Write an equation in point-stope form for the line through the given point with the given slope.

Answer:

Step-by-step explanation:

Assuming the density is the same for both lollipops, we can calculate what volume is required to make the 2158.7kg the same density of the smaller lollipop.  

Small Lollipop

r = 2cm

V=4 /3πr^3

V = 33.51 cm^3

Mass is 50 g in 33.51 cm^3, so the density is:

50g/(33.51 cm^3) = 1.492 g/cm^3

We have 2158.7kg in the larger lollipop.  That is 2158700 grams.

Find the volume required to contain 2158700 grams with a density of 1.492 g/cm^3.  :

       (2158700 grams)/(1.492 g/cm^3) = 1446775 cm^3

V=4 /3πr^3

1446775 cm^3 = (4/3)*π*r^3

r = 70.12 cm

Hi!

If they each got the same, then they each got 1/3 of the total $360. Therefore, we can divide 360 by 3. We can do this by dividing 36 by 3, 36/3, and that's 12. Then add the 0! 120.

Your sentence could be: "The amount of money each worker got can be represented by 360/3, which is $120."

Hope this helps! :D

Answer: Since Marcus hired 3 people and paid them $360 altogether, it should be easy to figure this out through dividing. 360/3 or 360 divided by 3 = 120. You can put three into 360 one-hundred and twenty times. So, your answer would be that each worker got $120.

Answer:

HF = 14.9

Step-by-step explanation:

Answer:

Width = 10 inches

Step-by-step explanation:

Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.

We can establish the following values to help us solve for the width of a rectangle:

Perimeter (P) = 68 inches

Length (L) = 14 + W inches

Width (W) = unknown

P =  2(L + W)  ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.

Divide both sides by 2:

[tex]\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}[/tex]

[tex]\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}[/tex]

Substitute the value of the Perimeter and the length (L) into the formula:

[tex]\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}[/tex]

Combine like terms on the right-hand side, and simplify the left-hand side of the equation:

[tex]\displaystyle\mathsf{34\:=14\:+2W}[/tex]

Subtract 14 from both sides:

34 - 14 = 14 - 14 + 2W

20 = 2W

Divide both sides by 2 to solve for the width (W):

[tex]\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}[/tex]

W = 10 inches

Therefore, the width of the rectangle is 10 inches.

Verify whether the derived value for the width is correct:

P = 2L + 2W

68 = 2(14 + 10) + 2(10)

68 = 2(34) + 20

68 = 48 + 20

68 = 68 (True statement).  

Thus, the length of the rectangle is 34 inches, and the width is 10 inches.

Answer:

I believe the answer is A.

Answer: 30%

Step-by-step explanation:

It increased by 15 so it increased by 15/50=30/100=30%

I hope this helped!

Answer:

8x-24

Step-by-step explanation:

First you do:

8×x which is 8x

Then you do:

8×-3 which is -24

Then you put it into 1 expression:

8x-24

Answer:

8−24

Thank You!

Answer:

y = 6x - 3

Step-by-step explanation:

Answer:

60 yards

Step-by-step explanation:

300 = 2(30 + w) + 2(w)

300 = 60 +2w + 2w

300 = 60 + 4w

240 = 4w

60 = w

Answer:

19 quarters and 13 nickles

Step-by-step explanation:

You have 32 coins in your pocket consisting of nickels and quarters with a total value of $5.40

How many nickels and quarters do you have?

Step 1: Setup Coin Value and Coin Total Equation:

Coin Value Equation → 0.05n + 0.25q = $5.40 where n = nickels and q = quarters

Coin Total Equation → n + q = 32

Step 2: Rearrange Coin Total Equation in terms of nickels (n)

n = 32 - q ← Revised Coin Total Equation

Step 3: Plug in our Revised Coin Total Equation for n into our Coin Value Equation:

0.05(32 - q) + 0.25q = $5.40

0.05(32) - 0.05(q) + 0.25q = $5.40

1.6 - 0.05q + 0.25q = $5.40

1.6 + (0.25 - 0.05)q = $5.40

1.6 + 0.2q = $5.40

Step 4: Subtract 1.6 from each side of the equation to isolate q

1.6 - 1.6 + 0.2q = $5.40 - 1.6

0.2q = 3.8

Step 5: Divide each side of the equation by 0.2 to isolate q

0.2q

0.2

=

3.8

0.2

q = 19

Step 6: Using our value for q, Solve for n using our Coin Total Equation:

n + 19 = 32

Subtracting 19 from both sides, we get n + 19 - 19 = 32 - 19

n = 13

Summarizing our word problem, we see that 19 quarters and 13 nickels adds up to $5.40

