(15, 2); perpendicular to 5x - y = 2
(a) Write the equation of the line in slope-intercept form.
(b) Write the equation of the line in standard form.

Answer:

y <= 40

Step-by-step explanation:

Let's call the number of people traveling by van "x", and the number of people buying train tickets "y". We know that the total number of people in the group is 40, so we can write the equation:

x + y = 40

And we also know that the van can hold up to 12 people, so we can write the inequality:

0 <= x <= 12

Now, to find the number of train tickets, we just need to substitute

x = 40 - y into the second inequality:

0 <= 40 - y <= 12

Expanding and solving for y, we get:

0 <= 40 - y <= 12

-40 <= -y <= -28

y >= 28

y <= 40

So the number of train tickets needed (y) is equal to or greater than 28 and equal to or less than 40.

Answer:

Inequality:    12 + x ≤ 40

Solution:   x ≤ 28

Step-by-step explanation:

Let x be the number of train tickets that the group will need.

As the van holds 12 people and the rest will buy train tickets, an expression for the total number of people is:

If the group is up to 40 people then 12 + x will be less than or equal to 40:

Therefore, the inequality that can be used to find the number of train tickets that the group will need is:

To solve the inequality, subtract 12 from both sides:

⇒ 12 + x - 12 ≤ 40 - 12

⇒ x ≤ 28

Therefore the number of train tickets that the group will need is less than or equal to 28 tickets.

Answer: the answer is sos not please help me dude

Step-by-step explanation:

but you use kami and go to files and download the pdf use kami

The twins are 6 years old, and the oldest sister is 13 years old (since they were born seven years after their older sister).

7.3% of women under the age of 35. 6.9% of females aged 35 to 37. 6.8% of women aged 38 to 40 were female. 5.1% of females aged 41 to 42.

Starting out, let's assign some variables.

Let x represent the sister's older sister's age in years.

The twins' age is then x – 7. (since they were born seven years after their older sister).

We are told that the product of the three siblings' ages is 2693 more than the sum of their ages. This can be expressed algebraically as:

x(x - 7)(x - 7) = x + (x - 7) + (x - 7) + 2693

Simplifying this equation gives:

x³ - 21x² + 98x - 2693 = 0

We can see that x = 13 is a root of the equation, since:

13³ - 21(13)² + 98(13) - 2693 = 0

This means that (x - 13) is a factor of the equation.

We can use polynomial division or synthetic division to divide the equation by (x - 13) and obtain a quadratic equation:

x² - 8x + 207 = 0

The solutions of this quadratic equation are:

x = (8 ± sqrt(8² - 4(1)(207))) / 2 = 4 ± sqrt(241)

Since x represents the age of the older sister, which must be a positive integer, the only valid solution is:

x = 13

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The probability that the both balls would be white when drawn at random from each urn would be = 1 7/45

The number of colour that is found in two urns = 2( white and yellow).

The first urn contains the following:

5 white balls

4 yellow balls

The total number of balls = 9 balls.

The probability of getting a white ball = 5/9

The second urn contains the following:

3 white balls

2 yellow balls

The total number of balls = 5 balls

The probability of getting a white ball = 3/5

Therefore the probability that both balls are white;

= 5/9 + 3/5

= 25+27/45

= 52/45

= 1 7/45

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The function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Consider the equation :

y = 30.5(0.7)ˣ

Plug in x=0,

y= 30.5(0.7)⁰ = 30.5 *1 = 30.5

The point is (0,30.5)

Similarly, when we plug in x=1 and x=2, we get y=21.35 and y=14.95 respectively

The other 2 points in (x, y) form are (1,21.35) and (2, 14.95)

These points are matching with the points on the graph

So, the function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

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Answer:

20 + .50M   = 10 + .80M     subtract .50M, 10 from both sides

10  = .30M     divide both sides by .30

10 / .30  = M   =  about 33 + 1/3 miles driven equalize the cost

[Jana used  " -.50M"  in the original set up instead of  " +.50M"   ]

Step-by-step explanation:

The amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.

Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.

Given that the interest is compounded continuously.

For the given situation the formula of compound interest is:

[tex]A = Pe^{rt}[/tex]

where, A is the amount = $12300

P is the principal amount

r is the rate = 4% = 0.04

t is the time = 8 years

Substituting the values we have:

[tex]12300 = Pe^{(0.04)(8)}\\\\P = \frac{12300}{e^{(0.04)(8)}} \\\\P =8932.461[/tex]

Hence, the amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.

