Put the numbers in order from smallest to largest.


3.6

4.9

4.2

3.1

5.0

4.5

Step 1

Find the slope of the line M

we have

[tex]5x-3y=2[/tex]

isolate the variable y

[tex]3y=5x-2 \\ \\y=\frac{5}{3}x-\frac{2}{3}[/tex]  

the slope of the line is [tex]\frac{5}{3}[/tex]

Step 2

Find the slope of the line perpendicular to line M

we know that

if two lines are perpendicular , then the product of their slopes are equal to minus one

so

[tex]m1*m2=-1[/tex]

we have

[tex]m1=\frac{5}{3}[/tex]

Find m2

[tex]m2=-1/m1[/tex]

[tex]m2=-1/(5/3)[/tex]

[tex]m2=-\frac{3}{5}[/tex]

therefore

the answer is

[tex]-\frac{3}{5}[/tex]

divide 18 by 3

18 / 3 = 6

 there are 6 girls on the team

I believe this problem has the following clue:

digit in the tens place is the largest number. digit in tenths place is less than the digit located in the hundredths place. the digit in the ones place is greater than the digit in the hundredths place

From this clue, we can say that the number is:

86.23

As x increases without bound, the graph of f(x)  approaches y=0 increases without bound .

We have function [tex]f(x)=3(2.5)^x[/tex]

From the graph we can see that as x decreases without bound  the graph of f(x) approaches y=0.

Also the exponential function in the graph is approaching y=0 as x decreases on the left side of the curve.

Here as the exponential function here the power is x variable and the exponential function cannot be negative for any value of x.

Therefore as x increases without bound, the graph of f(x)  approaches y=0 increases without bound .

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Step-by-step explanation:

i took the test :)

Final answer:

To find the other number when the product of two numbers is 40 and one of the numbers is 5/11, we divide 40 by 5/11 to solve for the unknown number. The other number is found to be 88.

Explanation:

The question asks to find the other number when the product of two numbers is 40 and one of the numbers is given as 5/11. To do this, we can set up an equation where the product of 5/11 and the unknown number (which we can call 'x') is equal to 40.

The equation would be: (5/11) × x = 40. To solve for x, we need to do some algebraic rearrangement by dividing both sides of the equation by 5/11. This brings x into the numerator on the left side and shifts the 5/11 to the denominator on the right side. Therefore, we get x = 40 × (11/5).

Next, we multiply 40 by 11/5. This calculation results in x = 88. Thus, the other number is 88.

The total commission that she will earn on the sale of these two vehicles is $4,250.

The midpoint is the exact middle of a line segment which divides the line into two equal lengths. Hence, the coordinate of K is (11, 16)

We can obtain the distance between the coordinates of JM thus :

Distance = y2 - y1 ; x2 - x1

Distance = (8 - 5) ; (5 - (-6) = (3, 11)

Hence, the change in the coordinates is (3, 11)

Therefore, the coordinates of K can be obtained thus :

(8 + 3) ;(5 + 11) = (11, 16)

Hence, the coordinate of K is (11, 16)

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At a mean of 95 pounds per passenger and standard deviation of 35 pounds, multiplying this with the total number of passengers = 200, results in:

absolute mean = 95 * 200 = 19,000

absolute std dev = 35 * 200 = 7,000

Calculating for the z score:

z = (x – u) / s

where x is sample value = more than 20,000; u is the sample mean = 19,000; s is std dev = 7,000

z = (20,000 – 19,000) / 7,000

z = 0.143

From the distribution tables,

P (z = 0.14) = 0.5557

Therefore a 55.57% chance that it will be more than 20,000 pound limit

Final answer:

Using the Central Limit Theorem, we calculate the probability that the total weight of passengers' baggage exceeds 20,000 pounds for an airplane with 200 passengers to be approximately 0.0217.

Explanation:

To solve this problem, we use the Central Limit Theorem which states that if we have a large enough sample size, the distribution of the sample means will be approximately normally distributed regardless of the original distribution's shape. Given that the mean weight of an individual passenger's baggage is 95 pounds with a standard deviation of 35 pounds, and that there are 200 passengers, we can calculate the mean and standard deviation of the total baggage weight.

The mean total weight, μtotal, is calculated as the product of the mean individual weight and the number of passengers, so μtotal = 95 pounds × 200 = 19,000 pounds. The standard deviation of the total weight, σtotal, is calculated as the standard deviation of the individual weight multiplied by the square root of the number of passengers, so σtotal = 35 pounds × √200 ≈ 494.97 pounds.

Using the standard normal distribution, we find the z-score for the probability that the total weight exceeds 20,000 pounds by subtracting the mean from the limit and dividing by the standard deviation: z = (20,000 - 19,000) / 494.97 ≈ 2.02.

Looking up this z-score in a standard normal table or using a calculator, we find that the probability of the total baggage weight exceeding 20,000 pounds is approximately 0.0217.

Answer :  Option B is correct.

Explanation :

Since we have given that

f(x) = x+1

and

g(x) =x

and when we divide f(x) with g(x) i.e.

[tex]\frac{f(x)}{g(x)}[/tex]

And we know the division algorithm , i.e.

[tex]f(x)=g(x).q(x) +r(x)[/tex],

Where q(x) represents quotient and r(s) denotes remainder

So, we write it in this manner ,

[tex]x+1=x.1+1\\\\\text{Remainder becomes 1}[/tex]

Hence, Remainder = 1

So, Option B is correct.

After solving the equation, the equivalent equation obtained which has an infinite solution will be equal to -2(x + 5). Hence, option D is correct.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

-5(x + 2) + 3x

Now, solve the equation,

-5x - 10 + 3x

= -5x + 3x - 10

= - 2x - 10

So, the equivalent equation will be,

-2(x + 5), it has an infinite solution because it is the same equation.

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The example of a function is:

  The price of a piece of cloth and the length of the cloth.

We know that a function is a relation in which each element of a set is mapped to a single element of the other set.

i.e. an element has just one image.

1)

The time it takes to mow a lawn and the age of the person mowing the lawn.

This is not a example of function since, the time taken by two person's of different age may be same to mow a lawn.

This means that there is  more than one image of a single element i.e. time.

2)

The distance to school and the time you spend at school.

The time one spend at school at different days may be different even if the distance to school is same.

3)

The price of a movie ticket and the height of the customer.

Two person's with different height will buy a movie ticket at the same cost.

Hence, this relation won't be a function.

4)

The price of a piece of cloth and the length of the cloth.

As we know that the price of a cloth is fixed according to the length.

Hence, the relation is a function.

( As corresponding to each price we have a unique length if a piece of clothing )