Let f(x)=2x-1 and g(x)=4-x^2. Find (f o g)(x).

Answer:

The below graph represents this scenario.

Step-by-step explanation:

Given,

The deposited amount, P = $ 21,

Annual interest rate, r = 2.4 % = 0.024,

Thus, the simple interest after x years,

[tex]y=P\times r\times t[/tex]

[tex]=21(0.024)(x)[/tex]

[tex]=0.0504x[/tex]

If x-axis shows the number of years and y axis represents the simple interest after x years,

So, y = 0.0504x is a line passes through the origin which will show the given scenario,

( shown below )

Also, x ≥ 0 ( number of years can not be negative )

To find the number of luggage still lost after 5 days, at least 2% of the given day's lost luggage will still be lost after 5 days.

To find the number of luggage still lost after 5 days, we can use the concept of complementary events.

Since 98% of lost luggage is located by the airlines within 5 days, that means 2% of the lost luggage is still not located.

Therefore, at least 2% of the given day's lost luggage will still be lost after 5 days.

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the answer would be b. C=(2,0), A=(0,1), T=(1,4)

all x's move 2 to the right and no change in y

Solution: If a shape is being translated neither it's shape nor size changes.When we translate a shape we just move a shape or geometrical figure by certain distance either horizontally or vertically or both horizontally and vertically.

Coordinates of Triangle CAT is →C(0,0), and A(-2,1), and T(-1,4).

In option (a) vertices C has not been translated , but A and T are translated.Which is Untrue because we have to move all the vertices by same value. But x and y can have different value.

In option (b) all the coordinates C,A,and T is being translated along→ x by 2 units , horizontally right, but not translated in vertical direction.  

C(0,0)⇒C(0+2,0+0)→C(2,0)

A(-2,1)⇒C(-2+2,1+0)→C(0,1)

T(-1,4)⇒C(-1+2,4+0)→C(1,4)

In option C, Coordinates of A and B are changed but not of C, So in this case translation can't happen.

In option D , C is being translated 2 units horizontally left ,  but amount of translation in A and T are different.

So , Option (b) is true.

Answer:

It rises to the left and rises to the right.

Step-by-step explanation:

Let

x----------> charge per hour to rent a jet sky in dollars

y----------> the total cost to rent a jet sky in dollars

we know that

First Jet Sky Company

[tex]y=24.00+2.25x[/tex] ---------> equation [tex]1[/tex]

Second Jet Sky Company

[tex]y=23.00+2.50x[/tex] ---------> equation [tex]2[/tex]

we know that

To find the number of hours for which the costs are the same

equate equation [tex]1[/tex] and equation [tex]2[/tex]

The intersection both graphs is the solution of the problem

using a graph tool

see the attached figure  

the intersection point is [tex](4,33)[/tex]

That means

For [tex]x=4\ hours[/tex]

the cost of the rent is [tex]y=\$33[/tex] in both companies

therefore

the answer is

[tex]4\ hours[/tex]

For 4 hours of booking, the charges paid to both the companies should be same. And the charge will be $ 30.

Let x be the number of hours of booking per jet ski.

First company charges $24.00 plus $2.25 per hour to rent a jet ski.

So, the total cost paid for x hours to the first company will be,

[tex]C_1=24+2.25x[/tex]

Second company charges a fee of $23.00 plus $2.50 per hour to rent the same jet ski.

So, the total cost paid for x hours to the second company will be,

[tex]C_2=23+2.5x[/tex]

Now, the charge paid to both the companies should be same. For this condition, the number of hours of booking per jet ski should be,

[tex]C_1=C_2\\24+2.25x=23+2.5x\\1=0.25x\\x=4[/tex]

Therefore, for 4 hours of booking, the charges paid to both the companies should be same. And the charge will be,

[tex]24+2.25\times4=\$33[/tex].

For visuals, refer the attached graph.

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Answer:B

Step-by-step explanation: The distance traveled by a truck driving at a constant speed compared with time.

Answer:

D)48 × 1 6 = 8 Use the relationship between multiplication and division to explain that 8 ÷ 1 6 = 48 because 48 × 1 6 = 8.

Step-by-step explanation:

By setting up a ratio based on the known miles per gallon, we can determine that Deon would be able to drive 281.5 miles using 11 gallons of gas.

This problem can be solved by setting up a proportion to find out how many miles Deon would drive using 11 gallons of gas. First, we know that Deon can drive 408 miles with 16 gallons of gas. This forms a ratio of 408/16 which simplifies to 25.5. This means Deon can drive 25.5 miles for every gallon of gas. Using this, we can determine how far he would travel with 11 gallons by multiplying the miles per gallon (25.5) by 11.

Therefore, Deon would drive 281.5 miles using 11 gallons of gas.

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To find the area in the right tail more extreme than z= 3.01 in a standard normal distribution, we calculate the p-value as the probability of observing a value more extreme than the test statistic. In this case, the p-value is approximately 0.0103.

