1. Transform the polar equation to a Cartesian (rectangular) equation: 2. Transform the Cartesian (rectangular) equation to a polar equation: y^2 = 4x

Hey there! I'm happy to help!

We know that the ice cream store makes 144 quarts in eight hours. What about in one hour? Let's divide this by eight to find out.

144/8=18

So, they make 18 quarts every hour. We want to figure out how many can be made in 12 hours. So, we just multiply 18 by 12!

18(12)=216

Therefore, 216 quarts of ice cream could be made in 12 hours.

Have a wonderful day! :D

The ice cream store will make 216 quarts of ice cream in 12 hours.

Division is breaking a number up into an equal number of parts.

Given that, An ice cream store makes 144 quarts of ice cream in 8 hours.

Since, they make 144 quarts of ice cream in 8 hours

Therefore, in 1 hour they will make = 144/8 = 18 quarts

So, in 12 hours = 18x12 = 216 quarts.

Hence, The ice cream store will make 216 quarts of ice cream in 12 hours.

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Answer: 0.584

Step-by-step explanation:

We have:

5 discs

6 jump ropes

3 balls

12 pieces of sidewalk.

5 + 6 + 3 + 12 = 26

If all of them have exactly the same probability of being removed, then:

in the first selection, we do not want to remove a jump rope, so we can remove one disc, one ball or one piece of sidewalk.

The total number of those objects is:

5 + 3 + 12 = 20.

Then the probability of removing one of those objects is:

P1 = 20/26 = 0.769

Now in the second selection, we have the same situation, but now we have 25 objects in total, and because in the previous selection we removed one ball, or one disc, or one piece of sidewalk, the total number of these things now is 19.

So the probability of removing another object of that set is:

P2 = 19/25 = 0.76

The joint probability is equal to the product of the individual probabilities, so we have:

P = P1*P2 = 0.769*0.76 = 0.584

In domain and range of a relation, if R be a relation from set A to set B, then

• The set of all first components of the ordered pairs belonging to R is called the domain of R.

Thus, Dom(R) = {a ∈ A: (a, b) ∈ R for some b ∈ B}.

• The set of all second components of the ordered pairs belonging to R is called the range of R.

Thus, range of R = {b ∈ B: (a, b) ∈R for some a ∈ A}.

Therefore, Domain (R) = {a : (a, b) ∈ R} and Range (R) = {b : (a, b) ∈ R}

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval is  [tex]49.85 < \mu < 54.15[/tex]

This means that there is 95% chance that the true population mean is within this interval

Step-by-step explanation:

From the question we are told that

    The  sample size is n = 30  

    The sample mean is  [tex]\= x = 52[/tex]

    The population standard deviation is  [tex]\sigma = 6[/tex]

Given that the confidence level is 95% then the level of confidence is evaluate as

             [tex]\alpha = 100 - 95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is

                 [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

            [tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]

           [tex]E = 2.147[/tex]

The  95% confidence interval is mathematically represented as

          [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

         [tex]52 - 2.147 < \mu < 52 + 2.147[/tex]

         [tex]49.85 < \mu < 54.15[/tex]

Answer:

6 out of 25

Step-by-step explanation:

At origin, the value of the function is [tex]0[/tex]

and then it again becomes zero for the first time is at $2$

but the function isn't repeating itself (it's going downwards)

at $x=4$, it's exactly same, hence the period is $4$

Answer:

F. [tex] \frac{3}{2} [/tex]

Step-by-step explanation:

[tex] \frac{a + 2b}{b} = \frac{7}{2} [/tex]

Cross multiply:

7b= 2(a +2b)

Expand:

7b= 2a +4b

Bring all common variables to 1 side:

7b -4b= 2a

3b= 2a

divide by 2 on both sides:

[tex] \frac{3}{2} b = a[/tex]

divide by b on both sides:

[tex] \frac{3}{2} = \frac{a}{b} \\ \frac{a}{b} = \frac{3}{2} [/tex]

Answer:

y > 1

Step-by-step explanation:

-2(7 + y) > -8(y + 1)

-14 -2y > -8y -8

-2y +8y > -8 +14

6y > 6

6y/6 > 6/6

y > 1

Answer:

combined like terms and then follow  the order of operations.

Step-by-step explanation:

Answer: Please Give Me Brainliest, Thank You!

#1, #2, #3 do, but #4 doesn't

Step-by-step explanation:

#1

18/9=2

6/3=2

#2

30/3=10

40/4=10

#3

28/14=2

36/18=2

Answer:

( -5,-7)

Step-by-step explanation:

f(x)= 2x+3 g(x)=-4x-27

Set the two functions equal

2x+3 = -4x-27

Add 4x to each side

2x+3+4x = -4x-27+4x

6x+3 = -27

Subtract 3

6x+3 - 3 = -27-3

6x = -30

Divide each side by 6

6x/6 = -30/6

x =-5

Now we need to find the output

f(-5) = 2(-5) +3 = -10+3 = -7

Answer:

Step-by-step explanation:

big burgewr

Answer:

  his path

Step-by-step explanation:

In order to determine the total distance driven from one place to another, you need to know the path taken.

Answer:

x= 5.5

Step-by-step explanation:

(segment piece) x (segment piece) =    (segment piece) x (segment piece)

x*4 = 11*2

4x = 22

Divide each side by 4

4x/4 = 22/4

x =5.5

Answer:

105/4 or 26.25 mi

Step-by-step explanation:

hillsdale to fairfax 8 7/8 = 71/8

fairfax to yardley = 17 3/8 = 139/8

71/8 + 139/8 = 105/4 or 26 2/8

Answer:

3 weeks

Step-by-step explanation:

6 quarts = 12 pints

12 divided by 3 = 4

Step-by-step explanation:

1 quart = 2 pints

6 quarts = 2 x 6 = 12 pints

12 ÷ 4 = 3

He can have 3 weeks

Answer:

52

Step-by-step explanation:

1. We see if we cube both sides of the second equation, then it looks more similar to the first equation (E = x^3 + 1/x^3)

(1/x + x)^3 = 4^3

1/x^3 + 3/x + 3x + x^3 = 64

2. Now we rearrange, because we see x^3 + 1/x^3 in the first equation in this equation

x^3 + 1/x^3 + 3x + 3/x = 64

3. We look at 3x + 3/x and see that it looks like the second equation, so we try factoring it

x^3 + 1/x^3 + 3(x + 1/x) = 64

we know x + 1/x = 4, so 3(x + 1/x) = 12

x^3 + 1/x^3 +12 = 64

4. Now we subtract and get our answer

x^3 + 1/x^3 = 52

Answer:

Step-by-step explanation:

a) First differences of the f(x) values in the table are ...

  19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162

The second differences are not constant:

  18 -6 = 12, 54 -18 = 36, 162 -54 = 108

But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.

__

b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...

  9, 15, 33, 87, 249

__

c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...

  (x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)

Answer: I think this is it:

The parent function of the function represented in the table is exponential. If function f was translated down 4 units, the f(x)-values would be decreased by 4. A point in the table for the transformed function would be (4,87)

Step-by-step explanation: I got it right on Edmentum!

Answer:

The  95% confidence interval is  [tex]98.27 < \mu < 102.53[/tex]

This interval means that there 95% confidence that the true mean is within this interval  

Yes i would agree with my friend because the lower and the upper limit 95% confidence interval for mean points scored at home is greater than 98 points

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  20

   The  sample mean is  [tex]\mu = 100.4[/tex]

     The standard deviation is  [tex]\sigma = 4.86[/tex]

Given that the confidence level is  95% then the level of significance is mathematically evaluated as

                [tex]\alpha = 100 - 95[/tex]

               [tex]\alpha = 5\%[/tex]

                [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is  

           [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{ \sqrt{n} }[/tex]

substituting values

            [tex]E = 1.96 * \frac{ 4.86 }{ \sqrt{20 } }[/tex]

           [tex]E = 2.13[/tex]

The  95% confidence interval is  mathematically represented as

          [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

         [tex]100.4 - 2.13 < \mu < 100.4 + 2.13[/tex]

          [tex]98.27 < \mu < 102.53[/tex]

Answer:

16

Step-by-step explanation:

It’s a ratio.

x/12=21/28

21x=12*28

21x=336

x=336/21

x=16

Answer:

Step-by-step explanation:

● h(x) = 2-2x

The domain is {-3,-2,1,5}

● h(-3) = 2-2×(-3) = 2+6 = 8

● h(-2) = 2 -2×(-2) = 2+4 = 6

● h(1) = 2-2×1 = 2-2 = 0

● h(5) = 2-2×5 = 2-10 = -8

The range is {-8,0,6,8}

Answer:

y=15x+126

Step-by-step explanation:

the slope is

15 because -8-(-9) is 1 and 6-(-9) is 15 and y is over x so slope 15

To find y intercept start from -8,6 and add 15 to the y value every time you add one to the x value

you will add 8 times and you get 126 as the intercept

Answer:

(A) 1

(B) -2

(C) 3.5

(D) -0.5

Step-by-step explanation:

We can treat each thermometer like a vertical number line and read the values on each.

A is right on 1.

B is right on -2.

C is in the middle of 3 and 4, so 3.5

D is in the middle of 0 and -1, so -0.5

Hope this helped!

Answer:

Collinear occurs when the two points has the same gradient,

So, for this question any line that forms by any three points would be collinear.

Hence, EBF,DGC,MGN,BGA are all collinears

Step-by-step explanation:

Answer:

z(s) is in the acceptance region. We accept H₀  we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine

Step-by-step explanation:

We must evaluate the differences of the means of the two machines, to do so, we will assume a CI  of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).

New machine

Sample mean                  x₁ =    25

Sample variance               s₁  = 27

Sample size                       n₁  = 45

Old machine

Sample mean                    x₂ =  23  

Sample variance               s₂  = 7,56

Sample size                       n₂  = 36

Test Hypothesis:

Null hypothesis                         H₀             x₂  -  x₁  = d = 0

Alternative hypothesis             Hₐ            x₂  -  x₁  <  0

CI = 90 %  ⇒  α =  10 %     α = 0,1      z(c) = - 1,28

To calculate z(s)

z(s)  =  ( x₂  -  x₁ ) / √s₁² / n₁  +  s₂² / n₂

s₁  = 27     ⇒    s₁²  =  729

n₁  = 45    ⇒   s₁² / n₁    = 16,2

s₂  = 7,56   ⇒    s₂²  = 57,15

n₂  = 36     ⇒    s₂² / n₂  =  1,5876

√s₁² / n₁  +  s₂² / n₂  =  √ 16,2  + 1.5876    = 4,2175

z(s) = (23 - 25 )/4,2175

z(s)  =  - 0,4742

Comparing z(s) and  z(c)

|z(s)| < | z(c)|  

z(s) is in the acceptance region. We accept H₀  we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine

The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean

Answer:

ABC = 148, 3*148 = 444

Step-by-step explanation:

We know that 111 = 3*  37, so all numbers of the form BBB has the factor 37.

So we need a multiple of 37 such thant when multiplied, we get three digits the same as the middle digit.

Try 4*37 = 148, 148*3 = 444, bingo, we got the right combination.

So ABC is 148.

Answer:

  288 square inches

Step-by-step explanation:

Assuming your "altitude" is the height of the prism--the distance between bases, the lateral area is the sum of the areas of the six rectangular faces. Each of those has an area of ...

  (8 in)(6 in) = 48 in^2

so the 6 of them will have an area of ...

  lateral area = 6×48 in^2 = 288 in^2

_____

Comment on nomenclature

'Altitude' is usually associated with the height of a triangle. In the case of a regular polygon, the 'altitude' of a triangular section of the polygon is called the 'apothem', and is often designated using the letter 'a'. If the polygon is regular, the apothem can be calculated from the side length and the number of sides, but it is often given in problems involving area, perimeter, and/or volume.

The distance between the parallel bases of a prism is often referred to as the prism height or length. The use of the word 'altitude' is confusing in this case.

Since the lateral area is the product of the perimeter of the base and the distance between bases, we have to assume that your 'altitude' refers to the distance between bases. Otherwise, there is not sufficient information to work the problem.

Answer:

No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4

Step-by-step explanation:

Equations : x + y + z = 17 [ Total times taken to score ]

1x + 2y + 3z = 33 [ Total Score ]

Also, y = x + 3

Putting the value of 'y' in both equations :

x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14  (i)

1x + 2 (x + 3) + 3z = 33 →  x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)

Solving these equations :

From (i), z = 14 - 2x

Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27

42 - 3x = 27 → 3x = 15 → x = 5

y = x + 3 = 5 + 3 → y = 8

z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4

Answer:

4

Step-by-step explanation:

Graphed using the given range equation. The shaded area is the possible range, extending to infinity, infinity from 0, -1.

Answer/Step-by-step explanation:

The inequality, x ≤ 7, has solutions that includes values that is equal to 1 or less than 7.

This can be represented on a number line as shown in the number line graphed in the attachment below.

A full circle or shaded "o" indicates that the number 7 is included in the solution.

The arrow points from 7 to the left, telling us that the value of x are all numbers from 7 and below.