³b¹⁸

Therefore,

(a⁻⁷ . b⁻²)⁻⁹ =  a⁶³b¹⁸

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Answer:

4 feet × 16 feet × 25 feet

4 feet × 20 feet × 20 feet

and 4 feet × 40 feet × 10 feet

Answer:

v = 2

Step-by-step explanation:

So we are trying to solve for v in the given equation.

6(5 - 8v) + 12 = -54

Distribute the 6 on the left side.

30 - 48v + 12 = -54

Combine like terms.

42 - 48v = -54

Subtract 42 from both sides.

-48v = -54 - 42

Combine like terms.

-48v = -96

Divide both sides by -48.

v = 2

And now we have the answer of v = 2.

I hope you find my answer helpful.

Answer:

d

Step-by-step explanation:

Answer:

when x=2

-2×2+4y=16

4y=16+4

y=20/4=5

again

x=-8

-2×-8+4y=16

4y=16-16

y=0/4=0

Answer:21.9

Step-by-step explanation:

Answer:

yes, true

Step-by-step explanation:

Answer:

the answer is true because they dont intersect

Step-by-step explanation:

Assuming that 6.8 means the area of the triangle, the height would be 1.94.

If this is incorrect, please, don't refrain to tell me. Thank you.

For a, 7/-8 and -(7/8) are both equivalent to -7/8 because they have 1 negative sign. It doesn't matter where it is on the fraction as long as there is only 1 negative sign.

For b, -2/-3 is equivalent to 2/3 because the double negatives cancel each other out to equal a positive.

Answer:

\(\frac{-7}{8}\) = \(-\frac{7}{8}\)

\(\frac{2}{3}\) = \(\frac{-2}{-3}\)

Step-by-step explanation:

the negative can just move down on -7

the negatives cancel out on -2/-3 to make 2/3

Answer:

The maximum height that the rocket will reach is 271 feet.

Step-by-step explanation:

We first calculate the time, t it takes the rocket to reach maximum height from v = u - gt. Since u = initial velocity = 128 ft/s, v = velocity at maximum height = 0  ft/s and g = acceleration due to gravity = 32 ft/s².

So, v = u - gt.

t = (u - v)/g

= (128 ft/s - 0 ft/s)/32 ft/s²

= 128 ft/s ÷ 32 ft/s²

= 4 s.

We calculate the maximum height from

y - y₀ = ut - 1/2gt² where y₀ = 15 ft and all other variables are as above.

Substituting these values into the equation, we have

y - y₀ = (u - 1/2gt)t

y - 15 ft = (128 ft/s - 1/2 × 32 ft/s² × 4 s) × 4 s

y - 15 ft = (128 ft/s - 64 ft/s)4 s

y - 15 ft = 64 ft/s × 4 s

y - 15 ft = 256 ft

y = 256 ft + 15 ft

y = 271 ft

So, the maximum height that the rocket will reach is 271 feet.

If the length of one side of the rhombus is 6m and the radius of the rhombus as 4 m then the area of the rhombus is 24 m².

What is the area of the rhombus?

The Area of a Rhombus = A = ½ × d1 × d2,

Where d1 and d2 are the diagonals of the rhombus.

The area of a rhombus can be found using the formula:

Area = (diagonal 1 x diagonal 2) / 2

or

Area = (base x height) / 2

We are given the length of one side of the rhombus as 6 m, which means the length of the other side is also 6 m since all sides of a rhombus are congruent. We are also given the radius of the rhombus as 4 m, which is half the length of the diagonal.

Using the Pythagorean theorem, we can find the length of the other diagonal:

diagonal 2 = 2(radius) = 2(4) = 8 m

Now we can use the formula to find the area of the rhombus:

Area = (diagonal 1 x diagonal 2) / 2

Area = (6 m x 8 m) / 2

Area = 24 m²

Therefore, the area of the rhombus is 24 m².

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Answer:

f(3) ≈ 17.310

Step-by-step explanation:

e = 2.71828

Step 1: Define

f(x) = e2x - 1 + 2

x = 3

Step 2: Substitute and evaluate

f(3) = e2(3) - 1 + 2

f(3) = 6e + 1

f(3) = 16.3097 + 1

f(3) = 17.3097

f(3) ≈ 17.310

The value of (f . g)(x ) = 6x³-13x²+6x and the function represents the area of the rectangle

Area is the measure of a region's size on a surface. The area of a rectangle is expressed as;

A = l×w

where l is the length and w is the width.

length = f(x) = 3x²-2x

width = g(x) = 2x-3

therefore area =( f . g)(x)

= (3x²-2x)(2x-3)

3x²(2x-3) -2x( 2x-3)

6x³-9x²-4x²+6x

= 6x³-13x²+6x.

