A target survey found that 4 out of 5 customers who entered the store made a purchase. If this store recorded 22,853 purchased last week, estimate the number of customers who entered the store

Answer:

The dimensions that will produce a maximum area of the rectangular region is 50 meters or 5000/Pi

Step-by-step explanation:

From the question given, let us recall the following formula

The perimeter = 200 which is,

P=2L + C

where L is = length of the rectangular region

The circumference of a circle denoted as C

The Circumference of the semi-circle is denoted as,

C=Pi x D, which is  D=C/Pi.

Thus the equation becomes,

200 = 2L+C

A=L x (C/Pi)

We now have Two equations and three variables, from these two equations, we can get a single equation,

200=2L+C means that C = 200-2L

For C in the Area equation. Substitute 200-2L:

A=Lx (C/Pi) which is  A = Lx (200-2L)/Pi.

We Simplify: A = (1/Pi)(-2L² + 200L)

Now take a  derivative of A with respect to L: dA/dL = (1/Pi)(-2L + 200)

(1/Pi)(-2L+200)=0

Let Solve for L: L = 50.

when L is 50 we have the MAXIMUM area. this is a negative quadratic so it MUST therefore not be a minimum but maximum

Then,

Plug in L=50 into the formula for A: A = 50(200-2(50))/Pi = 5000/Pi.

Final answer:

To find the dimensions that maximize the area of the rectangular region for a 200-meter running track with semicircle ends, we can use the perimeter constraint and optimization techniques to solve for the variable x that will give the maximum area when substituted back into the area formula. Therefore, the dimensions of the rectangular region that yield the largest area are [tex]\( x = 50 \) and \( y = \frac{100}{\pi} \).[/tex]

Explanation:

The student is asking about optimizing the area of a rectangular region with semicircles on each end, with a constraint on the perimeter. This is a typical optimization problem that can be solved using calculus, where we need to maximize the area function A(x) = x*y subject to the perimeter constraint P = 2x + πy = 200, considering y as the diameter of the semicircles.

To maximize the area, we'd typically take the derivative of the area function with respect to one of the variables, substitute the relationship given by the perimeter constraint, and solve for the variable that will give us the maximum area. However, since this is a high school level question, it might be expected that the student uses algebraic methods instead of calculus.

To find the value of \( x \) that maximizes the area [tex]\( A(x) = \frac{x(200 - 2x)}{\pi} \)[/tex], we'll follow the steps you provided.

1. Express \( y \) in terms of \( x \) using the perimeter constraint:

  Given that the perimeter of the rectangle is \( 200 \), we have:

 [tex]\[ P = 2x + 2y = 200 \][/tex]

  Rearranging for \( y \):

 [tex]\[ 2y = 200 - 2x \] \[ y = \frac{200 - 2x}{2} \] \[ y = \frac{200 - 2x}{\pi} \][/tex]

2. Substitute \( y \) in the area formula:

  Now, we substitute the expression for \( y \) in terms of \( x \) into the formula for the area:

[tex]\[ A(x) = x \times \left( \frac{200 - 2x}{\pi} \right) \][/tex]

3. Maximize the area:

  To maximize \( A(x) \), we'll find the critical points by taking the derivative of \( A(x) \) with respect to \( x \), setting it equal to zero, and solving for \( x \).

 [tex]\[ A'(x) = \frac{dA}{dx} = \frac{d}{dx} \left( x \times \frac{200 - 2x}{\pi} \right) \] Using the product rule, we get: \[ A'(x) = \frac{d}{dx} \left( x \right) \times \frac{200 - 2x}{\pi} + x \times \frac{d}{dx} \left( \frac{200 - 2x}{\pi} \right) \] \[ A'(x) = \frac{1}{\pi} (200 - 2x) - \frac{2x}{\pi} \][/tex]

  Setting \( A'(x) \) equal to zero and solving for \( x \):

 [tex]\[ \frac{1}{\pi} (200 - 2x) - \frac{2x}{\pi} = 0 \] \[ 200 - 2x - 2x = 0 \] \[ 200 - 4x = 0 \] \[ 4x = 200 \] \[ x = \frac{200}{4} \] \[ x = 50 \][/tex]

So, \( x = 50 \) maximizes the area. To find the corresponding value of \( y \), we substitute \( x = 50 \) into the expression we found for \( y \):

[tex]\[ y = \frac{200 - 2 \times 50}{\pi} = \frac{200 - 100}{\pi} = \frac{100}{\pi} \][/tex]

Therefore, the dimensions of the rectangular region that yield the largest area are [tex]\( x = 50 \) and \( y = \frac{100}{\pi} \).[/tex]

Answer:

choose choice c:  slope is  (2/3) and y-intercept is 2

Step-by-step explanation:

2x - 3y = -6

Convert this equation to Slope-Intercept form.

