After spending many hours studying for your math class (I am being hopeful here!) you decide to reward yourself with a case of soda. Unfortunately the store only had a warm case left (the Kent students got there first and got all of the cold ones). You buy several bags of ice and decide to chill it at home. When you get home the temperature of the soda is 76 degrees F and you proceed to pack it in ice. After ten minutes the temperature has cooled to 70 degrees F. If the soda is best served at 60 degrees F or cooler, how much longer must you wait to enjoy your soda? Note that you have not been given the temperature of the surroundings, but you should be able to figure out what that should be (you are packing it in ice that is at the freezing point of water so...).

Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

Answer:

m = 3/4

Step-by-step explanation:

The horizontal change in x is 4 and the vertical change 3.  The slope is therefore m = rise / run = 3/4.

Answer:

Slope is equal to the change in y over the change in x , or rise over run.

m=change in / y change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).

m=y2−y1/x2−x1

Substitute in the values of x and y into the equation to find the slope.

m=10−(13)/7−(11) Simplify.

m=34

Step-by-step explanation:

what? ;-;.............

Answer:

31.5 units²

Step-by-step explanation:

Area = ½*base*height

Height of the triangle on the grid = 9 units

Base = 7 units

Area = ½*9*7

Area = ½*63

Area = 63/2

Area = 31.5 units²

Complete question is;

The paraboloid z = 5 − x − x² − 2y² intersects the plane x = 1 in a parabola. Find parametric equations for the tangent line to this parabola at the point (1, 2, -4).

Answer:

x = 1

y = (2 + t)

z = (-4 - 8t)

Step-by-step explanation:

We are given the paraboloid z = 5 − x − x² − 2y²

That it intersects the plane x = 1 and tangent to the point (1, 2, -4).

Thus, the position of the tangent is;

r_o = (1, 2, -4).

Direction vector is; v = (x, y, z)

Let's put 1 for x into the paraboloid.

z = 5 − 1 − 1² − 2y²

z = 3 - 2y²

Now, let's use vectors to find the parametric equation, where;

x = 1

y = t

z = 3 - 2t²

Thus, the Directional vector is now;

v = (1, t, 3 - 2t²)

Derivative of this directional vector is;. v' = (0, 1, -4t)

Putting 2 for t gives;

v' = (0, 1, -4(2))

v' = (0, 1, -8)

Multiplying this derivative by T gjves;

tv' = (0, t, -8t)

The final direction vector will be;

r = r_o + tv'

r = (1, 2, -4) + (0, t, -8t)

r = (1, (2 + t), (-4 - 8t))

Thus our parametric equation is;

x = 1

y = (2 + t)

z = (-4 - 8t)

The perimeter of the rectangular bedroom is 126 feet.

To find the perimeter of the rectangular bedroom, we need to add up the lengths of all four sides.

The distance between the points (14, 22) and (14, -10) is 22 - (-10) = 32 feet, since these two points lie on a vertical line.

The distance between the points (14, -10) and (-17, -10) is 14 - (-17) = 31 feet, since these two points lie on a horizontal line.

The distance between the points (-17, -10) and (-17, 22) is 22 - (-10) = 32 feet, since these two points lie on a vertical line.

The distance between the points (-17, 22) and (14, 22) is 14 - (-17) = 31 feet, since these two points lie on a horizontal line.

Therefore, the perimeter of the rectangular bedroom is;

P = 32 + 31 + 32 + 31

P = 126 feet.

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Answer:

The answer is D. 3

Step-by-step explanation:

A number refers to the expression of a quantity or a magnitude. In mathematics, a number represents a fixed quantity of something or generally of a number system.

The numbers have a fixed order that determines their value.

The numbers are in order of:

Unit = 8

Ten = 3

Hundred = 5

Unit of thousand = 7

Ten thousand = 2

Hundred thousand = 4

Million unit = 1

10 million = 4

And a hundred million represented by = 3.

No, the relationship on the table is not proportional

From the question, we have the following parameters that can be used in our computation:

x   y

____ ____

6 -2

7 -1

8 0

9  1

On the table of values, we can see that:

Using the above as a guide, we have the following:

The relationship is not a proportional relationship

This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)

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My own multi-step combination problem is given below:

To solve this problem, Amanda  need to use the formula for combinations and it is:

nCr = n! / (r! x (n-r)!)

where:

n = total number of items to select from

r is the number of items to select.