Therefore the value of (f . g) (x) is 6x³-13x²+6x.

and the function represents the area of the rectangle.

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The required image of the given point (12, -4) dilation by a scale factor of 1/4 and centered at the origin is (-3, 1)

Coordinate, is represented as the values on the x-axis and y-axis of the graph

Given that,

To determine the image of  (12, -4) after dilation by a scale factor of 1/4 centered at the origin.

For the point, we have a dilation factor of 1/4,

So dilated coordinate,

= (1/4(12),   1/4(-1))

= (3, -1)

To form the image across the origin

= - (3, -1)

= (-3, 1)

Hence, the required image of the given point (12, -4) with a scale factor of 1/4 and centered at the origin is (-3, 1)

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Answer:

1/2

Step-by-step explanation:

1/2 simply because when long division is used to convert it in decimal, it is gonna be the largset

Based on a mean of 3 calls for service per day, there is a 22.4% probability of exactly two calls and a 79.9% probability of receiving more than one call in a randomly selected day.

In order to calculate the probabilities, we will use the Poisson distribution, which is commonly used to model the number of events occurring in a fixed interval of time or space when these events occur with a known constant mean rate.

i. To find the probability of exactly two calls for service in a randomly selected day, we can use the Poisson probability mass function (PMF). The PMF for the Poisson distribution is given by:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where:

P(x; λ) represents the probability of x events occurring given a mean rate of λ.

e is the base of the natural logarithm, approximately 2.71828.

λ is the average number of events occurring per interval.

x is the number of events we are interested in (in this case, two calls for service).

Substituting the values into the formula, we get:

P(x = 2; λ = 3) = (e^(-3) * 3^2) / 2!

Calculating this expression, we find that P(x = 2; λ = 3) ≈ 0.224 or 22.4%.

Therefore, the probability of exactly two calls for service being received in a randomly selected day is approximately 0.224 or 22.4%.

ii. To find the probability of more than one call for service in a randomly selected day, we can use the complementary probability. The complementary probability is equal to 1 minus the probability of zero or one call for service.

P(x > 1; λ = 3) = 1 - [P(x = 0; λ = 3) + P(x = 1; λ = 3)]

Using the Poisson PMF, we can calculate:

P(x > 1; λ = 3) ≈ 1 - [(e^(-3) * 3^0) / 0!) - (e^(-3) * 3^1) / 1!]

Simplifying this expression, we find that P(x > 1; λ = 3) ≈ 0.799 or 79.9%.

Therefore, the probability of receiving more than one call for service in a randomly selected day is approximately 0.799 or 79.9%.

These probabilities are derived using the Poisson distribution, which is suitable for modeling the occurrence of events with a known average rate.

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For the required value of the given complex numbers z₁z₂ = 32(cos 255° + isin 255°).

Complex numbers are those that expand on the idea of real numbers by incorporating an illogical element.

The formula for a complex number is "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit, which is equal to the square root of -1.

"A" stands for the complex number's real component, and "b" stands for the imaginary component.

We multiply the magnitudes of two complex numbers and add their arguments to determine their product.

Let's compute z₁z₂ with the supplied values.

Given:

z₁ = 8(cos 45° + isin 45°)

z₂ = 4(cos 210° + isin 210°)

We add the arguments and multiply the magnitudes to find z₁z₂:

Magnitude of z₁ = 8

Magnitude of z₂ = 4

Argument of z₁ = 45°

Argument of z₂ = 210°

Now, let's calculate z₁z₂:

Magnitude of z₁z₂ = (Magnitude of z₁) × (Magnitude of z₂) = 8 × 4 = 32

Argument of z₁z₂ = (Argument of z₁) + (Argument of z₂) = 45° + 210° = 255°

Therefore, z₁z₂ = 32(cos 255° + isin 255°).

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The correct question =

Given z₁ = 8(cos 45° + isin 45°) and z₂ = 4(cos 210° + isin 210°), what is z₁z₂?