A particular college has a 45% graduation rate. If 215 students are randomly selected, answer the following. a) Which is the correct wording for the random variable? rv X = the number of 215 randomly selected students that graduate with a degree v b) Pick the correct symbol: n = 215 n c) Pick the correct symbol: P = 0.45 d) What is the probability that exactly 94 of them graduate with a degree? Round final answer to 4 decimal places. e) What is the probability that less than 94 of them graduate with a degree? Round final answer to 4 decimal places. f) What is the probability that more than 94 of them graduate with a degree? Round final answer to 4 decimal places. g) What is the probability that exactly 98 of them graduate with a degree? Round final answer to 4 decimal places. h) What is the probability that at least 98 of them graduate with a degree? Round final answer to 4 decimal places. 1) What is the probability that at most 98 of them graduate with a degree?

Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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Answer:

\(200 \frac{43 \\ \)

The probability that the person is over 40 given that he or she is a root beer drinker is 62.75%

The fact that

The ratio of the event space's size to the sample space's size represents an event's probability.

The total number of outcomes equals the size of the sample space.

The number of outcomes in the event you are interested in is the event space.

so

P = event space size divided by sample space size

step 1

determine the likelihood that the person is over 40 years old.

The sample size is 255.

event space size = 85

P=85/255------> P=1/3

step 2

determine the likelihood that they consume root beer.

The sample size is 255.

event space size = 75

P=75/255------> P=5/17

step 3

determine the likelihood that the individual is over 40 years old or that

They consume root beer.

so

P=(1/3)+(5/17)——-> P=(17*1+3*5)/51------> P=32/51-----> 0.6275——> 62.75%

therefore, the response is

32/51 or 62.75%

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1. The population variances are equal;
2. The samples are independent;
3. The populations are normally distributed.

All of these choices are required conditions for ANOVA:

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Answer:

5

Step-by-step explanation:

f(1) means what is the value when x=1. y is at 5.

Answer:

f(1)=5

Step-by-step explanation: If you plug in 1 for x on the graph, then y is equal to 5.

Answer:

$20.01

Step-by-step explanation:

Simply subtract $29.99 from $50.00 so, your problem should be set up like this:

You substitute the numbers with 10s, but there cannot be more than one.

Answer:

$20.01

Step-by-step explanation:

You should subtract 50.00 and 29.99, and since there are three zeros, you have to borrow from the five, making it a four. Then, you make the first zero into a 10, then borrow from that one, making it a nine, same with the second zero. Then, for the third zero, you only borrow one from the second zero, turning the second one into a nine and the third on into a 10. You then start the subtracting process. This is the first part to the problem:

50.00 - 29.99 = ?

Then, this is what you should have after:

49.91(0) - 29.99 = ?

This is what you get after:

20.01

Then, add the dollar sign. You will get:

$20.01

Hope it helped!

a. The truth set for the predicate "6/d is an integer" with a domain of Z (the set of all integers) is the set of all integers that divide 6 evenly, which are {-6, -3, -2, -1, 1, 2, 3, 6}.

b. The truth set for the predicate "6/d is an integer" with a domain of Z+ (the set of all positive integers) is the set of all positive integers that divide 6 evenly, which are {1, 2, 3, 6}.

c. The truth set for the predicate "1 ≤ x2 ≤ 4" with a domain of R (the set of all real numbers) is the set of all real numbers between 1 and 4, including 1 and 4 themselves. So the truth set is [1, 4] .

d. The truth set for the predicate "1 ≤ x2 ≤ 4" with a domain of Z (the set of all integers) is the set of all integers whose square is between 1 and 4, including 1 and 4 themselves. So the truth set is {-2, -1, 1, 2}.

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The radius of the container is approximately 8.99 cm. We can use the formula for the volume of a cylinder, which is V = πr^2h, where V is the volume, r is the radius, and h is the height. In this case, we know that the volume is 3,560 cm3 and the height is 14 cm.

So, we can plug in these values and solve for r: 3,560 = πr^2(14)
Dividing both sides by 14π gives:  r^2 = 80
Taking the square root of both sides gives:  r = √80 ≈ 8.94 cm
The radius of the container is approximately 8.94 cm. In summary, Emma received a cylinder of Tootsie Rolls with a volume of 3,560 cm3 and a height of 14 cm. Using the formula for the volume of a cylinder, we found that the radius of the container is about 8.94 cm.
We'll use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.

