y=-3x + 4
y = 3x - 2
What solution does this system have? How do you
know? Justify(explain).

Answer:

[tex](g*f)(x) = 34[/tex]

Step-by-step explanation:

For sake of clarity, [tex](g * f)(x) = g(f(x))[/tex]

First, find [tex]f(1)[/tex]

[tex]f(1) = 2(1)^2 - 2(1) - 4\\f(1) = 2-2-4 \\f(1)=-4[/tex]

Then, take what you got for [tex]f(1)[/tex] and plug that into [tex]g(x)[/tex].  In this case, [tex]f(1) = -4[/tex]

[tex]g(-4) = -5(-4) + 14\\g(-4)= 20 + 14\\g(-4) = 34[/tex]

Please make sure to mark brainliest if this satisfies your

Answer:

The range would be 50.

Step-by-step explanation:

Range is found by putting a list or set of numbers in order, then subtracting the lowest number from the highest.

32, 61, 63, 52, 82

82 - 32 = 50

Answer:

389.19 m²

Step-by-step explanation:

The surface area of the box = area of the two equal triangles + area of the 3 different rectangles

✔️Area of the two equal triangles:

Area = 2(½*base*height)

base = 7 m

height = 8 m

Area of the two triangles = 2(½*7*8) = 56 m²

✔️Area of rectangle 1:

Area = Length*Width

L = 13 m

W = 7 m

Area of rectangle 1 = 13*7 = 91 m²

✔️Area of rectangle 2:

L = 13 m

W = 8 m

Area of rectangle 2 = 13*8 = 104 m²

✔️Area of rectangle 3:

L = 13 m

W = 10.63 m

Area of rectangle 3 = 13*10.63 = 138.19 m²

✅Surface Area of the box = 56 + 91 + 104 + 138.19 = 389.19 m²

Answer:

x = -8

Step-by-step explanation:

these angles are vertical, therefore they are equal

x + 78 = 70

x = -8

Answer:

m ÷ 7

Step-by-step explanation:

"Quotient" means you're dividing, so this just means you're dividing m by 7.

The total area of the regions between the curves is 1/3 square units

The total cost for making the first 10 units is 7.79

From the question, we have the following parameters that can be used in our computation:

y = √x and y = x²

With the use of graphs, the curves intersect at

x = 0 and x = 1

So, the area of the regions between the curves is

Area = ∫x² - √x

Integrate

[tex]Area = \frac{x^3}{3} - \frac{2x^\frac32}{3}[/tex]

Recall that x = 0 and x = 1

So, we have

[tex]Area = (\frac{0^3}{3} - \frac{2 * 0^\frac32}{3}) - (\frac{1^3}{3} - \frac{2 * 1^\frac32}{3} )[/tex]

Evaluate

Area =  0 + 1/3

Evaluate

Area =  1/3

Hence, the total area of the regions between the curves is 1/3 square units

Given that

MC(x) = √(x + 30)

Integrate to calculate the cost function

So, we have

[tex]C(x) = \frac{2}{3}(x + 30)^\frac23[/tex]

For the first 10, x = 10

So, we have

[tex]C(10) = \frac{2}{3}(10 + 30)^\frac23[/tex]

Evaluate

C(10) = 7.79

Hence, the total cost for making the first 10 units is 7.79

Read more about area at

brainly.com/question/15122151

#SPJ4

Answer:

4+4−8

Step-by-step explanation:

The function trapezium_integrator uses the Trapezium Rule to approximate the value of a definite integral. It takes four parameters: f, which represents the function to be integrated, start and end, which specify the interval of integration, and num_traps, the number of trapeziums used to approximate the integral.

In the Trapezium Rule, the interval of integration is divided into multiple trapeziums of equal width. The area of each trapezium is calculated as the sum of the lengths of its parallel sides divided by 2, multiplied by its height (the difference between the function values at the two endpoints of the trapezium). The areas of all trapeziums are then summed to obtain an approximation of the integral.

The function calculates the width of each trapezium by dividing the interval length by the number of trapeziums. It then uses a for loop to iterate over the trapeziums, accumulating their areas. The final result is returned as the approximation of the integral.

By dividing the interval into smaller trapeziums, the Trapezium Rule provides a reasonably accurate estimate of the integral. However, for highly oscillatory or irregular functions, a large number of trapeziums may be required to achieve sufficient accuracy. In such cases, more sophisticated numerical integration methods may be more appropriate.

