The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?

Answer:

4 and 8

Step-by-step explanation:

x1 = 4

x2 = 8

To find the length and width of a rectangle given its area and the relationship between its dimensions, set up and solve an equation by following the step-by-step process.

Given: The width of a rectangle is 3 inches less than its length and the area is 340 square inches.
To solve: Let the length be 'x' inches, then the width is 'x - 3' inches. Set up the equation 'x(x - 3) = 340', solve for 'x' to find the length and width.

Step-by-step:

Answer:

Ming says that 0.24 > 14

1

4

because 0.24 = 24

2

4

. Which best explains Ming's error?

Step-by-step explanation:

Answer and explanation:

Given : Vowels a,e,i,o or u.

To find : How many three-letter codes can we make using only vowels ?

Solution :

1) If we assume that repetition is allowed then

The three letter code can form

[tex]5\times 5\times 5=125[/tex] ways

Number of three-letter codes can we make using only vowels is 125.

2) If we assume that repetition is not allowed then

The three letter code can form

[tex]5\times 4\times 3=60[/tex] ways

Number of three-letter codes can we make using only vowels is 60.

The expression for (f + g)(x) is [tex]\rm 5x^3+2x-1[/tex] and this can be determined by using the arithmetic operations and the given data.

Given :

The following steps can be used in order to determine the value of (f + g)(x):

Step 1 - Write the given functions.

[tex]\rm f(x) = 5x^3-2[/tex]     --- (1)

[tex]\rm g(x) = 2x + 1[/tex]      --- (2)

Step 2 - Now, to determine the value of (f + g)(x), add both function f(x) and g(x).

f(x) + g(x) = (f + g)(x)

Step 3 - Substitute the value of f(x) and g(x) in the above expression.

[tex]\rm (f + g)(x) = 5x^3-2+2x+1[/tex]

Step 4 - Simplify the above expression.

[tex]\rm (f + g)(x) = 5x^3+2x-1[/tex]

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Using the binomial distribution, it is found that there is a 0.1296 = 12.96% probability that he makes all 4 shots.

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

For each throw, the player either makes it or misses it. The probability of making each throw is the same, independent of other throws, thus, the binomial distribution is used to solve this question.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, with X having two possible outcomes.

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

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

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

And p is the probability of a success on a single trial.

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

[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]

0.1296 = 12.96% probability that he makes all 4 shots.

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The population of the small town percent decreased by approximately 8.4%.

To find the percent decrease in the population of the small town, we can use the formula for percent decrease:

Percent Decrease = [(Initial Value - Final Value) / Initial Value] * 100

Given that the initial population was 983 and the final population was 901, we can plug these values into the formula:

Percent Decrease = [(983 - 901) / 983] * 100

Now, calculate the numerator:

Percent Decrease = [82 / 983] * 100

Divide and multiply:

Percent Decrease = 0.0835 * 100

Now, calculate the percent decrease to the nearest tenth of a percent:

Percent Decrease ≈ 8.4%

So, the population of the small town decreased by approximately 8.4%.

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Final answer:

The reported probability of 1 in 101,270 for matching all four lotto numbers is equivalent to a decimal probability of approximately 0.00000987.

Explanation:

The Louisiana Lottery Commission's lotto game entails participants matching all 4 numbers out of a pool of 41. The reported probability of achieving this feat is 1 in 101,270. To express this probability, we utilize the ratio of successful outcomes to total possible outcomes. Consequently, the probability of matching all four numbers is 1/101,270, equivalent to approximately 0.00000987 in decimal form. This minute probability underscores the challenging nature of the lotto game, highlighting the rarity of successfully predicting and matching the specified set of numbers within the given range.

Answer:

18.00

Step-by-step explanation:

60+40=100

(a)  Volume of  1st cup  =  (1/3)pi *(4/2)^2 * 8  =   32/3 pi in^3

 scoops  =  (2000/3)pi / ( 32/3) pi  =  2000/32  = 62.5  =  63

(b)  Volume of  2nd cup  =  (1/3)pi *(8/2)^2 * 8  =   128/3 pi in^3

scoops  =  (2000/3)pi / ( 128/3) pi  =  2000/128  = 15.625  =  16

that ratio means for every 7 boys there are 8 girls

 so 42 boys / 7 = 6

now 6*8 = 48

 there are 48 girls

Hudson earned $880 at pizza deliveries and $520 at mowing the lawn.

A System of Linear Equations is when we have two or more linear equations working together.

Given that, Hudson mowed lawns during the day and worked at a pizza place in the evenings. Hudson earned a total of $1,400. also he earned $360 more at the pizza place than mowing lawns

Let he earn x at deliveries and y at mowing,

Therefore, establishing a system of equations,

x+y = 1400

x-y = 360

Adding both the equations,

2x = 1760

x = 880

y = 1400-880

y = 520

Hence, Hudson earned $880 at pizza deliveries and $520 at mowing the lawn.

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the answer is c.6 i just took the test.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given data is:

56 32 48 52 51 53 48 38 35 42 40 46 54 50

In order to get the value of the upper quartile, first arrange he given data in ascending form, we get

32, 35, 38, 40, 42, 46, 48, 48, 50, 52, 53, 54, 56

The upper quartile is:48, 50, 52, 53, 54, 56

The value of upper quartile is given as:

[tex]\frac{52+53}{2}[/tex]

=[tex]\frac{105}{2}[/tex]

=[tex]52.5[/tex]

Thus, the value of the upper quartile will be 52.5.

To find the height of the rectangular prism, divide the volume by the area of the base.

To find the height of the rectangular prism, we need to divide the volume by the area of the base. The formula for the volume of a rectangular prism is V = lwh, where l, w, and h represent the length, width, and height, respectively. The formula for the area of the base is A = lw.

In this case, the volume is given as (x3-3x2+5x-3) and the area of the base is (x -2). So, we need to divide the volume by the area of the base, which gives us:

(x3-3x2+5x-3)/(x -2).

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Final answer:

The greatest common factor (GCF) of the numerator and denominator in the rational expression (7x+14)/(2x²+x-6) is x+2. Thus, option C is correct.

Explanation:

To find the greatest common factor (GCF) of the numerator and denominator of the given rational expression (7x+14)/(2x²+x-6), we need to factor both the numerator and the denominator separately.

For the numerator 7x+14, we can factor out a 7:

7x + 14 = 7(x + 2)

For the denominator 2x² + x - 6, we need to factor it as a quadratic expression. This can be done by finding two numbers that multiply to give -12 (the product of the coefficient of x² and the constant term) and add up to 1 (the coefficient of x). These numbers are 3 and -4, so the denominator can be factored as:

2x² + x - 6 = (2x - 3)(x + 2)

Now we can see that the common factor between the numerator and the denominator is x + 2. Therefore, the GCF is x + 2, which corresponds to option (c).