Bonus: The probability that our administrators are athletic is .79. The probability that they are
intelligent is .89. The probability that they are both athletic and intelligent is.83. What is the
probability that if we choose an administrator, randomly, that he/she is not athletic?

Answer:

Step-by-step explanation:

4. Nicole can make 7 quarts of lemonade with 10 cups of sugar.

If 3/4 cup of sugar is used to make 1 quart of lemonade and 10 cups of sugar are available, then you multiply 3 times 10 (when multiplying fractions, you only multiply with the numerator, not the denominator) which will give you 30.

Now, you can write it as 30/4. Using simple division, you find that 30/4 is 7.5 (or 7 and 1/2), and because we're trying to find how many full quarts we can make using 10 cups of sugar, your answer will be 7.

5. Each person will get 0.83 repeating (or 5/6) boxes of raisins.

In this problem, we have 6 people and we have to share 5 boxes of raisins among all of them. We know that each person can't get 1 because there would have to be 6 boxes (1 for each person), so we have a fraction (or decimal, depending on where you're at).

Dividing 5/6, you'll simply get 5/6 because you can't simply this any further, but if you were to write this as a fraction, you'd get 0.83 repeating (over the 3).

6. Each class will receive 30 boxes of cracker jacks.

We know that there are 153 boxes of cracker jacks available, and this needs to then be split among 5 different classes. So, to find the answer, we have to divide 153 by 5. In doing that, we get 30.6, but because we're trying to find the whole number that the classes will receive, as you can't get a fraction of a box (at least, I assume), then each class will get 30 with 3 boxes remaining.

Answer:

Stable. They're solid in they're emotions

Step-by-step explanation:

The new statement becomes "If the dog jumps in the lake, then it can't come in the house".

Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.

We have a statement:

R → S: If the dog jumps in the lake, then it gets wet.

S > T: If the dog gets wet, then it can’t come in the house.

After applying the law of syllogism to form a new statement:

R→T:

If the dog jumps in the lake, then it can't come in the house.

Thus, the new statement becomes "If the dog jumps in the lake, then it can't come in the house".

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Answer:

I think it's y - 21 = 4 (x - 1)

Step-by-step explanation:

im sorry if it's wrong

Answer:

x ≥ 6.

Step-by-step explanation:

Given : Kathy swims at least 6 laps every day.

To find: Write an inequality to show how long Kathy swims each day.

Solution : We have given that Kathy swims at least 6 laps every day.

We can see from given statement Kathy can swim 6 laps or greater then 6 laps in a day.

Then we use greater than or equal to sign  ( for at least)

Since x ≥ 6.

Therefore, x ≥ 6.

Answer:

Probability of getting a green ball is more than that of getting a white ball.

Step-by-step explanation:

There are in all (5+3= 8) outcomes of the experiment. There are 5 outcomes in favour of the event of getting a green ball as there are 5 identical green balls in the bag.

Therefore, P(a green ball) = 5/8

In the same way,P(a white ball) = 3/8

Thus, clearly the probability of getting a green ball is more than that of getting a white ball.

Answer:

f(x) = 3x^2 + 2

Step-by-step explanation:

Answer:

A. is the correct answer tnx to the points

The function f(x) = 1/[(x-1)(x+4)] is a rational function with two vertical asymptotes and one horizontal asymptote, which is graphed below.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The function f(x) = 1/[(x-1)(x+4)] is a rational function with two vertical asymptotes and one horizontal asymptote.

The vertical asymptotes occur when the denominator, (x-1)(x+4), is equal to zero. This happens when x = 1 or x = -4.

Therefore, the graph will have two vertical asymptotes at x = 1 and x = -4.

The horizontal asymptote can be found by looking at the behavior of the function as x approaches positive or negative infinity. As x gets very large in either direction, the terms (x-1) and (x+4) become insignificant compared to x².

Hence, the correct option is (B) f(x) = 1/[(x-1)(x+4)].  

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Answer:

Step-by-step explanation:

in 6 years we know that it will be half,  because that's what "half life" means

in 3 years it's only  loses  1/2 * 1/2 = 1/4 of it's mass

in 1 year it's only loses 1/6 * 1/2 = 1/12 of it's mass

from that we can make the formula that

current weight of radium  = Wr

Mass of radium orginal = Mo

year of time = t   ( must be in years, not days, months or weeks )

Wr = (1/12)*t* Mo

let x be the amount of times she visited the movie theater

[tex]70+12.5x=245\\\\12.5x=175\\\\x=14[/tex]

Alyssa needs to make 14 visits to earn a free movie ticket.

