A pyramid has a square base with a side length of 7 centimeters. If the volume of the pyramid is 196 cubic centimeters, what is its height in centimeters? 4 cm 12 cm 8 cm 7cm 21 cm​

The surface area of prism would be, 352 square inches

We know that;

Surface are of rectangular prism = 2(lb + bh + lh)

Where, l - Length of prism

b - width of prism

h - Height of prism

Here, It is given that, a rectangular prism measures 8 inches in width, 12 inches in length, and 4 inches in height.

To find the surface area of prism

l = 12 inches

b = 8 inches

h = 4 inches

Hence, We get;

surface area =  2(lb + bh + lh)

                    = 2(12 x 8 + 8 x 4 +12 x 4)

                    = 2(96 + 32 + 48)

                     = 352 square inches.

Therefore, the surface area of prism = 352 square inches

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Answer:

To find the sum of all integers between 18 and 75, we need to add up all the integers from 18 to 75. We can do this using the formula for the sum of an arithmetic series:

sum = (n/2) x (first term + last term)

where n is the number of terms in the series.

In this case, the first term is 18, the last term is 75, and we need to find the number of terms. We can do this by subtracting the first term from the last term and adding 1:

number of terms = last term - first term + 1

= 75 - 18 + 1

= 58

Now we can substitute these values into the formula:

sum = (n/2) x (first term + last term)

= (58/2) x (18 + 75)

= 29 x 93

= 2673

Therefore, the sum of all integers between 18 and 75 is 2673.

The equivalent expression is log (yz/x²)

We have,

Using the logarithmic concept.

log a + log b = log ab

log a - log b = log (a/b)

log x² = 2 log x

Now,

We will use,

log_2 x = log x

Now,

-2 log x + 4 log y + 4 log z

= (4 log y + 4 log z) -2 log x

= log (yz) - log x²

= log (yz/x²)

Thus,

The equivalent expression is log (yz/x²)

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Stacy's monthly payment for her loan of $870 with $254 in interest over 2 years is $41.50.

Payment is the transfer of money or goods in exchange for a service, product, or any other item of value. It is a form of exchange that is used in many different types of transactions, ranging from the purchase of a cup of coffee to the purchase of a house.

To solve this problem, we will use the formula for calculating the monthly payment when a loan has been taken out for a specific amount of time and with a certain amount of interest. The formula is:

Monthly Payment = (Loan Amount + Interest) / Number of Months

In this case, the loan amount is $870, the interest is $254, and the number of months is 24 (2 years). Plugging these numbers into the equation, we can calculate the monthly payment:

Monthly Payment = ($870 + $254) / 24
Monthly Payment = $41.50

Therefore, Stacy's monthly payment for her loan of $870 with $254 in interest over 2 years is $41.50.

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This is about hypothesis testing. The various steps required to determine whether elderly dementia patients really do take longer to fall asleep than average are given below.

The stages involved in testing a hypothesis are as follows:

1) First, state your hypotheses.

Elderly dementia sufferers fall asleep in the same length of time as the ordinary person (H0) (μ = 7)

An alternative hypothesis (Ha) is that elderly dementia patients sleep more slowly than the general population (μ  > 7)

2) Determine the degree of importance in step two.

The problem does not specify the degree of relevance (α). Assume that α = 0.05.

3) Calculate the test statistic in step three.

To compare the sample mean to the population mean, we may use a one-sample t-test. The t-test formula is as follows:

t = (x - μ) / (s / √n)

where:

x = sample  mean (7.2)

μ  = population mean  (7)

s =  sample standard  deviation (1.1)

n = sample  size  (8)

Plugging in the values,  we obtain the folowing:

t = (7.2  - 7) / (1.1 / √ 8) = 1.62

4) Determine the crucial value in step four.

We must use the t-distribution to ascertain the critical value because this is a one-tailed test with a sample size of fewer than 30, and the population standard deviation is unknown. n - 1 equals 7 degrees of freedom.

The crucial value is 1.895 when using a t-table with 7 degrees of freedom and a one-tailed test with = 0.05.

Step 5: Make a choice and analyze the outcomes

We are unable to reject the null hypothesis since the computed t-value (1.62) is lower than the critical value (1.895).


