Mathematics High School

A density curve for all of the possible weights between 0 pounds and 1000 pounds is in the shape of a rectangle. What is the value of the density curve in this interval?

Answers

Answer 1
0.001
1000 times .001 gives you 1
It's correct on apex
Answer 2

Answer:

The area under the curve is one.

Step-by-step explanation:

A density curve for all of the possible weights between 0 pounds and 1000 pounds is in the shape of a rectangle. What is the value of the density curve in this interval?

The area under the curve is one.

Reason

Lets draw an histogram. On the vertical axis is the frequency distribution. horizontal axis is the weights. the interval between the bars will be 1.

the height of the bars will be the frequency distribution.

we get the area of the bars by multiplying the bars width and height. add up all with the other weight.

we get 1

Related Questions

Please help me with a simple math problem.

What is the value of b?

A. 1.5
B. 3
C. 3.75
D. 4.5

Answers

You would take 7.5 and divide it by 2 which will give you C. 3.75
3.75 is the answer because the top and bottom line are the same and then you divide 7.5 by 2.


giving away all these points to the lucky person who can explain how to get the answer (Law of Cosines) !!!

Answers

Law of Cosines:  c^2 = a^2 + b^2 - 2ac cost C

Here,        (missing side length)^2 = 9^2 + 6^2 - 2(9)(6) cos (37 deg)

Just evaluate this to find the missing side length.

A local company manufactures netbook computers. Their profit function is given by this equation: y equal minus x to the power of 2 plus 120 x plus 3000 where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day. What is the maximum profit that the company can make? (Hint: Find the vertex of the parabola.)

Answers

Answer by BlueSky06

The equation described above can also be written as,                    y = -x² + 100x + 4000To get the number of notebooks that will give them the maximum profit, we derive the equation and equate to zero.                  dy/dx = -2x + 100 = 0The value of x from the equation is 50. Then, we substitute 50 to the original equation to get the profit.                    y = -(50^2) + 100(50) + 4000 = 6500Thus, the maximum profit that the company makes is $6,500/day. 
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Answer: $6,600

Step-by-step explanation:

Given: The profit function is given by the equation:

[tex]y=-x^2+120x+3000[/tex],where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day.

To find the maximum profit, first we need to find critical point of the function.

For that, first differentiate the above function w.r.t. x, we get

[tex]y'=-2x+120[/tex]

Now, Put [tex]y'=0[/tex], we get

[tex]-2x+120=0\\\\\Rightarrow\ x=60[/tex]

Again differentiate the above function w.r.t. x, we get

[tex]y"=-2<0[/tex]

By second derivative test, at x=60 , attains its maximum value.

Now, the Maximum profit will be :

[tex]y=-(60)^2+120(60)+3,000=6,600[/tex]

Hence, the maximum profit that the company can make = $6,600

Please help with geometry

Answers

It's a equilateral triangle. The area of the white region is the area of a sector minus the area of a triangle.
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]

The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]

The area of the segment:
[tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]

The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]

Compute the area of a triangle with sides. 15 × 15 × 18

Answers

You can find the area using Heron's formula.
A=√(s(s-a)(s-b)(s-c)),
where a,b,c are sides of the triangle,
and s=(a+b+c)/2 - half perimeter of a triangle.
a=15,
b=15
c=18
s=(15+15+18)/2=48/2=24
s=24
s-a=24-15=9
s-b=24-15=9
s-c=24-18=6

A=√(24*9*9*6)=√(4*6*6*9*9) = 2*6*9=108
A=108

Which points in the scatter plot are outliers?

Select EACH CORRECT ANSWER

point A

point F

point H

point K

point M

Answers

F and K are definitely outliers of the plot
F and K are the answers.

