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3 years ago

The black triangles are similar. Find the value of x. No links please!!

Mathematics

1 answer:

igor_vitrenko [27]3 years ago

8 0

9514 1404 393

Answer:

Step-by-step explanation:

The altitude of the triangle is 12/21 = 4/7 of the marked side. If we assume that the marked sides are the ones that are corresponding, then ...

x = (4/7)(28)

x = 16

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In studies for a medication, 3 percent of patients gained weight as a side effect. Suppose 643 patients are randomly selected.

timofeeve [1]

Part a)

It was given that 3% of patients gained weight as a side effect.

This means

$p = 0.03$

$q = 1 - 0.03 = 0.97$

The mean is

$\mu = np$

$\mu = 643 \times 0.03 = 19.29$

The standard deviation is

$\sigma = \sqrt{npq}$

$\sigma = \sqrt{643 \times 0.03 \times 0.97}$

$\sigma =4.33$

We want to find the probability that exactly 24 patients will gain weight as side effect.

P(X=24)

We apply the Continuity Correction Factor(CCF)

P(24-0.5<X<24+0.5)=P(23.5<X<24.5)

We convert to z-scores.

$P(23.5 \: < \: X \: < \: 24.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 1.20) \\ = 0.051$

Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.

P(X≤24)

We apply the continuity correction factor to get;

P(X<24+0.5)=P(X<24.5)

We convert to z-scores to get:

$P(X \: < \: 24.5) = P(z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P(z \: < \: 1.20) \\ = 0.8849$

Part c)

We want to find the probability that

11 or more patients will gain weight as a side effect.

P(X≥11)

Apply correction factor to get:

P(X>11-0.5)=P(X>10.5)

We convert to z-scores:

$P(X \: > \: 10.5) = P(z \: > \: \frac{10.5 - 19.29}{4.33} ) \\ = P(z \: > \: - 2.03)$

$= 0.9788$

Part d)

We want to find the probability that:

between 24 and 28, inclusive, will gain weight as a side effect.

P(24≤X≤28)=

P(23.5≤X≤28.5)

Convert to z-scores:

$P(23.5 \: < \: X \: < \: 28.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{28.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 2.13) \\ = 0.1494$

3 0

3 years ago

There are 213 calories in three ounces of a certain ice cream. How many calories are there in one pound?

miv72 [106K]

Answer:

1,136 calories.

Step-by-step explanation:

1. Considering that there are 16 ounces in one pound, and the question is asking for one pound, I would think that there would only need to be 16 ounces observed.

2. Through calculations of the given number of oz, there are 71 calories per oz. By multiplying that by 16 (the number of oz in a lb), there are a total of 1,136 calories in a lb.

4 0

3 years ago

Gavin needs to read at least 150 pages of his book this week. he has already read 82 pages. how many more pages p must gavin rea

Nataly_w [17]

I'm doing the same thing right now and I'm lost.

7 0

3 years ago

Maci and I are making a small kite. Two sides are 10". Two sides are 5". The shorter diagonal is 6". Round all your answers to t

Art [367]

Answer:

A. 4".

B. Approximately 9.54".

C. Approximately 13.54".

Step-by-step explanation:

Please find the attachment.

Let x be the distance from the peak of the kite to the intersection of the diagonals and y be the distance from the peak of the kite to the intersection of the diagonals.

We have been given that two sides of a kite are 10 inches and two sides are 5 inches. The shorter diagonal is 6 inches.

A. Since we know that the diagonals of a kite are perpendicular and one diagonal (the main diagonal) is the perpendicular bisector of the shorter diagonal.

We can see from our attachment that point O is the intersection of both diagonals. In triangle AOD the side length AD will be hypotenuse and side length DO will be one leg.

We can find the value of x using Pythagorean theorem as:

$(AO)^2=(AD)^2-(DO)^2$

$x^{2}=5^2-3^2$

$x^{2}=25-9$

$x^{2}=16$

Upon taking square root of both sides of our equation we will get,

$x=\sqrt{16}$

$x=\pm 4$

Since distance can not be negative, therefore, the distance from the peak of the kite to the intersection of the diagonals is 4 inches.

B. We can see from our attachment that point O is the intersection of both diagonals. In triangle DOC the side length DC will be hypotenuse and side length DO will be one leg.

We can find the value of y using Pythagorean theorem as:

$(OC)^2=(DC)^2-(DO)^2$

Upon substituting our given values we will get,

$y^2=10^2-3^2$

$y^2=100-9$

$y^2=91$

Upon taking square root of both sides of our equation we will get,

$y=\sqrt{91}$

$y\pm 9.539392$

$y\pm\approx 9.54$

Since distance can not be negative, therefore, the distance from intersection of the diagonals to the top of the tail is approximately 9.54 inches.

C. We can see from our diagram that the length of longer diagram will be the sum of x and y.

$\text{The length of the longer diagonal}=x+y$

$\text{The length of the longer diagonal}=4+9.54$

$\text{The length of the longer diagonal}=13.54$

Therefore, the length of longer diagonal is approximately 13.54 inches.

3 0

3 years ago

Baba Clothing store is a having a 5% off sale on all of its clothing. Which expression represents the discounted price if p is t

Irina18 [472]

Answer:

The total of the prices of all of the baby shirts and sweaters that the store sold during the sale was $420.00. It's possible that 12 sweaters and 8 shirts are sold a bargen

Step-by-step explanation:

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2 years ago