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3 years ago

For f(x)= 2x-5 and g(x)= 3-x , find (f (times) g)(-2)

1 answer:

8 0

$f(x)= 2x-5 \\g(x)= 3-x \\\\f(-2)= 2 \cdot (-2)-5 =-4-5=-9\\\\g(-2)=3-x=3-(-2)=3+2=5\\\\ (f \cdot g)(-2)=f(-2)\cdot g(-2)= (-9)\cdot 5=-45$

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Question 2

lina2011 [118]

Answer:

The firefighter should extend the ladder at 54° of elevation.

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

Tangent Ratio:

$\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}$

The woman is trapped at 91 feet up from the ground, and the firetruck is 67 feet away from the building.

The wall, the ground, and the ladder form a right triangle, where θ is the horizontal angle of the ladder.

Being the height of the woman the opposite leg and the distance where the firetruck is parked, the adjacent leg:

$\displaystyle \tan\theta=\frac{91}{67}=1.3582$

The angle is calculated as the inverse tangent:

$\theta=arctan(1.3582)\approx 54^\circ$

The firefighter should extend the ladder at 54° of elevation.

4 0

3 years ago

Mr. Hills horses, all together, eat 395 pounds of oats each month. If Mr. Hills has 5 horses, and each horse eats the sane amoun

Marizza181 [45]

I would say 80, because without an estimate it'd be 79 and 79x5=395. So 80x5=400, which is the estimate of 395. So 80 is the answer

8 0

3 years ago

Average box of crackers is 24.5 ounces with standard deviation of. 8 ounce. What percent of the boxes weigh more than 22.9 ounce

34kurt

Answer:

97.7% of of the boxes weigh more than 22.9 ounces.

15.9% of of the boxes weigh less than 23.7 ounces.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 24.5 ounces

Standard Deviation, σ = 0.8 ounce

We are given that the distribution of boxes weight is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(boxes weigh more than 22.9 ounces)

P(x > 22.9)

$P( x > 22.9) = P( z > \displaystyle\frac{22.9 - 24.5}{0.8}) = P(z > -2)$

$= 1 - P(z \leq -2)$

Calculation the value from standard normal z table, we have,

$P(x > 22.9) = 1 - 0.023 =0.977= 97.7\%$

97.7% of of the boxes weigh more than 22.9 ounces.

b) P(boxes weigh less than 23.7 ounces)

P(x < 23.7)

$P( x < 23.7) = P( z < \displaystyle\frac{23.7 - 24.5}{0.8}) = P(z < -1)$

Calculation the value from standard normal z table, we have,

$P(x < 23.7) =0.159= 15.9\%$

15.9% of of the boxes weigh less than 23.7 ounces.

7 0

3 years ago

Write a rule for determining the sign of the product when multiplying a positive and a negative integer

Flura [38]

1 Negative+ 1 Negative = A positive

1 negative + 1 positive = A negative

1 positive + 1 positive = A positive

Hope this helped :)

5 0

3 years ago

Read 2 more answers

Hi hi. I have a legit question now.

pochemuha

Answer:

A. 25.14%

B. 0.99%

C. 100%

D. 86.07%

Step-by-step explanation:

μ = 52, σ = 3

Each problem gives you an x value and asks you to find a probability. First calculate the z score(s), then look up in a table or use a calculator.

z = (x − μ) / σ

A. Find P(x < 50)

z = (50 − 52) / 3

z = -0.67

P(z < -0.67) = 0.2514

B. Find P(x > 59)

z = (59 − 52) / 3

z = 2.33

P(z > 2.33) = 1 − 0.9901 = 0.0099

C. Find P(x > 40)

z = (40 − 52) / 3

z = -4

P(z > -4) = 1 − 0 = 1

D. Find P(48 < x < 57)

z₁ = (48 − 52) / 3

z₁ = -1.33

z₂ = (57 − 52) / 3

z₂ = 1.67

P(-1.33 < z < 1.67) = 0.9525 − 0.0918 = 0.8607

I used a z score table. For more accurate answers, use a calculator.

8 0

2 years ago