The volume (V) is 3,560 cm³, and the height (h) is 14 cm. We need to solve for the radius (r). First, we'll rearrange the formula to isolate r: r² = V / (πh)
Now, we'll plug in the given values for V and h: r² = 3,560 cm³ / (π × 14 cm)
r² ≈ 80.71 cm²
To find the radius (r), we'll take the square root of this result: r ≈ √80.71 cm² ≈ 8.99 cm.

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Answer:

division

you divide 3 into 12 getting you 4=y

By constructing these arcs and connecting the appropriate points, we ensure that the newly drawn line passing through point C is parallel to line AB. Remember to use a straightedge to draw the lines accurately and ensure that the arcs intersect correctly.

To construct a line that passes through point C and is parallel to line AB, the best next step is to use a compass to mark an arc centered at point C that intersects line AB at two distinct points.

Here are the steps:

1) Take a compass and set its width to a convenient distance.

2) Place the compass point on point C and draw an arc that intersects line AB at two different points, let's call them D and E.

3) With the compass width still set, place the compass point on point D and draw an arc that intersects the previously drawn arc.

4) Without changing the compass width, place the compass point on point E and draw another arc that intersects the previous arc.

5) Label the point where the two new arcs intersect as F.

6) Draw a straight line passing through point C and point F. This line will be parallel to line AB.

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Answer:

3(x-2)=16

3x-6=16

3x=16+6

=22

x=22÷3

=22/3

=7/1/3

Answer:

Let x be the current page number.

If the sum of the two next pages is 101, we can set up the following equation:

x + (x+1) = 101

Simplifying this equation, we get:

2x + 1 = 101

Subtracting 1 from both sides, we get:

2x = 100

Dividing both sides by 2, we get:

x = 50

Therefore, the current page number is 50, and the next page number is 51.

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

Rational

Step-by-step explanation:

This can be reduced to a ratio of 1/2. Numbers that can be expressed as ratios are rational.

P(54 < X1 + X2 + X3 < 72) is approximately 0.8972.

-The sum of independent normal random variables is also a normal random variable. Therefore, X1 + X2 + X3 is also a normal random variable with mean

E(X1 + X2 + X3) = E(X1) + E(X2) + E(X3) = 10 + 20 + 30 = 60 and variance Var(X1 + X2 + X3) = Var(X1) + Var(X2) + Var(X3) = 12.

So, X1 + X2 + X3 ~ N(60, 12).

-To find P(54 < X1 + X2 + X3 < 72), we standardize the random variable as follows:

\(Z = \frac{(X1 + X2 + X3 - 60)}{\sqrt{12} }\)

-Then, we need to find \(p(\frac{(54-60)}{\sqrt{120} } < Z < \frac{(72-60)}{\sqrt{12} }\).

Simplifying, we get P(-1.73 < Z < 1.73).

Using a standard normal table or calculator, we can find that this probability is approximately 0.8972.

Therefore, P(54 < X1 + X2 + X3 < 72) is approximately 0.8972.

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Answer:

2/3

Step-by-step explanation:

Scaling can be reversed by using reciprocal factors. Because the scale factor from S to M is 2/3​​, the scale factor from M to S 2/3.

The scale factor from M to S will be 2/3.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

For example, 50 meters is very big so we cannot measure it but if we can convert it into 50 mm such that the scale ratio is maintained then it will be easy to draw.

Given,

Scale factor M to S

M/S = 3/2

By cross multiplication

2M = 3S

S/M = 2/3

S/M will be scale factor S to M.

Hence "The scale factor from M to S will be 2/3".

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Answer:

The answer is 15 because that absolute value for anything is 15. No matter what number

Step-by-step explanation:

Answer:

A:33

B:22

C:74

Step-by-step explanation:

A:

2x2x2=8

5x5=25

8+25=33

B:

7x7=49

3x3x3=27

49-27=22

C:

8x8=64

square root of 100 is 10

64+10=74

i hope this helps :)

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

x = 51°

Step-by-step explanation:

The angle I shaded in yellow is a flat angle which measures 180°.

Use the 129° to find x.

