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2 years ago

Find the area of the figure

Mathematics

1 answer:

cupoosta [38]2 years ago

4 0

Answer:

Step-by-step explanation:

It's a trapezoid.

The formula of an area of a trapezoid:

$A=\dfrac{b_1+b_2}{2}\cdot h$

b₁, b₂ - bases

h - height

(look at the picture)

Use the Pythagorean theorem to calculate the length x:

$x^2+12^2=15^2$

$x^2+144=225$ subtract 144 from both sides

$x^2=81\to x=\sqrt{81}\\\\x=9$

Substitute:

$b_1=9+12+9=30\\b_2=12\\h=12$

[tex]A=\dfrac{30+12}{2}\cdot12=(42)(6)=252[/txt]

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g In a certain rural county, a public health researcher spoke with 111 residents 65-years or older, and 28 of them had obtained

Marat540 [252]

Answer:

95% confidence interval for the percent of the 65-plus population that were getting the flu shot is [0.169 , 0.331].

Step-by-step explanation:

We are given that in a certain rural county, a public health researcher spoke with 111 residents 65-years or older, and 28 of them had obtained a flu shot.

Firstly, the Pivotal quantity for 95% 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 residents 65-years or older who had obtained a flu shot = $\frac{28}{111}$ = 0.25

n = sample of residents 65-years or older = 111

p = population proportion of residents who were getting the flu shot

Here for constructing 95% confidence interval we have used One-sample z test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.25-1.96 \times {\sqrt{\frac{0.25(1-0.25)}{111} } }$ , $0.25+1.96 \times {\sqrt{\frac{0.25(1-0.25)}{111} } }$ ]

= [0.169 , 0.331]

Therefore, 95% confidence interval for the percent of the 65-plus population that were getting the flu shot is [0.169 , 0.331].

7 0

2 years ago

What is 2x + 11y when x = 4 and y = 2? A. 30 B. 38 C. 48 D. 136

Alla [95]

The correct answer is A

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10 people who build at the same rate can frame a house in 6 days. What fractional part of a house can 4 people frame a house in

Alina [70]

10 people who build at the same rate can frame a house in 6 days. That means it will take one person $10\times6=60$ days to finish the house.

Which means that it will take 4 people $\frac{60}{4}=15$ days to finish the house.

So, the fractional part of the house 4 people can frame in 3 days will be $\frac{3}{15}=\frac{1}{5}$

Thus, Option D is the correct answer.

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3 years ago

Create and describe a function related to your field (or intended field). Give a detailed explanation of the domain (input) and

Andru [333]

An example of a domain that can be illustrated from the information given will be D(x) = 32.

<h3>Domain and range</h3>

An example based on the information given is "A gas tank in John's car can hold 20 gallons of gas and the car gets 32 miles for every gallon".

John fills up the tank and then goes on a trip. In this case, the distance that will be travelled on one tank will be:

D(x) = 32x

In the above function, it should be noted that the number of gallons can be from 0 to 20. Since he gets 32 miles per gallon, the car can travel 640 miles.

In this case, the domain is the number of gallons that can be used. The number of miles will be the range.

Learn more about domains on:

brainly.com/question/2264373

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2 years ago

Which of the following is an example of the compliment rule being applied to

UNO [17]

Answer:

Hello There!!

Step-by-step explanation:

I think the answer is B. The probability of not drawing a club or jack from a deck of cards.

hope this helps,have a great day!!

~Pinky~

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