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2 years ago

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A gardener has 10 pounds of soil. He used 58 of the soil for his garden. How many pounds of soil did he use in his garden?

1 answer:

mars1129 [50]2 years ago

8 0

Answer:

Step-by-step explanation:

58% of 10 pounds = 0.58 × 10 pounds = 5.8 pounds

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For positive acute angles AA and B,B, it is known that \tan A=\frac{28}{45}tanA= 45 28 and \cos B=\frac{3}{5}.CosB= 5 3 . Fi

MrRa [10]

Answer:

$\cos(A + B) = \frac{23}{265}$

Step-by-step explanation:

Given

$\tan A=\frac{28}{45}$

$\cos B=\frac{3}{5}$

Required

$\cos(A+B)$

In trigonometry:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

We need to solve for cosA, sinA and sinB

Given that:

$\tan A=\frac{28}{45}$ and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

$x =28$ and $y = 45$

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

$z^2 = x^2 + y^2$

$z = \sqrt{x^2 + y^2$

$z = \sqrt{28^2 + 45^2$

$z = \sqrt{2809$

$z = 53$

From here, we can calculate sin and cos A

$\sin A= \frac{opposite}{hypotenuse}$ and $\cos A= \frac{adjacent}{hypotenuse}$

$\sin A= \frac{x}{z}$

$\sin A= \frac{28}{53}$

$\cos A= \frac{y}{z}$

$\cos A= \frac{45}{53}$

To angle B.

Give that

$\cos B=\frac{3}{5}$ and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

$a = 3$ and $b = 5$

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

$c^2 = a^2 + b^2$

$5^2 = 3^2 + b^2$

$25 = 9 + b^2$

Collect like terms

$b^2 = 25 - 9$

$b^2 = 16$

$b = \sqrt{16$

$b = 4$

From here, we can calculate sin B

$\sin B= \frac{opposite}{hypotenuse}$

$\sin B = \frac{b}{c}$

$\sin B = \frac{4}{5}$

Recall that:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

and

$\cos B=\frac{3}{5}$ $\sin B = \frac{4}{5}$ $\sin A= \frac{28}{53}$ $\cos A= \frac{45}{53}$

$\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}$

$\cos(A + B) = \frac{135}{265} - \frac{112}{265}$

$\cos(A + B) = \frac{135-112}{265}$

$\cos(A + B) = \frac{23}{265}$

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2 years ago

The table showed price paid per concert ticket on a popular online auction site. What was the average price paid per ticket

allochka39001 [22]

Answer: Can you upload a picture of the question?

Step-by-step explanation:

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3 years ago

Round 9,631.4725 to the nearest thousandth

pychu [463]

The answer would be 9,631.473. Since there is a 5 after the two, you round up one value. Hope this helps!

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2 years ago

Read 2 more answers

United Blood Services is a blood bank that serves more than 500 hospitals in 18 states. According to their website, a person wit

Anna11 [10]

Answer:

a) 0.06 = 6% probability that a person has both type O blood and the Rh- factor.

b) 0.94 = 94% probability that a person does NOT have both type O blood and the Rh- factor.

Step-by-step explanation:

I am going to solve this question treating these events as Venn probabilities.

I am going to say that:

Event A: Person has type A blood.

Event B: Person has Rh- factor.

43% of people have type O blood

This means that $P(A) = 0.43$

15% of people have Rh- factor

This means that $P(B) = 0.15$

52% of people have type O or Rh- factor.

This means that $P(A \cup B) = 0.52$

a. Find the probability that a person has both type O blood and the Rh- factor.

This is

$P(A \cap B) = P(A) + P(B) - P(A \cup B)$

With what we have

$P(A \cap B) = 0.43 + 0.15 - 0.52 = 0.06$

0.06 = 6% probability that a person has both type O blood and the Rh- factor.

b. Find the probability that a person does NOT have both type O blood and the Rh- factor.

1 - 0.06 = 0.94

0.94 = 94% probability that a person does NOT have both type O blood and the Rh- factor.

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2 years ago

Oscar wants to put $1000 in a bank account that

Feliz [49]

Answer:

he would end up with 3000$ in 10 years with simple interest

Step-by-step explanation:

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2 years ago