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2 years ago

Given f(x) = 3x^2 + 2x – 1 and g(x) = 4x-5 find ( g of f) (-2)

Mathematics

2 answers:

pishuonlain [190]2 years ago

7 0

Answer:

Step-by-step explanation:

Evaluate f(- 2) then substitute the value obtained into g(x)

f(- 2) = 3(- 2)² + 2(- 2) - 1 = 3(4) - 4 - 1 = 12 - 5 = 7 , then

g(7) = 4(7) - 5 = 28 - 5 = 23

miv72 [106K]2 years ago

4 0

$\text{Given that,}\\\\f(x) = 3x^2 +2x -1\\\\f(-2)=3(-2)^2 +2(-2) -1 = 12-4-1=7\\\\g(x) = 4x -5\\\\\text{Now,}\\\\(g \circ f) (-2)\\\\=g(f(-2))\\\\=g(7)\\\\=4(7)-5\\\\=28-5\\\\=23$

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In a survey of 600 students, 80% said they liked pop music. How many students liked pop music?

Licemer1 [7]

Answer:

480 students

Step-by-step explanation:

600 x .80

4 0

2 years ago

The resting heart rate for an adult horse should average about µ = 47 beats per minute with a (95% of data) range from 19 to 75

KatRina [158]

Answer:

a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean:

$\mu = 47$

(95% of data) range from 19 to 75 beats per minute.

This means that between 19 and 75, by the Empirical Rule, there are 4 standard deviations. So

$4\sigma = 75 - 19$

$4\sigma = 56$

$\sigma = \frac{56}{4} = 14$

a. What is the probability that the heart rate is less than 25 beats per minute?

This is the p-value of Z when X = 25. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{25 - 47}{14}$

$Z = -1.57$

$Z = -1.57$ has a p-value of 0.0582.

0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. What is the probability that the heart rate is greater than 60 beats per minute?

This is 1 subtracted by the p-value of Z when X = 60. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{60 - 47}{14}$

$Z = 0.93$

$Z = 0.93$ has a p-value of 0.8238.

1 - 0.8238 = 0.1762

0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. What is the probability that the heart rate is between 25 and 60 beats per minute?

This is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 25. From the previous two items, we have these two p-values. So

0.8238 - 0.0582 = 0.7656

0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

3 0

2 years ago

joe puts $790.00 into a savings account that pays 5.5% simple interest. he leaves the money in his account for two years.

Dmitrij [34]

Answer: $879.29

Step-by-step explanation:

790(1.055)^2

790(1.113025)

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6 0

2 years ago

The lateral area of a cylinder is 325 pi inch^2. The radius is 13 in. Find the surface area and volume. Please show all work!!!

USPshnik [31]

Answer:

Surface area = 663π in².
Volume = (676/3)π in² ≈ 225.33 π in²

Explanation:

1) We know the radius and the lateral area.

2) With the radius you can find the areas of the top and the bottom.

For that, you use the formula:

area of the top = area of the bottom = π r²

∴ π (13 in)² = 169π in² (each)

3) Then, the surface area is the sum of the lateral area and the two bases (top and bottom)

surface area = lateral area + bottom area + top area = 325π in² + 2×169π in² = 663π in².

3) You can also find the height of the cylinder.

Use the formula: lateral area = 2π r h

∴ h = lateral area / [2 π r]

⇒ h = 325 π / [ 2π (13) ] = 12.5 in

4) With the height you can find the volume.

Use the formula: V = (4/3) π r³

∴ V = (4/3) π (13 in)³ = (676/3)π in² ≈ 225.33 π in²

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3 years ago

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Lemur [1.5K]

Answer:

The area of the triangular sail is 216 ft²

Step-by-step explanation:

Since the sail is triangular, we solve the area using the area of a triangle

Area of triangle = 1/2 of base × height

base is 18 and height is 24

Area = 1/2 × 18 × 24

= 9×24

= 216 ft²

5 0

3 years ago