How much is 30% of 190?

What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth

uysha [10]

Answer:

The perimeter of the trapezoid is $38.25\ units$

Step-by-step explanation:

we know that

The perimeter of the trapezoid is the sum of its four side lengths

so

In this problem

$P=QR+RS+ST+QT$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

$Q(8, 8), R(14, 16), S(20, 16),T(22, 8)$

step 1

Find the distance QR

$Q(8, 8), R(14, 16)$

substitute the values in the formula

$d=\sqrt{(16-8)^{2}+(14-8)^{2}}$

$d=\sqrt{(8)^{2}+(6)^{2}}$

$d=\sqrt{100}$

$QR=10\ units$

step 2

Find the distance RS

$R(14, 16), S(20, 16)$

substitute the values in the formula

$d=\sqrt{(16-16)^{2}+(20-14)^{2}}$

$d=\sqrt{(0)^{2}+(6)^{2}}$

$d=\sqrt{36}$

$RS=6\ units$

step 3

Find the distance ST

$S(20, 16),T(22, 8)$

substitute the values in the formula

$d=\sqrt{(8-16)^{2}+(22-20)^{2}}$

$d=\sqrt{(-8)^{2}+(2)^{2}}$

$d=\sqrt{68}$

$ST=8.25\ units$

step 4

Find the distance QT

$Q(8, 8),T(22, 8)$

substitute the values in the formula

$d=\sqrt{(8-8)^{2}+(22-8)^{2}}$

$d=\sqrt{(0)^{2}+(14)^{2}}$

$d=\sqrt{196}$

$QT=14\ units$

step 5

Find the perimeter

$P=10+6+8.25+14=38.25\ units$

6 0

3 years ago

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A purse contains $2.95 in quarters and dimes. The number of quarters exceeds the number of dimes by 2. Find the number of quarte

abruzzese [7]

Answer:

9 quarters and 7 dimes

Step-by-step explanation:

1 quarter = $0.25

1 dime = $0.10

9 (0.25) = $2.25

7 (0.10) = $0.70

2.25 + 0.70 = $2.95

4 0

3 years ago

How do u write twenty-seven hundreths

erma4kov [3.2K]

0.27 would be the answer

3 0

3 years ago

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One True Love? A survey that asked whether people agree or disagree with the statement ‘‘There is only one true love for each pe

sertanlavr [38]

Answer:

99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

Step-by-step explanation:

We are given that a survey that asked whether people agree or disagree with the statement ‘‘There is only one true love for each person." has been conducted. The result is that 735 of the 2625 respondents agreed, 1812 disagreed, and 78 answered ‘‘don’t know."

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of people who disagree with the statement = $\frac{1812}{2625}$ = 0.69

n = sample of respondents = 2625

p = population proportion of people who disagree with statement

Here for constructing 99% confidence interval we have used One-sample z proportion statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.58 & 2.58}

P(-2.58 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.58) = 0.99

P( $-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

99% confidence interval for p = [ $\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.69-2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }$ , $0.69+2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }$ ]

= [0.667 , 0.713]

Therefore, 99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

5 0

3 years ago

What must be true for lines a and b to be parallel lines? Check all that apply.

Dima020 [189]

Answer:

Option (1), (2) , (7) and (8) is correct.

Step-by-step explanation:

Given: a║b and d and c be transversal , We have to find the value of x and measure of angle 1 and 2.

Since, a║b and d be a transversal then ,

∠BXZ = ∠AZP = 58° ( corresponding angles )

Thus, m∠2 = 58°

∠BYC = ∠XYZ = (4X-10)° (vertically opposite angles)

Since, a║b and c be a transversal then,

∠XYZ = ∠QZU = (4X-10)° (Corresponding angles)

Thus, m∠1 = (4X-10)°

Also, Since, 'a' is a straight line.

Sum of angles on a straight line is 180°.

⇒ ∠PZA + ∠PZQ + ∠QZU = 180°

⇒ 58° +(3X-1)°+(4X-10)° = 180°

⇒ 58° + 7x - 11 = 180°

⇒ 47° + 7x = 180°

⇒ 7x = 180°- 47°

⇒ 7x = 133°

⇒ x = 19°

Put x = 19 in (3X-1)° and (4X-10)° , we get

(3X-1)° = (3(19)-1)° = 56°

(4X-10)° = (4(19)-10)°= 66

Thus, (3X-1)° ≠ (4X-10)°

Thus, option (1), (2) , (7) and (8) is correct.

5 0

3 years ago

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