The volume of a rectangular pyramid is 120 cm3. If the height of the base is 5 cm and the height of the pyramid is 12 cm, what is the length of the base of the pyramid?

a) Consider the experiment of picking 3 tax returns at random as 3 related experiments (due to the fact that it is without replacement); then, as for the first time one selects a tax return,

As for the second time we grab a tax return, there are 69 tax returns in total and 9 of them contain errors; thus,

Similarly, as for the third picking round,

Finally, the probability of experiment a) is

Rounded to one decimal place, the probability of event a) is 65.7%

b) Similarly, in the event of all three tax returns containing errors,

Thus,

The probability of event b) is 0.2%. It is quite unusual.

c) The condition 'at least one of those containing errors' includes the cases when 1, 2, or 3 tax returns of the ones selected have errors. Notice that

Therefore,

And we found the probability of picking 3 tax returns without any errors in part a); thus,

The probability of event c) is 34.3%.

d) Analogously to part c), the probability of selecting at least one without errors is

The probability of event d) is 99.8%, and it is not improbable at all.

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer:

DP=9

Step-by-step explanation:

DS=4

DP=5

DP=DS+DP=4+5=9  

DP=9

Answer:

in sequence, -7, 3, 43, -27

Step-by-step explanation:

Rate of change of the function, dC/dW = 3

Let the cost be represented as C

Let the wight be represented as W

The rate of change of the function can be calculated using the formula:

Answer:

x=2 and y=-1

Step-by-step explanation:

x−y=3

x−y+y=3+y(Add y to both sides)

x=y+3

Substitutey+3forxin−2x+y=−5:

−2x+y=−5

−2(y+3)+y=−5

−y−6=−5(Simplify both sides of the equation)

−y−6+6=−5+6(Add 6 to both sides)

−y=1

−y

−1

=

1

−1

(Divide both sides by -1)

y=−1

Substitute−1foryinx=y+3:

x=y+3

x=−1+3

x=2(Simplify both sides of the equation)

I hope this Helps and have a great day

Answer:

650 tickets for the main floor and 475 tickets for the balcony were sold.

Step-by-step explanation:

From the information given, you can write the following equations:

x+y=1125 (1)

8x+6y=8050 (2), where:

x is the number of tickets for the main floor

y is the number of tickets for the balcony

First, you can solve for x in (1):

x=1125-y (3)

Second, you can replace (3) in (2):

8(1125-y)+6y=8050

9000-8y+6y=8050

9000-2y=8050

9000-8050=2y

950=2y

y=950/2

y=475

Third, you can replace the value of y in (3) to find x:

x=1125-y

x=1125-475

x=650

According to this, the answer is that 650 tickets for the main floor and 475 tickets for the balcony were sold.

Answer:

1) \((3.5)^{2} ; \frac{57}{5}; 6\sqrt{3}; 9.8; \sqrt{75}\)

2) I found their alternate forms. So in the order the #'s were given its 10.4;12.3;8.7;9.8;11.4

3)\(x\sqrt{75};9.8x;6x\sqrt{3};\frac{57x}{5}; x(3.5)^{2}\)

4) I chose a negative number to base my calculations off (-2) then found their alternate from's. In order they were given its -20.8; -24.5; -17; -19.6; -22.8

Answer:

Rs 750 .

Step-by-step explanation:

We need to find 16 ⅔ % of Rs 45,00 .

So , we can write 16 ⅔ % as 50/3 %.

= \(\dfrac{50}{\cancel3}\times Rs ,\cancel{ 4500 }^{1500}\times\dfrac{1}{100}\)

=\(\red{ Rs 750 }\)

We have the next expression:

Now, solve the parentheses using the next property:

Therefore:

Which represents the product of two powers.

But, we need to find two quotients:

Then, we can rewrite the next expression:

To make fractions, we use the next property:

Then:

The result expression for the product of two powers:

The result for the product of two quotients:

Answer:

0.05 or 5%

Step-by-step explanation:

The formula for simple interest is as follows:

A = P(1+rt), with A representing the final amount, P representing the initial amount, r being the rate, and t being time. Plugging our values in, we have

5610 = 4400(1+5.5r). We know that 5 years and 6 months is 5.5 because 6 months = 0.5 years

5610 = 4400(1+5.5r)

expand

5610 = 4400 + 24200r

subtract 4400 from both sides to isolate the variable and its coefficient

1210 = 24200r

divide both sides by 24200 to isolate the variable

r = 0.05 or 5% as 0.05 * 100 = 5

To calculate the weighted mean of student 40's exam scores with exam 1 weighted twice that of the other 3 exams, you will need to use the weights provided in the spreadsheet. First, locate student 40's scores for all four exams on the second sheet of the spreadsheet. Then, apply the weights provided to each exam score.