2x - 3y  - 2x  = -6 - 2x

-3y  =  -6  - 2x

Divide both sides by -3

y = (-6  - 2x)/ (-3)

y =  2  +  2x/3

slope is  (2/3) and y-intercept is 2

Step-by-step explanation:

length x width x height is how to get the answer

Take the numbera and plug them into the equation.

Once youve finished you should get the answer.

Exact form: 105/8

Decimal form: 13.125

Mixed number form: 13 1/8

Answer: 13.125 cubic inches.

Or 13 1/8 cubic inches.

Step-by-step explanation: Volume is length×width×height

Multiply the given dimensions:

(3/2)(5/2)(7/2) = 105/8

Simplify that to get 13.125

or 13 1/8 cubic inches. we

Answer:

Vanessa made 6.25 batches of appetizers last weekend and made 18.75 batches of appetizers this weekend.

Step-by-step explanation:

Let b represent the number of appetizers Vanessa made last weekend.

Since Vanessa made 4 times what made last weekend, let the number of appetizers she made this weekend by represented by 4 × b.

Total batches of appetizers made for the two weekends = 25

Thus, to determine the batches of appetizers made last weekend we perform this operation:

[tex]4 \times b = 25[/tex]

[tex]4b = 25[/tex]

Divide both sides by 4

[tex] \frac{4b}{4} = \frac{25}{4} [/tex]

[tex]b = 6.25[/tex]

Hence, Vanessa made 6.25 batches of appetizers last weekend.

Since total batches of appetizers made by Vanessa for the two weekends is 25, to determine what she made this weekend we say:

[tex]25b - 6.25b = 18.75b[/tex]

Thus, Vanessa made 18.75 batches of appetizers this weekend. By implication, she made 6.25 batches + 18.75 batches of appetizers = 25 batches of appetizers for the two weekends.

Answer:

The funnel will fill the container in about 10 times

Step-by-step explanation:

To solve this question, the principal thing to do is to calculate the volumes of the cone-shaped funnel and the cylinder to actually know the number of times we will need to fill the funnel so as to fill the cylinder,

These number of times can simply be calculated by dividing the volume of the cylinder by the volume of the cone-shaped funnel.

Mathematically, we proceed as follows;

Volume of the cone funnel = 1/3 ×π× [tex]r^{2}[/tex]× h, where r and h represents the radius and height of the cone respectively.

From the question D = 6 inches, and mathematically r = D/2 = 6/2 = 3 inches and h = 7 inches

Plugging the values we have in the question, the volume = 1/3 ×π×[tex]3^{2}[/tex]×7 = 21π [tex]inches^{3}[/tex]

For the cylindrical receptacle, we have the volume calculated as π× [tex]r^{2}[/tex]× h

Where r = 4 inches and h = 13 inches.

Plugging these values we have ; π × [tex]4^{2}[/tex]× 13 = 208π [tex]inches^{3}[/tex]

Now the number of times is simply = volume of cylindrical container/volume of cone-shaped funnel

= 208π/21π = 208/21 = 9.9 which is approximately 10 times

Answer:

y = -4x + 6

Step-by-step explanation:

For a slope-intercept equation, you need to isolate the y. For this equation, just subtract 4x from both sides to get y on it's own.

Answer:

 Slope = 2.286/2.000 = 1.143

Step-by-step explanation:

To convert 8x - 7y + 8 = 0 to slope-intercept form, first, isolate y by moving terms, then divide by the coefficient of y to find the slope and intercept values as per the equation y = mx + b.

To change the equation 8x - 7y + 8 = 0 to slope-intercept form (y = mx + b), you need to solve for y. Here's the step-by-step process:

Move the term 8x to the right side by subtracting 8x from both sides, giving -7y = -8x - 8.

