If f(x) = x² + 5 and g(x) = 3x, find (f o g)(x) and (g o f)(x) .

The probability of the sample mean is 0.2008.

What is probability?
Probability is the quality or state of being probable the extent to which something is likely to happen or be the case.

Sol-Let x be a continuous random variable that has a normal distribution with
μ=48 and σ=8
Thus,
X~N(48,8^2/16)
The standardized value of x is obtained by :
Z= X-48/√8^2/16~N(0,1)

The probability that the sample mean x for a random sample of 16 taken from this population will be between 49.62 and 52.80 can be obtained as:

P(49.62<x<52.80)

P=(49.62-48/√8^2/16<x-48/√8^2/16<52.80-48/√8^2/16)

=P(0.81<Z<2.4)

=P(Z<2.4)-P(Z<0.81)

=0.9918-0.7910

=0.2008
There for the probability is 0.2008.

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to convert Fahrenheit to Celcius we have to apply the next formula:

C°= (F°-32) x 5/9

Replacing:

C = (103-32)x 5/9

C = 71 x 5/9

C = (71 x5)/9 = 355/9

You can write the relation between distance and time, as follow:

y = kx

where y is the distance, x is the time and k is the constant of proportionality.

k can be obtained with the given information, as follow:

k = 90/30 = 3

Then, the equation of the relationship is:

y = 3x,

for a time of 10 seconds, the distance traveled is:

y = 3(10) = 30

Hence, the answer is:

y = 3x , 30 feet

Answer:

yes it's is shown in the diagram below and prosperity more than your expectation for me too anymore I just

To complete the perfect trinomial, we add (5/2)² to the given equation and get:

Subtracting 6 we get:

Therefore:

Finally, we get:

Answer:

The second one is the Multiplicative Property of Zero.
The fourth one is the Commutative property.

Answer:

The second and third one

Step-by-step explanation:

After conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.

So, 11/3÷2/3:

Therefore, after conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.

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Given Data:

Total working hours is = 51 hours.

Pay rate=$8.45.

OT rate=1.5 times the regular pay rate.

Regular working hours is 40 hours.

Regular pay can be determined as,

Thus, the regular pay is $338.

The OT rate can be determined as,

Thus, the overtime rate is $ 12.68.

The overtime pay can be determined as,

Thus, the overtime pay is $139.43.

The gross pay can be determined as,

Thus, the gross pay is $ 447.425.

The order of the values using the basic unit of meters from smallest to largest. is: 109000 mm < 2.6 km < 41.7 hm

What are the units of measurement of distance or length?

Distance is the gap between any two points under consideration.

The basic unit for measuring distance is the meter.

There are larger as well as smaller units for measuring length or distance which are based on the unit of meter.

The units are as follows:

millimeter, mm = 0.001 m

centimeter, cm = 0.01 m

decimeters, dm = 0.1 m

meter, m = 1 m

kilometer, km = 1000 m

hectometer, hm = 100 m

Now to compare the given quantities making the units same as two quantities can only be compared only when there units are same :

Considering the given values;

2.6 km = 2600 m

109,000 mm = 109 m

41.7 hm = 4170 m

Therefore, after comparison arranging the quantities in order from smallest to largest is 109000 mm < 2.6 km < 41.7 hm

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We will get 406 after multiplication .

What does multiply mean?

   58 * 7 = 406

We will get 406 after multiplying .

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Data Input

1 Adult + 2 children

The price for all three family members

$76

Procedure

Adult ticket = $28

1 Adult + 2 children = $76

2 children = 76 - 1 adult

2 children = 76 - 28

2 children = 48

children = 48/2

children = 24

Therefore

hello

to solve this question, we have to use trigonometric ratios and in this case, it was specified to use tangent

from the image above, we can see that we have the value of angle and opposite and we need to look for adjacent

trigonometric ratio is given as SOH CAH TOA

now, let's use the formula of tangent to solve this problem

from the calculations above, the value of x is equal to 20.48

4 basketballs

Explanation

Step 1

Ms. Banks divides 18 basketballs evenly among 3 bag

divide the 18 basketballs by 3 bags

Step 2

now, she takes 2 from each bag, so

Hence, the answer is 4 basketballs.

