PLEASE HELP! The roof of the house rises 12 feet across the a 30-foot span.

In a random sample of 49 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3410 w

GREYUIT [131]

Answer:

$2948 and $4030

Step-by-step explanation:

The CI is sample mean +/- s/sqrt(n)

t(0.95,df=63 critical values are |t|>1.669

90% CI is 3489+/-1.669*(2595/8) since sqrt(64)=8

the interval is 541.38

round to 541

the interval is 3489+/-541

($2948,$4030) is the 90% CI for the mean.

5 0

3 years ago

Find equations of both the tangent lines to the ellipse x^2 + 4y^2 = 36 that pass through the point (12, 3).y = (smaller slope)y

Bingel [31]

Answer:

x+y=15

Step-by-step explanation:

Given equation of $x^2+4y^2=36$

Differentiating both side $2x+8y\frac{dy}{dx}=0$

$\frac{dy}{dx}=\frac{-x}{4y}$

It passes through the point (12,3) so

$\frac{dy}{dx}=\frac{-12}{4\times 3}=1$

So equation of tangent passing through (12,3) is

$y-12=-1(x-3)$ as $y-y_1=-m(x-x_1)$

So x+y =15 will be the equation of tangent which passes though the point (12,3)

5 0

3 years ago

A common blood test performed on pregnant women to screen for chromosome abnormalities in the fetus measures the human chorionic

goldfiish [28.3K]

Answer:

(a) The proportion of women who are tested, get a negative test result is 0.82.

(b) The proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

Step-by-step explanation:

The Bayes' theorem states that the conditional probability of an event E $_{i}$ , of the sample space S, given that another event A has already occurred is:

$P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum\liits^{n}_{i=1}{P(A|E_{i})P(E_{i})}}$

The law of total probability states that, if events E₁, E₂, E₃... are parts of a sample space then for any event A,

$P(A)=\sum\limits^{n}_{i=1}{P(A|B_{i})P(B_{i})}$

Denote the events as follows:

X = fetus have a chromosome abnormality.

Y = the test is positive

The information provided is:

$P(X)=0.04\\P(Y|X)=0.90\\P(Y^{c}|X^{c})=0.85$

Using the above the probabilities compute the remaining values as follows:

$P(X^{c})=1-P(X)=1-0.04=0.96$

$P(Y^{c}|X)=1-P(Y|X)=1-0.90=0.10$

$P(Y|X^{c})=1-P(Y^{c}|X^{c})=1-0.85=0.15$

(a)

Compute the probability of women who are tested negative as follows:

Use the law of total probability:

$P(Y^{c})=P(Y^{c}|X)P(X)+P(Y^{c}|X^{c})P(X^{c})$

$=(0.10\times 0.04)+(0.85\times 0.96)\\=0.004+0.816\\=0.82$

Thus, the proportion of women who are tested, get a negative test result is 0.82.

(b)

Compute the value of P (X|Y) as follows:

Use the Bayes' theorem:

$P(X|Y)=\frac{P(Y|X)P(X)}{P(Y|X)P(X)+P(Y|X^{c})P(X^{c})}$

$=\frac{(0.90\times 0.04)}{(0.90\times 0.04)+(0.15\times 0.96)}$

$=0.20$

Thus, the proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

6 0

4 years ago

A child care center has three rooms, and the same number of children are in each room. If c children attend the center, write an

raketka [301]

Answer:

Number of children in each room = c / 3

Step-by-step explanation:

Given:

Number of rooms in care center = 3

Number of children attend the center = c

Find:

Number of children in each room

Computation:

Number of children in each room = Number of children attend the center / Number of rooms in care center

Number of children in each room = c / 3

4 0

3 years ago

10p - (3p - 4) = 4(p + 1) + 9

andrezito [222]

Answer:

p = 3

Step-by-step explanation:

distribute parenthesis on both sides of the equation

10p - 3p + 4 = 4p + 4 + 9 ( simplify both sides )

7p + 4 = 4p + 13 ( subtract 4p from both sides )

3p + 4 = 13 ( subtract 4 from both sides )

3p = 9 ( divide both sides by 3 )

p = 3

6 0

3 years ago