12. Look for Relationships In the graph of a
vertical motion model shown, how is the initial
velocity related to the vertex of the parabola?

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

x = 4

Step-by-step explanation:

Given

4.5x = 18 ( divide both sides by 4.5 )

x = 4

Answer:

x=4

Step-by-step explanation:

to isolate x, we need to divide both sides by 4.5, and 18/4.5 is equal to 4, so x=4.

Answer: 5

Step-by-step explanation:

Answer: Another factor is 3x + 5.

Step-by-step explanation:

please view the attachment for the steps.

The other factor of the polynomial (6x² + x - 15) would be (3x + 5). Hence option 2 is true.

Given that the polynomial is,

6x² + x - 15

And, The polynomial has a factor of 2x - 3.

Now apply the factorization method to solve for the  factor,

6x² + x - 15

6x² + (10 - 9)x - 15

6x² + 10x - 9x - 15

2x (3x + 5) - 3 (3x + 5)

(2x - 3) (3x + 5)

Since The polynomial has a factor of 2x - 3.

Hence, the other factor would be (3x + 5). So option 2 is true.

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a) Joint probabilities:

P(Female and Brand 1) ≈ 0.09

P(Female and Brand 2) ≈ 0.06

P(Female and Brand 3) ≈ 0.22

P(Male and Brand 1) ≈ 0.25

P(Male and Brand 2) ≈ 0.17

P(Male and Brand 3) ≈ 0.21

b) Marginal probabilities:

P(Female) ≈ 0.37

P(Male) ≈ 0.63

P(Brand 1) ≈ 0.34

P(Brand 2) ≈ 0.23

P(Brand 3) ≈ 0.43

c) Conditional probabilities (given gender):

P(Brand 1 | Female) ≈ 0.243

P(Brand 2 | Female) ≈ 0.162

P(Brand 3 | Female) ≈ 0.595

P(Brand 1 | Male) ≈ 0.397

P(Brand 2 | Male) ≈ 0.270

P(Brand 3 | Male) ≈ 0.333

a) Joint probabilities:

The joint probabilities represent the probability of two events occurring together. In this case, we want to calculate the probabilities of each combination of gender and brand.

P(Female and Brand 1) = 9/100 = 0.09

P(Female and Brand 2) = 6/100 = 0.06

P(Female and Brand 3) = 22/100 = 0.22

P(Male and Brand 1) = 25/100 = 0.25

P(Male and Brand 2) = 17/100 = 0.17

P(Male and Brand 3) = 21/100 = 0.21

b) Marginal probabilities:

The marginal probabilities represent the probabilities of each individual event, regardless of the other variable. Here, we want to calculate the probabilities of each gender and brand separately.

P(Female) = (9 + 6 + 22)/100 = 0.37

P(Male) = (25 + 17 + 21)/100 = 0.63

P(Brand 1) = (9 + 25)/100 = 0.34

P(Brand 2) = (6 + 17)/100 = 0.23

P(Brand 3) = (22 + 21)/100 = 0.43

c) Conditional probabilities (given gender):

The conditional probabilities represent the probabilities of choosing a specific brand given the gender. We can calculate these by dividing the joint probabilities by the corresponding marginal probabilities for each gender.

P(Brand 1 | Female) = P(Female and Brand 1) / P(Female) = 9/37 ≈ 0.243

P(Brand 2 | Female) = P(Female and Brand 2) / P(Female) = 6/37 ≈ 0.162

P(Brand 3 | Female) = P(Female and Brand 3) / P(Female) = 22/37 ≈ 0.595

P(Brand 1 | Male) = P(Male and Brand 1) / P(Male) = 25/63 ≈ 0.397

P(Brand 2 | Male) = P(Male and Brand 2) / P(Male) = 17/63 ≈ 0.270

P(Brand 3 | Male) = P(Male and Brand 3) / P(Male) = 21/63 ≈ 0.333

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Answer:

147 is one such number and least number. This discussion on What is the least number which when divided by 8, 12 and 16 leaves 3 as the remainder in each case, butwhen divided by 7 leaves no remainder?

Notice that the prime factorization of \(20^{20}\) and \(10^{10}\) are \(2^{40}\cdot5^{20}\) and \(2^{10}\cdot5^{10}\), respectively. also, notice that both of their prime factorizations contain only 2 and 5.