I hope this helps you

[tex]y = -1.25 x^{2}+ 5[/tex]  is the needed quadratic function in standard form.

A quadratic equation is one with a single degree 2-variable and has the general form  [tex]a x^{2} + bx + c = 0.[/tex]  a, b, and c is the constant value, and x consists of a variable.

The quadratic equation's x-intercepts are (-5, 0). That indicated that the quadratic equation's two elements are (x + 5) and (x -0).

f(x) = a (x + 5) (x - 0) (x - 0)

= ax+5a

f(x) = [tex]ax^{2} +5x[/tex]

The quadratic equation's graph goes through (4, 0). Therefore, we must change equation 1 to read x = 4 and f(x) = 0.

0 = a × 4² + (5 × 4)

0 = a × 16 +20

a = [tex]\frac{-20}{16}[/tex]

=-1.25

The quadratic equation is known to have the form ax² + bx + c = 0.

f(x) = -1.25[tex]x^{2}[/tex] + 5x  

Consider y= F(x)

∴ The required quadratic equation of function in the standard form is Y = -1.25 x² + 5x.

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Answer: No

Step-by-step explanation:

The graph fails the vertical line test, and thus the graph does not represent a function.

The question wants the "lowest common multiple" of 6 and 9, so first, lets find some of the miltiples of 6 and 9:

We can see that 18 is a commom multiple of 6 and 9, and is also the smallest, so the lowest common multiple of 6 and 9 is 18. So the least number of gift bags and bows that Rachel can buy is 18.

A)

In order to check this sentence, we need to convert the value from foot to yard.

Knowing that 1 yard is equal 3 feet, we have that:

So Debbie's affirmation is incorrect, therefore we disagree.

B)

First we need to calculate the area of the table cloth.

Converting the length to foot, we have:

Now, calculating the area (which is the product of the length and the width), we have:

If each square foot is $0.25, we just need to multiply the area by the cost of one square foot in order to find the cost of the fabric for the table cloth:

So the cost is $30.

Denominator has been factorized on the right.

Now we need to write this fraction as a sum of two fraction.

when x = 8 we have following

Similarly when x =-4 A = 17/12 these are the constants

Answer:

x=\frac{1}{4}(h-12y-2)x=4

Step-by-step explanation:x=\frac{1}{4}(h-12y-2)x=

4

1

(h−12y−2)

Step-by-step explanation:

We are given the equation h=4(x+3y)+2h=4(x+3y)+2 .

Simplifying for x, we get,

h=4(x+3y)+2h=4(x+3y)+2

i.e. h=4x+12y+2h=4x+12y+2

i.e. 4x=h-12y-24x=h−12y−2

i.e. x=\frac{1}{4}(h-12y-2)x=

4

1

(h−12y−2)

Thus, the equation for x is x=\frac{1}{4}(h-12y-2)x=

4

1

Answer:

152 cm

Step-by-step explanation:

Perimeter of kite= 2(a+b)

P= 2(AB+CD) = 2(29+47) = 2 *(76) = 152 cm.

If something remains unclear, be free to ask questions!

The total surface area Paul is required to paint is 36 yard square.

He needs to buy paint to cover all outside surfaces of his shed .

2 sides of shed are rectangles with a base of 12ft and a side of 6 ft.

Therefore,

area of a rectangle = lw

where

area of the rectangle = 12 × 6

area of the rectangle = 72 ft²

The rectangle are two.

Hence, area of the two rectangular faces = 72 + 72  = 144 ft²

The other two sides are squares with sides of 6 ft.

Therefore,

area of the two squares = 6² + 6² = 36 + 36 = 72 ft²

The roof consists of four triangles,

2 of the triangles have a base of 6 feet and a height of 6 feet.

