3. College Students (10 points)
In Fall 2019, there were approximately 16.6 million undergraduate students in degre
granting postsecondary institutions. This represents a 5% decrease from the Fall 200
number of students. How many undergraduate students were there in 2009?
Source: https://nces.ed.gov/fastfacts

Answer:

9.1

Step-by-step explanation:

3(9.1)=27.3

27.3÷3=×

×=9.1

[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]

23 is a prime number, therefore there are two possibilities:

[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]

or

[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]

[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]

Now, we check if any of these solutions is also a solution to the second equation:

[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]

Therefore, 3 is not a solution.

[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]

Therefore, 4 is a solution.

[tex]\text{II.}[/tex]

[tex](x-3)!=23[/tex]

We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.

So, the only solution is [tex]x=4[/tex].

Answer:

Zeros: 0, 1, and 7

Step-by-step explanation:

Given function: f(x) = 3x(x - 1)²(x - 7)²

To find the zeros (also known as the x-intercepts) of the function, first substitute f(x) = 0 into the equation and simplify.

1. Substitute f(x) = 0:

[tex]\sf f(x) = 3x(x - 1)^2(x - 7)^2\\\\\Rightarrow 0 = 3x(x - 1)^2(x - 7)^2[/tex]

2. Divide both sides by 3:

[tex]\sf \dfrac{0}{3} = \dfrac{3x(x - 1)^2(x - 7)^2}{3}\\\\\Rightarrow 0=x(x-1)^2(x-7)^2[/tex]

3. Separate into possible cases:

[tex]\sf a)\ x = 0\\b)\ (x - 1)^2 = 0\\c)\ (x - 7)^2 = 0[/tex]

4. Simplify:

[tex]\sf a)\ x = 0\ \textsf{[ already simplified ]}[/tex]

[tex]\sf b)\ (x - 1)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 1)^2}=\sqrt{0}\\\\\Rightarrow x-1=0\ \textsf{[ add 1 to both sides ]}\\\\x-1+1=0+1\\\\\Rightarrow x=1[/tex]

[tex]\sf c)\ (x - 7)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 7)^2}=\sqrt{0}\\\\\Rightarrow x-7=0\ \textsf{[ add 7 to both sides ]}\\\\x-7+7=0+7\\\\\Rightarrow x=7[/tex]

Therefore, the zeros of this function are: 0, 1, and 7.

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Using the normal distribution, it is found that 7.64% of of sample means are greater than 8.8 hours.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 8.4, \sigma = 1.77, n = 40, s = \frac{1.77}{\sqrt{40}} = 0.2799[/tex]

The proportion of sample means greater than 8.8 hours is one subtracted by the p-value of Z when X = 8.8, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{8.8 - 8.4}{0.2799}[/tex]

Z = 1.43

Z = 1.43 has a p-value of 0.9236.

1 - 0.9236 = 0.0764.

7.64% of of sample means are greater than 8.8 hours.

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Answer:

Define different tipes of discontuinity of a function .also,write the condition for increasing, decreasing and concave of function

Answer:

Step-by-step explanation:

Let :

C = number of cats

D = number of dogs

Raul's pet store has a play area that can fit up to 30 cats and dogs.

C + D = 30

The pet store never has more than 8 cats in the play areas.

(there can never be 9 or more cats)

As or the number of dogs :

C + D = 30

C = 30 - D

Since we know that C < 9. To get the number of dogs allowed, we just plug in 30 - D for C.

30 - D < 9

30 - 9 < D

or

(dogs have to be 22 or more)

The average time taken to travel to Toronto by  the swarm of Rasberry Crazy Ants  is 12,947 Years

To arrive at the solution above, we need to look at the information given and the information assumed.

Step 1 - Information given:

Step 2 - Information assumed:

The swarm are travelling to the location of the student which is assumed to be Toronto.

Hence,

Time taken for the swam to get to Toronto (TTS) =

Distance between Austin, Texas and Toronto (DBTT) / Average distance covered per day by the Rasberry Ants. (ADC)

Estimated distance between Austin Texas and Toronto = 2592.6 Kilometers

Time travelled per day by the ants (In Km) = 0.00054864

Thus,

TTS  = DBTT/ADC

= 2592.6 /0.00054864

≈ 4,725,503.06 days or

≈ 12,947 Years

The answer to both questions is NO.

The average life expectancy in Toronto (as at 2022) is 80 years. Assuming I was born today, it is expected that the time between now and when my last grand child will die is about:

80 x 3 = 240 years.

Given that the ants have to travel 12,947  to get to Toronto, the possibility of my grand children seeing them is zero.

Besides, even if they by chance got to Toronto and infested my grandchildren's residence, they would have nothing to worry about because Rasberry Crazy Ants are 100% harmless.

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Answer:

From what my calculations said its 20%

Answer:

The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways. for some constant k. The k is called the constant of proportionality. Therefore a chance of probability is a binary table.

Step-by-step explanation:

Answer

(0,3)

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\texttt{Yes, there's a local maximum at -9,} [/tex] [tex] \texttt{and it is 9} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

By Observing the graph, we can easily conclude that there's a local maxima at -9

[tex] \textsf{And f(-9) = 9} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

thomas age:44

huilan age: 29

Step-by-step explanation:

h = t + 15

t + t + 15 = 73

2t = 73 - 15

2t = 58

t = 29

Answer:

Yes.

