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3 years ago

If B is the midpoint of AC and AB = 4x + 14 and BC = x + 20, determine how long AC is.

Mathematics

2 answers:

Serhud [2]3 years ago

5 0

Answer:

44 units

Step-by-step explanation:

Since B is the mid-point of AC

AB=BC

or,4x+14=x+20

or, 4x-x=20-14

or 3x=6

or,x=6/3=2

AC=AB+BC

= 4x+14+x+20

= 4(2) + 14 +2 +20

= 8+14+22

=44 units

olchik [2.2K]3 years ago

5 0

Answer:

44 units

Step-by-step explanation:

We know that B is the midpoint of AC, so by definition, AB = BC. Thus, set the two expressions equal and solve for x:

AB = BC

4x + 14 = x + 20

3x = 6

x = 2

Given that x = 2, plug this into the expression for AB and BC and add them to get AC:

AC = AB + BC = 4 * 2 + 14 + 2 + 20 = 44

Hence, AC is 44 units.

Hope this helps!

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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 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

Amy is using a drawing program to complete a construction with which she is almost finished. Which construction is she completin

Vedmedyk [2.9K]

Given options : Two intersecting circles are drawn with a radius in each marked. the image will be linked.

Given options : An equilateral triangle inscribed in a circle

A square inscribed in a circle

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Note. When we join an intersection point of two circles and centers of the circles it would form an equilateral triangle that would be inscribe inside a common portion of both circles..

Therefore, an equilateral triangle inscribed in a circle would be correct option.

She is completing an equilateral triangle inscribed in a circle.