To weight exam 1 twice that of the other 3 exams, you will need to multiply the exam 1 score by 2 and leave the other three scores as they are. Once you have adjusted the weights accordingly, you can calculate the weighted mean using the formula:

weighted mean = (weight1 * score1 + weight2 * score2 + weight3 * score3 + weight4 * score4) / (weight1 + weight2 + weight3 + weight4)

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.

Answer:

b6 2hich method

Step-by-step explanation:

I solv3 this

Two triangles if the side between any two corners of one triangle cornor corresponds to the side between the corresponding two angles of the second triangle corner are said to be congruent by the ASA rule.

Create a point F' on ray AC such that BF' is equal to DE.

Angle BAF' = angle BAC, which equal to

angle EDF, AB = DE (given), so ∆ DEF

= ∆ ABP

Point F' has two possibilities: F' is equal to point C please.

If F' is not on C, line AC and ray BC intersect only at C, so F' is not on ray BC. Therefore the angle ABF' is not = the angle ABC. But this is a contradiction. Because angle ABF' = angle DEF (because ∆ DEF = ∆ ABF') and angle DEF = angle ABC (given). So, this case does not occur.

Therefore, F' = C must be true.

∆ABC = ∆ABF' = ∆DEF.

The reasonwe only need some parts to

prove congruence of triangles is that from these parts we can (in Euclidean geometry) derive other parts. This is because the basic axioms and definitions allow us to make "guesses" that turn out to be true every time.

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Answer:

<7

Step-by-step explanation:

<5 and <7 are cut by the same transversal, so that should be the answer!

Hope that helps!

Total money Gillian spend on both cotton shirts and wool shirts = $300

Cost of per cotton shirt = $15

Cost of per wool shirt = $ 20

According to question,

The number of wool shirts Gillian will buy will be at least 3, but less than half the number of cotton shirts she buys.

So, by option when we use the data of Option 'A'

Number of cotton shirts =13

Cost incurred on cotton shirt is given by

13×15=195

Number of wool shirts = 4

Cost incurred on wool shirt is given by

4×20=80

Total cost incurred on both the shirts is given by 195+80=275

If we use option 'B' we spend only $230

If we use option 'C' , it does not satisfy the question as it is mentioned in the question that number of wool shirt must be less than half of number of cotton shirt

If we use option 'D' , we spend $325 which is much higher than $300

Therefore, option A is the correct answer.

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Answer: 4 times 3 equals 12, and that plus 6 is 18.  18 divided by 5 is not 4, sorry if i interpreted your statement wrong, but that is incorrect, or my brain is melting. Help.

Step-by-step explanation:

L is the slope 1 and K is the slope 2.

Given,

From the graph:

To find the graphing lines  and slopes

Now, According to the question:

Analysis the graph :

1) we can see that the line L : when level changed by one the vertical changed by one. The change in both directions is the same.

So, The slope is 1 .

The line K has aslope 2: when level changed by one, the vertical changed by two.

2) Slope is 1/3 : It means that when level changed by three, the vertical changed by one .

and, To see the graph.

Hence, L is the slope 1 and K is the slope 2.

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6.29117647059

This is the answer

Answer: 6.29117647059

Step-by-step explanation:

divide the problem :)

Answer: 27/40

Step-by-step explanation:

27/40 is already simplified.

The simplified fraction form of 27/40 is 27/40.

To simplify the fraction 27/40, we can find the greatest common divisor (GCD) of the numerator (27) and the denominator (40) and divide both by that value.

The GCD of 27 and 40 is 1, which means they have no common factors other than 1.

Since there is no common factor other than 1, the fraction 27/40 is already in its simplest form.

Therefore, the simplified fraction form of 27/40 is 27/40.

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The statement "A high value of the correlation coefficient r implies that a causal relationship exists between x and y" is False.

A high correlation coefficient (r) indicates a strong linear relationship between x and y, but it does not necessarily imply causation.