According to Newton's Law of Cooling, if a body with temperature T 1 is placed in surroundings with temperature T 0, different from that of T 1, the body will either cool or warm to temperature T(t) after t minutes, where: T(t) = T 0 + (T 1 - T 0)e kt and k is a constant. A cup of coffee with temperature 140°F is placed in a freezer with temperature 0°F. The constant k ≈ -0.0815. Use Newton's Law of Cooling to find the coffee's temperature, to the nearest degree Fahrenheit, after 15 minutes. The temperature is about a0degrees Fahrenheit.

Answers

We can substitute the given values into the equation for T, given the surrounding temperature T0 = 0, initial temperature T1 = 140, constant k = -0.0815, and time t = 15 minutes.
T = 0 + (140 - 0)e^(-0.0815*15) = 140e^(-1.2225) = 41.23°F
Final answer:

Using Newton's Law of Cooling, the coffee's temperature after 15 minutes when placed in a freezer with a temperature of 0°F is approximately 76°F.

Explanation:

According to Newton's Law of Cooling, the temperature of an object changes at a rate proportional to the difference between its temperature and the temperature of its surroundings. In the given problem, we have a cup of coffee initially at 140°F placed in a freezer at 0°F, aimed to find the coffee's temperature after 15 minutes. The constant k is given as -0.0815.

We can plug these values into the equation T(t) = T0 + (T1 - T0)ekt. Therefore, the temperature of the coffee after 15 minutes can be calculated as T(15) = 0 + (140 - 0)e-0.0815*15.

Computing this gives us a value of approximately 76°F. Thus, after 15 minutes, the coffee's temperature, to the nearest degree Fahrenheit, is 76°F when placed in a freezer with a temperature of 0°F according to Newton's Law of Cooling.

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Three numbers are in the ratio of 6:5:1. What are the numbers if the difference between the smallest and largest is 30?
a.48, 40, 18B.36, 30, 6
c.24, 20, 4D.180, 150, 30

Answers

Given that the ratios between 3 numbers is 6:5:1 and the difference between the largest and the smallest number is 30, then the numbers will be as follows:
difference in ratio between large and smallest number is:
6-5=5
thus:
largest number=6/5*30=36
medium number=5/5*30=30
smallest number=1/5*30=6

Answer: B.36, 30, 6 

What is the best way to randomly choose these 500 members?

Answers

The best way to randomly pick would be to enter all the names into a computer and let it pick the names.
 The last choice is the correct answer

CDs and DVDs Solve by setting up a system of linear equations with 2 variables and 2 unknowns. CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost $127.73?

Answers

6 CDs and 2 DVDs would cost $147.68.

Let c be the cost of a CD and d be the cost of a DVD.

We know that c = d+5.96.

We also know that 5c+2d = 127.73.

Substituting our value of c from the first equation into the second one, we have
5(d+5.96)+2d = 127.73

Using the distributive property,
5*d+5*5.96+2d = 127.73
5d+29.80+2d = 127.73

Combining like terms,
7d+29.80 = 127.73

Subtract 29.80 from both sides:
7d+29.80-29.80=127.73-29.80
7d = 97.93

Divide both sides by 7:
7d/7 = 97.93/7
d = 13.99
c = d + 5.96 = 13.99+5.96 = 19.95

6 CDs and 2 DVDs would be
6(19.95)+2(13.99) = 147.68

The relationship between the total cost and the costs of CDs and DVDs are represented by a linear function.

The cost of 6 CDs and 2 DVDs is $147.68

Let:

[tex]C \to CDs[/tex]

[tex]D \to DVDs[/tex]

From the question, we have:

[tex]C = D + 5.96[/tex]

[tex]5C + 2D = 127.73[/tex]

Substitute [tex]C = D + 5.96[/tex] in [tex]5C + 2D = 127.73[/tex]

[tex]5 \times (D + 5.96) + 2D = 127.73[/tex]

[tex]5D + 29.8 + 2D = 127.73[/tex]

Collect like terms

[tex]5D + 2D = 127.73 - 29.8[/tex]

[tex]7D = 97.93[/tex]