Divide by -7 to isolate y, resulting in y = (8/7)x + 8/7.

Therefore, the equivalent equation in slope-intercept form is y = (8/7)x + 8/7.

Answer:

its d on edg

Step-by-step explanation:

just did the test

Answer

y = RootIndex 3 StartRoot x + 3 EndRoot + 3

Step-by-step explanation:

Took quiz

Answer:

Well I have two that i really enjoy which is Lund and Melanie Martinez

Step-by-step explanation:

Both of their music is amazing I enjoy listening to it all the time there is more i love but i would recommend this two

Answer: Drake, Ariana Grande, Justin Bieber, Shawn Mendes Etc

Step-by-step explanation:

Answer:

1740 cubic feet

Step-by-step explanation:

Given:

A tank is in the shape of a rectangular prism.

Area of base = 116 square feet

Height of the tank = 30 feet

Question asked:

How many cubic feet of water would the tank contain when it is filled halfway?

Solution:

Area of rectangular base = 116 square feet

[tex]Length\times breadth=116[/tex]

As we know:

[tex]Volume\ of\ rectangular\ prism=length\times breadth\times height[/tex]

                                                 [tex]=116\times30=3480\ cubic\ feet[/tex]

That means capacity of tank is 3480 cubic feet.

When it is filled halfway, it will contain =

[tex]\frac{1}{2} \ of\ volume=\frac{1}{2}\times3480=1740\ cubic feet[/tex]

Thus, tank will contain 1740 cubic feet of water when it is filled halfway.

Answer:

12 m3

Step-by-step explanation:

Answer:

12m3

Step-by-step explanation:

Answer:

4(5) -7

Step-by-step explanation:

4(5) -7

The product of 4 and 5 means that 4 and 5 are multiplied together.

"7 less than," means subtracting 7.

That means you get 4(5) - 7

Answer:

-2 or (0,-2)

Step-by-step explanation:

The slope intercept form is y=mx+b, where m represents the slop and b represents the y intercept. Since b here is -2, so is the y intercept's y value. The coordinate of the y intercept is (0,-2). Hope this helps!

Answer:$5075

Step-by-step explanation:

$5075

Hope this helps

Pls gimme brainlest.

Answer:

The iguana can is larger

Step-by-step explanation:

Plug in the measurements into the equation for a cylinder (V=πr^2h) to find out which volume is bigger. Remember to divide the diameter by 2 to radius.

(Hampster) V≈196.35 < V≈226.19 (Iguana)

Answer: 5F < 5( X + x )

Step-by-step explanation:

Let each finger = F and

The index finger = X

The shortest index finger = x

the combined length of all 5 of her fingers on one hand should be less than 5 times the length of index finger

From the statement above, we get

5F < 5X

Tessa add the second shortest index finger.

That is

5F < 5( X +x)

Answer: 10 units

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

Answer:

70 golf balls

Step-by-step explanation:

54+18+24-12-14=70

Answer: D “she dips a corner of her sleeve / like a brush into water”

Step-by-step explanation:

The simile from Cathy Song's poem "Girl Powdering Her Neck" is identified in the line that compares the subject's form to 'polished ivory' and her cheek to 'the spring', using the words 'like' and 'as'.

The student asks which excerpt from Cathy Song's poem "Girl Powdering Her Neck" is an example of a simile. A simile is a figure of speech that compares two different things using the words 'like' or 'as'. In the provided excerpts, the simile is found in the line:

From head to foot her lovely form is fair
As polished ivory. Like the spring, her cheek
Presents a radiant bloom...

This line compares the subject's fair form to polished ivory and her cheek to the spring, suggesting freshness and radiance. The use of 'like' and 'as' confirms these comparisons as similes.

The required solution to the expression 45 + 35 - 25 ÷ 13 is approximately 78.077.

To solve the expression 45 + 35 - 25 ÷ 13, we need to follow the order of operations (PEMDAS/BODMAS).

First, we perform the division operation:
25 ÷ 13 = 1.923 (rounded to three decimal places).

Then, we perform the addition and subtraction operations from left to right:
45 + 35 = 8080 - 1.923
             = 78.077 (rounded to three decimal places).

Therefore, the answer to the expression 45 + 35 - 25 ÷ 13 is approximately 78.077.