Let the divisor of 20^20 that is a multiple of 10^10 be:

\(2^y\cdot5^x\cdot2^{10}\cdot5^{10}\\=2^{10+y}\cdot5^{10+x}\)

where y and x are positive integers.

We can have y equal to 0, 1, 2, ... 30 before the exponent of 2 exceeds 40, and we can have x equal to 0, 1, 2, ... 10 before the exponent of 5 exceeds 20.

That is 11*31= 341 numbers in total.

There are (40+1)(20+1)=861 factors in 20^20, which means that the final answer is:

\(\boxed{\frac{341}{861}}\)

also are you, by any chance, the same guest who posted the same question in web2.0?

Answer:

B!!!!

Step-by-step explanation:

Answer:

 D. (900 mi)/(? hours)

Step-by-step explanation:

The given fraction has miles in the numerator and hours in the denominator. To write a proportion, you need to equate that to a fraction that has miles in the numerator and hours in the denominator. The (miles, hours) pair of interest is (900 miles, ? hours), so the necessary proportion is...

Answer:

7 quarts.

Step-by-step explanation:

First, let's convert all the units to quarts. There are 2 pints in 1 quart, so 5 pints of orange sherbet is equivalent to 5/2 = 2.5 quarts. Similarly, 7 pints of vanilla ice cream is equivalent to 7/2 = 3.5 quarts. The recipe calls for 6 quarts of lemonade and 2.5 quarts of orange sherbet, for a total of 6 + 2.5 = 8.5 quarts of liquid. Since the punch bowl holds 4 gallons, which is equivalent to 4 * 4 = 16 quarts, Jasmine needs to add 16 - 8.5 = 7.5 quarts of ginger ale to the punch bowl. Since 1 quart is equivalent to 2 pints, Jasmine needs to add 7.5 * 2 = <<7.5*2=15>>15 pints of ginger ale to make one bowl of punch. Thus, the correct answer is 7 quarts.

Tell me if this helped :)

graph c is the right answer

Step-by-step explanation:

by solving the linear equation with one variable

we have constant value for y= - 3

so

x changes and y remain same

as we know

the 2nd coordinate show y axis in order pair

so we have to look

for change of x but no Change in y coordinate in order pair

which is in graph c

(0,-3),(1,-3)

so graph c is the answer

i hope you get it

100% of the F2 generation plants are expected to be tall and produce round fruit.

The given information suggests that F1 and F1 represent heterozygous tall and round plants, respectively. When these two genotypes are crossed, we can predict the possible genotype and phenotype combinations of the offspring by using a Punnett square.

The Punnett square for this cross would be:

F1     F1

F2 F1F1 F1F1

F1F1 F1F1

From this square, we can see that all of the F2 generation plants will be homozygous for both tallness and roundness. This is because the F1 generation is heterozygous for both traits, so when they are crossed, the recessive alleles are masked by the dominant alleles.

Therefore, the genotype of all F2 plants will be F1F1, and they will all be tall and round.

In summary, 100% of the F2 generation plants are expected to be tall and produce round fruit.

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Answer:

x = -12

Step-by-step explanation:

\( {7}^{ - 9} \times {7}^{ - 3} = {7}^{x} \)

the base is equal so we can add the number above

\( {7}^{ - 9 + ( - 3)} = {7}^{x} \)

\( {7}^{ - 12} = {7}^{x} \)

the base is equal so is the number above

-12 = x

Answer:

x = 14.4

Step-by-step explanation:

Using dilations, the following equation can be written to show the relationship between the two similar triangles:

x/4 = (6.5 + 2.5)/2.5

x/4 = 9/2.5

Cross multiply

x*2.5 = 9*4

2.5x = 36

2.5x/2.5 = 36/2.5

x = 14.4

Answer:

look at the picture

Step-by-step explanation:

The population of interest in this study is the youth population aged 15-24 years in British Columbia.

b) The sampling frame in this study is the list of colleges and high schools that were visited by the police department.

c) The bias in this survey is called social desirability bias.

Many students who have used cannabis may be afraid or hesitant to admit it to a uniformed police officer due to social stigma, fear of legal consequences, or other reasons.