Divide both sides by 7

[tex]D = 13.99[/tex]

Substitute [tex]D = 13.99[/tex] in [tex]C = D + 5.96[/tex]

[tex]C = 13.99 + 5.96[/tex]

[tex]C = 19.95[/tex]

The cost of 6 CDs & 2 DVDs is represented as:

[tex]Cost =6C + 2D[/tex]

So, we have:

[tex]Cost =6 \times 19.95 + 2 \times 13.99[/tex]

[tex]Cost =147.68[/tex]

Hence, the cost of 6 CDs & 2 DVDs is $147.68

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The perimeter of a square window is 360 cm find the length of one side

Answers

Final answer:

To find the length of one side of a square window with a perimeter of 360 cm, we use the formula for the perimeter of a square, resulting in each side being 90 cm long.

Explanation:

To find the length of one side of a square window when the perimeter is 360 cm, we can use the formula for the perimeter of a square, which is P = 4s, where P represents the perimeter and s represents the length of one side. Given that the perimeter is 360 cm, we can set up the equation 360 = 4s. Dividing both sides of the equation by 4 gives us s = 90 cm.

Therefore, the length of one side of the square window is 90 cm.

Iridium -192 has a half life of 74 days after 148 days, how many milligrams of 900 mg sample will remain?

Answers

[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &900\\ t=\textit{elapsed time}\to &148\\ h=\textit{half-life}\to &74 \end{cases} \\\\\\ A=900\left( \frac{1}{2} \right)^{\frac{148}{74}}\implies A=900\left( \frac{1}{2} \right)^2\implies A=225[/tex]

The amount that remained out of the 900 mg sample after 148 days is 225 milligrams.

Given,

Iridium -192 has a half-life of 74 days.

We need to find out after 148 days how many milligrams of the 900 mg sample will remain.

Here the initial amount is 900mg.

What is half life?

It is the time at which the initial amount of a substance is reduced to half its amount.

The formula used with half-life:

[tex]N_{t} =N_{0} (\frac{1}{2})^\frac{t}{t_\frac{1}{2} }[/tex]

Where

N_t = Amount after time t

N_0 = initial amount

t_1/2 = half-life value of the substance.

t = time.

We have,

N_0 = 900 mg

t_1/2 = 74 days.

t = 148 days.

Substituting the values in the formula,

We get,

N_t = 900 ( 1/2 ) ^148/74

N_t = 900 ( 1/2 )^2

N_t = 900/4

N_t = 225 mg

We see that the amount that remains after 148 days is 225 milligrams.

Thus the amount that remained out of the 900 mg sample after 148 days is 225 milligrams.


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I need your help here! 15 pointa and brainliest. If you cant do it, at least give me the formula to this so I can solve it.

Answers

see the attached picture for the answer. You will need to write the sentence required.

Answer:

0.40 formula x3.9 standardwise. Sorry if this doesnt help. I tried.

Step-by-step explanation:

There are 9.5 ounces of juice in a container. an additional 1.75 ounces of juice are poured into the container each second. how many ounces of juice are in the container after 6 seconds? enter your answer in the box. ounces

Answers

20 ounces of juice because u take 9.5+1.75 . 6 times and get 20 that is how it is 20 ounces of juice 

For this case, the first thing we must do is define variables.

We have then:

x: time in seconds

y: number of ounces

We then have an equation of the form:

[tex] y = mx + b
[/tex]

Where,

b: initial amount of juice

m: amount of juice added every second.

Substituting values we have:

[tex] y = 1.75x + 9.5
[/tex]

For 6 seconds later we have:

[tex] y = 1.75 (6) +9.5

y = 20
[/tex]

Answer:

20 ounces of juice are in the container after 6 seconds

please help asap 50 pts

Answers

Answer: The answer is B

Step-by-step explanation:

The smaller the coefficient, the wider the graph would be. So the smallest number, if positive, 1/5 is the widest and the largest 7 is the narrowest.

