A fenced enclosure consists of a rectangle (length L and width 2R) attached to a semicircle with a radius R as pictured below. Note: there is fencing between the rectangular and semi-circular portions. The enclosure is to be built to have a total area (the entire shaded region), A, of 2000 ft2. The cost of the fence is $20/ft for curved sections and $30/ft for straight sections. Analytically (show all of your steps using algebra and calculus in the write up), find the minimum cost to build the fence and the dimensions of the enclosure. Show all equations that you derive and use. This part should be done entirely in the write-up: no coding. It is fine to do this by hand and include a high-resolution picture in the writeup rather than using Equation Editor. Hint: you will need to use two equations in order to find the cost as a function of only R or L. Construct a plot to graphically determine the values of R and L (x-axis) that minimize the total cost (y-axis) of the fence. Using the MIN function, determine the R and L that minimize cost and what that cost is Do your answers in A, B and C all agree? Why or why not?

Answer:

Step-by-step explanation:

Length: (25 yd)(3 ft/yd) = 75 ft.

Width: (8 lanes)(3 yd/lane)(3 ft/yd) = 72 ft.

The length and width are 75 ft and 72 ft, respectively.

Answer:

length; 75 ft

width; 72 ft

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

The response variable is also known as the dependent variable. It depends on another factor which is the independent variable to cause change/ response to it.

In this study, they want to test if an increase in the number of Math workshop which is the independent variable will cause a change in the final exam scores which is the dependent variable. The response to this inquiry is thus the final exam score which is also known as the response variable.

Answer:

The quotient is [tex]10x+16[/tex]

The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]

Step-by-step explanation:

(See my image for my work)

Once the problem is set up, we need to figure out how to make [tex]x^3[/tex] become [tex]10x^4[/tex]. To do this, we must multiply it by [tex]10x[/tex].

This becomes the first number at the top of our work.

Now, we need to create the second row. To do this, we need to multiply all of the terms on the left by [tex]10x[/tex] and then multiply it by a negative.

Once that is done, we need to subtract these two rows.

After we subtract, we are left with [tex]16x^3-20x^2+26x-10[/tex]

Now we can do the same thing. This time, the number that we must multiply by is 16, so that is the next term on top

Next, we multiply the terms on the left by 16 and then subtract them from the previous expression

This leaves us with [tex]34x^2+10x+22[/tex].

As this has a smaller power than the left-hand side, this is our remainder, which we need to divide by the left hand side.

Our quotient is the number that we have found on the top.

This gives us the answer of

The quotient is [tex]10x+16[/tex]

The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]

(Sorry. This process is hard to do in this form, so I had to write it by hand.)

Answer:

the quotient is 10x + 16

the remainder is 28x² + 10x + 22

Answer:

[tex]\dfrac{90}{341}[/tex]

Step-by-step explanation:

3rd grade:

Number of girls = 16

Number of boys = 15

Total number of students = 31

4th grade:

Number of girls = 15

Number of boys = 18

Total number of students = 33

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Probability of picking a boy from 3rd grade, [tex]P_{1} = \dfrac{15}{31} ..... (1)[/tex]

Probability of picking a boy from 4th grade, [tex]P_{2} = \dfrac{18}{33} ..... (2)[/tex]

These are two independent events of picking a boy from 3rd grade and 4th grade.

So, probability the captain chooses 2 boys in the first pick can be found by multiplying (1) and (2) above.

[tex]P = P_{1} \times P_{2}\\\Rightarrow \dfrac{15}{31} \times \dfrac{18}{33}\\\Rightarrow \dfrac{90}{341}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the occupants not wearing seat belts and occupants wearing seat belts. The population proportion of occupants not wearing seat belts and occupants wearing seat belts would be p1 and p2 respectively.

P1 - P2 = difference in the proportion of occupants not wearing seat belts and occupants wearing seat belts.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 > p2

p1 - p2 > 0

it is a right tailed test

Sample proportion = x/n

Where

x represents number of success

n represents number of samples.

For occupants not wearing seat belts,

x1 = 31

n1 = 2823

P1 = 31/2823 = 0.011

For occupants wearing seat belts,

x2 = 16

n2 = 7765

P2 = 16/7765 = 0.0021

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (31 + 16)/(2823 + 7765) = 0.0044

1 - pc = 1 - 0.0044 = 0.9956

z = (P1 - P2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.011 - 0.0021)/√(0.0044)(0.9956)(1/2823 + 1/7765) = - 0.0089/0.00145462023

z = 6.81

From the normal distribution table,

p < 0.00001

0.00001 < 0.05, we would reject the null hypothesis.

