If f(x) = x² and g(x) = x - 3, then g(f(x)) = ?

Samantha works at a nursery where sh pots plants. It takes her 1-1/2 hours to pot 12 plants. So, Samantha takes7.5 minutes to pot one plant.

Samantha takes 1-1/2 hours to pot 12 plants. To find out how long it takes her to pot one plant, we need to divide the total time taken by the number of plants potted.

There are a few steps we can take to simplify the calculation. First, we can convert 1-1/2 hours to a decimal by adding 1 to 1/2, which gives us 1.5 hours. Then, we can divide 1.5 hours by 12 plants to find the time it takes to pot one plant.

1-1/2 hours = 1.5 hours

Time taken to pot one plant = 1.5 hours / 12 plants

Time taken to pot one plant = 0.125 hours per plant

Finally, we can convert hours to minutes by multiplying by 60.

0.125 hours per plant = 7.5 minutes per plant

Therefore, it takes Samantha 7.5 minutes to pot one plant.

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Question:

Samantha works at a nursery where she pots plants. It takes her 1 1/2 hours to pot 12 plants. How many plants can Samantha pot in 1 hour? (Please give me the equation you used.)

Answer:

Answer is C...........................

Step-by-step explanation:

Answer:

C.) y = -2x

Step-by-step explanation:

To solve for y, u gotta divide both sides by -2 to get y by itself. When u do that, u get -2x.

Answer:

Step-by-step explanation:

Given functions:

Linear functions have the form of

Therefore functions 1. and 4. are linear functions, the other two aren't

Answer:

J (7,0)

Step-by-step explanation:

(x,y)

ordered pair x,y

point J = (7,0)

The future value of the loan is approximately $10,070.29.

To find the interest on the loan, we can use the formula:Interest = Principal × Rate × Time

Given:

Principal (P) = $6000

Rate (R) = 8% per year (0.08 as a decimal)

Time (T) = 6 months (0.5 years)

Plugging in the values into the formula:

Interest = $6000 × 0.08 × 0.5 = $240

Therefore, the interest on the loan is $240.

To find the future value of the loan, we can use the formula for simple interest:

Future Value = Principal + Interest

Given:

Principal (P) = $6000

Interest = $240

Plugging in the values into the formula:

Future Value = $6000 + $240 = $6240

Therefore, the future value of the loan is $6240.

For the second scenario:

Given:

Principal (P) = $9275

Rate (R) = 7.57% per year (0.0757 as a decimal)

Time (T) = 13 months (13/12 years)

To find the interest, we can use the same formula:

Interest = Principal × Rate × Time

Plugging in the values into the formula:

Interest = $9275 × 0.0757 × (13/12) = $795.29

Therefore, the interest on the loan is approximately $795.29.

To find the future value of the loan, we can use the same formula as before:

Future Value = Principal + Interest

Plugging in the values into the formula:

Future Value = $9275 + $795.29 = $10,070.29

Therefore, the future value of the loan is approximately $10,070.29.

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Answer:

Angle B = 51.06 degrees

Step-by-step explanation:

arcsin(7/9)=Angle B

Therefore, Angle B = 51.06 degrees

Answer:

Use the quadratic formula to solve. Show work describe solution.

Step-by-step explanation:

The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.

The quadratic formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.

For example, let's say we have the equation 2x^2 + 5x - 3 = 0.

Here, a = 2, b = 5, and c = -3.

Plugging these values into the quadratic formula, we get:

x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)

Simplifying the expression inside the square root:

x = (-5 ± sqrt(49)) / 4

x = (-5 ± 7) / 4

We get two solutions:

x = (-5 + 7) / 4 = 1/2

x = (-5 - 7) / 4 = -3

So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.

These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.

Based on the information, the y-intercept is (0, 6.5).

The function is increasing.

Based on the information, we can use the variable x. This will be:

0 = 6.5 + 5.25%x

-6.5 = 5.25%x

x = -6.5 / 5.25% ≈ -123.81

There's no x intercept due to the negative value which doesn't make sense in this scenario.

In order to find the y-intercept, we set x = 0 and evaluate b(x):

b(0) = 6.5 + 5.25% × 0 = 6.5

Therefore, the y-intercept is (0, 6.5).

The function b(x) is increasing since the coefficient of x is positive (5.25%). This means that as the number of engines produced (x) increases, the time it takes to manufacture the engines also increases.

