6. Solve P = C + rC for r.

Answer:

B. (-1, -4)

Step-by-step explanation:

Answer:

answer a -4, 1

i think

The number 0.00006 is greater than 0.000002 by 30 times.

Two numbers , 0.00006 and 0.000002 are given.

We have to find out that by how many times 1st is greater by the 2nd.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as multiplication , division , etc.

As per the question ;

Numbers are 0.00006 and 0.000002.

Let's divide them to find how many times 1st is greater by the 2nd.

So ;

0.00006 ÷ 0.000002

Multiply by 10^6 and divide by 10^6

We get ;

\(\frac{0.00006 * 10^6}{0.000002*10^6}\)

or

60 / 2

= 30 times

Thus , the number 0.00006 is greater than 0.000002 by 30 times.

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The value of the variable of the rectangular prism 'x' will be 7.

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

The equation is given below.

308 = 2(10 · x) + 2(2 · x) + 2(2 · 10) + 6(5 · 5) - 2(5 · 5)

Simplify the equation, then we have

308 = 2(10 · x) + 2(2 · x) + 2(2 · 10) + 6(5 · 5) - 2(5 · 5)

308 = 20x + 4x + 40 + 150 - 50

308 = 24x + 140

24x = 168

x = 7

The value of the variable of the rectangular prism 'x' will be 7.

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Answer:

5(-2m - 4) is equivalent to 10m + 20.

Answer:

D) 10m+20

Step-by-step explanation:

To solve for this, we have to solve -5(-2m-4).

To do this, distribute (multiply) -5 to both of the numbers in the parathesis:

-5x-2m

=10m

-5x-4

=20

10m+20

So, D is the correct answer.  Hope this helps :)

The derivate of the logarithmic function is :

f'(x) = [(4*x^3 + 2*e^2x)/(x^4 + e^2x)]

Remember that for the natural logarithm g(x) = ln(x), we have:

dg/dx = 1/x

Here we have the function:

f(x) = ln(x^4 + e^2x).

The derivate will be one over the argument (for what we wrote above) times the derivate of the argument, we will get:

f'(x) = [1/(x^4 + e^2x)]*(4*x^3 + 2*e^2x)

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Answer:

Please see attached photo!

Step-by-step explanation:

The area of a regular pentagon is 58 ft2. thus option B is correct.

Apothem for a regular polygon is a line segment that originates from the center of the regular polygon and touches the mid of one of the sides of the regular polygon.

It is perpendicular to the regular polygon's side it touches.

Given; An apothem has a length of 4 feet and each side has a length of 5.8 feet.

The area of any regular polygon can be calculated as:

Area = number of sides (n) x 0.5 x length of sides (s) x apothem (a)

Area = 5 x 0.5 x 4 x 5.8

Area = 58

Hence, the area of a regular pentagon is 58 ft2. thus option B is correct.

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Answer:

30/182 = 15/91.

Step-by-step explanation:

PROBABILITY: the likelihood of an event.

There are a total of 14 shirts in the basket.

Of the 14, 8 (8/14) of them are white, and 6 (6/14) of them are black.

The probability of picking a black shirt is 6 in 14, or 6/14.

The probability of picking a white shirt is 8 in 14, or 8/14.

WITHOUT REPLACING: This means that you take one without putting it back. (There will be one less).

6/14 × 5/13 = 30/182.

30/182 = 15/91.

The probability of randomly picking a black t-shirt from the basket, and then another one without putting the first one back is 15/ 91.

Probability refers to a possibility that deals with the occurrence of random events.

There are a total 14 shirts in the basket.

Out of the total of 14, 8 (8/14) of them are white, and 6 (6/14) of them are black.

The probability of picking a black shirt = 6/14.

The probability of picking a white shirt = 8/14.

The probability of randomly picking a black t-shirt from the basket, and then another one without putting the first one back

= 6/14 × 5/13

= 30/182.

= 15/91.

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Answer:

Slope: -8/3

Step-by-step explanation:

y + 3 = -8 (x-4)

y+3 = -8x + 32

y = -8/3x + 29

Therefore, the slope is -8/3.

The slope is :

Solution:

Givens :

To determine the slope, it's important to know the form of the equation first.

The forms are:

This equation matches point slope perfectly.

\(\rule{350}{4}\)

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Extra info

The point of the line is \(\bf{(4,-3)}\).

Opportunity cost is the price of giving up an option. An opportunity cost is the price you pay for selecting a particular option over another. Opportunity cost is the benefits you lose by choosing one alternative over another one.”

The value of the next-highest-valued alternative use of a resource is what economists mean when they talk about its "opportunity cost." You cannot, for instance, read a book at home during the time you would have spent seeing a movie and spend the money you would have spent on something else.

Opportunity cost is frequently referred to as the second-best option. The loss of benefit that would have been realized if a different option had been taken is sometimes referred to as the alternative cost. The loss of advantage as a result of a change in decision is another way to explain it.

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We must select at least 10 numbers from the given set to guarantee that at least one pair of these numbers adds up to exactly 22.

To guarantee that at least one pair of numbers from the given set adds up to exactly 22, we need to use the Pigeonhole Principle.
Let's first look at all possible pairs that add up to 22. They are (4,18), (6,16), (8,14) and (9,13). There are four such pairs.
Now, let's assume we select only 9 numbers from the given set. It is possible that we don't select any of the numbers from the four pairs that add up to 22. In that case, we won't have any pair of numbers that add up to 22.
However, if we select 10 numbers from the given set, by the Pigeonhole Principle, we are guaranteed to have at least one pair of numbers that add up to exactly 22. This is because we have 10 pigeons (numbers) and 4 holes (pairs that add up to 22). At least two pigeons must land in the same hole.

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Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept

We can use the data given in writing out our equation

390.6 = 14x

If 14 gallons = 390.6 miles

 1 gallon = x miles

x = 390.6 / 14

x = 27.9 miles

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Fourteen eleventh graders prefer math and eight tenth graders prefer English.

A survey is a study that seeks to gather information about people sometimes involving the preferences of the people.

From the table, we can see that fourteen eleventh graders prefer math and eight tenth graders prefer English.

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Answer:

a) Height = OC = 13.3cm

b) Perimeter = 48.4cm

Step-by-step explanation:

a) Given:

ODC is a right angle triangle and

ABCD is part of it.

AB = 6 cm

CD = 15 cm

BC = 8 cm

∠BCD = 90 degrees

AB is parallel to DC

Find attached the diagram obtained from the given information.

From the diagram, ∆OAB is similar to ∆ODC.

∠OBA = ∠OCD = 90 degrees

To find the height, we would apply the similar triangles theorem.

The ratio of corresponding sides are equal and the angles are congruent.

OB/BA = OC/CD

OC = OB+BC = OB+8

OB/6 = (OB+8)/15

15OB = 6(OB+8)

15OB = 6OB + 48

9OB = 48

OB = 48/9 = 16/3

OC = 16/3 + 8

OC = 13⅓ cm = 13.3cm

Height = OC = 13.3cm

b) To get perimeter, we have to first determine OD (the hypotenuse of ∆OCD) as it is a right angled triangle

Using Pythagoras theorem

Hypotenuse ² = opposite ² + adjacent ²

OD² = OC² + CD²

OD² = (13⅓)² + 15²

OD² = 1600/9 + 225 = 3625/9

OD = √(3625/9)

OD = 20.1

Perimeter of ∆ODC= OC + CD + OD

= 13.3 + 15 + 20.1

Perimeter = 48.4cm

Answer: 15000

Step-by-step explanation: Step by step solution for calculating 135 is 0.9 percent of what number

We already have our first value of 135 and the second value of 0.9. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1135 = 0.9% × Y

STEP 2135 =

0.9

100

× Y

Multiplying both sides by 100 and dividing both sides of the equation by 0.9 we will arrive at:

STEP 3Y = 135 ×

100

0.9

STEP 4Y = 135 × 100 ÷ 0.9

STEP 5Y = 15000

Finally, we have found the value of Y which is 15000 and that is our answer.

You can easily calculate 135 is 0.9 percent of what number by using any regular calculator, simply enter 135 × 100 ÷ 0.9 and you will get your answer which is 15000

The expected number of matchings goes to infinity as N › [infinity].

Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].

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Answer:

(4y)2 - (5)2 which is in the form a2 - b2

= (4y + 5) (4y - 5)

Step-by-step explanation:

The number that Dextor is thinking of is 7

5.

It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Let the number based on the information be x

The statement is that three more than double his number is the same value as seven less than four times his number. This will be:

(2 × x) + 3 = (4 × x) - 7

2x + 3 = 4x - 7

Collect like terms

4x - 2x = 7 + 3

2x = 10

Divide

x = 10 / 2

x = 5

The number is 5.

