Find the slope of the line if it exists.

nina can swim 8/7 laps in one minute

given that

nina can swim 4 laps in 7/2 minutes

we have to calculate that how many laps can nina swim in 1 minute

then 4 laps= 7/2 minutes

then 4*2 /7 =1 minute

           8/7=1 minute

  thus nina can swim 8/7 laps in one minute

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In the graph we have a parabola, and its equation is y = (x - 2)^2 - 3

In the graph, we can see a parabola.

We only need to identify 3 parts, which are the two x-intercepts (if it has) and the y-intercept.

Remember that if the vertex and the y-intercept. Remember that if the vertex is (h, k) and the leading coefficient is a, then we can write the equation as:

y = a*(x - h)^2 + k

In the image we can see that the vertex is (2, -3), then:

y = a*(x - 2)^2 - 3

And the y-intercept is y = 1, then if we evaluate in x = 0 we should get y = 1, replacing that we get:

1 = a*(0 - 2)^2 - 3

1 = a*4 - 3

1 + 3 = a*4

4/4 = a = 1

Then the quadratic equation is y = (x - 2)^2 - 3

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Answer:

  B.  False

Step-by-step explanation:

You want to compare the lateral surface areas of a cone and cylinder, where the slant height of the cone is twice the height of the cylinder. Your proposition is that the cone's lateral area is half that of the cylinder.

Effectively, the lateral area of a cone is the area of a triangle whose base is the circumference of the cone, and whose height is the cone's slant height. The formula for the lateral area of a cone of radius r and slant-height s is ...

  A = πrs

For the given dimensions (s=2h), the lateral area is ...

  A = πr(2h) = 2πrh

The lateral area of a cylinder is the area of a rectangle whose base is the circumference of the cylinder, and whose height is the cylinder's height. The formula for the lateral area of a cylinder of radius r and height h is ...

  A = 2πrh

The lateral areas of the given figures are both 2πrh, so one is not half the other.

The proposition is False.

Answer:

y2-y1/x2-x1

-8--3/0-2

Step-by-step explanation:

-8+3/-2=-5/-2=5/2

Rene's limeade has a weaker flavor as calculated by division of fractions.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

Concentration of Jaylan's limeade [tex]=\frac{3}{4} \div\frac{1}{5} = \frac{15}{4} =3.75[/tex]

Therefore as calculated by division of fractions, concentration of Jaylan's limeade is 3.75 cups of water for 1 cup of lime juice.

Concentration of Rene's Limeade[tex]=\frac{2}{3} \div\frac{1}{6} = \frac{12}{3} =4[/tex]

Therefore as calculated by division of fractions, concentration of Rene's limeade is 4 cups of water for 1 cup of lime juice.

Hence Rene's limeade has a weaker flavor as calculated by division of fractions.

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Answer:

a). 16, 25, 36, 49, 64

b). ???

Step-by-step explanation:

16 + 9 = 25

25 + 11 = 36

36 + 13 = 49

49 + 15 = 64

I don't think b is possible

Answer: 46.5 by 19.5

Step-by-step explanation:

P=perimeter of panel. L=length. W=width

L=3W-12

P=2L+2W

132=2(3W-12)+2W

132=6W-24+2W

132=6W+2W-24

132=8W-24

156=8W

W=19.5

P=2L+2W

132=2L+2(19.5)

132=2L+39

2L=93

L=46.5

46.5 by 19.5

This is probably what steps your friend took, or something similar.

5x+4x-68 = 34-8x

9x = 34-8x-68

9x = -8x-34

9x+8x = -34

17x = -34

x = -34/17

x = -2

However, the error is when they subtracted 68 from both sides (line 2).

Instead, they should have added 68 to each side to undo the -68 on the left hand side.

----------------------------

Here's what the steps should look like (one variation of it anyway)

5x+4x-68 = 34-8x

9x = 34-8x+68

9x = -8x+102

9x+8x = 102

17x = 102

x = 102/17

x = 6 is the correct value of x

--------------------------

Check:

5x+4x-68 = 34-8x

5*6+4*6-68 = 34-8*6

30+24-68 = 34-48

54-68 = 34-48

-14 = -14

We get the same thing on both sides after replacing each x with 6, so it confirms x = 6 is the solution.

If you were to try x = -2, then you would end up with -86 = 50 which is a false statement. So that rules out x = -2 as a solution.

Answer:

2n-67

Step-by-step explanation:

Twice a number means 'multiply by 2' so we can write 2 x n. We can also write this in a simpler form- 2n

'67 decreased' means minus 67 off your answer so therefore the answer must be:

2n-67

Love answering your questions by the way :)

Using the Pythagorean theorem, the missing sides are:

1. 5

2. 13

3. √15

4. 3

The Pythagorean theorem is given as: c² = a² + b², where c is the longest side and a and b are the other two legs.

