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3 years ago

14

The ratio of faculty members to students at a college is 1:15. If there are 675 students, then how many faculty members are ther

e?

1 answer:

Tresset [83]3 years ago

6 0

Answer:

The number of faculty member is 45.

Step-by-step explanation:

Ratio of faculty members to students = 1 : 15

Number of students = 675

Total = Number students + faculty members

Let the total be t

Let the faculty member be f

Representing the ratio, we have:

$\frac{15}{16} * t = 675\\\frac{15t}{16} = 675\\15t = 16 * 675\\15t = 10800\\\frac{15t}{15} =\frac{10800}{15} \\t = 720$

Therefore, the total number of both the students and faculty member is 720. To get the number of faculty member:

Total = Number students + faculty members

$720 = 675 + f\\f = 720 - 675\\f = 45$

The number of faculty member is 45.

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If f(x) = 2x²+2 and g(x) = x² - 1 ,find (f- g)(x).

mestny [16]

Step-by-step explanation:

(F-g) (X)

= f(x) - g(x)

(2x² + 2 )-(x²-1) =

3x²+3

4 0

3 years ago

Rick and Sara have two children, Marcos and Jade. Use the clues to determine their ages. Rick is 4 years younger than Sara. Marc

Morgarella [4.7K]

Step-by-step explanation:

Let age of rick = x

age of sara = y

age of marcos = a

age of jade = b

Rick is 4 years younger than Sara.

x = y - 4

Marcos is 3 years older than Jade.

a = b + 3

Rick's age is twice the age of Marcos and Jade's ages combined.

x = 2(a+b)

The youngest is 9 years old.

The youngest is jade because rick and sara are the parents and marcos is older than she is.

b = 9

How old is each??

a = b + 3

a = 9 + 3 = 12

Marcos is 12 years old

x = 2(a+b)

x = 2 (12 + 9)

x = 2 (21) = 42

Rick is 42 years old

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42 = y - 4

y = 42 + 4 = 46

Sara is 46 years old

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3 years ago

Solve the inequality.

zysi [14]

Answer:

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Step-by-step explanation:

3(1+1)<9

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1 year ago

Read 2 more answers

Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteerin

NISA [10]

Answer:

The 95% confidence interval would be given by (5.139;5.861)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Confidence interval

Assuming that $\bar X =5.5$ and the ranfom sample n=1086.

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=1086-1=1085$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that $t_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139$

$5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861$

So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

5 0

3 years ago

Find the measure of the the sides of DEF then classify it by it sides. <br> D(8,-6) E(-1,-3) F(-2,5)

Mama L [17]

Answer:

Part a) The measure of the sides of triangle DEF are

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

Part b) Is a scalene triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the coordinates

D(8,-6) E(-1,-3) F(-2,5)

step 1

Find the length side DE

D(8,-6) E(-1,-3)

substitute in the formula

$d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}$

$d=\sqrt{(3)^{2}+(9)^{2}}$

$d_D_E=\sqrt{90}\ units$

step 2

Find the length side EF

E(-1,-3) F(-2,5)

substitute in the formula

$d=\sqrt{(5+3)^{2}+(-2+1)^{2}}$

$d=\sqrt{(8)^{2}+(-1)^{2}}$

$d_E_F=\sqrt{65}\ units$

step 3

Find the length side DF

D(8,-6) F(-2,5)

substitute in the formula

$d=\sqrt{(5+6)^{2}+(-2-8)^{2}}$

$d=\sqrt{(11)^{2}+(-10)^{2}}$

$d_D_F=\sqrt{221}\ units$

step 4

Classify the triangle by the measure of its sides

we have

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

so

Is a scalene triangle, because is a triangle in which all three sides have different lengths.

6 0

3 years ago