Learn more about definite integral here:

https://brainly.com/question/30760284

#SPJ11

This is a binomial experiment because it meets all the necessary conditions: a fixed number of trials (20 people in the group), independence of each trial (assuming eye color is independent), two possible outcomes (green eyes or not), a constant probability of success (9% for having green eyes), and the random variable representing the count of successes (number of Americans in the group with green eyes, denoted as X).

To argue that this is a binomial experiment, we need to check if the following conditions are met:

1. The experiment consists of a fixed number of trials: In this case, we are considering a fixed number of trials equal to 20, as we have a random group of 20 American people.

2. Each trial is independent: We assume that the eye color of each person in the group is independent of the others.

3. There are only two possible outcomes for each trial: The outcomes are either having green eyes or not having green eyes.

4. The probability of success is constant for each trial: The probability of an American having green eyes is fixed at 9% for each individual in the population.

5. The random variable X represents the count of successes: In this case, X represents the number of Americans in the group with green eyes.

Since all these conditions are satisfied, we can conclude that this is a binomial experiment.

To know more about binomial experiment refer here:

https://brainly.com/question/32104221#

#SPJ11

Answer:

909.09

Step-by-step explanation:

400 divided by 44% is about 909.09.

Step-by-step explanation:

the correct answer is exponent because 6 is its power.

hope this answer will help u.

have a great time.

After considering the given data we conclude that the new point generated is (2,3), under the condition that g(x) is transformed by [tex]-g[4(x+2)][/tex].

To evaluate the new point after the transformation of point (2,-3) by -g[4(x+2)], we can stage x=2 and g(x)=-3 into the expression [tex]-g[4(x+2)][/tex]and apply  simplification to get the new y-coordinate. Then, we can combine the new x-coordinate x=2 with the new y-coordinate to get the new point.
Stage x=2 and g(x)=-3 into [tex]-g[4(x+2)]:[/tex]
[tex]-g[4(2+2)] = -g = -(-3) = 3[/tex]
The new y-coordinate is 3.
The new point is (2,3).
Hence, the new point after the transformation of point (2,-3) by [tex]-g[4(x+2)][/tex] is (2,3).
To learn more about transformation
https://brainly.com/question/29788009
#SPJ4

Answer:

y=3x

Step-by-step explanation:

Correct Question:

He counts 18 female students, 16 male students, and 6 teachers. There are

720 people in the auditorium. Consider the probability of selecting one person

at random from the auditorium.

Which of these statements are true?

Choose all that apply.

A:  The probability of selecting a teacher is 6%.

B : The probability of selecting a student is 85%.

C : The probability of selecting a male student is 32%.

D : The probability of selecting a female student is 45%.

Step-by-step explanation:

Option B  and D are correct because

The total number of people in one cross section = 18 + 16 + 6 = 40.

A = The probability of selecting a teacher is = (6/40)x100 = 15 % not equal to 6 %

B = The probability of selecting a male student is = (34/40)x100 = 85%

C = The probability of selecting a male student is = (16/40)x100 = 40 % not equal to 32 %

D : The probability of selecting a female student is = (18/40)x100= 45%

Answer:

Range = [0, ∞)

Step-by-step explanation:

Range is the y-values

For this question y starts at 0 and just continually goes up so:

Range = [0, ∞)

Answer: 92.5

So to find median all we have to do is rearange it from low - high and get the middle number

71  81  89  92  93  94  94  99

So take this and you know the middle is right in between 92 and 93

71  81  89  92      |      93  94  94  99

All you have to do then is take the mean of 92 and 93 (so do [92+93]/2)

Answer is 92.5

Answer:

the yield is 7.68%

Step-by-step explanation:

The calculation of the yield is given  below:

we know that

Yield is

= Annual dividend ÷ Price per share

= $4.15 ÷ $54

= 7.68%

Here we divide the annual dividend by the price per share in order to determine the yield  

hence, the yield is 7.68%  

And, the same would be considered

Answer:

X= 4. Y = 3.

Step-by-step explanation:

If you have a graphing calculator, put the first equation into Y1. And second equation into Y2. Then, find the intersection of the two equations. That's how you find your answer.

Answer:

3x - 4 = 14

+4. +4

3x = 18

÷3. ÷3

x = 6

The calculated value of z = 2.80 > the Critical value of z = -1.645, we reject the null hypothesis.

Hence, the claim that the proportion is at least 34% is rejected.

Therefore, the researcher's claim is true that the figure is higher for fathers in Littleton.

Null hypothesis:

H0: p ≥ 0.34

Alternative hypothesis:

Ha: p < 0.34

where:p = proportion of Littleton fathers who do not help with childcare

Here, the level of significance, α = 0.05

Level of significance = α = 0.05

The test statistics for a proportion is given as z-test.  