1. Missing side = √(3² + 4²) [Pythagorean theorem]

Missing side = 5

2. Missing side = √(12² + 5²) [Pythagorean theorem]

Missing side = 13

3. Missing side = √(4² - 1²) [Pythagorean theorem]

Missing side = √15

4. Missing side = √((√10)² - 1²) [Pythagorean theorem]

Missing side = √(10 - 1) = √9

Missing side = 3

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The number in each of the set of blank boxes is 10

From the first number set of stamps, we see that the sum of each row is;

5 + 5 + 5 + 5 = 20

There are four rows. Thus;

Total sum of set of stamps = 20 + 20 + 20 + 20

Total sum of set of stamps = 80

Now, for the blank set of stamps, we see that there are 8 boxes which are al equal. Now, for this 8 boxes t have same sum as that of the initial set of stamps, it means they must sum up to 80.

If the number in each box is x, then;

8x = 80

x = 80/8

x = 10

Thus, the number in each of the set of blank boxes is 10

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Step-by-step explanation:

[tex] 3\sqrt{8} + \sqrt{114} [/tex]

Answer:

x = 4 and x = 7

Step-by-step explanation:

→ Find the sum of both the angles

3x + x + 74 = 4x + 74

6x + x + 13 = 7x + 13

→ Equate both equations to 90

4x + 74 = 90

7x + 13 = 90

→ Minus 74 and 13

4x = 16

7x = 77

→ Divide by 4 and 7 respectively

x = 4 and x = 7

Considering the concepts of parallel lines and alternate interior angles, it is found that Mitch created diagram C.

Parallel lines are lines that never intersect. For this problem, lines l and k are parallel, that is, they are the horizontal lines.

When two parallel lines are crossed by a transversal, the alternate interior angles are between the two parallel lines, one in each side.

Since 1 and 2 are alternate interior angles, Mitch created diagram C.

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The rate of margin used is 37.5% . The cost price of the batch of plywood is $312.5. Fence post sell for $16. The selling price was $133.33

Margin is the difference between the Selling price and the cost price. The price at which a item is sold is called the selling price and the price at which an item is bought is called the cost price.

The given markup is 60%.

We know that margin=markup÷(1+markup)

markup=60%

Substituting the values we get the rate of margin:

[tex]=\frac{\frac{60}{100} }{1+\frac{60}{100} } \\=\frac{60}{160}\\ =37.5[/tex]

Hence the rate of margin is 37.5 %.

Selling price for the plywood=$500

We know that selling price=cost price ÷(1-margin)

Let the cost price be x

[tex]x=500(1-\frac{37.5}{100} )\\x=312.50[/tex]

The cost price is $ 312.50 .

Now cost of fence = $10

Selling price of fence=cost price÷(1-margin)

substituting the values we get:

Selling price =10÷0.625

or, selling price= $16

Therefore the selling price is $16 .

Now we know that Markup percentage= profit÷ cost price

Substituting the values we get:

[tex]60\% = \frac{50}{CP}\\or,\frac{60}{10}=\frac{50}{CP}\\or,CP=83.33[/tex]

Therefore sell price=cost price+ profit

or, sell price=83.33+50

or, sell price =133.33

The sell price is $133.33

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The value of the f(x) = (x + 4) / x at x = 4 is equal to - 1 / 4.

In this problem we have the following rational equation, which is equivalent to the following sum of functions:

f(x) = (x + 4) / x = 1 + 4 / x = g(x) + h(x)

Then, we must find both the derivatives of the functions g(x) and h(x) by using the definition of derivative:

g(x):

g'(x) = [1 - 1] / h

g'(x) = 0 / h

g'(x) = 0

h(x):

h'(x) = [4 / (x + h) - 4 / x] / h

h'(x) = [4 · x - 4 · (x + h)] / [h · (x + h) · x]

h'(x) = - 4 · h / [h · (x + h) · x]

h'(x) = - 4 /[(x + h) · x]

If h = 0, then:

h'(x) = - 4 / x²

Then, the first derivative of the function is f(x) = - 4 / x². Now we evaluate the function at x = 4:

f(4) = - 4 / 4²

f(4) = - 1 / 4

The value of the f(x) = (x + 4) / x at x = 4 is equal to - 1 / 4.

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Answer:

10%

Step-by-step explanation:

firstly express as a fraction then multiply the fraction by 100% , that is

[tex]\frac{2}{20}[/tex] × 100% = 2 × 5 = 10% of the flowers are roses

The profit function is P(x) = ( - x² / 5000 ) + 13.9x - 75000.

50,000 baseball game tickets were sold at $4 per ticket.

When the price is raised to $5, then 45,000 tickets were sold.

The variable and fixed costs for the ballpark owners are $0.10 and $75,000 respectively.

Let's say x is the number of tickets sold, and P is the profit.

