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IrinaK [193]
3 years ago
5

Given that QR¯∥ST¯, identify the length of PT¯.

Mathematics
1 answer:
wariber [46]3 years ago
3 0

Answer:

PT = 16.3 units

Step-by-step explanation:

From the picture attached,

From ΔPQR and ΔPST,

QR ║ST [Given]

PQ is a transversal line.

Therefore, ∠PST ≅ ∠PQR [Corresponding angles]

∠P ≅ ∠P [Common angle]

ΔPQR ~ ΔPST [By AA property of similarity of two triangles]

Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.

\frac{PQ}{PS}=\frac{PR}{PT}

\frac{12+28}{28}= \frac{PT+7}{PT}

\frac{40}{28}=1+\frac{7}{PT}

\frac{10}{7}-1=\frac{7}{PT}

\frac{10-7}{7}=\frac{7}{PT}

PT = \frac{49}{3}

PT = 16.3 units

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Use the sample data and confidence level given below to complete parts a through d.
Sholpan [36]

Answer:

Step-by-step explanation:

Given that a research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1096 and x=542 who said yes.

i.e. sample size = n=1096\\

who said yes =x=542\\

Sample proportion = p=\frac{542}{1096} =0.4945

Std error of proportion = \sqrt{\frac{p(1-p)}{n} } \\=\sqrt{\frac{0.4945(1-0.4945)}{1096} } \\=0.0151

Margin of error 95% = 1.96 (se)\\=0.0296

Hence confidence interval for proportions

=(0.4945-0.0296, 0.4945+0.0296)\\= (0.4649,0.5241)

a) Point estimate =0.4945

B) Margin of error = 0.0296

C) Conf interval = (0.4649,0.5241

D) We are 95% confident that for large random samples representing the population, the proportion of yes will lie between these two values.

4 0
3 years ago
SECTION B
lapo4ka [179]

Answer: The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.

Step-by-step explanation:

Order the dataset from least to greatest:

-38 → -13 → -9 → -2 → 14 → 28

Then find the values that lies in the middle:

-38 → -13 → <u>-9 → -2</u> → 14 → 28

Since there are 2 values, find the average of those 2 values:

\frac{-9+(-2)}{2} =\frac{-11}{2} =-5.5

The median value = -5.5.

The median value of data set B is -5.5, which is less than the median value of  3.1 in dataset A.

3 0
3 years ago
The volume of a cylinder is 75 cubic inches. What is the radius of the base of the cylinder?
Papessa [141]

Answer:

the radius of the base of the cylinder is 5 cubic inches

Step-by-step explanation:

6 0
3 years ago
If DA equals 6 units, AB equals 16 units, and HE equals 36 units, what does EF equal?​
yuradex [85]

Answer:

B. 96 units

Step-by-step explanation:

DA is 6 units and HE is 36 units. There are the same side, but HE is 6 times larger.

AB is 16 units, but since all the sides on the left shape are 6 times larger, EF has to be 16*6, which is 96 units.

Hope this helps

5 0
4 years ago
JK=9x−5 KL=7x+3 find JL
lianna [129]

Answer:

JL = 16x-2

Step-by-step explanation:

From the diagram, we can see that;

JL = JK + KL

Thus;

JL = 9x-5 + 7x + 3

JL = 9x + 7x -5 + 3

JL = 16x -2

6 0
3 years ago
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