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SVETLANKA909090 [29]
3 years ago
15

Find the gradient and y intercept of 3x+4y=5

Mathematics
1 answer:
noname [10]3 years ago
3 0

Answer:

gradient = - \frac{3}{4} , y- intercept = \frac{5}{4}

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + 4y = 5 ( subtract 3x from both sides )

4y = - 3x + 5 ( divide terms by 4 )

y = - \frac{3}{4} x + \frac{5}{4} ← in slope- intercept form

with slope m = - \frac{3}{4} and y- intercept c = \frac{5}{4}

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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 <em>E</em>_{i}, of the sample space <em>S,</em> given that another event <em>A</em> 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 <em>E</em>₁, <em>E</em>₂, <em>E</em>₃... are parts of a sample space then for any event <em>A</em>,

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

Denote the events as follows:

<em>X</em> = fetus have a chromosome abnormality.

<em>Y</em> = 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
What is the simplified form of (4x^2)^3
barxatty [35]

Answer:

i guess the answer is 64x^5

Step-by-step explanation:

(4x^2)^3

=64x^5

7 0
2 years ago
What is 36 to 21 ratio in simplest form?
OLga [1]
36:21 in simplest form is 12:7, because 3 goes into both 36 and 21. Simplifying ratios is essentially the same thing as simplifying fractions. Once we have 12:7, we can't reduce any further, because 7 is prime.

Hope this helps!
7 0
3 years ago
How many ways can 4 people sit in a row of 7 ​chairs?
Ghella [55]

7\cdot6\cdot5\cdot4=840

6 0
3 years ago
Read 2 more answers
2z + 4x + 9y -y + 3
kotegsom [21]

Answer:

Step-by-step explanation:

2z+4x+9y-y+3

2z+4x+8y+3

=2z+4x+8y+3

8 0
3 years ago
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