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1 year ago

Find the coordinates of a point on a circle with radius 18 corresponding to an angle of 190°

1 answer:

8 0

The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).

What is transforming coordinates?

Polar coordinates (r,θ) are transformed into Cartesian coordinates (x, y) using the formulas x = r cos(θ), and y = r sin(θ).

This problem is under the concept of transforming polar coordinates (r,θ) to cartesian coordinates (x, y).

For this problem the polar coordinates are r = 18 and θ = 190°.

Convert these polar coordinates into a cartesian coordinates as,

x = r cos(θ) = 18 cos(190°) = -17.73

y = r sin(θ) = 18 sin(190°) = -3.13

The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).

To know more about the transforming coordinates, click on the below link

brainly.com/question/2689696

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If f(x)=3x+2,find f(f^-1(14)).

lisov135 [29]

Answer: 14

Step-by-step explanation:

f(x) = 3x + 2

To find f⁻¹, swap the x's and y's and solve for y --> Note: f(x) is y

x = 3y + 2

x - 2 = 3y

$\dfrac{x-2}{3}=y$

$\implies f^{-1}(x)=\dfrac{x-2}{3}$

$\implies f^{-1}(14)=\dfrac{14-2}{3}$

$\implies f^{-1}(14)=\dfrac{12}{3}$

$\implies f^{-1}(14)=4$

f(f⁻¹(14)) = f(4)

f(4) = 3(4) + 2

= 12 + 2

= 14

NOTE: the simplified version is .... f and f⁻¹ cancel out, leaving you with 14

4 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

3 years ago

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year; 4 years.

Mekhanik [1.2K]

Answer: $2880

Step-by-step explanation:

I = P • r • t

I = 12000 • 0.06 • 1460/365 (I used 1340/365 because there are 365 days in a year. 4 years = 1460)

I = 2880

8 0

3 years ago

which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 11?

gtnhenbr [62]

The graph of y = f(x) will shift down 11 units.

3 0

3 years ago

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What happens to the value of the expression 3 y over 2 y as y increases

vladimir1956 [14]

It starts becoming bigger :)

8 0

3 years ago