This can lead to underreporting or inaccurate reporting of cannabis use.

d) The bias that can result from the sampling frame used is known as selection bias.

The sample of students selected may not be representative of the entire youth population in British Columbia.

For example, if certain schools or colleges were excluded from the sampling frame, it may not provide a comprehensive representation of all youth in the province.

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The probability that 2 out of 10 call center representatives will be rated as unsatisfactory is approximately 0.002853, or 0.2853%.

To find the probability that 2 out of 10 call center representatives will be rated as unsatisfactory, we can use the binomial probability formula.

The formula is:
P(X=k) = (n C k) * p^k * (1-p)^(n-k)

Where:
P(X=k) is the probability of getting exactly k successes in n trials
n is the number of trials (sample size), which is 10 in this case
k is the number of successes (call center representatives rated as unsatisfactory), which is 2 in this case
p is the probability of success (call center representatives rated as unsatisfactory), which is 5% or 0.05

Using this information, we can calculate the probability as follows:

P(X=2) = (10 C 2) * 0.05^2 * (1-0.05)^(10-2)

Calculating this equation gives us:

P(X=2) = (10 C 2) * 0.05^2 * 0.95^8

The combination formula (10 C 2) can be calculated as:

(10 C 2) = 10! / (2! * (10-2)!)

Simplifying further:

(10 C 2) = 10! / (2! * 8!)

Calculating 10! and 8! gives us:

(10 C 2) = 10 * 9 / (2 * 1)

Simplifying:

(10 C 2) = 45

Substituting the values back into the equation:

P(X=2) = 45 * 0.05^2 * 0.95^8

Calculating this equation gives us:

P(X=2) = 0.002853

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The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

-5639801 this the answer all you have to do is multiply 2 three times by itself which equals 8 then multiply 5 six times by itself and you get 15625 then multiply 7 eight times by itself and that equals 5764801 the multiply 8 x 15625  which will be 125000 then subtract that by 5764801 and you should get -5639801

The length of x is 3√10 units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the hypotenuse c. Pythagoras, a Greek philosopher who was born around 570 BC, is remembered by the theorem's name. The theorem has likely been proved the most times of any mathematical theorem using a variety of techniques.

As per the given data:

Perpendicular = 9 units

Base = 3 units

Using Pythagoras theorem to find x (hypotenuse):

\(x^2 = 9^2 + 3^2\\x^2 = 81 + 9\\x^2 = 90\\x = \sqrt{90}\\x = \sqrt{9\times10}\\x = 3\sqrt{10}\)units

Hence, the length of x is 3√10 units.

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Answer:

Wheres the question

Step-by-step explanation:

To find the time until the ball hits the ground, you need to solve the quadratic as the height equals zero.

0 = -16t^2+50t

This gives us a classing quadratic that you can factor or use the quadratic formula to solve.

x = 0, x = 25/8

If you graph this, think of y = 0 as the ground, so when the parabola intersects the x-axis on the right that represents how much time would have passed.

Hope this helps you out! Good luck with your homework! Stay safe and stay healthy.

30 hours of use by the Washington family sprinkler and 35 hours of use by the Bennett family sprinkler.

We can find how long was each sprinkler used by substitution method.

Let W = hours of use by the Washington family

65 - W = hours of use by the Bennett family

According to the question we get

15W + 40(65 -W) = 1850

15W + 2600 - 40W = 1850

-25W = -750

W = 30

Now, put the value of W in 65 - W to calculate the hours used by the Bennett family

65 - W = 65 - 30 = 35

Thus, the amount of time used for sprinklers by the Washington family and the Bennett family is 30 hours and 35 hours, respectively.

--The given question is incomplete, the complete question is

"The Washington family and the Bennett family each used their sprinklers last summer. The water output rate for the Washington family's sprinkler was 15L per hour. The water output rate for the Bennett family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850L. How long was each sprinkler used?"--

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In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.

That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.

We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.

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Answer:

3460 m

Step-by-step explanation:

There are 1000 meters in a kilometer and since Doreen walks 3.46 km, she must walk 3460 m.

3.46 x 1000 = 3460

Answer:

3.46 km = 3.46*1000m = 3460 m

Answer:

4.1

Step-by-step explanation: