No links, I just need an explanation on how to do this, like step by step because I don't understand. T-T

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

Area of a triangle = (base x height) / 2

if the base is 3 and height is 4

Area = (3x4)/2 = 6 sq units

if the base is 4 and height is 8

Area = (4x8)/2 = 16 sq units

if base is 3 and height is 8

Area = (3x8)/2 = 12 sq units

The team attempted 30 three-point shots.

Let x be the number of three-point shots the team attempted.

We know that the team attempted 50% more two-point shots than three-point shots, so the number of two-point shots is 1.5x.

We also know that 50% of the two-point shots were successful and 40% of the three-point shots were successful, so we can set up the following equation:

(1.5x)(0.5) + (x)(0.4) = 54

Solving for x yields x = 30.

Therefore, the team attempted 30 three-point shots.

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43 feet try it dw it will be correc6

Answer:

15 yards is bigger than 43 feet

Step-by-step explanation:

There are 3 feet in one yard

Multiply 15 by 3:

45 feet

Answer:

$786

Step-by-step explanation:

50, 60, 72

find the difference between the first and second hour earnings to get 10.

get the difference of the second and third to get 12.

we realize that they are in increasing with even numbers from 10 going further, ie, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28....etc

to get the total earnings for the 24 hrs, you have to keep on adding the next even number till you reach the 24th hour

you will get $786.

a. The 90% confidence interval for the proportion of all American households who have at least one dog is (0.636, 0.704). This means we can be 90% confident that the true proportion of all American households who have at least one dog lies within this range.

b. The 90% confidence means that if we were to repeat this poll many times with different samples of American households, we would expect 90% of the resulting confidence intervals to contain the true proportion of all American households who have at least one dog

a) To construct a 90% confidence interval for the proportion of all American households who have at least one dog, we can use the following formula:

CI = p ± zsqrt((p(1-p))/n)

where:

CI is the confidence interval

p is the sample proportion (67% or 0.67 in decimal form)

z is the z-score corresponding to the level of confidence (90% or 1.645 for a one-tailed test)

n is the sample size (750)

Plugging in the values, we get:

CI = 0.67 ± 1.645sqrt((0.67(1-0.67))/750)

CI = 0.67 ± 0.034

Therefore, the 90% confidence interval for the proportion of all American households who have at least one dog is (0.636, 0.704). This means we can be 90% confident that the true proportion of all American households who have at least one dog lies within this range.

b) In this context, 90% confidence means that if we were to repeat this poll many times with different samples of American households, we would expect 90% of the resulting confidence intervals to contain the true proportion of all American households who have at least one dog.

In other words, we can be reasonably sure that our sample proportion of 67% is a good estimate of the true proportion, with a margin of error of about 3.4 percentage points, based on the sample size and the level of confidence we have chosen.

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The value of "m' that makes the expression equivalent is 0.2584

Given the expression 12 (–1.4m + 0.4) = m + 0.2

We need to solve for the value of m from the expression.

Expand using the distributive law:

12(-1.4m) + 12(0.4) = m +  0.2

16.8m + 4.8 = m + 0.2

Collect the like terms:

-16.8m - m = 0.2 - 4.8

-17.8m = -4.6

m = 4.6/17.8

m = 0.2584

Hence the value of "m' that makes the expression equivalent is 0.2584

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The statement that gives a unit rate is "for every day, Trey's cat ate 1.5 cups". So correct answer is option B).

This statement represents the amount of cat food consumed per unit of time, which is 1.5 cups per day. A unit rate is a comparison of two measurements in which one of the numbers is 1, making it easier to compare different rates. So, the correct option is B).

In this case, the unit rate would be 1.5 cups per day. Option A and C are not unit rates because they express the amount of cat food consumed over a varying number of days, while option D is not a unit rate because it expresses the amount of cat food consumed in a fractional amount of a day.