The formula for calculating z-score for a proportion is: z = (p - P) / sqrt[P(1 - P) / n]

where:

P = Population proportion

p = Sample proportion

n = Sample size

The calculated value of z-statistics can be compared with the critical value of z-score from the standard normal distribution table at a particular level of significance.

If the calculated value of z is greater than the critical value of z, then we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Calculating the z-statistic:

Here, Sample size n = 225

Sample proportion

p = 97/225

= 0.4311

Population proportion

P = 0.34z

= (p - P) / sqrt[P(1 - P) / n]z

= (0.4311 - 0.34) / sqrt[(0.34)(0.66) / 225]z

= 2.80

Since the alternative hypothesis is one-tailed (Ha: p < 0.34), the critical value of z at α = 0.05 can be found as follows:

The critical value of z = zα

= -1.645

Since the calculated value of z = 2.80 > the Critical value of z = -1.645, we reject the null hypothesis.

Hence, the claim that the proportion is at least 34% is rejected.

Therefore, the researcher's claim is true that the figure is higher for fathers in Littleton.

To know more about normal distribution visit:

https://brainly.com/question/15103234

#SPJ11

Answer:

7 + 2i is the simplified form

Step-by-step explanation:

Null hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. Alternative hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.

The median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605.

The median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.As per the given question, Central Airlines claims that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. But, this claim is being challenged by the Association of Travel Agents, who believes that the median price is less than $605. Hence, we need to test whether the median price is less than $605 or not.Hence,Null hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. Alternative hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.

Learn more about Null hypothesis here:

https://brainly.com/question/30821298

#SPJ11

Answer: ±√2

Step-by-step explanation: A fraction is undefined when its denominator is =0 or undefined. so we need to get 2/3x²-6=0 or undefined. so we can also do 3x^2-6=0. Solving yields ±√2!

Answer:

the answer is B)

4√24x^3/2x

Solution:

The answer is B

Step-by-step explanation:

I just took the test.

She decreased her candy intake by 15%

Answer:

3 inches

Step-by-step explanation:

got it right on edg

Therefore, the solution to the given system of differential equations, with the initial conditions x(0) = 3 and y(0) = 3, is:

x_(t) = 146t + 24yt + 3

y_(t) = (876t + 21) / ((-144) - 10t)

To solve the given linear system of differential equations, let's rewrite the system in a more standard form:

dx/dt = 146 + 24y

dy/dt = 12x + 20y

We'll use the initial conditions x_(0) = 3 and y_(0) = 3 to find the specific solution.

To solve the system, we can use the method of integrating factors.

Solve the first equation:

dx/dt = 146 + 24y

Rearrange the equation to isolate dx/dt:

dx = (146 + 24y) dt

Integrate both sides with respect to x:

∫dx = ∫(146 + 24y) dt

x = 146t + 24yt + C_(1) ---(1)

Solve the second equation:

dy/dt = 12x + 20y

Rearrange the equation to isolate dy/dt:

dy = (12x + 20y) dt

Integrate both sides with respect to y:

∫dy = ∫(12x + 20y) dt

y = 6x + 10yt + C_(2) ---(2)

Now, we'll apply the initial conditions x_(0) = 3 and y_(0) = 3 to find the values of C_(1) and C_(2).

From equation (1), when t = 0, x = 3:

3 = 146(0) + 24(3)(0) + C_(1)

C_(1) = 3

From equation (2), when t = 0, y = 3:

3 = 6(0) + 10(3)(0) + C_(2)

C_(2) = 3

Now, substituting the values of C_(1) and C_(2) back into equations (1) and (2), we get:

x = 146t + 24yt + 3

y = 6x + 10yt + 3

Simplifying further:

x = 146t + 24yt + 3

y = 6(146t + 24yt + 3) + 10yt + 3

x = 146t + 24yt + 3

y = 876t + 144y + 18 + 10yt + 3

x = 146t + 24yt + 3

y - 154y - 10yt = 876t + 18 + 3

(-144y) - 10yt = 876t + 21

y = (876t + 21) / (-144 - 10t)

Therefore, the solution to the given system of differential equations, with the initial conditions x(0) = 3 and y(0) = 3, is:

x_(t) = 146t + 24yt + 3

y_(t) = (876t + 21) / ((-144) - 10t)

To know more about differentiation:

https://brainly.com/question/31230190

#SPJ4

Answer:

Y = 10 I believe

Step-by-step explanation:

To solve this we need to find what number, times 6, equals 18 - it's fairly easy to find the answer is three.

So what, minus seven, equals 3?