This is our y intercept

This is our slope.

So our equation is

Here v is visits

Answer:

volume is 36.25inches

145/4

Step-by-step explanation:

L= 3 5/8inches

W= 2 1/2inches

H= 4inches

VOLUME = L×W×H

3 5/8 × 2 1/2 × 4 =

29/8 × 5/2 × 4 = 36.25inches

36.25→145/4

Answer + Step-by-step explanation:

y = 2x + 1 represents a linear function then the its graph is a line

To draw the line we have to determine two points that lie on that line

If x = 0 → y = 2(0) + 1 = 1 then the point A(0,1) lies on the line

If x = 2 → y = 2(2) + 1 = 5 then the point B(2,5) lies on the line

Now all we have to do is joining the points A and B with a line

The line AB represents our graph

If the first term is 25 and the common difference is 4. Then the 97th term of the sequence will be 409.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The sequence is given below.

25, 29, 33, ...., so on

Then the first term is 25. And the common difference is 4.

Then the 97th term will be given as

[tex]\rm a_n = a + (n - 1)d[/tex]

where

n = 97

a = 25

d = 4

Then we have

a₉₇ = 25 + (97 - 1)4

a₉₇ = 25 + 96 x 4

a₉₇ = 25 + 384

a₉₇ = 409

Then the 97th term of the sequence will be 409.

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Using the normal distribution, it is found that 25.14% of the batteries will last more than 420 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]

In this problem, we have that the mean and the standard deviation are given, respectively, by:

[tex]\mu = 400, \sigma = 30[/tex].

The proportion of the batteries will last more than 420 hours is one subtracted by the p-value of Z when X = 420, hence:

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

[tex]Z = \frac{420 - 400}{30}[/tex]

Z = 0.67

Z = 0.67 has a p-value of 0.7486.

1 - 0.7486 = 0.2514.

0.2514 = 25.14% of the batteries will last more than 420 hours.

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Answer:

[tex]y\approx24.129[/tex]

Step-by-step explanation:

[tex]y=0.05-10\ln x;\: x=0.09\\y=0.05-10\ln(0.09)\\y\approx24.129[/tex]

Answer:

24.129

the answer is that and I need 20 characters

The area of the shaded region is [tex]154cm^2[/tex]

The formula for solving the area of a circle is:

[tex]\pi r^2[/tex]

Where [tex]\pi[/tex]= 3.14

r= 7cm

To find the area, we would input the values together

[tex]3.14 * 7^2[/tex]

= 3.14 * 49

= 153.86cm^2

Rounded to the nearest tenth would be:

154cm^2

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Answer:

18

Step-by-step explanation:

36 divided by two is 18 therefore 18+18  is 36

Answer:

A solar panel is the best way to transform electrical energy into other forms of energy

Answer:

Problem 21:

Slope = -3
y-intercept = (0, 7)

Problem 23:

Slope = 1
y-intercept = (0, -2)

Problem 22:

Slope = [tex]\frac{2}{3}[/tex]
y-intercept = (0, 1)

Step-by-step explanation:

In the slope formula, the coefficient of x (the number times x) is the slope. The number added or subtracted from it is the y-intercept.

In problem 21, -3 is the coefficient of x, so thats the slope. 7 is what's being added, so that is the y-intercept.

In problem 23, 1 is the coefficient of x (a singular x is the same as 1, or -1 if the variable is negative), so thats the slope. -2 is what's being subtracted, so that is the y-intercept.

In problem 22, [tex]\frac{2}{3}[/tex] is the coefficient of x, so thats the slope. 1 is what's being added, so that is the y-intercept.

hope this helps!

Answer: I think it's 30km per hour.

Step-by-step explanation:

So first you have to find what speed the cyclist is going per hour. So first I did 90/3 and that gave me 30.

Answer:

  6. 14.9 years

  7. 4.8 years

  8. 28.91 years

Step-by-step explanation:

Exponential growth or decay is described by the function ...

  y = a·b^t

where 'a' is the initial value, and 'b' is the growth (or decay) factor. The growth (or decay) factor is one added to the growth rate.