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Answer:

8

Step-by-step explanation:

1+2+3=6

4+5+6=15

15-6=9-1=8

Answer:

1. (36 - 8) + (7b + 4) = 28 + 7b + 4 = 7b + 32

Answer: 7b + 32

2. (7x^2 - 3x + 2) + (5x - 2) = 7x^2 + 2x = 2x + 7x^2

Answer: 2x + 7x^2

3. (5y^2 - 2y + 1) - (y^2 + y + 3) = 4y^2 - 3y - 2

Answer: 4y^2 - 3y - 2

4. (-7a^4 - a + 4a^2) - (-8a^2 + a - 7a^4) = -7a^4 - a + 4a^2 + 8a^2 - a + 7a^4

Simplifying the expression, we get:

-7a^4 + 7a^4 + 4a^2 + 8a^2 - a - (-a) = 12a^2

Answer: 12a^2

5. (2x^2 - 7x^3 + 8x) + (-8x^3 - 3x^2 + 4) = -15x^3 - x^2 + 8x + 4

Answer: -15x^3 - x^2 + 8x + 4

6. (4m^2 - 2m + 4) - (2m^2 + 2m - 5) = 2m^2 - 4m + 9

Answer: 2m^2 - 4m + 9

Correct me if I'm wrong.

Step-by-step explanation:

Answer:85.7 miles per hour

Step-by-step explanation:

Answer:

O y=_5x+4 it is equation the line that is parallel

The equation of line passes through the point (-2, 2) will be;

⇒ y = 1/5x - 12/5

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 5, -4) and (0, -3).

Now,

Since, The equation of line passes through the points (- 5, -4) and (0, -3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 3 - (-4)) / (0 - (-5))

m = 1 / 5

Hence, The slope of parallel line = 1/5

Thus, The equation of line with slope 1/5 and passes through the point (-2, 2) is,

⇒ y - (-2) = 1/5 (x - 2)

⇒ y + 2 = 1/5x - 2/5

⇒ y = 1/5x - 2/5 - 2

⇒ y = 1/5x - 12/5

Therefore, The equation of line passes through the point (-2, 2) will be;

⇒ y = 1/5x - 12/5

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Answer:

80 cubic units

Step-by-step explanation:

Area for rectangular prism is l*w*h

2*8*5=80

Answer:

Step-by-step explanation:

For question 1:The answer is 36-k.

Question 2: The answer is 61.

Question 3: The answer is 162.

The area of the polygon is 37.81 units and the perimeter is 33.02 units.

The given points are in order, we have:

a(-3, 2)

f(2, -3)

b(0, 5)

c(3, 2)

d(5, 4)

e(7, 2)

g(0, -1)

Using the distance formula, we can find the lengths of the sides of the polygon. Then, we can add up the lengths of all the sides to find the perimeter of the polygon.

As per the shown figure,

Length of side fa = 7.07 units

Length of side ef = 7.07 units

Length of side de = 7.6 units

Length of side cd = 2.8 units

Length of side bc = 4.24 units

Length of side ab = 4.24 units

The perimeter of the polygon is:

= fa + ef + de + cd + bc + ab

= 7.07 + 7.07 + 7.6 + 2.8 + 4.24 + 4.24

= 33.02 units

The area of the polygon is:

= area of rectangle (1) + area of sqare (2)

= 7.07 × 4.24 + 2.8 × 2.8

= 37.81 units

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We can expect the mean length of ears in the next generation to be 31.6 cm.

It is given that the narrow sense heritability (h2) is 0.70, which means that 70% of the total variation in maize ear length is due to genetic factors.

Let the mean length of ears in the original population be µ and the mean length of ears in the selected plant be x. Then, we can use the formula for response to selection to find the expected mean length of ears in the next generation:

x' = µ + h2 * (x - µ)

Substituting the given values, we get:

x' = 28 + 0.70 * (34 - 28) = 31.6 cm

Therefore, we can expect the mean length of ears in the next generation to be 31.6 cm.