Answer:

9/4

Step-by-step explanation:

Answer:

9/2.25 = 4

Step-by-step explanation:

9/x = 4

x = 9/4 or 2.25

Answer:

1 1/2 pound

Step-by-step explanation:

If each coin weighs 3/4 ounces and she picked up 6 then you do 3/4 x 6/1 which equals 18/4 and since there is 16 ounces in a pound it simplifies to 1 2/4 or 1 1/2 pounds

Answer: to number 1 :The area of the square increases by 96% to number 2:  increase in width = 50%

Step-by-step explanation

Answer:

Click the picture and u will see the answer.

#CarryOnLearning

The summation of the given function from 1 to 4 is 10.5x³.

The given parameters:

[tex]\Sigma \ x^3 \times \Delta x, \ \ \ \Delta x = 2 + \frac{i}{4} \\\\[/tex]

The summation of the given function from i = 1, to i = 4, is calculated as follows;

[tex]\Sigma \ x^3 \times \Delta x = x ^3 (2 + \frac{1}{4} ) + x ^3 (2 + \frac{2}{4} ) + x ^3 (2 + \frac{3}{4} ) + x ^3 (2 + \frac{4}{4} )\\\\= x^3(10\frac{1}{2} )\\\\=\frac{21}{2} x^3\\\\= 10.5x^3[/tex]

Thus, the summation of the given function from 1 to 4 is 10.5x³.

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Answer:

15 installments

Step-by-step explanation:

3900 = Σ [tex]\left \ {{x=n} \atop {x=1}} \right.[/tex]   400 - 20*(n - 1)

Answer:

3

Step-by-step explanation:

3 months baseball = 18 x 3 = 54

3 months soccer = 15 x 3 = 45

54-45 = 9

9 / 3 = 3

David plays baseball 3 more times than soccer each month.

David plays 3 more times baseball than soccer each month.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

David plays baseball for 3 months, and each month he plays 18 times.

Also, David plays soccer for 3 months, and each month he plays 15 times.

In 3 months, David plays baseball = 18 x 3 = 54

Also, in 3 months, David plays soccer = 15 x 3 = 45

The more number of times David plays baseball than soccer

= 54 - 45

= 9

In 3 months, David plays 9 more times baseball than soccer.

In one month, David plays 9/3 = 3 more times baseball than soccer.

3 more times David plays baseball than soccer each month.

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Answer:

Option D

Step-by-step explanation:

Step 1:  Determine the correct option

Option A, this option doesn't work because -3.46 is not greater than -2 1/3.  Although the number 3 is greater than 2, these numbers are negative therefore the bigger the negative number, the smaller the number actually is.

Option B, this option doesn't work because 16/5 is not greater than 6.  If we convert 16/5 into a decimal we get 3.2 and this number isn't bigger than 6.

Option C, this option doesn't work because once again it states that -3.46 is greater than -2 1/3 when in reality it's actually smaller.

Option D, this option does work because everything goes according the way it should.  -3.46 is smaller than -2 1/3 and -2 1/3 is smaller than -3/4 and -3/4 is smaller than 16/5 and 16/5 is smaller than 6.

Answer:  Option D

========================================================

Explanation:

x = Jose's speed in mph

x+35 = Kayla's speed since she drives 35 mph faster than Jose

Jose gets a 2.1 hour head start and it takes Kayla 1.2 hours to reach him. So this means Jose has been driving for 2.1+1.2 = 3.3 hours when Kayla reaches him. The distance he travels is

distance = rate*time

d = r*t

d = x*3.3

d = 3.3x

while Kayla's distance equation is

d = r*t

d = (x+35)*1.2

d = 1.2x+42

Since Kayla meets up with Jose at the 1.2 hour mark, this means the two distances they travel is the same. Set their distance expressions equal to one another. Solve for x.

3.3x = 1.2x+42

3.3x-1.2x = 42

2.1x = 42

x = 42/(2.1)

x = 20

Jose's speed is 20 mph, while Kayla's speed is x+35 = 20+35 = 55 mph.

Jose's fairly slow speed is probably due to a number of factors such as heavy traffic, icy roads, or poor visibility. Kayla probably got a bit of a break with more favorable conditions.

Since Jose travels at 20 mph and does so for 3.3 hours, he travels d = r*t = 20*3.3 = 66 miles. Kayla travels d = r*t = 55*1.2 = 66 miles as well. We get the same number each time to help confirm the answer.