Correlation measures the strength and direction of a relationship between two variables, while causation implies that one variable directly affects the other. It is important to remember that correlation does not equal causation.

Thus, the given statement is False.

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The expected real rate of interest can be calculated by subtracting the expected inflation rate from the yield of the Treasury bill. In this case,  the expected real rate of interest is 1.5%.

The real rate of interest represents the return on an investment adjusted for inflation. It indicates the actual purchasing power gained from an investment after accounting for the erosion of value due to inflation. To calculate the expected real rate of interest, we subtract the expected inflation rate from the nominal interest rate.

In this scenario, the one-year Treasury bill yields 4.5%, which is the nominal interest rate. The expected inflation rate is 3%. To determine the expected real rate of interest, we subtract the expected inflation rate from the nominal interest rate: 4.5% - 3% = 1.5%.

Therefore, the expected real rate of interest is 1.5%. This means that after adjusting for the expected inflation rate of 3%, the investor can expect a real return of 1.5% on their investment in the one-year Treasury bill.

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Answer:

10n=10n

Step-by-step explanation:

n-10+9n-3=10n-13

n+9n

10n-10-3=10n-13

-10-3

10n-13=10n-13

    +13        +13

10n=10n

The mean absolute deviation (MAD) and mean absolute percent error (MAPE) are both measures used to assess the accuracy or variability of a dataset. However, they differ in terms of the type of data they analyze and the way they express the deviation.

Mean Absolute Deviation (MAD):

MAD measures the average absolute difference between each data point and the mean of the dataset.

It provides information about the dispersion or spread of the data.

MAD is calculated by taking the absolute value of the differences between each data point and the mean, summing these values, and then dividing by the total number of data points.

MAD is expressed in the same units as the original data.

Mean Absolute Percent Error (MAPE):

MAPE measures the average percentage difference between each data point and its corresponding value in a reference dataset (often a forecast or predicted value).

It provides information about the relative error or accuracy of a model or prediction.

MAPE is calculated by taking the absolute value of the percentage difference between each data point and its corresponding reference value, summing these values, and then dividing by the total number of data points.

MAPE is expressed as a percentage.

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2a plus 6 equl eight i hink so

Answer:

Solve the given system first

Find b:

Find a:

Verify the options for correctness:

Answer:

  7/9

Step-by-step explanation:

Evaluate the expression at x=8-. You can see from the graph that p(8-) = 3.

  \(\displaystyle \lim_{x\to8^-}{\frac{3p(x)-2x}{15-3x}}=\frac{3(3)-2(8)}{15-3(8)}=\frac{-7}{-9}=\boxed{\frac{7}{9}}\)

The stability margin of a closed-loop control system increases as the magnitude of the step change in the set point decreases.

The stability margin of a closed-loop control system refers to the ability of the system to remain stable despite disturbances or changes in the input. When the magnitude of the step change in the set point decreases, it means that the change is smaller. This smaller change results in less disruption to the system and allows the control system to respond more effectively and maintain stability. The stability margin increases because the system has more room to adjust and can compensate for smaller changes in the set point. As a result, the system becomes more robust and less prone to instability. Therefore, as the magnitude of the step change in the set point decreases, the stability margin of the closed-loop control system increases.

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Answer:

10 red pencils because 10 is double 5 so it would be 5:10 which simplifies to 1:2

Answer:

10

Step-by-step explanation:

ratio 1 : 5

for 5 blue pencils ratio = 1

x red pencils ratio. = 2

simply 5B = 1

xR = 2

5B × 2 = R

R = 10

Therefore 10 red pencils are required

c) The measures of spread for Mrs. Hampton’s class data are given as follows:

d) The better measure of spread is the interquartile range, as the measure of 0 is an outlier.

First we consider the dot plot, which shows the number of times that each observation appears in the data-set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data-set.

The data-set is composed by 26 values, hence the first quartile is the element at the position:

0.25 x 26 = 6.5 (between 6th and 7th).

Both are the same, of 5.

The third quartile is of:

0.75 x 26 = 19.5.

Hence it is of 8.

Thus the IQR is calculated as follows:

IQR = 8 - 5  = 3.

The range is the difference between the highest and the lowest value, hence:

Range = 10 - 0 = 10.

The high range is only due to the outlier of zero, hence the IQR is the better measure of spread.

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