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The probability that the next marble selected is white is given as follows:

63%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of a total of 65 trials, 41 white marbles were selected, hence the probability that the next marble selected is white is given as follows:

p = 41/65

p = 0.6308.

p = 63%. (rounded to the nearest percent).

We have that, out of the 65 selections:

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Answer:63%

Step-by-step explanation:

The radius of the barrel which has the shape of a cylinder would be = 5 ft. That is option C.

To calculate the radius of the barrel, the formula that should be used is the formula for the volume of a cylinder which is given below;

Volume of cylinder = πr²h

where;

π = 3.14

height = 10ft

radius = ?

Volume = 785.4 ft³

That is;3.

785.4 ft³ = 3.14× r² × 10

make r the subject of formula;

r² = 785.4/3.14×10

r = √ 785.4/3.14×10

= √ 785.4/31.4

= √25.01273885

r = 5ft

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Answer:

A confidence interval and hypothesis test will yield the same results when the null hypothesis value is outside the calculated confidence interval. In other words, if the null hypothesis falls outside the confidence interval, the null hypothesis is rejected at the same level of significance used to calculate the confidence interval. Conversely, if the null hypothesis falls inside the confidence interval, it cannot be rejected.

Null hypothesis: The proportion of college students who believe that freedom of the press is secure or very secure in this country has not changed from 2016.

Alternative hypothesis: The proportion of college students who believe that freedom of the press is secure or very secure in this country has changed from 2016.

We can test this hypothesis using a two-sample z-test for proportions, where the two proportions being compared are the proportion of students who believed freedom of the press was secure or very secure in 2016 and the proportion who believed this in 2017. The test statistic is calculated as:

z = (p1 - p2) / sqrt( p(1-p) * (1/n1 + 1/n2) )

where p1 is the proportion of students who believed freedom of the press was secure or very secure in 2016, p2 is the proportion who believed this in 2017, n1 is the sample size for 2016, n2 is the sample size for 2017, and p is the pooled proportion of successes.

If the test statistic falls outside the critical values for the chosen level of significance, the null hypothesis can be rejected and we can conclude that the proportion of college students who believe that freedom of the press is secure or very secure in this country has changed from 2016.

Step-by-step explanation:

The absolute value of f(24) is 25165824 for the given recurrence relation.

As per the question, the recurrence relation as:

f(n) = 2 × f(n-1)

f(1) = 3

As we know that the geometric series is described as a series representing the sum of the terms in a finite or infinite geometric sequence.

This is a geometric sequence with a = 3 and r = 2.

The formula for the nth term of a geometric sequence is:

f(n) = ar⁽ⁿ⁻¹⁾

Substitute a = 3 and r = 2, we get:

f(n) = 3×2⁽ⁿ⁻¹⁾

So, the absolute value of f(24):

|f(24)| = 3 × 2⁽²⁴⁻¹⁾

|f(24)| = 3 × 2²³

|f(24)| = 25165824

Therefore, the absolute value of f(24) is 25165824.

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0.8942 = 89.42% probability of the mean IQ score of people in the sample is less than 98.

The Normal (or Gaussian) distribution is the most common continuous probability distribution. The function calculates the likelihood that an event will occur between any two real number limits as the curve gets closer to zero on either side of the mean. The area beneath the normal curve is always one.

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation, the z-score of a measure X is:

[tex]\text{z}=\dfrac{\text{x}-\mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

This is the P-value of Z when X = 98.

[tex]\text{z}=\dfrac{\text{x}-\mu}{\sigma}[/tex]

[tex]\text{z}=\dfrac{(98 -100)}{15}[/tex]

[tex]\text{z}=-0.133[/tex]

z = -0.133 has a P-value of 0.8942

Hence, 0.8942 = 89.42% probability of the mean IQ score of people in the sample is less than 98.

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The volume of the triangular pyramid is 150 cubic units.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

We have to find the volume of triangular pyramid

Volume = 1/3×B×h

B is the area of base

B=1/2×10×6

B=30 units

Height = 10 units

Volume = 1/2×30×10

=150 cubic units

Hence, the volume of the triangular pyramid is 150 cubic units.

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The solution is, the profit is 18.

