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4 years ago

Solve for x Please help

Mathematics

1 answer:

Elodia [21]4 years ago

5 0

Answer:

The answer to your question is below

Step-by-step explanation:

1) Alternate interior angles measure the same

10x - 10° = 100°

10x = 100° + 10°

10x = 110°

x = 110° / 10°

x = 11°

2) Alternate exterior angles measure the same

x + 99° = 90°

x = 90° - 99°

x = -9°

3) Supplementary angles measure 180°

(6x + 12) + (14x + 8) = 180°

6x + 12 + 14x + 8 = 180°

20x + 20 = 180

20x = 180 - 20

20x = 160

x = 160 / 20

x = 8

4) Alternate exterior angles measure the same

26x + 1 = 131°

26x = 131° - 1°

26x = 130°

x = 130° / 26°

x = 5

5) Consecutive interior angles measure 180°

x + 100 + 85° = 180°

x + 185 = 180

x = 180 - 185

x = -5

6) Corresponding angles measure the same

7x - 7 = 70

7x = 70 + 7

7x = 77

x = 77 / 7

x = 11

7) Supplementary angles measure 180°

(12x + 8) + (100°) = 180°

12x + 8 + 100 = 180

12x + 108 = 180

12x = 180 - 108

12x = 72

x = 72 / 12

x = 6

8) Consecutive interior angles measure 180°

18x + 8x - 2 = 180°

26x = 180 + 2

26x = 182

x = 182 / 26

x = 7

9) Corresponding angles measure the same

27x + 7 = 28x + 3

27x - 28x = 3 - 7

-1x = -4

x = -4/-1

x = 4

10) Consecutive interior angles measure 180°

(x + 107) + (x + 87) = 180

x + 107 + x + 87 = 180

2x + 194 = 180

2x = 180 - 194

2x = -14

x = -14 / 2

x = -7

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D = r * t is the formula that will be used to find the distance traveled.
Serenity: d = 17 * 2
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Mystic: d = 20 * 2
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Complete this statement 24x^4a^2+30x^2a^3=6x^2a^2 ( )

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24x⁴a² + 30x²a³ = 6x²a²(4x² + 5a)

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3 years ago

A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an incr

ss7ja [257]

Answer:

a) There is a 12.11% probability that exactly 1 man has the marker.

b) There is a 85.07% probability that more than 1 has the marker.

Step-by-step explanation:

There are only two possible outcomes: Either the men has the chromosome, or he hasn't. So we use the binomial probability distribution.

Binomial probability

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

In this problem, we have that:

30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure, so $\pi = 0.30$

(a) If 10 men are selected randomly and tested for the marker, what is the probability that exactly 1 man has the marker?

10 men, so $n = 10$

We want to find P(X = 1). So:

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{10,1}.(0.30)^{1}.(0.7)^{9} = 0.1211$

There is a 12.11% probability that exactly 1 man has the marker.

(b) If 10 men are selected randomly and tested for the marker, what is the probability that more than 1 has the marker?

That is $P(X > 1)$

We have that:

$P(X \leq 1) + P(X > 1) = 1$

$P(X > 1) = 1 - P(X \leq 1)$

We also have that:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = 0) = C_{10,0}.(0.30)^{0}.(0.7)^{10} = 0.0282$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0282 + 0.1211 = 0.1493$

Finally

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1493 = 0.8507$

There is a 85.07% probability that more than 1 has the marker.

3 0

3 years ago

Lydia baked a total of 144 chocolate chip cookies and peanut butter treats for Valentine's Day. Initially, the ratio of chocolat

andre [41]

Let $x$ be the chocolate chip cookies, so the peanut butter treats will be $144-x$ .
We know that the cookies and the treats are in a ratio of 5:3, so: $\frac{cookies}{treats} = \frac{5}{3} = \frac{x}{144-x}$
Now we can solve for $x$ :
$\frac{5}{3} = \frac{x}{144-x}$
$5(144-x)=3x$
$720-5x=3x$
$8x=720$
$x= \frac{720}{8}$
$x=90$

We now know Lydia has 90 chocolate chip cookies, and $144-x=144-90=54$ peanut butter treats.

Then, Lydia's friend ate $\frac{3}{5}$ of her cookies, so her friend ate $\frac{2}{5} (90)=36$ cookies. Therefore, Lydia has $90-36=54$ cookies left.
Now we can calculate the total amount of baked goods after her friend ate the cookies:
$144-54=90$
Therefore, our remainder treats will be:
$90-x$

We also now that after her friend ate 54 cookies and some treats, the new ratio is 6:1, and that's all we need to set up our new equation and solve it to find how many treats she ate:
$\frac{cookies}{treats} = \frac{6}{1} = \frac{54}{90-x}$
$6(90-x)=54$
$540-6x=54$
$6x=486$
$x= \frac{486}{6}$
$x=81$

Finally, if she ate 81 out 90 treats, we can conclude the Lydia has left with 9 peanut butter treats.

3 0

4 years ago

Read 2 more answers

NEED HELP ASAP PLEASE HELP ASAP THANKS 15 points

Brilliant_brown [7]

Answer:

The correct answer is B.

Step-by-step explanation:

1/4 = .25

.25 < .32

5 0

3 years ago

Read 2 more answers