Plz help me answer this

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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we have

[tex] 2x + 5y = 10 [/tex]

we know that

the formula to calculate the slope is equal to

[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]

Let

[tex] A( 5,0)\\B( 0,2) [/tex]

Step [tex] 1 [/tex]

Find the slope AB

[tex] mAB=\frac{(2-0)}{(0-5)} \\ \\ mAB=-\frac{2}{5} [/tex]

therefore

the answer is the option B

[tex] -\frac{2}{5} [/tex]

the graph in the attached figure

The unknown number is 46.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Let the number be x.

The sum of 74 and four times a number is 258,

⇒ [tex]74+4x=258[/tex]

⇒ [tex]4x=258-74[/tex]

⇒ [tex]x=\frac{184}{4}[/tex]

⇒ [tex]x=46[/tex]

Hence we can conclude that the unknown number is 46.

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Answer:

The ball will hit at 2.83 seconds.

Step-by-step explanation:

It is given that,

Velocity with which a ball is thrown up is, v = 10 ft/s

Initial height, h = 100 ft

The equation for the height of an object as a function of t is given by :

[tex]h(t)=-16t^2+10t+100[/tex]...............(1)

Where

t is the time in seconds

h is the ball's height measured in feet

We have to find the time when the ball hits the ground. It can be calculated by solving the quadratic equation of equation (1). On solving we get the value of t as :

t = 2.832 seconds

So, at 2.83 seconds the ball will hit the ground. Hence, this is the required solution.                        

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 required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.

Given that,
To simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

= 2x − 6y + 3x² + 7y − 14x.
= 3x² + 2x -14x + 7y -6y
= 3x² -12x + y

Thus, the required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.

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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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The constant term will be the product of -p and -q.

A trinomial is an algebraic expression that has three non-zero terms and has more than one variable in the expression.

Given that the factors of a trinomial are (x - p) and (x - q) we need to determine the constant term of the trinomial:

We know that a trinomial in its factors form can be written as,

x² + (α+β)x + αβ, where α and β are factors.

So, here the constant term of the trinomial will be (-p) × (-q) = pq.

Hence the constant term will be the product of -p and -q.

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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.

Answer:

Factors of 60 are:

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

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!

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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