Learn more about PEMDAS here:

https://brainly.com/question/20876480

#SPJ4

Answer:x= -1

Step-by-step explanation:

The train's average speed was calculated by using the formula for average speed (Total distance \/ Total time), resulting in approximately 64.4 km/h, after converting the total journey time from minutes to hours.

To calculate the average speed of the train, we can use the formula:

Average speed = Total distance \/ Total time

First, we find the total time taken by the train for its journey:

Departure time: 17:22

Arrival time: 18:14

Total time = Arrival time - Departure time

Total time = 18:14 - 17:22

Total time = 52 minutes

To convert minutes to hours (since speed is in km/h), we divide by 60:

Total time in hours = 52 / 60 ≈ 0.87 hours

Now, we can plug in the given distance and calculated time into the formula:

Average speed = 56 km / 0.87 hours ≈ 64.4 km/h

Hence, the train's average speed was approximately 64.4 km/h, rounded to 1 decimal place.

Answer:

x = -7

Step-by-step explanation:

Steps of solution:

The roots are:

Correct answer option is:

Answer:

B,     x =  -7

Step-by-step explanation:

Answer:

The answer to your question is distance = 24 mi

Step-by-step explanation:

Data

speed = 12 mph

time = 2 hours

distance = ?

Process

To solve this problem, use the speed formula. Speed is a variable that measures the distance travel by a body over time.

speed = distance / time

-Solve for distance

distance = speed x time

-Substitution

distance = 12 x 2

-Result

distance = 24 mi

Answer:

24miles

Step-by-step explanation:

12/1 = x/2

where the numerator is the miles and the denominator the hours

cross multiply

12×2 and dived by 1 to yet your answer.

Answer:

The answer would be 15

Step-by-step explanation:

90÷6=15

Final answer:

To determine the needed x-value when the required value of y is -108.5, substitute the value of y into the fit line equation and solve for x. The rounded x-value is 100.

Explanation:

To determine the needed x-value when the required value of y is -108.5 using the fit line equation y = -2.61x + 152.51, we can substitute the value of y into the equation and solve for x.

-108.5 = -2.61x + 152.51

Subtract 152.51 from both sides: -108.5 - 152.51 = -2.61x

Simplify: -261.01 = -2.61x

Divide both sides by -2.61: x = -261.01 / -2.61

Rounding to the nearest whole number, x = 100.

Answer:

p=4 d=2

Step-by-step explanation:

To do this, we can set up a system of equations.

Special Deal 1:

2p+4d=16

Special Deal 2:

4p+7d=30

Now we can set this up for elimination, and try to eliminate the p variable.

Let's do this by multiplying the entire equation for Special Deal 1 by 2.

2(2p+4d=16)

4p+8d=32

Now we can eliminate p by subtracting the equation for special deal 2, by the equation for special deal 1.

4p+8d=32 minus

4p+7d=30 equals

d=2

Now we can plug that into the original equation to find the cost of p.

2p+4(2)=16

2p+8=16

Subtract 8 from both sides.

2p=8

p=4

Therefore, a pizza costs $4 and a drink costs $2.

Answer: p=4 d=2

Step-by-step explanation:

just did the assignment, it's right

Answer:

The answer to your question is 10 ft

Step-by-step explanation:

We can observe that all the sides have a length but the first to the left.

Also, we know the corners meet at right triangles, so to calculate the length of the missing side, we must add to sides.

But these sides must be the ones that are in front of it (6 ft and 4 ft)

Then    ? = 6 + 4

               10 ft

Answer:

B

..............................................

Answer: I believe it would be B(3,-3), Please correct me if I'm wrong, but thats the way I was taught when dealing with scale factors.

Step-by-step explanation:

Answer:

  B.   Figure A was rotated 180° about the midpoint of FF'

Step-by-step explanation:

Points ABC are oriented clockwise, as are points A'B'C', so two reflections or rotation are involved. Segment AB is directed in the opposite direction of segment A'B', so the rotation must be 180°. These effects cannot be accomplished by translation or single reflections, nor can they be accomplished by rotation of 90°.

The midpoints of segments joining a point and its image all intersect at the center of rotation of 180°. The appropriate choice is B:

  Figure A was rotated 180° about the point in the middle of the line segment connecting F and F' to create Figure B.