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3 years ago

PLEASE HELP ASAP THE DETAILS ARE BELOW.What is the value of x?

Mathematics

1 answer:

Aloiza [94]3 years ago

6 0

Answer:

x = 30°.

Step-by-step explanation:

The dashes on the three lines indicate that the three lines are of equal lengths. The smaller triangle made out of the three lines (the one with two vertices on the circumference of the circle and one at the center of the circle) is an isosceles triangle. All three of the triangle's interior angles are 60° since it is isosceles.

The line (the one with arrows on its ends) touches the circle at only one point. That line is a tangent to the circle. That line is perpendicular to the segment that connects the center of the circle to the point of tangency. The angle between the two will be 90°.

The largest triangle includes three angles:

The angle with the center of the circle as its vertice: 60°;
The right angle due to the tangent to the circle: 90°;
The angle x°.

What is the value of x?

The three interior angles of a triangle add up to 180°. As a result,

60° + 90° + x° = 180°

x = 180 - 90 - 60 = 30.

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Quadrilaterals ABCD and PQRS shown below are two similar figures. Find the values of x and y.

nadezda [96]

Answer:

x = 12, y = 16

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

$\frac{AD}{PS}$ = $\frac{DC}{SR}$ , substitute values

$\frac{20}{2x+6}$ = $\frac{18}{27}$ ( cross- multiply )

18(2x + 6) = 540 ( divide both sides by 18 )

2x + 6 = 30 ( subtract 6 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

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and

$\frac{AB}{PQ}$ = $\frac{DC}{SR}$ , substitute values

$\frac{y}{24}$ = $\frac{18}{27}$ ( cross- multiply )

27y = 432 ( divide both sides by 27 )

y = 16

3 0

3 years ago

Peter works at a bookstore. He packed 3 identical paperbacks and 2 identical textbooks in a box. The total mass of the books was

Alexus [3.1K]

If we let p and t be the masses of the paper and textbook, respectively, the equations that would best represent the given in this item are:

(1) 20p + 9t = 44.4

(2) (20 + 5)p + (9 + 1)t = 51

The values of p and t from the equation are 0.6 and 3.6, respectively. Thus, each paperback weighs 0.6 pounds and each textbook weighs 3.6 pounds.

Yw and pls mark me brainiest

5 0

2 years ago

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Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally dis

nikitadnepr [17]

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = the interval of time between the eruptions

So, X ~ N( $\mu=72, \sigma^{2} =23^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 minutes is given by = P(X > 82 min)

P(X > 82 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{82-72}{23}$ ) = P(Z > 0.43) = 1 - P(Z $\leq$ 0.43)

= 1 - 0.6664 = 0.3336

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let $\bar X$ = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes is given by = P( $\bar X$ > 82 min)

P( $\bar X$ > 82 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{82-72}{\frac{23}{\sqrt{13} } }$ ) = P(Z > 1.57) = 1 - P(Z $\leq$ 1.57)

= 1 - 0.9418 = 0.0582

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let $\bar X$ = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is given by = P( $\bar X$ > 82 min)

P( $\bar X$ > 82 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{82-72}{\frac{23}{\sqrt{34} } }$ ) = P(Z > 2.54) = 1 - P(Z $\leq$ 2.54)

= 1 - 0.9945 = 0.0055

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 minutes, then we conclude that the population mean must be more than 72, since the probability is so low.

6 0

3 years ago

1/5,6/30 tell if it forms a porportion

Marianna [84]

1/5=6/30 if thats what you mean

5 0

3 years ago

PLEASE ANSWER FAST!!!

NemiM [27]

Answer:

A- 3,000 = 50(60) + b

B- 2,100 = 50(42) + b

Step-by-step explanation:

i just did it

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3 years ago

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