Step-by-step explanation:

In mathematics, a number line ends in arrows on both sides, signifying it going infinite in the positive and negative directions.

Answer:

Yes.

Step-by-step explanation:

A number line is infinite in both directions it faces. This means left or right there is a infinite amount of numbers.

Answer:

1/2(6-8), 1/2(-3+7)=-1,2

Answer: C - (-1, 2)

Step-by-step explanation:

The quotient is -27m/ 55.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Given:

(9mn²)(−3m*6n)÷33m*10n³

=9mn² *(-18mn) / 330mn³

= -162m²n³/ 330mn³

= -27m/ 55

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Inequalities help us to compare two unequal expressions. The inverse of p>q is p<q.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the inequality that p is greater than q, therefore, the inverse of it will be p smaller than q. Thus, The inverse of p>q is p<q.

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The area of the sector, to 4 decimal places, is: 78.6794 cm².

Area of sector = ∅/360 × πr².

Given the following:

Area of sector = 46/360 × π(14²)

Area of sector ≈ 78.6794 cm²

The area of the sector is approximately 78.6794 cm².

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: [ - 10,- 8] \cup[ - 2,0] \cup[2,5][/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The intervals in which a function is decreasing has a negative slope. and for given graph, the required intervals are :

[tex]\qquad \tt \rightarrow \: [ - 10,- 8] \cup[ - 2,0] \cup[2,5][/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

[tex]\triangleright[/tex]Hii! [tex]\triangleleft[/tex]

     _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex] Equation: [tex]\bullet[/tex] y=43x-3 ✅

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]

Do you need to know the equation of the line with a slope of -43 and a y-intercept of (0,-3)? No problem! Luckily, there's a formula to find it! (:

The slope intercept formula, [tex]\boldsymbol{y=mx+c}[/tex], comes in handy when we need to find the equation of a line!

In this formula,

--                                         ↩

This particular question provides us both "m" and "c."

Stickin the values

[tex]\boldsymbol{y=43x+(-3)}[/tex]

Simplify!

[tex]\boldsymbol{y=43x-3}[/tex]

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. \: Dream big. }[/tex]

--

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--

Answer:

The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Multiplication of slope of two perpendicular lines is = -1

first line is  y= [tex]\frac{1}{3}[/tex]x +6

slope of this line is [tex]\frac{1}{3}[/tex]

So the slope of the second line is : [tex]\frac{-1}{3}[/tex]

Equation of line would be written by using :

(y - y1) = m(x - x1)

here the line passing through (-4,5)

put the values in equation

y -5 =[tex]\frac{-1}{3}[/tex][x - (-4)]

3y - 15 = -x -4

3y = -x +11

y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

So The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

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Answer:

Step-by-step explanation:

Answer:

The formula is: y = y•e^(-k•x)

In this specific case the function is: 512•e^(-x/1.44)

The number of players in the round 7 is 4

Answer:

C. 261

Step-by-step explanation:

45 times 7= 315

326-315=11

125 times 2=250

250+11=261

so the answer is C. $261

Considering that the mean of the normal distribution is the same as the median, the median is of 88%.

It states that, for a normally distributed random variable:

For the normal distribution, the median is the same of the mean, that is, the median is of 88%.

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Because both lines have the same slope but different y-intercepts, we conclude that the lines are parallel.

Here we have the two lines:

6x - 2y = -2

y = 3x + 12

If we write both of these in the slope-intercept form, we get:

y = (-2 - 6x)/-2  = 3x + 1

y = 3x + 12

So, as you can see, both lines have the same slope but different y-intercepts. That means that the two lines are parallel, so they never do intercept.

Then we can conclude that the correct option is parallel.

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El costo en la opción uno es menor que el de la opción dos, asi que la primera es la más conveniente.

En la primera opción, el par de zapatos cuesta $90, y el segundo par tiene un descuento del 25%.

Entonces el costo por 2 pares es:

C = ($90 + $90)*(1 - 25%/100%)

Donde le aplicamos un descuento del 25% al total del costo de los dos zapatos, resolviendo esto obtenemos:

C = ($180)*(0.75) = $135.

En la segunda opcion tenemos que los pares cuestan $90, pero esta vez le aplicamos un descuento del 40% al segundo par.

C = $90 + $90*(1 - 40%/100%) =

C = $90 + $90*(0.6) = $144

Así, vemos que en la primera opción el costo es menor, entonces esa es la mejor opción.

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Answer:

D -6, 15

Step-by-step explanation:

Because 3,11 is the middle, and 12,7 is the other end, you can do

12 - 3 = 9

3 - 9 = 6

then

11 - 7 = 4

11 + 4 = 15

so

6 is you x and 15 is your y

Answer:

y = 21x + 413

Step-by-step explanation:

Use y = mx + b

m represents the slope which in this case is 21.

b represents the y - intercept which in this case is 413.

Now, just fill in the variables.

y = 21x + 413

Hope this helps!