180° - 129° = 51°

Answer:

32 degrees

Step-by-step explanation:

180 - 116 = 64

64/2 = 32

Answer:

32°

Step-by-step explanation:

as it is an isosceles triangle from the sides mentioned above

so the other unknown angle is also x

interior angles of triangle sum up 180

so 116 + 2x = 180

2x = 180 -116

2x = 64

x = 32°

Step-by-step explanation:

Base of smaller pink triangle

= (3m + 6m) - 7m = 2m.

Area of smaller pink triangle

= 0.5(2m)(5m) = 5m².

Area of bigger pink triangle

= 0.5(6m)(5m) = 15m².

Hence total area shaded = 5m² + 15m² = 20m².

By the limit comparison test, the series ∑(1+9^n)/(4n) from n=1 to infinity diverge

We are asked to determine whether the series ∑(1+9^n)/(4n) from n=1 to infinity is convergent or divergent.

We can use the ratio test to determine the convergence of the series. Let's compute the ratio of the (n+1)th term to the nth term:

[(1+9^(n+1))/(4(n+1))] / [(1+9^n)/(4n)]

= (1+9^(n+1))/(1+9^n) * (n/ (n+1))

As n approaches infinity, the term (n/(n+1)) approaches 1, and the ratio becomes:

(1+9^(n+1))/(1+9^n)

Since the ratio does not approach a finite value as n approaches infinity, the ratio test is inconclusive. Therefore, we cannot determine the convergence of the series using the ratio test.

However, we can use the limit comparison test with the series 1/n^p, where p=1/2. Let's compute the limit of the ratio:

lim n→∞ [(1+9^n)/(4n)] / [1/n^(1/2)]

= lim n→∞ (n^(1/2) * (1+9^n))/(4n)

= lim n→∞ (n^(1/2) + 9^n/ (4n^(1/2)))

Since the first term approaches infinity as n approaches infinity and the second term approaches zero, the limit diverges. Therefore, by the limit comparison test, the series ∑(1+9^n)/(4n) from n=1 to infinity diverges.

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The range of scores between the upper and lower quartiles of a distribution is called the interquartile range. The median is the score that divides a distribution into two equal halves, while quartiles divide a distribution into quarters.

The range of scores between the upper and lower quartiles of a distribution is called the interquartile range. The interquartile range (IQR) is the difference between the 75th percentile (upper quartile) and the 25th percentile (lower quartile). It is used to measure the spread of the middle 50% of the data, providing a sense of the distribution's variability. Percentiles are a way of dividing a distribution into hundredths, often used to describe a student's performance relative to their peers.
Quartiles are three values ​​that divide the statistical data into four parts, each containing the same observation. A quarter is a type of quantity. First quartile: Also called Q1 or lower quartile. Second quartile: Also called Q2 or median. Third quarter: Also called Q3 or upper quarter.

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The distance from -4 to 1 is 5 units.

The correct number line and expression to find the distance from -4 to 1 are:

Number line: -4 -3 -2 -1 0 1

Expression: |-4 - 1|

To find the distance, we subtract the smaller number (-4) from the larger number (1) and take the absolute value:

|-4 - 1| = |-5| = 5

Therefore, the distance from -4 to 1 is 5 units.

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Answer:

n ≤ 4

Step-by-step explanation:

Which means you should start at four (make sure it's a close circle) pointing to the left. I hope it helps.

Answer:

522 miles

Step-by-step explanation:

406÷7=58

58×9=522

The most likely cause for the change in pH after bubbling CO2 through the solution is the formation of carbonic acid.

When CO2 is bubbled through an aqueous solution, it can react with water to form carbonic acid (H2CO3). This reaction occurs due to the dissolution of CO2 in water, which undergoes a chemical equilibrium process. Carbonic acid is a weak acid that can release hydrogen ions (H+) into the solution, thus lowering the pH. The presence of carbonic acid lowers the pH value compared to the original pH of the solvent.

This phenomenon is commonly observed when CO2 is dissolved in water, such as in carbonated beverages. The carbonic acid formed from the reaction with CO2 contributes to the acidic properties of the solution. Therefore, the most likely cause for the change in pH after bubbling CO2 through the solution is the formation of carbonic acid, leading to a decrease in pH.

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We have the next system of equations

y=-5 ....(1)

y=4x+19​ ...(2)

we substitute the first equation into the second equation and we have

-5=4x+19

then we clear x

-4x=19+5

-4x=24

x=24/-4

x=-6

the solution is

x=-6

y=-5