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Mashcka [7]
1 year ago
11

The foundation of a building is in the shape of a rectangle, with a length of 20 meters (m) and a width of 18 m. To the nearest

meter, what is the distance from the top left corner of the foundation to the bottom right corner?
Mathematics
1 answer:
wariber [46]1 year ago
4 0

Answer:

27m

Step-by-step explanation:

It's the Pythagorean Theorem.

20^2+18^2=c^2

400+324=c^2

724=c^2

take the square root of both sides

26.9m=c

to the nearest meter = 27

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In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly d
____ [38]

Complete question is;

In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.

Answer:

P(has diabetes | positive) = 0.442

Step-by-step explanation:

Probability of having diabetes and being positive is;

P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)

We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.

Thus;

P(positive & has diabetes) = 0.08 × 0.95 = 0.076

P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)

P(negative & has diabetes) = 0.004

P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)

We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease

Thus;

P(positive & no diabetes) = 0.92 × 0.1 = 0.092

P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)

P(negative &no diabetes) = 0.828

Probability that a person selected having diabetes actually has the disease is;

P(has diabetes | positive) =P(positive & has diabetes) / P(positive)

P(positive) = 0.08 + P(positive & no diabetes)

P(positive) = 0.08 + 0.092 = 0.172

P(has diabetes | positive) = 0.076/0.172 = 0.442

8 0
2 years ago
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times
rusak2 [61]

Answer:

x=30\\y=68\\z=82

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

y+z=5x

The third angle is 14 more than the second

z=y+14

And remember that the sum of these three angles must be equal to 180.

x+y+z=180

Let's take these equations

y+z=5x\\z=y+14\\x+y+z=180

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

x+y+z=180\\x+(y+z)=180\\x+(5x)=180

Distribute the + sign

x+5x=180

Combine like terms;

6x=180

Divide by 6.

x=\frac{180}{6}\\ x=30

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example z=y+14

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

x+y+z=180\\30+y+(y+14)=180

Distribute the + sign and Combine like terms;

30+y+y+14=180\\44+2y=180\\

Subtract 44 to isolate 2y.

2y=180-44\\2y=136

Now divide by 2.

y=\frac{136}{2}\\ y=68

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82

5 0
2 years ago
$5000 was invested into an investment that pays 4.25% simple interest. The total value of the investment amounted to $6593.75. H
Basile [38]

Answer:

7.5 years

Step-by-step explanation:

P = $5000,

R = 4.25%,

A = $6593.75,

N =?

SI = A - P = 6593.75 - 5000 =$1593. 75

\because \: SI = \frac{ PNR}{100} \\  \\  \therefore \: 1593.75 =  \frac{5000 \times N \times 4.25}{100}  \\  \\  \therefore \: 1593.75 \times 100 = 21,250 \times N \\  \\ N =  \frac{159375}{21250}  \\  \\ N = 7.5 \: years \:

6 0
2 years ago
A relationship between x and y is defined by the equation y=3x +1/2 which statements are true of this relationship? Select all t
bezimeni [28]

Answer:

a.

b.

d.

Step-by-step explanation:

4 0
1 year ago
Which polynomials are prime? Check all that apply. 2x2+ 7x + 1 5x2 – 10x + 5 3x2 + 8 4x2 – 25 x2 + 36
aleksley [76]
The correct answer would be 2x2+ 7x + 1, 3x2 + 8    and x2 + 36. These polynomials cannot be reduced to a lower degree where the factors are integers so they should be prime. The factors are as follows:

<span>2x2+ 7x + 1             -0.1492189406 and -3.350781059
5x2 – 10x + 5         1 and 1
3x2 + 8                     1.632993162i and - </span>1.632993162i<span>
4x2 – 25                  5/2 and -5/2
x2 + 36                    6i and -6i</span>
6 0
2 years ago
Read 3 more answers
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