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Answer:

AC ≈ 6.25

Step-by-step explanation:

using the tangent ratio in the right triangle

tan36° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{AC}{8.6}[/tex] ( multiply both sides by 8.6 )

8.6 × tan36° = AC , then

AC ≈ 6.25 ( to 3 SF )

The algebraic expression for the amount of etergent remaining in the container isy = x - 13 - 4 - 73

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that;

13 4 73

Let's define the variable 'x' to represent the amount of detergent initially present in the container.

Then, if 'y' represents the amount of detergent remaining in the container, we can write an algebraic expression for it as:

y = x - 13 - 4 - 73

where:

13 represents the amount of detergent used on the first day

4 represents the amount of detergent used on the second day

73 represents the amount of detergent used on the third day

By subtracting the total amount of detergent used from the initial amount 'x', we get the remaining amount 'y'.

Therefore, the expression will be y = x - 13 - 4 - 73.

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The appropriate measure of variation (spread) for these data is the standard deviation, which is 2.287.

The appropriate measure of variation (spread) for these data is the standard deviation. Standard deviation is a measure of how much the data values vary from the mean (average) of the data set. It is calculated by taking the square root of the variance, which is the average of the squared differences between each data value and the mean.

To calculate the standard deviation for this data set, follow these steps:

1. Find the mean of the data set by adding up all of the data values and dividing by the total number of values. In this case, the mean is (4 + 7 + 2 + 3 + 4 + 2 + 1 + 3 + 9 + 8 + 5 + 1 + 3 + 2 + 3 + 2 + 4 + 3 + 6 + 5) / 20 = 3.65

2. Find the variance by subtracting the mean from each data value, squaring the result, and then finding the average of these squared differences. The variance for this data set is ((4 - 3.65)^2 + (7 - 3.65)^2 + (2 - 3.65)^2 + ... + (6 - 3.65)^2 + (5 - 3.65)^2) / 20 = 5.2275

3. Take the square root of the variance to find the standard deviation. The standard deviation for this data set is sqrt(5.2275) = 2.287

Therefore, the appropriate measure of variation (spread) for these data is the standard deviation, which is 2.287.

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The cost to wax the floor will be $2,184.03.

What is the area of any geometrical shape?

The area of a geometrical shape is a measurement of the extent of a two-dimensional surface. It is the measure of the amount of space inside the shape, which can be expressed in square units, such as square inches, square feet, or square meters.

Rectangle: area = length x width

Trapezoid: area = ((base1 + base2) / 2) x height

To find the area of the floor, we need to split the shape into two parts: a trapezoid on top and a rectangle on bottom.

The area of the trapezoid is: (33 + 19) / 2 * 14 = 385 square feet

The area of the rectangle is: 33 * 28 = 924 square feet

The total area is: 385 + 924 = 1309 square feet

Multiplying by the cost per square foot, we get:

1309 * 1.67 = 2184.03

Hence, the cost to wax the floor will be $2,184.03.

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Answer:

First, we need to find the area of Site A and Site B. The area of a rectangle is found by multiplying its length and width, so:

Site A: 60 m x 40 m = 2400 m^2

Site B: 45 m x 40 m = 1800 m^2

Next, we need to find the perimeter of each site, which is the distance around the edges of the rectangle. The perimeter is found by adding up the lengths of all four sides, so:

Site A: 2 x (60 m + 40 m) = 2 x 100 m = 200 m

Site B: 2 x (45 m + 40 m) = 2 x 85 m = 170 m

Finally, to find the total amount of rope needed, we add up the perimeters of both sites:

200 m + 170 m = 370 m

So, we need a total of 370 meters of rope to rope off both sites.

Answer:350

ITS NOT 370

The length of the hypotenuse BC in right  angled triangle ABC is 3.605 units.

A triangle is said to be right angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. Consequently, other names for this triangle include the right triangle and 90-degree triangle.

In right angle triangle if 90 degree angle is A then

[tex]AB^{2} +AC^{2} = BC^{2}[/tex]

And here length of altitude AB equals to 3 units and length of base  AC equals to 2 units And here length of hypotenuse BC equals to [tex]\sqrt{13}[/tex] units

[tex]AB^{2} +AC^{2} = BC^{2}[/tex]

[tex]3^{2} +2^{2} = \sqrt{13}[/tex]

[tex]\sqrt{13}[/tex]= 3.60555 unit

And here ans [tex]\sqrt{13}[/tex] is already give what we have to do just calculate the value of [tex]\sqrt{13}[/tex] which is = 3.605

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Heyy! Johnny Sins back with another answer for yall!

Lets see here....