The p-value, in statistics, measures the probability of obtaining results as extreme or more extreme than the observed data, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis, typically indicating statistical significance and supporting the alternative hypothesis.

To find the area in the right tail more extreme than z = 3.01 in a standard normal distribution, we need to calculate the p-value.

The p-value is the probability of observing a value more extreme than the test statistic.

In this case, we use the formula P(Z > z) to find the area in the right tail. Using the information given, P(Z > 3.01) ≈ 0.0103.

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To find the area in the right tail more extreme than z= 3.01 in a standard normal distribution, we calculate the p-value as the probability of observing a value more extreme than the test statistic. In this case, the p-value is approximately 0.0103.

The p-value, in statistics, measures the probability of obtaining results as extreme or more extreme than the observed data, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis, typically indicating statistical significance and supporting the alternative hypothesis.

To find the area in the right tail more extreme than z = 3.01 in a standard normal distribution, we need to calculate the p-value.

The p-value is the probability of observing a value more extreme than the test statistic.

In this case, we use the formula P(Z > z) to find the area in the right tail. Using the information given, P(Z > 3.01) ≈ 0.0103.

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To find the area in the right tail more extreme than z= 3.01 in a standard normal distribution, we calculate the p-value as the probability of observing a value more extreme than the test statistic. In this case, the p-value is approximately 0.0103.

The p-value, in statistics, measures the probability of obtaining results as extreme or more extreme than the observed data, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis, typically indicating statistical significance and supporting the alternative hypothesis.

To find the area in the right tail more extreme than z = 3.01 in a standard normal distribution, we need to calculate the p-value.

The p-value is the probability of observing a value more extreme than the test statistic.

In this case, we use the formula P(Z > z) to find the area in the right tail. Using the information given, P(Z > 3.01) ≈ 0.0103.

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1.

 18.98 per 1000

320,000 / 1000 = 320

18.98 x 320 = $6073.60

2. smoker: 9.36 * 100 = 936

 non smoker: 7.85 * 100 = 785

936 - 785 = $151

Answer:

d

Step-by-step explanation:

The proportion given to us is

[tex]\frac{16}{x} =\frac{x}{4}[/tex]

Next we cross multiply to get

[tex]16*4=x*x[/tex]

[tex]64=x^2[/tex]

[tex]x^2=64[/tex]

Take the sqrt on both side to get x

so

[tex]\sqrt{x^2}   = \sqrt{64}[/tex]

x=8

so the correct option is d .

Answer:

B. -6

Step-by-step explanation:

There is a mistake in the question. It would have to say:

Your football team gained four yards on first down and two yards on second down during its last possession

So, your team gained 4 + 2 = 6 yards.

Calling x, the additive inverse of 6, the following equation must be satisfied:

6 + x = 0

x = 0 - 6

x = -6

To find the area of a round footprint with a diameter of 42 cm, you use the formula for the area of a circle, A = πr². The radius is 21 cm, so the area is approximately 1382.74 cm².

To find the area of a round footprint, you use the formula for the area of a circle, which is πr², where r is the radius of the circle.

Therefore, the area of the fossilized footprint is approximately 1382.74 cm².

The average speed for the trip is calculated by using the formula of total distance divided by total time. For a total distance of 130 miles and total time of 2.42 hours, the average speed is approximately 53.72 mph.

In order to find the average speed for the entire trip, we need to use the formula which is total distance travelled divided by the total time taken. The total distance travelled is 100 miles at 60mph plus 30 miles at 40mph, which results in 130 miles.

Now, to find the total time taken, we divide the distance travelled by the speed, which is 100 miles at 60mph results in 1.67 hours and 30 miles at 40mph results in 0.75 hours. Hence, the total time taken is the sum of these two times which is 2.42 hours.

Applying the formula for average speed, i.e., total distance divided by total time, we get 130 miles divided by 2.42 hours results in approximately 53.72 mph which is the average speed for the trip.

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Answer:

Option a. $2,411.44

Step-by-step explanation:

In the table the profit of Mr. Brown's store in all quarters of 2012  was given.

In Quarter 1 Profit was = $9,841.28

In Quarter 2 profit was = $8,957.67

In Quarter 3 profit was = $7,429.84

In Quarter 4 profit was = $11,095.67

To find out the difference between the profits earned in the first quarter and the third quarter, we subtract it.

Difference between profits = 9,841.28 - 7,429.84 = $2,411.44

Answer would be Option a. $2,411.44

Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

The other angles in the isosceles triangle are 40°.

Option D is the correct answer

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Isosceles triangle:

One angle = 100°

We know that,

In an isosceles triangle, there are two equal sides and two equal angles opposite to the equal sides.

The sum of the three angles in the isosceles triangle is 180.

We already have,

One angle = 100°

The other two should be equal.

The sum should give us 180°.

Now,

40 + 40 = 80

100 + 80 = 180°

Thus,

The other angles in the isosceles triangle are 40°.

Option D is the correct answer

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