Answer:

  N is at -2 on the number line

Step-by-step explanation:

The location of point N can be found by writing the segment lengths as a proportion.

  ON : NP = 4 : 8

  8(ON) = 4(NP) . . . . . . . . "cross multiply"

  2(N -O) = (P -N) . . . . . divide by 4, show lengths ON and NP

  2(N -(-7)) = 8 -N . . . . . use given values of O and P

  3N = -6 . . . . . . . . . . . add N-14 and simplify

  N = -2 . . . . . . . . . . divide by 3

Point N is at -2 on the number line.

If the ratio of ON to NP is 4:8, point N lie on the -2 at the number line.

Point O is at -7.

Point P is at 8.

The ratio of ON to NP is 4:8.

The ratio 4:8 simplifies to 1:2. This means that ON is one-third of the total distance from O to P, and NP is two-thirds of the total distance.

The total distance from O to P is the sum of the distances between O and N, and between N and P.

As the ratio of ON to NP is 1:2, and the total distance is 15 (8 - (-7) = 15), we can set up the following equation:

ON/NP = 1/2

ON/(15 - ON) = 1/2

Now we can solve for ON:

2 × ON = 15 - ON

3 × ON = 15

ON = 5

So, ON is 5 units away from O.

Now O is at -7, point N is at -7 + 5 = -2 on the number line.

So, N is at -2.

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Answer:

a) 8/17

b) 4/17

c) 5/17

d) 48/187

Step-by-step explanation:

a) P(silver) = 16/34 = 8/17

b) P(blue) = 4/17

c) P(red) = 5/17

d) P(silver, not silver) = 8/17 × 18/33 = 144/561 = 48/187

The probability for each event are -

[A] -  8/34

[B] -  16/34

[C] -  10/34

[D] -  18/33

        P(A) = n(A)/n(S)

        where -

        n(A) = Number of outcomes favorable to event A.

       n(S) = Total number of outcomes

We have 16 silver cars, 8 blue cars and 10 red cars in a parking lot.

[A] -

P{silver} = 8/(16 + 8 + 10) = 8/34

[B] -

P{blue} = 16/(16 + 8 + 10) = 16/34

{C} -

P{red} = 10/(16 + 8 + 10) = 10/34

D) -

P{not silver} = 1 - 15/33 = 18/33

Therefore, the probability for each event are -

[A] -  8/34

[B] -  16/34

[C] -  10/34

[D] -  18/33

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Answer:

Let’s take a point each on the x, y, and z-axis as follows:

A (1, 0, 0) on x-axis

B (0, 1, 0) on y-axis and

C (0, 0, 1) on z-axis

unit vector

So, we have

|OA→| = 1 , |OB→| = 1, and |OC→| = 1

These vectors OA→, OB→, and OC→, each having magnitude 1 are Unit Vectors along the axes OX, OY, and OZ respectively. They are denoted by i⃗ , j⃗ , and k⃗  as shown in Fig. 1 above.

Step-by-step explanation:

The midpoint of a line segment divides the line segment into equal halves.

Point M is the midpoint of line segment VW.

So, we have:

[tex]VM = MW[/tex]

Substitute known values

[tex]4x - 1= 3x+3[/tex]

Collect like terms

[tex]4x - 3x = 1 + 3[/tex]

Evaluate like terms

[tex]x = 4[/tex]

Hence, the value of x is 4

The expression for VM is:

[tex]VM = 4x - 1[/tex]

So, we have:

[tex]VM = 4(4) - 1[/tex]

[tex]VM = 15[/tex]

Hence, the value of VM and MW is 15

The length of VW is the sum of both lengths.

So, we have:

[tex]VW = 15 + 15[/tex]

[tex]VW = 30[/tex]

Hence, the value of VW is 30

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Answer:

731 miles

Step-by-step explanation:

344 miles / 8 hours = 43 mph

17 hours * 43 mph = 731 miles

Answer:

(-5, -7)

Step-by-step explanation:

Answer:

[tex](-5,-7)[/tex]

Step-by-step explanation:

[tex]f(x)=2x+3[/tex]

[tex]g(x)=-4x-27[/tex]

[tex]2x+3=-4x-27[/tex]

[tex]6x+3=-27[/tex]

[tex]6x=-30[/tex]

[tex]x=-5[/tex]

[tex]f(-5)=2(-5)+3[/tex]

[tex]f(-5)=-10+3[/tex]

[tex]f(-5)=-7[/tex]

Therefore, the point of intersection is [tex](-5,-7)[/tex]