If 39 is added to a number, it will be 4 times as large as it was originally. What's the number?

There are 10 different ways to choose three products out of five.

What are permutation and combination?

Permutation and combination are mathematical concepts used to study the arrangements and selections of items.

Permutation: An arrangement of items, where order matters.

Combination: A selection of items, where order does not matter.

In this case, the manager has to choose three products out of five possibilities, which is a combination problem. To find the number of different ways to choose three products out of five, we can use the formula: nCr = n! / (r! (n - r)!).

n = 5 (number of items)

r = 3 (number of items to be chosen)

nCr = 5! / (3! (5 - 3)!) = 5! / (3! 2!) = (5 x 4) / (2 x 1) = 10.

Hence, there are 10 different ways to choose three products out of five.

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The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

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Answer:

18

Step-by-step explanation:

Answer: 18, 21, 24, 27, 30

Step-by-step explanation:

Answer:

He is in Track.

Step-by-step explanation:

Answer:

i think is what they meant

Step-by-step explanation:

Andre is running in an 80-meter hurdle race. There are 8 equally-spaced hurdles on the race track. The first hurdle is 12 meters from the start line and the last hurdle is 15.5 meters from the finish line. Estimate how far the hurdles are from one another. Explain your reasoning

Based on the data, the estimated number of lemon candies in the bag of 100 assorted candies is about 19.

In mathematics, proportion refers to the relationship between two quantities that are equivalent or have a constant ratio. It is usually expressed as a fraction or a ratio. For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion of flour to water is 2:1 or 2/1. Proportions are used in a variety of mathematical and real-world situations, such as solving problems involving ratios, rates, and percentages.

In the given question,

We can use a simple proportion to estimate the number of lemon candies in the bag. We know that Ridgette handed out a total of 6 lemon candies out of a total of candies. Therefore, the proportion of lemon candies in the bag is:

6/total candies = number of lemon candies/100

We can cross-multiply to solve for the number of lemon candies:

number of lemon candies = 6 x 100 / total candies

We can also use the information about the other flavors to estimate the total number of candies in the bag. The total number of candies is:

total candies = lemon + orange + grape + cherry

Using the information from the table, we can estimate the total number of candies:

total candies = 6 + 5 + 8 + 13 = 32

Therefore, the estimated number of lemon candies in the bag is:

number of lemon candies = 6 x 100 / 32 = 18.75

We can round this to the nearest whole number to estimate that there were about 19 lemon candies in the bag of 100 assorted candies.

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The value of the function \(\lim_{x \to \ -1} \frac{2}{(x + 1)^{2}}\) is ∞.

A value of the function, whenever the input values are substituted in the function then the function approaches some number.

And that number is a limit of the function.

Given:

A function,

f(x) = 2/{(x + 1)²}

And function increases without bounds as the values of x approach -1.

So,

\(\lim_{x \to \ -1} \frac{2}{(x + 1)^{2}}\)

= 2/(x² + 2x + 1)

= 2/{1 + (-2) + 1}

= 2/0

= ∞

Therefore, the function approaches infinity.

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The mean of brothers and sisters = 3

From the attached data set of brothers and sisters we can write the data values (frequency) as:

1, 5, 4, 2

We need to find the mean of brothers and sisters,

We know that the formula for the mean of data.

mean(\(\bar{x}\)) = sum of all data values / total number of data values

First we find the sum of all data values.

1 + 5 + 4 + 2 = 12

and the total number of data values = 4

Using above formula of mean,

mean(\(\bar{x}\)) = sum of all data values / total number of data values

mean(\(\bar{x}\)) = 12 / 4

mean(\(\bar{x}\)) = 3

Therefore, the required mean is: 3

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Find the complete question below.

Answer:

ur right

Step-by-step explanation:

The first table shows a proportional relationship between x and y.

A proportional relationship exist between two entities if an increase in one causes an increase in another or vice versa.

x             y

7            28

14           35

x               y

1               2

4               4

7                5

The first table shows a proportional relationship between x and y, for every value of x, y increases by almost 2 times.

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Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

Answer:

Gloria travelled 7.5 yards on the bus.

Step-by-step explanation:

8 miles is 14080 yards

14080 - 880 = 13200

13200 yards is 7.5 miles

Answer:

Q.1 a²+10a+24

splitting the middle.

a²+6a+4a+24

=a(a+6)+4(a+6)

(a+6)(a+4)

Q.2 x²+9x+18

splitting the middle

x²+6x+3x+18

x(x+6)+3(x+6)

(x+6)(x+3)

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer:

Step-by-step explanation:

What are the other colors?

if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2

similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....

depends on how many colors are there

Answer:

\(3x^{2} - 7x - 6\)

Step-by-step explanation:

\(2x^{2} - 6 + x^{2} - 7x\)

\(3x^{2} - 7x - 6\)

Answer: D

Step-by-step explanation:

The slope of a parellel line is the same slope as the original line. Parallel lines never touch. atherefore, the slope has to be the same, but the y-intercept can be different. The only answer choice with m=3 for slope is D.

D.

m=6/2

m=3

Answer:

D) m = 6/2

Step-by-step explanation:

Parallel lines have the same slope. This is because they go on forever without intersecting, so they must have the exact same steepness. You can see that all the answers are in fraction form, so you just need to determine which fraction is equal to 3. 6/2 is equal to 3: you can confirm this by dividing 6 by 2: the answer is three!

