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3 years ago

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Mathematics

1 answer:

shtirl [24]3 years ago

8 0

Answer:

d) 2y + x = 106

Step-by-step explanation:

Mean of the data = sum of the data / number of frequencies:

(40 + 38 + y + y + x + 32)/6 = 36
2y + x + 110 = 36*6
2y + x = 216 - 110
2y + x = 106

Correct choice is d

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Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is current

exis [7]

Answer:

n = 1, this means the interest compounds ANNUALLY.

Step-by-step explanation:

Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is currently $30,541.83. How often does the interest compound?

Compound Interest Formula

: A = P(1 + r/n)^nt

A = Amount after time t

P = Principal (Initial Amount Invested)

r = Interest rate

n = Number of times the interest is compounded

t = time in years

A = $30,541.83

r = 4.6% = 0.046

t = 30

P = $7,924

Hence,

$30,541.83 = $7924(1 + 0.046/n)^30n

Divide both sides by 7924

$30,541.93/$7924 = (1 + 0.046/n)^30n

$30,541.93/$7924 = (n + 0.046/n)^30n

3.8543576477 = (n + 0.046/n)^30n

We take the logarithm of both sides

log 3.8543576477 = log (n + 0.046/n)^30n

Solving for n,

n = 1

Therefore, from the calculation above, since n = 1, this means the interest compounds ANNUALLY.

6 0

2 years ago

A new test to detect TB has been designed. It is estimated that 88% of people taking this test have the disease. The test detect

Elodia [21]

Answer:

Correct option: (a) 0.1452

Step-by-step explanation:

The new test designed for detecting TB is being analysed.

Denote the events as follows:

D = a person has the disease

X = the test is positive.

The information provided is:

$P(D)=0.88\\P(X|D)=0.97\\P(X^{c}|D^{c})=0.99$

Compute the probability that a person does not have the disease as follows:

$P(D^{c})=1-P(D)=1-0.88=0.12$

The probability of a person not having the disease is 0.12.

Compute the probability that a randomly selected person is tested negative but does have the disease as follows:

$P(X^{c}\cap D)=P(X^{c}|D)P(D)\\=[1-P(X|D)]\times P(D)\\=[1-0.97]\times 0.88\\=0.03\times 0.88\\=0.0264$

Compute the probability that a randomly selected person is tested negative but does not have the disease as follows:

$P(X^{c}\cap D^{c})=P(X^{c}|D^{c})P(D^{c})\\=[1-P(X|D)]\times{1- P(D)]\\=0.99\times 0.12\\=0.1188$

Compute the probability that a randomly selected person is tested negative as follows:

$P(X^{c})=P(X^{c}\cap D)+P(X^{c}\cap D^{c})$

$=0.0264+0.1188\\=0.1452$

Thus, the probability of the test indicating that the person does not have the disease is 0.1452.

4 0

3 years ago

What is the volume of a square pyramid that has a base length of 5 inches and a height of 9 inches?

PtichkaEL [24]

Well since the for formula for these are b × h. We are gonna do...

5 × 9 which equals 45. So your answer is 45 cubic inches

hope this helps!

4 0

4 years ago

What is the equation of the line that passes through points (15,9) and (-2,9)

Vikki [24]

Answer:

y=9

Step-by-step explanation:

Slope: 9-9/-2-15=0

Therefore, y=0x+b

Plug values in: 9=0(-2)+b

0+b=9

b=9

Therefore, equation is y=9

7 0

3 years ago

Points are: A= (-2,7)B= (3,5)C= (1,0) To show that the triangle is a right triangle, show that the sum of the squares of the len

Gala2k [10]

The sum of the squares of the lengths is 58

The square of length of the hypotenuse is 58

From the question, we have

AB² = (-2-3)² +(7-5)²= 25+4 =29

BC² = (3-1)²+(5-0)²=4+25=29

AC² = (-2-1)²+(7-0)² = 9+49 = 58

Here we can see that,

AB²+BC² = AC²

The sum of the squares of the lengths of two sides (the legs) equals the square length of the third side (hypotenuse).

the sum of the squares of the lengths = AB²+BC² =29+29 = 58

the square of length of the hypotenuse= 58

Pythagoras Theorem:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

To learn more about pythagoras theorem visit: brainly.com/question/343682

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5 0

1 year ago