Therefore,

b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities

Answer:

336 is the answer

Step-by-step explanation:

hope this helps

Answer:

[tex](3x+1)^2[/tex]

Step-by-step explanation:

[tex]9x^2+6x+1=\\(3x+1)^2[/tex]

You can confirm this by working and expanding backwards:

[tex](3x+1)^2=\\(3x+1)(3x+1)=\\9x^2+3x+3x+1=\\9x^2+6x+1[/tex]

Hope this helps!

The factorized form of 9x² + 6x + 1 is indeed (3x + 1)².

To find the factorized form of the quadratic expression 9x² + 6x + 1 is (3x + 1)², we can expand the factorized form and compare it with the given expression to check if they are equal.

Expanding (3x + 1)² using the square of a binomial formula, we get:

9x² + 6x + 1

= 9x² + 3x + 3x + 1

= 3x (3x + 1) + 1 (3x + 1)

(3x + 1)² = (3x + 1)(3x + 1)

Comparing the expanded form of (3x + 1)² with the given expression 9x² + 6x + 1, we can see that they are equal.

Therefore, we have found that the factorized form of 9x² + 6x + 1 is indeed (3x + 1)².

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Answer:

Height of second tower = 17.32m

Step-by-step explanation:

I have attached a diagram depicting the question.

From the diagram, The first tower is depicted by side AEB and the second tower CD.

While d is the distance that separates the two towers and it's given as 15m.

Now, since the angle of depression of the second tower’s base is 60°, then for triangle BAC. Angle C = 60°.

Thus; using trigonometric ratios;

tan 60° = AB/AC.

This gives; AB = d*tan 60°

Similarly, for the triangle BED, BE = d*tan 30°

Since, AE = CD, thus ;

CD = AB − BE

CD = d (tan 60° − tan 30°)

CD = 15(1.7321 − 0.5774)

CD = 15 × 1.1547

CD ≈ 17.32 m.

So, height of second tower = 17.32 m

Answer:

Can you answer mine? I willl answer yours

Step-by-step explanation:

Answer:

Step-by-step explanation:espinal hola defryet iSight x0 do hulp

Answer:

(x-1)^2= -0.5

Step-by-step explanation:

I DID THE USA TEST PREP AND THIS ANSWER WAS CORRECT

Answer:

a

Step-by-step explanation:

A percentage is a way to describe a part of a whole. The correct matrix is C.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the table shows Amy's, Jenny's, and Meg's sales for the month of February. They get a 5% commission on their sales. Therefore, the commission on each product category and for each person can be calculated as shown below.

Commission on book sales for Amy, a₁₁ = 120 × 0.05 = 6

Commission on book sales for Jenny, a₁₂= 250× 0.05 = 12.5

Commission on book sales for Meg, a₁₃ = 215 × 0.05 = 10.75

Commission on Games sales for Amy, a₂₁ = 155 × 0.05 = 7.75

Commission on Games sales for Jenny, a₂₂= 106 × 0.05 = 5.3

Commission on Games sales for Meg, a₂₃ = 175 × 0.05 = 8.75

Commission on Tables sales for Amy, a₃₁ = 350 × 0.05 = 17.5

Commission on Tables sales for Jenny, a₃₂= 400 × 0.05 = 20

Commission on Tables sales for Meg, a₃₃ = 290 × 0.05 = 14.5

Now, the matrix can be made as shown below,

[tex]\left[\begin{array}{ccc}6&12.5&10.75\\7.75&5.3&8.75\\17.5&20&14.5\end{array}\right][/tex]

Hence, the correct matrix is C.

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Answer:

x = 0, 4/5

Step-by-step explanation:

The zero-product property states that if the product of a and b is zero, then either a = 0, b = 0, or both terms equal zero

Answer:

Yes.

Step-by-step explanation:

Answer:

si

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

The actual pressure when the gauge shows 33.58 would be 36.5.

Used the concept of the percentage that states,

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.

Given that,

Ali's tire pressure gauge shows a reading which is [tex]8 \%[/tex]lower than the actual pressure.

And, the gauge shows [tex]33.58.[/tex]

Let us assume that,

The actual pressure of Ali's tires = x

Hence, we can formulate the equation,

[tex]x \times (1 - 8\%) = 33.58[/tex]

Solve the equation for x,

[tex]x \times (1 - \dfrac{8}{100} ) = 33.58[/tex]

[tex]x \times (1 - 0.08) = 33.58[/tex]

[tex]x \times 0.92 = 33.58[/tex]

Divide both sides by 0.92;

[tex]x= \dfrac{33.58}{0.92}[/tex]

[tex]x = 36.5[/tex]

Therefore, The actual pressure of Ali's tires = 36.5

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The complete question is,

Ali's tire pressure gauge shows a reading which is 8% lower than the actual pressure.