Therefore,

area of the two triangles = 2 (1 / 2 × 6 × 6) = 36 ft²

The other two triangles have a base of 12 ft and a height of 6 ft.

area of the other triangle = 2(1 / 2 × 12 × 6) = 72 ft²

Hence,

total area the paint will cover = 72 + 36 + 72 + 144 = 324 ft² = 36 yard²

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ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following system of equations:

To graph, we calculate the intercepts in each equation to then draw the straight line corresponding to each equation, like this:

Now we graph:

EXPLANATION

Since the figure is like a pentagon, we need to add the interior angles in order to get the needed angle.

The first part of the figure is composed of a square with two right angles of 90 degrees and two angles of 135, making a total of 90+90+135+135 = 450 degrees.

The left needed angle should add a total of 540 degrees, by the Sum of Interior Angles of a Pentagon Theorem, as follows:

450 + bottom angle = 540

Subtracting -450 to both sides:

bottom angle = 540 - 450

Subtracting angles:

bottom angle = 90 degrees

In conclusion, the value of the bottom angle is 90 degrees.

If an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours, then Graph H  best represents this rate.

The graphs are attached

Given that the oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours,

hence the rate at which the shaft drills = 7 meter / 2 hours = 3.5 meters per hour

Since the drill goes into the ground, hence the rate is negative that is -3.5 meters per hour

The slope (rate of change) of a line (m) is given by:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

a) For graph F, the line passes through the point (0,0) and (10, -20). Hence:

Slope of the line , [tex]m = \frac{-20 - 0}{10 - 0}[/tex]

Slope of the line is - 2 meters per hour

b) For graph G, the line passes through the point (0,0) and (10, -70). Hence:

Slope of the line, [tex]m = \frac{-70 - 0}{10 - 0}[/tex]

Slope of the line is -7 meters per hour

c) For graph H, the line passes through the point (0,0) and (10, -35). Hence:

Slope of the line, [tex]m = \frac{-35 - 0}{10 - 0}[/tex]

Slope of the line is -3.5 meters per hour

d) For graph J, the line passes through the point (0,-3.5) and (10, -3.5). Hence:

Slope of the line, [tex]m = \frac{-3.5 - 3.5}{10 - 0}[/tex]

Slope of the line is 0 meters per hour.

Therefore, if an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours, then Graph H  best represents this rate.

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There would be 20 guests for the restaurants to cost the same

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, we have the following parameters:

Red Lobster

Rate per person = $30

Set up fee = $100

Olive Garden

Rate per person = $25

Set up fee = $200

So, the equations of the restaurants are

Red Lobster = 30g + 100

Olive Garden = 25g + 200

Where the number of guests is g

When the restaurants cost the same amount, we have

Red Lobster = Olive Garden

Substitute the known values in the above equation

So, we have

30g + 100 = 25g +200

Evaluate the like terms

5g = 100

Divide by 5

g = 20

Hence, the number of guests is 20

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Answer: (-1, 0)

The interval of decreasing refers to the interval of x-values where the graph is decreasing or going down.

If we look at the graph:

We can see that the graph starts to decrease or "go down" at values x = -1 and x=0. With this, we can conclude that the interval of decrease for the given graph is (-1, 0)

Percentage of a number

Find a number which

its a 100% percentage

henW

When 232 is 290%

Then find

X = (100%/290)• 232

Divide 232/29 = 10% = 8 exactly

Now multiply by 10 = 10• 8 = 80

Then 100% = 80

The better deal between the offer at Mystic Bank and Four Rivers Bank is the deal at Mystic Bank.

In order to determine which bank has the better offer, the future value of the investment options have to be determined.

The future value of an investment is a function of the amount investment, the number of compounding, the years of the investment and the interest rate.

When an investment is compounded semi-annually, it means that it grows exponentially twice in a year. When an investment is compounded quarterly, it means that is grows exponentially four times in a year.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Interest rate at Mystic bank = 10% /2 = 5%

Interest rate at Four Rivers Bank = 8% / 4 = 2%

Future value of the investment at Mystic bank :

$10,000 x (1.05)^(2 x 4) = $14,774.55

Future value of the investment at Four Rivers Bank :

$10,000 x (1.02)^(4 x 4) = $13,727.86

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