Answer:

b is ur answer

Step-by-step explanation:

The exchange rate between non-fixed currencies continuously fluctuates. The following table shows the exchange rate of pounds sterling to Israeli new shekel (plural shekalim) over a period of six days.

Days / £:INS
Monday: 1:6.0333
Tuesday: 1:5.8594
Wednesday: 1:5.7012
Thursday: 1:5.9462
Friday: 1:6.1715
Saturday: 1:6.0896

nate had 88.65 to convert into shekalim. the currency exchange he is using charges an 8% surcharge when converting currency. about how many more shekalim will nate recieve if he makes his trade on the day with the most favorable exchange rate than if he makes his trade on yhe day with the least favorable exchange rate?

Possible Answers
A. INS 41.69
B. INS 38.35
C. INS 31.68
D. INS 6.67

Answers

The correct answer is:

B) INS 38.35

Explanation:

The day with the best exchange rate is Friday; the rate is 1:6.1715. Converting 88.65£ with this rate, we have:

88.65(6.1715) = 547.103475.

Since he is charged an 8% surcharge, he gets to keep 100%-8% = 92% = 92/100 = 0.92 of this:

0.92(547.103475) = 503.335197

The day with the worst exchange rate is Wednesday, with a rate of 1:5.7012. Converting 88.65£ at this rate,

88.65(5.7012) = 505.41138. 4

0.92(505.41138) = 464.9784696

The difference between Friday and Wednesday is:

503.335197-464.9784696 = 38.3567274, or 38.35.

Nate would receive about 38.35 more shekalim if he made his trade on the day with the most favorable exchange rate than if he made his trade on the day with the least favorable exchange rate.

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The day with the best exchange rate is Friday; the rate is 1:6.1715. Converting 88.65£ with this rate, we have:

88.65(6.1715) = 547.103475.

Since he is charged an 8% surcharge, he gets to keep 100%-8% = 92% = 92/100 = 0.92 of this:

0.92(547.103475) = 503.335197

The day with the worst exchange rate is Wednesday, with a rate of 1:5.7012.

Converting 88.65£ at this rate,

88.65(5.7012) = 505.41138. 4

0.92(505.41138) = 464.9784696

The difference between Friday and Wednesday is:

503.335197-464.9784696 = 38.3567274, or 38.35.

Hence, Nate would receive about 38.35 more shekalim if he made his trade on the day with the most favorable exchange rate than if he made his trade on the day with the least favorable exchange rate.

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A 15 sector in a circle has an area of 11.9 m2 What is the area of the circle?

Answers

Given that the area of a 15° secant has an area of 11.9 m2, then the area of the circle will be given by:
(Total measure in degrees of the circle)/(measure in degrees of the secant)*(area of secant)
=360/15*11.9
=24*11.9
=285.6 m^2

Answer: 285.6 m^2

Elly buys 75 shares of stock in a mutual fund for a total investment of $450. She sells 50 shares of her stock for total proceeds of $400. Determine if Elly made a profit or loss, and how much per share.
a.
loss of $0.67 per share
b.
loss of $2 per share
c.
profit of $0.67 per share
d.
profit of $2 per share

Answers

We have been given that Elly buys 75 shares of stock in a mutual fund for a total investment of $450.

It means the cost of 1 share is given by

[tex]\frac{450}{75}\\ \\ =\$6[/tex]

Now, we have been given that she sells 50 shares of her stock for total proceeds of $400.

It means the cost of 1 share is given by

[tex]\frac{400}{50} \\ \\ \$8[/tex]

She purchased per share at $6 and sold per share at $8.

It means that she made a profit of [tex]8-6=\$2[/tex] per share.

Therefore, d is the correct option.