What is the actual pressure of Ali's tires when the gauge shows 33.58?

Answer:

I think it's 462. I'm sry if I'm wrong.

Answer:

  A.  A horizontal shift to the right 7.5 units

Step-by-step explanation:

Replacing x with x-7.5 shifts the graph 7.5 units to the right.

__

In general, g(x) = f(x-h)+k will shift h units right and k units up. In this problem there is no vertical shift.

Answer:

1) No, there is  not  enough evidence to support the claim that the vaccine was effective (P-value=0.104) .

The null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

being the subindex 1 for the experimental group and subindex 2 for the control group.

2) Test statistic z=-1.26

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

[tex]p_1=X_1/n_1=21/100000=0.0002[/tex]

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

[tex]p_2=X_2/n_2=30/100000=0.0003[/tex]

The difference between proportions is (p1-p2)=-0.0001.

[tex]p_d=p_1-p_2=0.0002-0.0003=-0.0001[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=P(z<-1.26)=0.104[/tex]

As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is  not  enough evidence to support the claim that the vaccine was effective.

Answer:

66

Step-by-step explanation:

So the volume of a cone is [tex]\pi r^2*\frac{h}{3}[/tex]

r = 3

h = 7

[tex]9\pi *\frac{7}{3} = 21\pi[/tex]

[tex]\frac{22}{7} *21=66[/tex]

Answer: $58.33

Step-by-step explanation:

Yes, Sasha is correct. The mean amount she makes is in a day.

Answer:

a: Yes, Sasha is correct. The mean amount she makes is $58.33 in a day

Step-by-step explanation:

edg2020

Rise over run. Or I believe. Like If I chose (-1,2) and (0,-1)  the rise or in this case since the line is going down, if I move down 4 units. I am one unit to the left of (0,-1) so 4/1 so rise/run

The equation of the line is y+2x+1 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

In the given graph,

Line intersect x-axis at -1/2

And intersect y-axis at -1

The points are (-1/2,0) and (0,-1)

The slope of the line m = -1-0/(0-(-1/2)) = -2

The required equation of the line that passes through the point (-1/2,0) and slope is -2,

y-0 = -2(x-(-1/2))

⇒y=-2x-1

⇒y+2x+1 = 0

The equation of the line is y+2x+1 = 0.

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Answer:[tex]8.75\ m^2[/tex]

Step-by-step explanation:

Given

Area of circle is [tex]A=45\ m^2[/tex]

Arc measure [tex]\theta =70^{\circ}[/tex]

and area of sector is given by

[tex]\Rightarrow \frac{\theta }{360^{\circ}}\times \text{Area of circle}[/tex]

[tex]\Rightarrow \frac{70}{360}\times 45[/tex]

[tex]\Rightarrow 0.194\times 45[/tex]

[tex]\Rightarrow 8.75\ m^2[/tex]

So, area of sector is [tex]8.75\ m^2[/tex]

Answer: x>-2

Step-by-step explanation:

To find the values of the inequality, you treat this like it would be any other equation.

[tex]-3x<6[/tex]

[tex]x>-2[/tex]

Answer:

8

Step-by-step explanation: because its even

Answer:

  straight angle

Step-by-step explanation:

A straight angle is one whose measure is 180°. Its formative rays point in opposite directions from the vertex and make a straight line.

Answer:

Option (1)

Step-by-step explanation:

System of equations has been given as

2x + 6y = 14

By dividing this equation by 2

x + 3y = 7 --------(1)

Second equation is,

-2x + 2y = -10

-x + y = -5 -------(2)

By adding equation (1) and equation (2)

(x + 3y) + (-x + y) = 7 - 5

2x = 2

x = 1

By putting x = 1 in the equation (1)

1 + 3y = 7

3y = 6

y = 2

So, we get exactly one solution pair (1, 2) where these lines are intersecting.

Therefore, the best category that defines the system of equations is Consistent/Independent

Option (1) will be the answer.

Answer:

0.864p

Step-by-step explanation:

A discount of 20% is (1 - .2) = .8

8% tax is 1.08

.8 * 1.08 = 0.864

That means the new price is 0.864p

As far as I'm concerned, it still exists

What do you mean becauae nothing happened

Answer:

 4π cm

Step-by-step explanation:

The length of an arc of a circle with radius r and central angle θ is given by ...

  s = rθ

where θ is in radians.

Here, your arc measures 60° = π/3 radians, so the arc length is ...

  s = (12 cm)(π/3) = 4π cm