__

This equation can be solved for t to get ...

  y/a = b^t . . . . . . . divide by a

  log(y/a) = t·log(b) . . . . take logarithms

  t = log(y/a)/log(b) . . . . divide by the coefficient of t

Note that the time period is in the same units as the growth rate. (If the growth rate is per quarter, then the value of t will be in quarters.)

__

The initial value is a=8000; the final value is y=35000; and the growth rate is 10%/4 = 0.025 per quarter. The above equation will give the time period in quarters.

  t = log(35000/8000)/log(1+0.025) ≈ 59.77 . . . quarters

Anisha will have $35,000 after 59.77/4 = 14.9 years.

__

No loan payment period is given, so we assume that the $43000 represents the repayment of the entire loan. The growth rate is 6% per year. The time required for the loaned amount to accumulate to a value of $43,000 is ...

  t = log(43,000/32,500)/log(1 +0.06) ≈ 4.80 . . . years

If the loan period is 4.80 years, Kevin will have paid 43,000 to pay it off.

__

The growth rate is 0.024/12 = 0.002 per month. The number of months to achieve the desired balance is ...

  t = log(3200/1600)/log(1 +0.024/12) ≈ 346.92 . . . . months

The balance in the account will be $3200 after 346.92/12 = 28.91 years.

_____

Additional comment

As a crude check on the answers, the "rule of 72" can be used. It says the doubling time is approximately 72 divided by the growth rate in percent. That is, a 10% growth rate will cause the value to double in approximately 72/10 = 7.2 years.

In the first problem, the value grows from 8000 to 35000, which represents a little more than 2 doublings (8000 to 16000 and 16000 to 32000). So, it is reasonable to expect the time period to be near 2 times 7.2 years, or 14.4 years. The value of 14.9 years is not unreasonable.

Answer:

Compound interest formula

[tex]\Large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]

where:

Given:

[tex]\begin{aligned}8000\left(1+\frac{0.1}{4}\right)^{4t} & = 35000\\(1.025)^{4t} & = \frac{35000}{8000}\\(1.025)^{4t} & = 4.375}\\\ln (1.025)^{4t} & = \ln 4.375\\4t \ln 1.025 & = \ln 4.375\\4t & = \frac{\ln 4.375}{\ln 1.025}\\t & = 0.25\left(\frac{\ln 4.375}{\ln 1.025}\right)\\t & = 14.9427947\end{aligned}[/tex]

Therefore, she will have $35,000 in 15 years.

Given:

[tex]\begin{aligned}32500\left(1+\frac{0.06}{1}\right)^{1t} & = 43000\\32500(1.06)^{t} & = 43000\\(1.06)^{t} & = \frac{43000}{32500}\\(1.06)^{t} & = \frac{86}{65}\\\ln (1.06)^{t} & = \ln \left(\frac{86}{65}\right)\\t \ln 1.06 & = \ln \left(\frac{86}{65}\right)\\t & = \dfrac{\ln \left(\frac{86}{65}\right)}{\ln 1.06}\\t & = 4.804621116\end{aligned}[/tex]

Therefore, Kevin will have paid $43,000 on the loan in 4 years and 10 months.

Given:

[tex]\begin{aligned}1600\left(1+\frac{0.024}{12}\right)^{12t} & = 3200\\1600(1.002)^{12t} & = 3200\\(1.002)^{12t} & = \frac{3200}{1600}\\(1.002)^{12t} & = 2\\\ln (1.002)^{12t} & = \ln 2\\12t \ln (1.002) & = \ln 2\\12t & = \dfrac{\ln 2}{\ln 1.002}\\t & = \frac{1}{12}\left(\dfrac{\ln 2}{\ln 1.002}\right)\\t & = 28.91000404\end{aligned}[/tex]

The balance of the account will be $3,200 in 28 years and 11 months.

Answer:

3pi/4

Step-by-step explanation:

can't really explain it that well, but I sure hope this helps!! :)

Answer:

15

Step-by-step explanation:

8² + 15² = c²

To find : Value of c

8² = 8 x 8 = 64

15² = 15 x 15 = 225

c² = 225

225 = 15 x 15 = 15²

So,

c² = 15²

c = 15