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The area of a cross section of the shape formed by the intersection of the solid and a plane parallel and 2 inches above the base is 20.93 cm².

Calculate the area of the cylinder.

A cylinder's surface area is determined by multiplying its base circumference by its height.

2r, where r is the cylinder's radius (5 cm), equals the circumference of the cylinder.

Therefore, the area of the cylinder is 2πr x 5 cm = 2π x 5 cm2 = 31.4 cm².

Calculate the area of the cone.

A cone's area is determined by multiplying its height by a factor of three times the base's radius.

2r, where r is the cone's radius (5 cm), equals the circumference of the cone.

Therefore, the area of the cone is 1/3 x 2πr x 5 cm = 2π x 5 cm2 / 3 = 10.47 cm².

Determine the cross section area.

The area of the cylinder less the area of the cone equals the area of the cross section.

Therefore, the area of the cross section is 31.4 cm2 - 10.47 cm2 = 20.93 cm².

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Answer:

$1417.5

Step-by-step explanation:

Given data

Principal=$4500

Rate = 9%

Time=3.5 years

The simple interest is given as

SI=PRT/100

substitute

SI= 4500*9*3.5/100

SI= 141750/100

SI= $1417.5

Hence the simple interest is $1417.5

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:

2(3) that's multiplication so the answer is A

Answer: you would use the last option

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Therefore, using simple exponential smoothing with a = 0.75, the forecast for water pump sales for February through May are:- February: 26.5 units,  March: 37.63 units, April: 72.66 units.

To use simple exponential smoothing with a = 0.75, we first need to calculate the forecast for January:
F1 = 25 (given)
Next, we calculate the forecast for February using the formula:
F2 = a * Y1 + (1 - a) * F1
F2 = 0.75 * 28 + 0.25 * 25
F2 = 26.5 (rounded to one decimal place)
We repeat this process for each month, using the previous month's forecast and the actual sales data for the current month. The results are as follows:
Month      Actual Sales    Forecast
-------------------------------------
January           28          25
February          72          26.5
March             98          37.63
April            126          72.66
- May: 101.17 units
Hi, I'd be happy to help you with your question. To use simple exponential smoothing with a smoothing constant α = 0.75 to forecast the water pump sales for February through May, given that the forecast for January was 25 units, follow these steps:
Step 1: Start with the given forecast for January, which is 25 units.
Step 2: Calculate the forecast for February using the formula:
Forecast_February = α * (Actual_January) + (1 - α) * Forecast_January
Step 3: Calculate the forecast for March using the formula:
Forecast_March = α * (Actual_February) + (1 - α) * Forecast_February
Step 4: Calculate the forecast for April using the formula:
Forecast_April = α * (Actual_March) + (1 - α) * Forecast_March
Step 5: Calculate the forecast for May using the formula:
Forecast_May = α * (Actual_April) + (1 - α) * Forecast_April
Please note that you have provided sales data for air-conditioning sales, but the question is about water pump sales. If you meant to ask about air-conditioning sales, you can use the given sales data to calculate the forecasts for February through May. If you need help with water pump sales, please provide the correct sales data for January through April, and I will gladly help you with the calculations.

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Answer:

12/13

Step-by-step explanation:

According to SOH CAH TOA;

cos theta = adjacent/hyp = 5/13

adj = 5

hyp = 13

Get the opposite

opp = √13²-5²

opp = √169-25

opp = √144

opp = 12

Get sin theta

sin theta = opposite/hyp

sin theta = 12/13

Hence the value of sin theta is 12/13

Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

The 3/5 + 2/7 = 31/35, which is a ratio of two integers. This shows that 3/5 + 2/7 is rational.

To show that 3/5 + 2/7 is rational, we need to write it as a ratio of two integers. To do that, we must first find the common denominator of 5 and 7.5 x 7 = 35, 7 x 5 = 35.

Therefore, the common denominator is 35.Now, we need to write both fractions as an equivalent fraction with a denominator of 35. We can do that by multiplying each fraction by the denominator it is missing.

3/5 × 7/7 = 21/35 2/7 × 5/5 = 10/35

Therefore, 3/5 + 2/7 = 21/35 + 10/35We can add these two fractions because they have the same denominator, which gives us: 31/35

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Answer:

in total she would spend 27.90 so she should bring C i got this by doing 7.80 x 3 because she is buying 3 medium pizzas then i did 0.75 x 6 and got 27.90 so at least bring 25-30 dollars with her

Step-by-step explanation: