A professor teaches a small lecture class with 25 students. For a certain class, 22 students attend the lecture. What is the experimental probability that a student is absent?

If two triangles are similar then the corresponding sides are in proportion. Thus,

AB / AU = BC / UV = AC / AV

AB / (20x+108) = 703 / 444

Where AB is equivalent to:

AB = AU + UB

AB = 20x + 108 + 273

AB = 20x + 381

Therefore going back to the first equation:

(20x + 381) / (20x + 108) = 703/444

444 (20x + 381) = 703 (20x + 108)

8880x + 169164 = 14060x + 75924

14060x - 8880x = 169164 – 75924

5180 x = 93240

x = 93240 / 5180

x = 18          (ANSWER)

The correct value of x is [tex]\(\frac{1}{20}\)[/tex].

To solve for x, we need to use the properties of similar triangles. The sides of similar triangles are proportional. Given that triangles AU V and ABC are similar, we can set up the following proportion:

[tex]\[\frac{AU}{AB} = \frac{UV}{BC} = \frac{AV}{AC}\][/tex]

We are given the lengths of the sides as follows:

- (AU = 20x + 108)

- (UB = 273) (which is part of AB, since (AB = AU + UB)

- (BC = 703)

- (UV = 444)

- (AV = 372)

- (AC = 589)

Using the proportion involving the sides AU, UB, UV, and BC, we have:

[tex]\[\frac{AU}{UB} = \frac{UV}{BC}\][/tex]

Substituting the given values, we get:

[tex]\[\frac{20x + 108}{273} = \frac{444}{703}\][/tex]

Cross-multiplying to solve for x, we have:

[tex]\[(20x + 108) \cdot 703 = 444 \cdot 273\][/tex]

Expanding both sides gives us:

[tex]\[14060x + 76184 = 121172\][/tex]

Subtract (76184) from both sides to isolate the term with x:

[tex]\[14060x = 121172 - 76184\] \[14060x = 49888\][/tex]

[tex]\[x = \frac{49888}{14060}\][/tex]

Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20, we get:

[tex]\[x = \frac{2494.4}{703}\][/tex]

Since (2494.4) is very close to (2496), and \(2496\) divided by (703) is (3.55), which is (20) times (0.1775), we can see that:

[tex]\[x = \frac{1}{20}\][/tex]

Therefore, the value of x is [tex]\(\frac{1}{20}\)[/tex].

Using the combination formula, it is found that it would be possible to elect 27,405 different leadership committees.

The order in which the students are selected to the committee is not important, which means that the combination formula is used to solve this question.

Combination formula:

[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]

In this problem, 4 students are chosen from a set of 30, thus:

[tex]C_{30,4} = \frac{30!}{4!26!} = 27405[/tex]

It would be possible to elect 27,405 different leadership committees.

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Amount of juice that cup B will hold than cup A when both are completely full is A: 18.8 cubic inches.  therefore, Option A: 18.8 cubic inches.

Amount of juice hold by Cup B which is in the shape of a cylinder having width 2 inches that is radius 1 inches and height 7 inches

πr^2h = π × 1^2 ×7 = 7π  cubic inches

Amount of juice hold by cup A which is in the shape of a cone having width 2 inches that is radius 1 inches and height 3 inches

1/3 × π × r^2 h

1/3 × π × 1^2 × 3  =  πcubic inches

Amount of juice that cup B will hold than cup A when both are completely full  = 7π - π = 6π cubic inches

= 6 × 3.14

= 18.84 cubic inches

Option A: 18.8 cubic inches

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Question

Look at the cups shown below (please note that images are not drawn to scale):

A cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches.

How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.

18.8 cubic inches

21.9 cubic inches

25.1 cubic inches

32.6 cubic inches

The original factorable polynomial 15z^2 + 10z can be rewritten in two different equivalent forms by factoring out the GCF to get 5z(3z + 2) and by applying the Zero Product Property to find its roots z = 0, -2/3.

To begin, we will create a factorable polynomial with a Greatest Common Factor (GCF) of 5z. An example might be: 15z^2 + 10z. This polynomial has two terms, and each term includes the GCF of 5z in its make up.

Now, let's rewrite this polynomial in two other equivalent forms using different methods of factorization and simplification.

Form 1: Factor by GCF

In this form, we factor out the GCF from the original polynomial. For our provided example, the GCF is 5z, so we get: 5z(3z + 2).

Form 2: Use the Zero Property

We can also rewrite this polynomial using the Zero Product Property. This naturally complements factoring because it allows us to set the factors equal to zero and solve for z. In this case, this provides the roots of the polynomial but not in factor form: z = 0, -2/3.

Therefore, the original polynomial and the different equivalent forms all represent the same relationship, just expressed in different manners.

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To create a factorable polynomial with a GCF of 5z, multiply it with another term like (4z+2). The resulting polynomial is 20z² + 10z. You can rewrite it in another equivalent form by factoring out the common term from each term, resulting in 2z(8z + 2) = 16z² + 4z.

To create a factorable polynomial with a GCF of 5z, we can start by multiplying 5z with another term. Let's say we multiply it with (4z+2). The polynomial becomes 5z(4z+2), which can be expanded to 20z² + 10z. This is one form of the polynomial.

To rewrite the polynomial in another equivalent form, we can factor out the common term from each term of the polynomial. Doing so, we get 5z(4z+2) = 5z * 4z + 5z * 2 = 20z² + 10z. Thus, the second equivalent form is 20z² + 10z.

The third equivalent form can be obtained by factoring out a common term, 2z, from each term: 5z(4z+2) = 2z * (2 * 4z + 2) = 2z(8z + 2) = 16z² + 4z.

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3^2/3 means squaring the number 3 to get 9, and then taking the cube root of 9, which is approximately 2.08008.

To calculate 3^2/3, we are dealing with an exponential expression where 3 is the base and 2/3 is the exponent. The exponent 2/3 means we must first square the base, which is 3, giving us 3 squared: 32 = 9. Next, we take the cube root (denominator of the fraction exponent) of this result since the exponent is 2/3, meaning the cube root of 9.

To find the cube root of 9, we look for a number which, when multiplied by itself three times, equals 9. Unfortunately, 9 is not a perfect cube, but using estimation or a calculator, we can find that the cube root of 9 is approximately 2.08008. Therefore, the exact expression for 32/3 remains (9)1/3 and the approximate decimal value is 2.08008.

To determine the length of the hypotenuse in a triangle with an angle measure of 92 degrees and a side length of 10 inches, we can use the sine ratio. Calculating the value of Sin(92 degrees) and dividing 10 by that value, we find that the hypotenuse is approximately 10.001525 inches.

A triangle brace with an angle measure of 92 degrees and a side length of 10 inches opposite this angle, and a base length of 12 inches adjacent to the given angle. To determine which of the given statements is correct, we need to use trigonometric ratios. We can use the sine ratio in this case.

The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the angle measure is 92 degrees and the side opposite is 10 inches. Let's calculate:

Sin(92 degrees) = Opposite/Hypotenuse

Sin(92 degrees) = 10/Hypotenuse

To solve for the hypotenuse, we can rearrange the equation:

Hypotenuse = 10/Sin(92 degrees)

Using a calculator, we can evaluate Sin(92 degrees) and then divide 10 by that value to find the hypotenuse:

Hypotenuse = 10/0.9998477 = 10.001525 inches (approximately)

Based on this calculation, the correct statement would be that the hypotenuse is approximately 10.001525 inches.

4 +12 = 16 crates

 16 x 32 = 512 juice boxes

 so both A & C are correct

Answer:

r(t) = 3t ; where t represents the time in minutes and r represents how far the paint is spreading.

A(r) = πr²

Part A:  

A[r(t)] = π (3t)² = 3.14 * 9t² = 28.26t²

Part B:

r(10) = 3(10) = 30

A(r) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit

Step-by-step explanation:

The value of f(-1) from the table given is 0

Table of functions are used to find the relationship between variables. The variables x and y can be written as coordinate (x, y)

In order to determine f(-1), we need the value of f(x) at the point where x is 1. From the table, the value of f(-1) is 0

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The probability helps us to know the chances of an event occurring. The theoretical probability that they have three dogs or three cats is 0.25.

The probability helps us to know the chances of an event occurring.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

As it is given that the pet can either be a dog or a cat, therefore,

The probability that all the three pets are dogs is:

[tex]\rm P(X= 3\ dogs) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]

The probability that all the three pets are cats is:

[tex]\rm P(X= 3\ Cats) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]

Now, we need to calculate the probability that all three pets are either dogs or cats, therefore, the probability can be written as,

[tex]\rm P(3\ Dogs\ or\ 3\ Cats) = P(X = 3\ dogs) + P(X = 3\ cats)[/tex]

                                [tex]= \dfrac{1}{8}+\dfrac{1}{8}\\\\=\dfrac{2}{8}\\\\ = \dfrac{1}{4} = 0.25[/tex]

Hence, the theoretical probability that they have three dogs or three cats is 0.25.

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there are 3600 seconds per hour

5280 feet per mile

1 foot per second = 3600/5280 = 0.681818 Miles per Hour

 60 seconds per minute

 so 1500/60 = 25 feet per second

25 x 0.681818 = 17.05 miles per hour

Answer:

(-4,-1) satisfies the given system of inequalities

Step-by-step explanation:

[tex]2x+y<-5[/tex]

[tex]-x+y>0[/tex]

To find out the solution we check with each option

(4,1) , x=4 and y=1 (Plug in x and y values in the given inequalities)

[tex]2(4)+1<-5[/tex]

[tex]9<-5[/tex] False

(-4,-1) , x=-4 and y=-1 (Plug in x and y values in the given inequalities)

[tex]2(-4)-1<-5[/tex]

[tex]-9<-5[/tex] True

Now plug it in second inequality

[tex]-(-4)-1>0[/tex]

[tex]3>0[/tex] True

(-8,-21) , x=-8 and y=-21 (Plug in x and y values in the given inequalities)

[tex]2(-8)-21<-5[/tex]

[tex]-37<-5[/tex] True

Now plug it in second inequality

[tex]-(-8)-21>0[/tex]

[tex]-13>0[/tex] False

(8,11) , x=8 and y=-11(Plug in x and y values in the given inequalities)

[tex]2(8)+11<-5[/tex]

[tex]-9<-5[/tex] false

To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.

The base is formed by the segment connecting point A and point B.

While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.

The formula for area of trapezoid is given as:

A = b (h1 + h2) / 2

Where,

b = base of the trapezoid  = 3 – (-4) = 7

h1 = shorter height = 2 – (-2) = 4

h2 = longer height = 2 – (-5) = 7

Therefore the area is:

A = 7 (4 + 7) / 2

A = 77 / 2

A = 38.5 

The answer is 38.5. I took this exam and I chose 38.5 and got it right, I hope this helps!

To make the most monkeys happy we need 20 number of pair of pears, peaches, and oranges. and 20 number of pair of peaches bananas and oranges.

In statistics, sampling distribution refers to the study of multiple random samples drawn from a particular population depending on a specified property. The acquired data paint a clear picture of the changes in the likelihood of the outcomes determined. As a consequence, the analysts are aware of the outcomes ahead of time, allowing them to plan their actions accordingly.

Given, A monkey is happy if it eats 3 types of fruit. There are 20 pears, 30 bananas, 40 peaches, and 50 oranges. to formulate the equation we need to divide them by 10 and make the pair of three.

Hence,

2pears + 3 bananas + 4 peaches + 5 oranges

2(pears + oranges +  peaches)  + 2(banana + peach + oranges) + peach +1 orange.

Therefore to make the most monkey happy. we need to make 20 pairs of pears, oranges, and peaches and 20 pairs of banana peaches and oranges.

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Answer:

Factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60