(d) profit of $2 per share

Elly made a profit of $2 per share.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can determine the average cost per share of the 75 shares of stock that Elly bought:

Average cost per share = Total investment / Number of shares

= $450 / 75 shares

= $6 per share

Next, we can determine the total proceeds from the sale of 50 shares:

Total proceeds = Number of shares sold x Price per share

= 50 shares x ($400 / 50 shares)

= $400

Elly paid $6 per share for the 75 shares she bought, and she sold 50 shares for $8 per share.

The difference between these prices will determine whether she made a profit or loss per share:

Profit or loss per share = Selling price per share - Average cost per share

= $8 per share - $6 per share

= $2 per share

Since the profit per share is positive, Elly made a profit.

Therefore,

Elly made a profit of $2 per share.

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Which story problems could be solved using the given equation? 6 divided by 1/2 = ? Choose exactly two answers that are correct.

A.
Mike spends a hour reading every night before bed. How many hours does Mike spend reading before bed in 6 days?



B.
Alice has 6 yards of ribbon. She uses yard of ribbon for each package she’s wrapping. How many packages can Alice wrap?



C.
A cup of milk is used for every serving in a recipe. How many servings can be made with 6 cups of milk?



D.
Charlie spent of his savings on 6 equally priced admission tickets to the zoo. What fraction of his savings did Charlie spend on each ticket?

Answers

Most likely D, the first three you don’t divide by 1/2.

can someone please help ill try to add the picture

Answers

check the picture below.

the lateral area, namely the area of the sides, is just the area of 4 rectangles.

left and right, 4x3 rectangles,

front and back, 15x3 rectangles,

so the lateral area of the box is just the sum of those areas,

 [tex]\bf \stackrel{\textit{left and right}}{(4\cdot 3)}~~~~+~~~~\stackrel{\textit{front and back}}{(15\cdot 3)}[/tex]

A forester wants to estimate the height of a tree. He is 6 ft tall and cast a shadow of 4 ft. If the shadow of the tree is 60 ft, how tall is the tree?

Answers

Since 4 is only 2/3 of 6, then you need to divide 60 into 3rds.
1/3 of 60=20
60+20=80!
Hopefully this is correct, but i will go check real quick!

Answer:

90 ft

Step-by-step explanation:

Given,

The 6 ft tall man casts 4 ft long shadow,

So, the ratio of the height of the man and its shadow = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]

Now, suppose the height of the tree that casts the shadow of 60 ft long is h ft,

So, the ratio of the height of tree and its shadow = [tex]\frac{h}{60}[/tex]

At the same time,

[tex]\frac{h}{60}=\frac{3}{2}[/tex]

[tex]h=60\times\frac{3}{2}=30\times 3=90[/tex]

Hence, the height of the tree is 90 ft

In the school band there are 4 trumpet players and f flute players. The total of trumpet and flute players is 12. Are there twice as much flute players as trumpet players? Explain.

Please help me really plz help i need it!
Thanks to those who took time for this....

Answers

if there are a total of 12 players and 4 are trumpet players than there are 8 flute players.

Twice are many trumpet players is 8 because you just do
[tex]4 \times 2 = 8[/tex]
so yes, there are twice as many flute players.

yes there is because there is 8 flute players and there are 4 trumpets and 8 is double then 4

The radius of a circular clock face is 13 centimeters. how do i find the circumfrence

Answers

The formula is 2pi(radius) so 13*2*pi=26pi

Hence, the circumfrence is [tex]81.64[/tex].

What is the circumference?

Circumference is the distance around a circle. We can find the circumference using either the diameter or radius of a circle. For shapes made of straight lines, we say they have a perimeter.

Here given that,

The radius of a circular clock face is [tex]13[/tex] centimeters.

The general formula of circumference of a circle is [tex]2\pi r[/tex].

As, [tex]r=13cm[/tex]

Substitue these values in the general formula then,

[tex]2\pi r=2(3.14)(13)\\\\=81.64[/tex]

Hence, the circumfrence is [tex]81.64[/tex].

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The local grocery store wants to know if the shoppers prefer Crest or Colgate toothpaste. The store gives all of its shoppers a value saver card, then uses a random number generator to select 30 card numbers and surveys those shoppers. Is this sampling method representative of the entire population and explain?