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Answer:

6.2 feet

Step-by-step explanation:

Answer:

his daughter is ten

hope this helps

Step-by-step explanation:

Answer:

(40÷5) +2 = 10

Step-by-step explanation:

his daughter is 10 years old

Answer:

- (x-1)^2 x (x+3)  is correct ans

Step-by-step explanation:

rewrite the expression

-x^3 - x^2 + 5x - 3

factor the expressions

x^3 + x^2 -2x^2 +2x=3x-3

factor the expression

-x^2 x (x-1)-2x x (x-1) +3 (x-1)

rewrite the expression

-(x-1) x (x^2 + 2x-3)

rewrite

-(x-1) x (x^2 + 3x - x - 3)

factor the expression

-(x-1) x (x^2+2x-3)

factor the expression

-(x-1) x (x x(x+3)-(x+3)

write in exponential form

-(x-1) x (x+3) x (x-1)

solution:

-(x-1)^2 x (x+3)

(Hope this helps can I pls have brainlist (crown)☺️)

In statistics, p hat is used as an estimator of the population proportion (p) of a categorical variable. It is the sample proportion of the variable, which is calculated as the number of occurrences of a particular category in the sample divided by the total sample size.

The reason why p hat is used is that it provides an estimate of the unknown population proportion based on a representative sample. By using p hat, we can draw inferences about the population proportion with a certain level of confidence. This is important in hypothesis testing and confidence interval estimation, where we want to make statements about the population based on the information gathered from a sample.

Using p hat as an estimator of p is also beneficial because it has desirable statistical properties, such as being an unbiased estimator, having a sampling distribution that approaches normality, and having a known standard error.

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The probability that the 3 companies will be the 3 with the best future earnings is 5/100 .

There are a total of 20 possible combinations of 3 companies that Mr. Way can sell stocks from. However, we are only interested in the probability of him selecting the 3 companies with the best future earnings. Since we do not know the actual future earnings of each company, we can assume that all 6 companies have an equal chance of being in the top 3.

Therefore, the probability of Mr. Way selecting the 3 companies with the best future earnings is the same as the probability of selecting any specific set of 3 companies out of the 6.

The number of ways to select 3 companies out of 6 is given by the combination formula, which is:

6! / (3! x 3!) = 20

Therefore, the probability of Mr. Way selecting the 3 companies with the best future earnings is 1/20. So, the answer is:

Probability = 1/20

This can also be written as a fraction, which is probability = 0.05 or 5/100

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The canopy of a parachute is a semicircle with a radius of 13 feet. Therefore, the correct option is 88.5 ft².

Area of a circle = πr²

where π = 3.14 and r = radius

We can double the area of a semicircle to get the area of a full circle and divide by 3 to get the area of each section (one-third) of the circle, which is equal to one-third of the semicircle.

Now, the area of the semicircle (canopy) of the parachute is given as follows:

Area of semicircle \(= πr²/2A\)

rea of semicircle \(= 3.14 × 13²/2\)

Area of semicircle \(= 3.14 × 169/2\)

Area of semicircle \(= 528.86/2\)

Area of semicircle \(= 264.43 ft²\)

The area of each of the three equal sections of the semicircle (canopy) of the parachute is given as follows:

Area of each section \(= (1/3) × (264.43)\)

Area of each section \(= 88.14 ft²\)

Approximately 88.5 ft² of each color (red, white, and blue) will be needed to make a single parachute canopy. Therefore, the correct option is 88.5 ft².

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Answer:

The range gives you the spread of the whole data set, the interquartile range gives you the spread of the middle half of a data set.

Step-by-step explanation:

Answer: The answers are 20% and 40%

Step-by-step explanation:

Cost price is $240,000

The percentage of $48000 will be

(48000/240000) × 100

= 20%

The percentage of $96000 will be

(96000/240000) ×100

= 40%

Answer:

(a , n ) = ( 1, - 4/7 )

Steps:

1- rewrite the expression

2- solve the equation

3- substitute the value of a

4- solve the equation

5- a possible solution is

6- check the solution

7- simplify

8- the ordered pair is a solution  

The radius of the sphere is approximately 5.22. The equation of the sphere is x^2 + y^2 + z^2 - 7x + 3y - 2z = 14.6784.