If the profit of a company made by the company is in the form a quadratic expressions but in the different forms as given in the question.

a). The prices that give a profit of zero dollars.

   Expression that is most useful,

   Factored form: -2(p - 3)(p - 9) = 0

   p = 3, 9

b). The profit when the price is zero .

   Standard form:

   Profit = -2p² + 24p - 54 = 0

   -p² + 12p - 27 = 0

   -p² + 3p + 9p - 27 = 0

   -p(p - 3) + 9(p -3) = 0

    (-p + 9)(p - 3) = 0

    p = 3, 9

c). The price that gives the maximum profit.

  Vertex form: -2(p - 6)² + 18

  Vertex of the given expression → (6, 18)

  Maximum profit will be at p = 6.

  Therefore, profit = -2(6 - 6)² + 18 = 18

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complete question:

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If p is the price of the item, then three equivalent forms for the profit are

Standard form: - 2 p^2 + 24p - 54

Factored form: -2(p - 3)(y-9)

Vertex form: -2(p-6)^2 + 18.

Which form is most useful for finding a. The prices that give a profit of zero dollars?

b. The profit when the price is zero?

c. The price that gives the maximum profit?​

Answer:

3√5

Step-by-step explanation:

We can calculate the lentgh of x using the following equation:

x² = 5×(5+4)

x² = 5×(5+4)

x² = 45

x = 3√5

The required there are 120 ways to choose a team captain, an assistant captain, and an equipment manager from a team of 10.

The number of ways 3 people can be selected from a team of 10 is given by the combination formula:

C(10, 3) = 10! / (3! (10 - 3)!)
            = (10 x 9 x 8) / (3 x 2 x 1)
            = 120

Thus, there are 120 ways to choose a team captain, an assistant captain, and an equipment manager from a team of 10.

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Answer:

π(5^2)(6) = 150π = 471.24

So 471.2 is the correct answer.

Step-by-step explanation:

Just plug in the given numbers into the given equation !

 V = pi (5^2) (6) = 150 pi = 471.2    units^3

Step-by-step explanation:

Let r be the radius of both the sphere and the cylinder, and let V be their common volume. The volume of a sphere with radius r is (4/3)πr^3, and the volume of a right cylinder with radius r and height 8 is πr^2(8) = 8πr^3. Since the sphere and the cylinder have the same volume, we can set these expressions equal to each other:

(4/3)πr^3 = 8πr^3

Dividing both sides by πr^3 and simplifying, we get:

4/3 = 8

This is a contradiction, since 4/3 is not equal to 8. Therefore, there is no common radius that would make the sphere and the cylinder have the same volume.

Answer:

600.5%

Step-by-step explanation:

6.005 × 100 is 600.5%

"per cent" means per hundred, so TIMES by 100 to change a number to a percent. DIVIDE by 100 to change a percent to a decimal number.

Some people memorize this as move the decimal two places to the right (decimal to percent) or left (percent to decimal)

Answer:18 laps for sure

Step-by-step explanation:

Let's say that Raina starts running when Shalhevet has already run for some time t (measured in laps). During this time, Shalhevet runs at a rate of 15 laps / t laps per lap, since she has run 15 laps in t laps.

We know that when Raina has run 5 laps, Shalhevet has run 15 laps. Since they run equally fast, we can say that Raina has caught up to Shalhevet and is now 10 laps behind.

Using this information, we can set up an equation to solve for the time t:

15/t = 5/(t-10)

Solving for t, we get t=25.

This means that when Raina has run 30 laps, Shalhevet has run 15 + (30-25)*(15/25) = 18 laps. Therefore, Shalhevet has run 18 laps when Raina has run 30 laps.

Shalhevet has run 6 sets of 15 laps each or 90 laps in total.

Two or more expressions with an Equal sign is called as Equation.

Raina and Shalhevet are running around a track.

When Raina has run 5 laps, Shalhevet has run 15 laps.

We have to find Raina has run 5 laps, Shalhevet has run 15 laps.

If Shalhevet runs 15 laps while Raina runs 5 laps, then the ratio of Shalhevet's laps to Raina's laps is 15:5 or 3:1.

This means that for every 3 laps Shalhevet runs, Raina runs 1 lap.