A. No, some shoppers may not buy toothpaste there.

B. Yes, all shoppers have a value card and the shoppers interviewed were chosen by a random number generator.

C. No, need a bigger sample.

D. No, the store should only ask women.

Answers

a, it is a biased ample because for example I may not go there to get toothpaste. Good luck

No, some shoppers may not buy toothpaste there.

The answer is option A.

What is an example of a word problem?

Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?

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The coordinate values of the vertices of △klm are integers. triangle klm has vertices located at (1, 1), (5, 4) and (5, 1). which set of coordinate pairs could represent the vertices of a triangle congruent to △klm?

Answers

The rest of the queastion is :
A) (-1, 1), (-1, 4), (2, 1)
B) (0, 0), (3, 4), (0, 5)
C) (-1, 1), (-4, 5), (-1, 5)
D) (0, 0), (-5, 0), (0, 4)
==============================

The distance between two points (x₁,y₁),(x₂,y₂) = d
[tex]d = \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} } [/tex]


we have K(1, 1), L(5, 4) and M(5, 1)
we will find the length between each two points.
KL = [tex]d = \sqrt{ (5-1)^{2} + (4-1)^{2} } [/tex] = 5
LM = [tex]d = \sqrt{ (5-5)^{2} + (1-4)^{2} } [/tex] = 3
KM = [tex]d = \sqrt{ (5-1)^{2} + (1-1)^{2} } [/tex] = 4

now check each group from the choices
the group that will give the same result will be the correct choice.
The correct choice is C
C) (-1, 1), (-4, 5), (-1, 5)

check the answer;
K'(-1, 1), L'(-4, 5), M'(-1, 5)

K'L' = [tex]d = \sqrt{ (-4+1)^{2} + (5-1)^{2} } [/tex] = 5
L'M' = [tex]d = \sqrt{ (-1+4)^{2} + (5-5)^{2} } [/tex] = 3
K'M' = [tex]d = \sqrt{ (-1+1)^{2} + (5-1)^{2} } [/tex] = 4

What is the y-intercept of the equation 5x - 6y = 18?

A.-6

B. -3

C .5

D. 18

Answers

The y-intercept is for x = 0.

Put the value of x = 0 to the equation 5x - 6y = 18:

5(0) - 6y = 18

0 - 6y = 18

-6y = 18    divide both sides by (-6)

y = -3 → B.

What is the equation of the line that passes through the points (–12, –8) and (–17, –16)?
A.
-17=-8/5(x-16)
B.
-16=8/5(x-17)
C.
+16=-4/5(x+10)
D.
y+16=8/5(x+17)

Answers

Last one


happy to help :)_

A circle has a circumference of 144\pi144π144, pi. what is the radius of the circle?

Answers

By definition, the circumference of a circle is given by:
 C = 2πR
 Where,
 R: radius of the circle.
 Substituting values we have:
 144π = 2πR
 By clearing R we have:
 R = 144/2
 R = 72 units
 Answer:
 The radius of the circle is:
 R = 72 units

PLEASE HELP: 22 points//And brainliest answer.

Picture is above

Answers

B. A square is a perfect shape, it will be symmetrical no matter how it is rotated.

Yes, the square is the only shape that will be the same no matter what side it is on.

Find the point on the curve y = √ 2 x + 4 which is closest to the point ( 3 , 0 ) .

Answers

Here you'll need differential calculus.

The distance between (3,0) and (x, sqrt(2)*x + 4) is given by the distance formula:

distance:  sqrt [ (3+x)^2 + (sqrt(2)*x + 4)^2 ]

Differentiate this, and then set the resulting derivative = to 0.  Solve for x.  Test your results to ensure that the distance d is actually the SMALLEST, given the root(s) x that you've found.

Write the coordinates of this point on the curve as ( x, f(x) ).
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