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In the Stackelberg case, Firm 1 has a higher profit (562.5 > 277.78) and Firm 2 has a lower profit (156.25 < 277.78) than in the simultaneous-move case.

1. In the Stackelberg case, let Firm 1 choose output y1 first, and then Firm 2 decides y2 after observing y1. Firm 1 is the leader and Firm 2 is the follower. Thus, the optimization problem for Firm 2 is as follows:

Max p(y1 + y2) * y2 - c2(y2), where y1 is chosen by Firm 1.

Thus, the profit function of Firm 2 is Π2(y1, y2) = (100 − 2(y1 + y2))y2 − 4y2

                                                                              = (100 − 2y1 − 2y2)y2

Differentiating with respect to y2, we obtain:

∂Π2(y1, y2) / ∂y2 = 100 − 2y1 − 4y2

Setting this equal to zero, we obtain:

50 − y1 = 2y2

Thus, Firm 2's best response function is: yˆ2(y1) = (50 − y1)/2

Now, Firm 1 knows that Firm 2 will choose yˆ2 given that it already chose y1.

Firm 1 chooses y1 to maximize its own profit, which is:

Π1(y1) = (100 − 2(y1 + yˆ2(y1)))y1 − 2y1

= (100 − 2y1 − 25 + 0.5y1)y1

= (75 − 1.5y1)y1

Differentiating with respect to y1, we obtain:

∂Π1(y1) / ∂y1 = 75 − 3y1

Setting this equal to zero, we obtain:

y1 = 25

Thus, yˆ1 = 25, and yˆ2 = (50 − y1)/2 = 12.5.

The profit of Firm 1 is Π1(y1) = (75 − 1.5y1)y1 = 562.5, and the profit of Firm 2 is

= Π2(y1, y2)

= (100 − 2y1 − 2y2)y2

= 156.25.2.

In the simultaneous-move case, the optimization problem for Firm 1 is as follows:

Max p(y1 + y2) * y1 - c1(y1) - c2(y2)

Similarly, the optimization problem for Firm 2 is: Max p(y1 + y2) * y2 - c1(y1) - c2(y2)

These two problems can be combined into a single problem by substituting

p(y1 + y2) = 100 − 2(y1 + y2) and

c1(y1) = 2y1 and c2(y2) = 4y2.

Thus, the profit function of each firm is:

Π1(y1, y2) = (50 − y1 − y2)y1Π2(y1, y2) = (50 − y1 − y2)y2

The first-order conditions for maximizing these profit functions are:

= ∂Π1(y1, y2) / ∂y1

= 50 − 2y1 − y2

= 0

∂Π2(y1, y2) / ∂y2 = 50 − y1 − 2y2 = 0

Solving these equations simultaneously, we obtain:

y1 = 16.67, y2 = 16.67, and Π1(y1, y2) = Π2(y1, y2) = 277.78.

Comparing this to the Stackelberg case, we see that both firms are worse off in the simultaneous-move case. In the Stackelberg case, Firm 1 has a higher profit (562.5 > 277.78), and Firm 2 has a lower profit (156.25 < 277.78) than in the simultaneous-move case. Thus, Firm 1 is better off in the Stackelberg case, and Firm 2 is worse off.

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Answer :    x=−5

Step-by-step explanation: Step 1: Simplify both sides of the equation.

−3−3x=−4(2x+7)

−3+−3x=(−4)(2x)+(−4)(7)(Distribute)

−3+−3x=−8x+−28

−3x−3=−8x−28

Step 2: Add 8x to both sides.

−3x−3+8x=−8x−28+8x

5x−3=−28

Step 3: Add 3 to both sides.

5x−3+3=−28+3

5x=−25

Step 4: Divide both sides by 5.

5x /5 =  −25 /5

x=−5

Answer:

x=−5

Answer:

Step-by-step explanation:

The theorem states that the square on the hypotenuse  (longest side) of a right triangle equal the sum of the squares on the other 2 sides.