When Raina has run 30 laps, she has run 30/5 = 6 sets of 5 laps each.

Therefore, Shalhevet has run 6 sets of 15 laps each, or 6 × 15 = 90 laps in total.

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Answer:

Down there

Step-by-step explanation:

1. 4189 cm cubed

2. Cost of one-time fee for a camping permit

3. A translation 11 units to the left and a reflect across the 'x'-axis

The given expression 3u(y - 3) - (y − 3) should be written in complete factored form as (3u - 1)(y - 3).

In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).

In this scenario and exercise, the simplest form of the given expression 3u(y - 3) - (y − 3) can be determined or calculated by simplifying it as follows;

3u(y - 3) - (y − 3) = 3uy - 9u - y + 3

On the other hand, the complete factored form of the given expression 3u(y - 3) - (y − 3) can be determined or calculated by simplifying it as follows;

3u(y - 3) - (y − 3) = (3u - 1)(y - 3)

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Answer:

if you're rough ding to the nearest tenth, in that case the answer is 9.3 ft

Using point-slope formula, the equation of line passing through the point is y = x + 3

To find the equation of the line that is passing through this point, we have to apply point-slope form of the equation.

y - y₁ = m(x - x₁)

We can substitute the values into the formula

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

y - 2 = x + 1

y = x + 1 + 2

y = x + 3

The equation of line is y = x + 3

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The residual is equal to 6.5.

The given equation is y=5x-2.5 and the coordinate point is (3, 6).

The residual is the difference between the predicted value and the real value. Using the equation, we find for the value of y using the given value of x.

y = -2.5 + 5x

y = -2.5 + 5(3)

y = 12.5

Residual=actual y value−predicted y value,

The difference between this value and the given value of y is 12.5 - 6 = 6.5

Therefore, the residual is equal to 6.5.

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The measurement which has four significant figures is option C. 11,890.

Significant figures of a given number are the numbers or digits which are significant and it conveys the accurate meaning of the digit.

Given is a table which shows the velocity of a certain object in different times.

There are certain rules for calculating the significant figures.

Zeroes at the end and the beginning are not significant.

Significant figures in 0.275 = 3

Significant figures in 750 = 2

Significant figures in 320050 = 5

Significant figures in 11,890 = 4

Significant figures in 10.4 × 10⁵ = 3

Thus the measurement 11,890 has 4 significant figures.

Hence the correct option is C.

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The probability that a student chosen randomly from the class has a brother is 13/30

From the attached two way table we can observe that the total number of students in the class = 20

To find the number of students having a brother, we need to add the number of students having a sister as well as brother i.e., 6 and the number of students having a brother but do not have a sister i.e.,7

so, we get the sum as 6 + 7 = 13

Let event A: a student chosen randomly from the class has a brother

n(A) = 13

The probability that a student chosen randomly from the class has a brother.

Using the definition of probability,

P(A) = n(A) / n(S)

P(A) = 13/20

This is the required probability.

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Find the complete question below.

The margin of error for the 95% confidence level is approximately 0.016.

In statistics, a critical value is a value that is used to determine the acceptance or rejection of a null hypothesis, in a hypothesis testing procedure. The critical value is compared to the test statistic to determine if the null hypothesis can be rejected or not. Critical values are based on the significance level (alpha) and the degrees of freedom of the test. They are typically obtained from statistical tables or calculated using software or a calculator. The critical value is the boundary between the rejection region and the non-rejection region, and it helps to determine the likelihood of obtaining a certain result by chance.

The sample proportion can be calculated by dividing the number of voters against school bond measures by the total number of voters in the sample:

p = 403/1000 = 0.403

For a 95% confidence level, the critical value is 1.960 (from the table in the prompt).

The margin of error:

m = z × [tex]\sqrt{\frac{p*(1-p)}{n} }[/tex]

Substituting the given values, we get:

m = 1.960 × [tex]\sqrt{\frac{0.403*(1-0.403)}{1000} }[/tex]

m ≈ 0.0155

Therefore, the margin of error for the 95% confidence level is approximately 0.016.

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The exact value of x is √1156 and it follows the Pythagorean triple

From the question, we have the following parameters that can be used in our computation:

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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