The perimeter of a rectangle can be found by adding the lengths of all four sides. If the length of the rectangle is three times its width, we can write the expression for the length as 3w. Therefore, the expression for the perimeter would be:

P = 2(width) + 2(length)

P = 2w + 2(3w)

P = 2w + 6w

P = 8w

So the perimeter of the rectangle can be represented by the expression 8w.

___________________________________________________________

Pretty easy huh? Well no worries just give me 5 stars and a thanks. 2 buttons. So simple huh?

Love, Johnny Sins :)

a) The probability that no one reports the loss or theft of their credit cards is 0.0498.

b) The probability that every credit card is lost or stolen is practically zero.

c) The probability that exactly six people report the loss or theft of their cards is 0.1042

d) The probability that at least nine people report the loss or theft of their cards is 0.2142

a. To calculate the probability that no one reports the loss or theft of their credit cards, we can use the Poisson distribution with an average of λ = 0.02% * 15,000 = 3.

The probability that no one reports the loss or theft of their credit cards is:

P(X = 0) = e^(-λ) * (λ^0 / 0!) = e^(-3) * (1 / 1) = 0.0498 or approximately 5%.

b. The probability that every credit card is lost or stolen is:

P(X = 15000) = e^(-λ) * (λ^15000 / 15000!)

Since λ is very small, the probability of all 15000 credit cards being lost or stolen in a month is practically zero.

c. To calculate the probability that six people report the loss or theft of their cards, we again use the Poisson distribution with an average of λ = 3.

The probability that exactly six people report the loss or theft of their cards is:

P(X = 6) = e^(-λ) * (λ^6 / 6!) = e^(-3) * (3^6 / 720) = 0.1042 or approximately 10.4%.

d. To calculate the probability that at least nine people report the loss or theft of their cards, we need to sum the probabilities for X = 9, 10, 11, ..., 15, since there are only 15,000 credit cards in total.

The probability that at least nine people report the loss or theft of their cards is:

P(X >= 9) = Σ(i=9 to 15) P(X = i) = Σ(i=9 to 15) e^(-λ) * (λ^i / i!)

This is a tedious calculation to do by hand, but we can use a calculator or software to find that P(X >= 9) is approximately 0.2142 or 21.42%.

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Answer:

y = (4/3)x - 2

Step-by-step explanation:

y intercept is (0, -2)

slope is 4/3

Using the equation  [tex]C =a (1 - r)^{t}[/tex] , 179.75 grams will remain after 2 hours

What is Exponential Decay?

Exponential Decay is the process of reducing an amount by a consistent percentage rate over a period of time using the formula [tex]C = a(1-r)^{t}[/tex]

Where a = 480 grams

r = 15.1% = 0.151

t = 2 hours

C = 480(1 - 0.151)^2

C = 480(0.849)^2

C = 346 grams

Therefore, 346 grams will remain after 2 hours

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Answer:

Yes, because 50x20= 5x10x2x10= (5x2)x(10x10)

So you can multiply 5x2 first and than add the zeros

The fuel consumption per liter of Lilly's car is  12.5 kilometers per liter .

Average mileage The average mileage of a vehicle is the ratio of the distance traveled by the vehicle and the total amount of fuel used for that distance.

You can specify:

where (d) is the distance traveled and (n) is the fuel consumption.

Lily's car consumes 8 liters per 100km. This is your car's mileage or efficiency.

average mileage = 100/8 = 12.5 kilometers per liter

Therefore, the fuel efficiency in kilometers per liter of a Lily car with a fuel efficiency of 8 liters per 100 kilometers is 12.5 kilometers per liter.

Complete Question - Lily’s car has a fuel efficiency of 8 liters per 100 kilometers. What is the fuel efficiency of Lily’s car in kilometers per liter ?

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Answer: look at the image for the answer and solution

Step-by-step explanation:

Answer:

roughly 88 but 87.9645943005...

Step-by-step explanation:

First, the formula for the circumference of a circle is 2pi(r), so plugging in 14 yards, you get 28pi roughly 88 but for an actual answer 87.9645943005

The probability of getting one club and one heart is 0.127.

p= [tex]\frac{13*13*2*1}{52*51}[/tex]=0.1275

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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The number of possible outcomes in the sample space of a wireless garage door opener with 16 switches can be determined using the concept of combination is 1.

Combination is a mathematical concept that refers to the number of ways that a set of objects can be selected from a larger set without regard to their order.

To determine the number of possible outcomes in the sample space, we can use the concept of combination. In this case, the objects are the 16 switches, and the larger set is the set of all possible settings for these switches (up or down).

To calculate the number of possible combinations, we can use the formula for combination, which is:

ⁿCₓ = n! / (x! * (n - x)!)

where n is the total number of objects (16 switches), and x is the number of objects selected (in this case, also 16 switches). The exclamation mark (!) represents the factorial function, which is the product of all positive integers up to and including the given integer.