Then,

P = ax + b

At P = 4,

4 = (50000)a + b                                                                                  ---------(1)

At P = 5,

5 = (45000)a + b                                                                                  --------(2)

Subtracting (2) from (1),

4 - 5 = (50000)a + b - (45000)a - b

- 1 = 5000(a)

a = ( - 1/5000)

So if a = ( - 1/5000),

Then,

4 = (50000)a + b

4 = (50000)( - 1 / 5000 ) + b

4 = -10 + b

b = 14

Therefore,

p(x) = ( - x /5000) + 14

Now, the profit function is:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Now, R(x) =  xp(x)

R(x) = x[ ( - x/5000) + 14]

R(x) = ( - x² / 5000 ) + 14x

The fixed cost is F(x) = $75000

Hence, the costs will be:

C(x) = 75000 + (0.10)x

Therefore the profit function is:

P(x) = R(x) - C(x)

P(x) = ( - x² / 5000 ) + 14x - 75000 - (0.10)x

P(x) = ( - x² / 5000 ) + 13.9x - 75000

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The complete question is mentioned below:

When the admission price for a baseball game was $4 per ticket, 50,000 tickets were sold. When the price was raised to $5, only 45,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ballpark owners are $0.10 and $75,000 respectively.

Find the profit P as a function of x, the number of tickets sold

Answer:6.986

Step-by-step explanation:

To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.

Answer: Standard deviation is 6.986.

Step-by-step explanation:

Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation

To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.

Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.

In this case standard deviation is 6.986.

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At this point, the canoe will be under a net force of 51.52 N.

The total mass of a canoe and a paddler is 100.0 kg. A river that runs from east to west is where the canoe is thrown in. The power of the water current on the canoe is 18.0 N. The paddler exerts a force of 36.0 N [E 37.0° N].

The Free Body Diagram is then displayed below.

The canoe's net force would then be indicated as follows:

F = (18 + 36 cos 37°) i + (36 sin 37°) j

F = 46.75 i + 21.67 j

Therefore the force's strength will be

|F| = √(46.75² + 21.67²)

|F| = √2655.15

|F| = 51.52 N

Thus, at this point, the canoe will be under a net force of 51.52 N.

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Answer:

F=9/5c+32

Step-by-step explanation:

Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:

9/5C = F-32

C=F−32

Then add 32 to both sides, giving you:

9/5C + 32 = F

C+32=F

Thus, you have:

F= 9/5C + 32F=

5

9

C+32

Answer:

[tex]F= \frac{9}{5}C + 32[/tex]

Step-by-step explanation:

Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:

[tex]\frac{9}{5}C = F-32[/tex]

Then add 32 to both sides, giving you:

[tex]\frac{9}{5}C + 32 = F[/tex]

Thus, you have:

[tex]F= \frac{9}{5}C + 32[/tex]

Answer:

{a, c, e, f, g}

Step-by-step explanation:

[tex]B'=\{a,b,c,d,e,f,g\}-\{a,b,c,d\}=\{e,f,g\} \\ \\ A \cup B=\{a,c,e,f,g\}[/tex]

The equation will be,

→ 5/10 = 12/24

Is 5/10 equivalent to 12/24?

→ 5/10 = 12/24

→ 24 × 5 = 12 × 10

→ 120 = 120

→ [ LHS = RHS ]

Hence, they are equivalent.

Answer:

[tex]-\frac{47}{64}[/tex] or [tex]\frac{1}{2}^{3} -6/\sqrt{64}[/tex]

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

Answer:

GCF = 2

Step-by-step explanation:

The number of nails in each box is: 1300, 1400, 600, 1200, and 500

Given 5000 nails in five boxes.

Let X denote the universal set.

Then n(X) = 5000.

Let A denote the first box,

B denote the second box,

C denote the third box,

D denote the fourth box, and

E denotes the fifth box.

The first and second boxes have 2700 nails altogether.

⇒n(A ∪ B) = 2700

The second and third boxes have 2000 nails altogether.

⇒n(B ∪ C) = 2000

The third and fourth boxes have 1800 nails altogether.

⇒n(C ∪ D) = 1800

The fourth and fifth boxes have 1700 nails altogether.

⇒n(D ∪ E) = 1700

We need to find out how many nails are there in each box.

That is to find out: n(A), n(B), n(C), n(D), and n(E).

Note that all these five sets are disjoint. This means that the intersection is empty.

n(A ∪ B ∪ C ∪ D) = n(A ∪ B) + n(C ∪ D) = 2700 + 1800 = 4500

n(E) = n(X) - n(A ∪ B ∪ C ∪ D) = 5000 - 4500 = 500

n(D) = n(D ∪ E) - n(E) = 1700 - 500 = 1200

n(C) = n(C ∪ D) - n(D) = 1800 - 1200 = 600

n(B) = n(B U C) - n(C) = 2000 - 600 = 1400

n(A) = n(A U B) - n(B) = 2700 - 1400 = 1300

Therefore, the number of nails in each box is 1300, 1400, 600, 1200, and 500.

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Answer: 85 in

Step-by-step explanation:

A=Area of rectangle. L=length of rectangle. W=width of rectangle

A=L*W

1445=L*17

1445/17=L*17/17

L=85 in