To find the centre of the sphere, we first need to find the midpoint of the diameter. Using the midpoint formula, we have:
Midpoint = ((5+2)/2, (-1-2)/2, (6+(-4))/2) = (3.5, -1.5, 1)
Therefore, the centre of the sphere is (3.5, -1.5, 1).
To find the radius of the sphere, we need to find the distance between the centre and one of the endpoints of the diameter. Using the distance formula, we have:
r = √[(5-3.5)^2 + (-1-(-1.5))^2 + (6-1)^2] = √[(1.5)^2 + (0.5)^2 + (5)^2] = √(27.25) ≈ 5.22
Therefore, the radius of the sphere is approximately 5.22.
The standard equation of a sphere with centre (h,k,l) and radius r is:
(x-h)^2 + (y-k)^2 + (z-l)^2 = r^2
Plugging in the values we found, we have:
(x-3.5)^2 + (y-(-1.5))^2 + (z-1)^2 = (5.22)^2
Expanding and simplifying, we get:
x^2 - 7x + 12.25 + y^2 + 3y + 2.25 + z^2 - 2z + 1 = 27.3284
Rearranging and simplifying further, we get:
x^2 + y^2 + z^2 - 7x + 3y - 2z = 14.6784
Therefore, the equation of the sphere is x^2 + y^2 + z^2 - 7x + 3y - 2z = 14.6784.

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The Tonga Trench is deeper than the Puerto Rico Trench.

Generally, Other major tectonic features in the region include the Mariana Trench, the Mariana Arc, the Volcano Arc, the Caroline Islands Arc, and the Palau Microplate.

The region is earthquake-prone and has experienced several large earthquakes in recent years, including a 7.7 magnitude quake in the Mariana Trench in 2020 and a 7.6 magnitude quake in the Solomon Islands in 2013. The region is also home to several active volcanoes, including the Kavachi volcano in the Solomon Islands and the Taal volcano in the Philippines.

The region is home to a wide variety of marine life, including whales, dolphins, sharks, sea turtles, and a variety of fish. The region is also home to some of the world's most spectacular coral reefs, including the Great Barrier Reef in Australia and the Tubbataha Reefs in the Philippines.

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There are 41 ways to distribute five distinguishable objects into three indistinguishable boxes.

The boxes are indistinguishable, there are 5 different ways to arrange the number of balls in each box: (5,0,0), (4,1,0), (3,2,0), (3,1,1), or (2,2,1).

There is 1 way to put all 5 balls in one box i.e (5,0,0)

(4,1,0): There are 5 choices for the 4 balls in one of the boxes.

(3,2,0): There are 10 choices for the 3 balls in the boxes.

(3,1,1): There are 10 choices for the 3 balls in one of the boxes, and we can simply split the last two among the other indistinguishable boxes.

(2,2,1): There are 10 options for one of the boxes with two balls, then 3 options for the second box with two balls, and one for remaining for the third.

Therefore the boxes with two balls are indistinguishable, we are counting each pair of balls twice so we have to divide by two.

So there are (10×3)/2=15 arrangements of balls as (2,2,1).

Hence the total number of arrangements for 3 indistinguishable boxes and 5 distinguishable balls is 1+5+10+10+15=41.

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Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

total number of marbles= 5+2+3+5 = 15 marbles

probability of a red marble - 2/15

probability of yellow marble - 5/15 = 1/3

Answer:

i) 2/15 ii) 1/3

Step-by-step explanation:

the number of marbles all together is 15

2 out of the 15 are red, so 2/15

5 out of 15 are yellow,so 5/15, simplified to 1/3

The probability that the described situation could occur as required in the task content is; 1 / 100.

It follows from the task content that the you selection is done such that there's replacement.

Since the treasure chest contains 10 different toys, the probability of selecting a crazy straw two times consecutively is;

= 1/10 × 1/10

= 1 / 100.

Ultimately, the probability that the given situation occurs as described is; 1 / 100.

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A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.

A slant asymptote exists of the form y = mx + b where m ≠ 0.

Vertical lines go up and down and are in the form of x = a, where a stands for the common x-coordinate of all locations, whereas horizontal lines go left to right and take the shape of y = b, where b stands for the y-intercept.

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's domain, the graph can never cross it. There may be multiple vertical asymptotes for a given function. All common factors are cancelled in the denominator, D(x).

A horizontal asymptote exists of the form y = k where x→∞ or x→ -∞ if the value of the one/both of the limits lim ₓ→∞ f(x) and lim ₓ→ -∞ f(x).

A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.

A slant asymptote exists of the form y = mx + b where m ≠ 0.

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Answer:¿De qué número 48 es el 20%:240

Step-by-step explanation:Estos son los pasos para mostrarle cómo encontrar el porcentaje del 20% de qué número = 48.

Answer:

x=3

y=4

z=1

Step-by-step explanation:

4x-2y+6z=10

-(4x+12y+4z=64)

= -14y+2z=-54

= -7y+z=-27

-7y+z=-27

+(5y-z=19​)

= -2y=-8

y=4

5(4)-z=19

20-z=19

z=1

x+12+1=16

x=3