Using this formula, we can calculate the number of possible combinations as follows:

=> 16! / (16! x (16 - 16)!)

=> 16! / (16! x 0!)

=> 1

Therefore, the sample space of possible codes for a wireless garage door opener with 16 switches is 1.

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The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.

A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:

Angle 2 = (Angle 1) / 0.25

For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.

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The triangle is scalene triangle as none of the sides of a triangle are equal to each other.

Triangles are classified into three types on the basis of its sides.

Equilateral triangle =  If all sides of a triangle are equal then it is known as equilateral triangle.

Isosceles triangle =  If any two sides of a triangle are equal then it is known as isosceles triangle.

Scalene triangle = If none of the sides of a triangle are equal then it is known as scalene triangle.

The question states that a triangle has side lengths 35cm, 46cm, and 68cm

so, none of the side are equal so the given triangle is scalene triangle

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Answer:

A.   112 units^2

Step-by-step explanation:

64 + 32 + 12 + 4 = 112

The total volume of compost required for 16 bowls is 67,493.33 cm³

The total weight of compost required for 16 bowls is 155,906.67 gm

The total amount of polythene required for 16 bowls is: 6400π cm²

(i) The volume of compost required per bowl can be calculated as follows:

V = (4/3)πr^3, where r is the radius of the sphere

The radius of each bowl can be calculated as:

r = (d/2) - t, where d is the diameter (21 cm) and t is the thickness (0.5 cm)

So, r = (21/2) - 0.5 = 10 cm

Plugging the value of r into the formula for volume:

V = (4/3)πr^3 = (4/3)π * 10^3 = 4186.67 cm³

The total volume of compost required for 16 bowls is:

16 * 4186.67 = 67,493.33 cm³

The total weight of compost required for 16 bowls is:

67,493.33 cm³ * 2.31 gm/cm³ = 155,906.67 gm

(ii) To find the total amount of polythene required to cover the outer surface of 16 bowls, we first need to calculate the surface area of one bowl.

The surface area of a sphere can be calculated as follows:

A = 4πr^2

Plugging the value of r into the formula for surface area:

A = 4πr^2 = 4π * 10^2 = 400π cm²

The total amount of polythene required for 16 bowls is:

16 * 400π cm² = 6400π cm²

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The fractions have values -

4. one-sixth plus five-sixths equals - Option 3 : 1

5. seven twelfths plus two-twelfths equals - Option 1 : 0

6. nine-tenths minus four-tenths equals - Option 4 : 2

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The first fractional statement is -

one-sixth plus five-sixths

The mathematical expression is -

1/6 + 5/6

Since the denominator is same just add the numerator.

(1 + 5) / 6

6/6

1

Therefore, the value is obtained as 1.

The second fractional statement is -

seven twelfths plus two-twelfths

The mathematical expression is -

7/12 + 2/12

Since the denominator is same just add the numerator.

(7 + 2) / 12

9/12

3/4

0.75 ≈ 0

Therefore, the value is obtained as 3/4.

The third fractional statement is -

nine-tenths minus four-tenths

The mathematical expression is -

9/10 - 4/10

Since the denominator is same just subtract the numerator.

(9 - 4) / 10

5/10

2

Therefore, the value is obtained as 2.

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4. Round each fraction to help you estimate the solution for the following equation:

one-sixth plus five-sixths equals

1. 0

2. one half

3. 1

4. 2

5. Round each fraction to help you estimate the solution for the following equation:

seven twelfths plus two-twelfths equals

1. 0

2. one half

3. 1

4. one and one half

6. Round each fraction to help you estimate the solution for the following equation:

nine-tenths minus four-tenths equals

1. one half

2. 1

3. one and one half

4. 2

A 5-card poker hand is dealt from a standard deck of cards and the number of distinct ways are there to form a hand with two pairs are 1326 ways.

To solve this problem, we got to use permutations and the combinations. Given that a 5-card poker hand is dealt from a standard deck of cards  and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.

Here 4 suits with 13 different kinds for each and every suit , so number of total outcomes are 13*4 = 52

Here we use combinations, and given that a 5-card poker hand is dealt from a standard deck of cards  and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.

The number of distinct ways are there to form a hand with two pairs are given by, C(52,2)

(52 * 51) / 2

(26 * 51)

1326 ways

Therefore, the  number of distinct ways are there to form a hand with two pairs are 1326 ways.

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Answer:

Step-by-step explanation:

1/4 is one bow.

1/4 *4 is 1 yard.

mel can make 4 bows.