Counting the small squares gives us these areas.

We see that

Sum of squares on hypotenuse = 25.

and sum of squares on the other 2 sides = 9 and 16  which equals 25.

the ratio is the relation(division) between 2 number

Step 1

Let

number 1= number of apples=8

number 2=total fruit = number of pears+ number of apples=5+8

number 2=13

Step 2

so, the ratio of apples to total fruit is 8/13

Answer:

10°

Step-by-step explanation:

Step 1:

∠EFG = 90°         Def. of Right Angle

Step 2:

∠EFH + ∠HFG = ∠EFG        Sum of an angle

Step 3:

7x + 2x = 90         Input Values

Step 4:

9x = 90        Combine Like Terms

Step 5:

x = 90 ÷ 9       Divide

Answer:

x = 10°

Hope This Helps :)

Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

Given,

In the question:

A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.

To find the how many possible 3-course meals are there?

Now, According to the question:

Let's know:

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N=n_1\) × \(n_2\) × \(n_3\)... ×\(n_n\)

In this problem, considering the number of salads, main courses and desserts, we have that:

\(n_1=4 , n_2=5,n_3=3\)

The total number of options is given by:

N = 4 × 5 × 3

N = 60

Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

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Line segments equation is :

D = [(x2x1 x 2 x 1)2 + (y2y1 y 2 y 1)2].

This is further explained below.

Generally, A shape known as an angle is created when two rays (or two line segments) converge on a single point to produce a shape. To determine how large the angle is, we will use degrees as our unit of measurement.

In conclusion,  Now that we have the coordinates of the two endpoints, let's figure out how to calculate the length of the line segment that connects them.

In this instance, we make use of the formula for calculating distance, which is written as D = [(x2x1 x 2 x 1)2 + (y2y1 y 2 y 1)2].

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Answer:

4x + 16 = 90

4x = 74, so x = 18.5

2y + 16 = 90

2y = 74, so y = 37

Answer:

sorry I don't know the answer

Let x be the no.of square feet for landscaping

Company A

Monthly consulting fee = $250

Cost of landscaping of 1 sq.feet = $10

Cost of landscaping of x sq.feet = $10x

So, Total charge by company A = 250+10x  ---1

Company B

Monthly consulting fee = $90

Cost of landscaping of 1 sq.feet = $12

Cost of landscaping of x sq.feet = $12x

So, Total charge by company B = 90+12x   ---2

Now we are supposed to find  how many square feet of landscaping will the two companies charge the same amount

So, Equate 1 and 2

\(250+10x=90+12x\\160=2x\\80=x\)

So, the two companies charge the same amount for 80 sq.feet

Total charge by company A for 80 sq.feet = 250+10(80)= $1050

Total charge by company B for 80 sq.feet = 90+12(90)=$1170

The area of region of the function f on the interval [1, 2] is found to be 3/2 square units using the integration.

In calculus, integration can be used to find the area of the region under a curve.

In this case, we want to find the area of the region under the graph of the function f on the interval [1, 2], where

f(x) = ∫3/2 square units.

We can start by graphing the function on the interval [1, 2]:

We can see that the graph of f is a horizontal line at y = 3/2 between x = 1 and x = 2.

Therefore, the area of the region under the graph of f on the interval [1, 2] is simply the area of a rectangle with base 1 and height 3/2:

Area = base x height

= 1 x 3/2

= 3/2 square units.

The area of the region under the graph of the function f on the interval [1, 2] is 3/2 square units.

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Answer:

1 cm: 200 cm (if they don't give units) (most likely this answer) (1:200)

if the units are centimeter and meter though, then it's

1:2

Step-by-step explanation:

there are 100 cm in 1 meter, so 1cm:2m

is actually 1cm : 200cm

Answer:

g = 8

Step-by-step explanation:

3g - 6 = 18

     +6   +6

3g = 24

divide by 3

g = 8

Answer:

The answer is G = 8

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Hoped this helped!

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