Hope this helps :)

Answer:

x = 9

Step-by-step explanation:

9 - 1 = 8

Answer:

x = 9

Step-by-step explanation:

Add 1 to each side:

x - 1 = 8

x = 9

Answer:

 3x ≤ -6

Step-by-step explanation:

"At most" means "less than or equal to." If x represents the number, then you have ...

  (three) times (a number) (is at most) negative 6 . . . . . English

      3       ·         x                ≤           -6 . . . . . . . . . . . . . . . . Math

__

  3x ≤ -6

Answer:

3x ≤ -6

Step-by-step explanation:

The ratio of the given 240 kg to 6 kg will be 40:1.

What is Ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

the ratio 240 kg to 6 kg.

It will be simple 240/6 :: 40 :1

Hence the ratio of the given data will be 40:1

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The probability of rolling a number greater than 2 on a fair 6-sided die would be; 4/6, or 2/3.

To find how many times a number greater than 2 will be rolled in 60 rolls, we can use the formula:

Number of times = Probability x Total number of rolls

So, the probability of 2/3, we can calculate as;

Number of times = 2/3 x 60

Number of times = 40

Therefore, we can predict that a number greater than 2 will be rolled approximately 40 times out of 60 rolls means that out of 6 possible outcomes, 4 of them will result in a number greater than 2.

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Answer:

#1  (0,-4)

#2  (5,0)

#3  (3,1)

Step-by-step explanation:

#1.  (-3, 2) (0, y)  slope = -2

slope = rise/run    therefore slope = -2/1  or down 2 and over 1

so from -3 to 0 you are going over 3 units (or 3 times)  Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6      so 2-6 = -4

so y intercept (b)  = -4 0r (0,-4)

#2   (-7,-4)  (x,0)  slope (m) = 1/3   -7+12=5    x=5

#3   (4,-3)   (x, 1)   slope (m) = -4   (4/-1)   Moving one unit in slope  means

-3=4=1 for Y and 4-1=3 for X    therefore the point is (3, 1)

Answer:

3/16

Step-by-step explanation:

16 pupils, 11 play both, 1 plays piano only and 1 flute only

⇒ 11 + 1 + 1 = 13 pupils who play at least one instrument

⇒ 16 - 13 = 3 pupils who don't play either instrument

⇒ Out of the 16 total pupils, 3 play neither, putting this into numbers:

\(\frac{3}{16}\) which is then also the answer.

The diagram that models the story is given as follows:

Right diagram.

The equation that models the story is given as follows:

c = 12 x 8.

The story is modeled applying the proportions from the units given in the context of the problem.

We have that the parameters are given as follows:

Hence the total number of charms that she purchased is given as follows:

c/12 = 8.

c = 12 x 8. (which is the equation that models this situation).

c = 104.

The diagram that represents a multiplication of 12 by 8 is the diagram that is composed by a successive addition of twelve times the number 8, hence it is the right diagram.

The complete problem is given by the image presented at the end of the answer.

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Answer:

90 feet

Step-by-step explanation:

perimeter = 30x2 + 15x2 = 90 feet

The buses will be 215miles apart in 4.67s

Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position. For example- If an object moves from A position to B, then the object's position changes.

The relationship between velocity and displacement is given as v= d/t

where v = velocity, d= displacement and t = time

therefore d= vt

the displacement of bus A = 35t miles

the displacement of bus B = 30t miles

the resultant displacement = 215miles

using Pythagoras theorem

(35t)²+(30t)²= 215²

1225t²+ 900t²=46225

t²(1225+900)=46225

t²(2125)= 46225

divide both sides 2125

t²=21.75

t= √21.75

t= 4.67s

therefore the buses will be 215miles apart in 4.67s

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The Total length of two sides based on the information will be 7x²+2x+1

The Length of the third side will be 4 x³-10x²-7.

Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Length of the third side = Perimeter - Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

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Answer:

g(x) = 4x² - x

General Formulas and Concepts:

Algebra II

Functions

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:                                                       \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

*Note:

Integrating a piecewise function requires you to integrate both parts.

Step 1: Define

Identify.

\(\displaystyle f(x) = \left \{ {{8x - 1 ,\ x \leq 4} \atop {31 ,\ x \geq 4}} \right.\)

\(\displaystyle \int {f(x)} \, dx = \left \{ {{g(x) + C ,\ x \leq 4} \atop {31x + C ,\ x \geq 4}} \right.\)

Step 2: Find function g(x)

We can see that the 2nd part of the piecewise function already has been integrated:

To find function g(x), we simply have the same setup:

The integration constant C is already included in the answer, so our answer is g(x) = 4x² - x.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration (Applications)

Answer:

y=3/2x-2

Step-by-step explanation:

Find the slope first:

\(m=\frac{y_{2-y_{1} } }{x_{2}-x_{1} } =\frac{1-(-2)}{2-0}=\frac{3}{2}\)

Then solve for y-intercept:

\(y=\frac{3}{2}x+b\\-2=\frac{3}{2}(0)+b\\-2=b\)

Now, write out your complete equation:

y=3/2x-2