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2 years ago

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Here are 15,000 students at college x. of those students, 1,700 are taking both ethics and metaphysics this semester. there are

2,200 total students taking ethics. 9,500 students are taking neither of these classes. how many students are taking metaphysics this term?

2 answers:

tekilochka [14]2 years ago

7 0

I think the answer is 1,600 totals students taking metaphysics

mars1129 [50]2 years ago

3 0

This can be solved using formula for Venn Diagrams:

Total = n(A)+ n(B) - n(both A and B) + n(neither A nor B)

Where, the n in front indicates number of items <u><em>[ n(A) is number of elements in set A ]</em></u>

We can take:

set A as students taking Ethics
set B as students taking Metaphysics

Given:

Tota = 15,000

n(A) = 2200

n(both A and B) = 1700

n(neither A nor B) = 9500

Substituting these into our formula, we get:

$15,000=2200+n(B)-1700+9500\\15,000=n(B)+10,000\\n(B)=15,000-10,000\\n(B)=5000$

Hence, 5000 students are taking metaphysics this term.

<u><em>*** If we want to know students taking </em></u><u><em>metaphysics ONLY</em></u><u><em>, we can subtract n(both A and B) from 5000. So we have $5000-1700=3300$ ***</em></u>

ANSWER:

Total students taking Metaphysics = 5000

Students taking Metaphysics only = 3300

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jok3333 [9.3K]

This is an isosceles right triangle (AB = BC & ∠ B=90° - Given)
Then the angles at the base are equal and ∠ CAB = ∠ ACB = 45°

Theorem: Segment DE, joining the midpoints of 2 sides is:
1st) parallel to the 3rd side and
2nd) equal to half the measurement of the 3rd side
So if the 3rd side (hypotenuse) = 9 units, DE = 9/2 = 4.5 units

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2 years ago

Joanie is organizing her closet. She has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. S

marin [14]

Answer:

Option A. 2

Step-by-step explanation:

To solve this problem we can write equations for each shirt color.

Let's call:

b = black shirts

g = gray shirts

w = white shirts

B = brown shirts

If you have 3 times more black shirts than gray shirts and buy 3 more black shirts then:

$b = 3g +3$ (i)

If you have 5 times more white shirts than gray shirts and gave a white shirt then:

$w = 5g -1$ (ii)

It has 2 times more gray shirts than brown camsas, then:

$g = 2B$ (iii)

It has the same amount of black and white shirts

$b = w$ (iv)

We want to find the number of gray shirts.

Then replace (iv) in (ii)

$b = 5g -1$ (v)

Now substitute (v) into (i) and clear g.

$5g -1 = 3g +3\\\\5g -3g = 3 +1\\\\2g = 4\\\\g = 2$

Joan has 2 gray shirts

5 0

2 years ago

Maggie brought $10 to the candy store she will buy a certain amount of fudge 1 pound cost to 2.30 if p represents the money magg

xxTIMURxx [149]

Question is Incomplete. Complete question is given below;

Maggie brought $10 to the candy store. She will buy a certain amount of fudge. One pound of fudge costs $2.30. If p represents the amount of fudge, in pounds, Maggie buys, which expression represents the money Maggie has left after visiting the candy store?

Answer:

The expression that represent the money Maggie has left after visiting the candy store is $(10-2.3p)$

Step-by-step explanation:

Given:

Money Maggie brought at store = $10

Cost of 1 pound of fudge = $2.30

Let the amount of fudge be p

We need to find the amount of Money Maggie has left with after visiting the store.

The amount of Money Maggie has left with can be calculate by subtracting the amount of fudge she bought multiplied by Cost of 1 pound of fudge with Money Maggie brought at store.

The equation can be framed as;

Money left = $10-2.3p$

Hence, The expression that represent the money Maggie has left after visiting the candy store is $(10-2.3p)$

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2 years ago

According to the rational root theorem, which number is a potential root of f(x) = 9x8 9x6 – 12x 7?

yaroslaw [1]

The options of the problem are

$A. 0\ B. \frac{1}{7}\ C. 2\ D. \frac{7}{3}$

we have

$9x^{8} +9x^{6} - 12x +7$

we know that

<u>The Rational Root Theorem </u>states that when a root 'x' is written as a fraction in lowest terms

$x=\frac{p}{q}$

p is an integer factor of <u>the constant term</u>, and q is an integer factor of <u>the coefficient of the first monomial</u>.

So

in this problem

the constant term is equal to $7$

and the first monomial is equal to $9x^{8}$ -----> coefficient is $9$

therefore

<u>the answer is the option </u>

D. $\frac{7}{3}$

7 0

2 years ago

Read 2 more answers

A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored

pickupchik [31]

Answer:

We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.

Step-by-step explanation:

<u>The complete question is</u>: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:

Number sampled: 1,000 (republican) , 800 (democrats)

Number in favor: 200 (republican) , 168 (democrats)

At the 0.02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.

Let $p_1$ = <u><em>proportion of Republicans in favor of lowering the standards</em></u>.

$p_2$ = <u><em>proportion of Democrats in favor of lowering the standards</em></u>.

SO, Null Hypothesis, $H_0$ : $p_1 \geq p_2$ {means that there is an equal or larger proportion of Republicans in favor of lowering the standards}

Alternate Hypothesis, $H_A$ : $p_1 < p_2$ {means that there is a larger proportion of Democrats in favor of lowering the standards}

The test statistics that would be used here <u>Two-sample z-test for</u> <u>proportions</u>;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of Republicans in favor of lowering the standards = $\frac{200}{1000}$ = 0.20

$\hat p_2$ = sample proportion of Democrats in favor of lowering the standards = $\frac{168}{800}$ = 0.21

$n_1$ = sample of Republicans = 1000

$n_2$ = sample of Democrats = 800

So, <u><em>the test statistics</em></u> = $\frac{(0.20-0.21)-(0)}{\sqrt{\frac{0.20(1-0.20)}{1000}+\frac{0.21(1-0.21)}{800} } }$

= -0.52

The value of z test statistics is -0.52.

<u>Now, P-value of the test statistics is given by the following formula; </u>

P-value = P(Z < -0.52) = 1 - P(Z $\leq$ 0.52)

= 1 - 0.6985 = 0.3015

Now, at 0.02 significance level, the z table gives a critical value of -2.054 for left-tailed test.

Since our test statistic is more than the critical value of z as -0.52 > -2.054, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.

Therefore, we conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.

7 0

2 years ago