First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:

5C3

=  5! / (3! x (5-3)!)

= 10

Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be

4C2

= 4! / (2! x  (4-2)!)

= 6

Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:

3C2

= 3! / (2! x  (3-2)!)

= 3

To have the total number of dinner menus, we have to multiply these three numbers together:

= 10 x 6 x 3

= 180

Therefore, one can say that Amanda have 180 different dinner menus that she can be create.

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Answer:

Step-by-step explanation:

dividing common base numbers with exponents is done by subtracting the denominator exponent from the numerator exponent.

3^(3/4) / 3^(3/8) = 3^[(6/8) - (3/8)]  = 3^(3/8)

numbers with exponents raised to exponents is completed by multiplying the exponents

3^(3/8)^(4/9) = 3^[(3/8)*(4/9)] = 3^(12/72) = 3^(1/6)

x = 1/6

Answer:

Letting L = distance per lap

4L + 8 = 6L + 4

2L = 4

L = 2 miles

She runs 16 miles each day

2 miles per Lap = 8 Laps on Saturday

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

100% sure and correct :) ❤️

Answer:

3 and 1 respectively.

Step-by-step explanation:

Subtract 3 from 4.

4 = 3 + x

4 - 3 = x

1 = x

Multiply 1 by 1.

The no. of pets friend has = 1

Answer:

The third one.

Step-by-step explanation:

o

oooo  <----Lol the on that looks like this

    o

Answer:

b

Step-by-step explanation:

The set of values that corresponds to the circle with a radius of three units and the center lying on the Y axis is:

A = 1, B = 1, C = 0, D = 3, E = 0.

The general equation of a circle is given by:

x^2 + y^2 + 2gx + 2fy + c = 0

In this case, since the circle has a radius of three units and the center lies on the Y axis, we can deduce the following information:

The center of the circle lies on the Y axis, which means the x-coordinate of the center is zero.

The radius of the circle is three units, which means the distance from the center to any point on the circle is three units.

Using the information above, we can substitute the values into the general equation to solve for the corresponding values:

Substituting the x-coordinate of the center (zero) into the equation, we have:

0^2 + y^2 + 2g(0) + 2fy + c = 0

y^2 + 2fy + c = 0

Since the center lies on the Y axis, the x-coordinate is zero, so the term with x (2gx) becomes zero.

Substituting the radius of the circle (three) into the equation, we have:

(3)^2 = 9

Therefore, the equation becomes:

y^2 + 2fy + c = 9

Comparing this equation with the general form of the circle equation, we can deduce the values of A, B, C, D, and E as follows:

A = 1 (coefficient of x^2)

B = 1 (coefficient of y^2)

C = 0 (constant term)

D = 3 (coefficient of x)

E = 0 (coefficient of y)

Hence, the set of values that corresponds to the circle is A = 1, B = 1, C = 0, D = 3, and E = 0.

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The equation that can be used to find the number of peaches Muriel has is; 2 + 3·x = 17

A mathematical equation is a statement that has two expressions, joined by the equals to, '=' sign.

The number of peaches Frances has = 17

Let x represent the number of peaches Muriel has

Therefore;

The number of peaches Frances has = 2 + 3·x

Which indicates through substitution property, that we get;

17 = 2 + 3·x

The equation that can be used to find the number of peaches Muriel has, x is; 17 = 2 + 3·x

Solving for x in the above equation, we get;

17 = 2 + 3·x

3·x = 17 - 2 = 15

x = 15 ÷ 3 = 5

The number of peaches Muriel has, x = 5 peaches

The 17 peaches Frances has and the indication that Frances has 2 more than 3 times the number of peaches Muriel has, indicates that the equation that could be used to find the the number of peaches Muriel has is; 17 = 2 + 3·x

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1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.

3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.

4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.

5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.

6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.

Answer:

135.06 feet

Step-by-step explanation:

Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.

opposite side = x

adjacent side = 150 feet

angle = 42°

tan(42°) = x/150 feet

150 feet * tan(42°) = x

x = 135.06 feet

The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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Sum of all angles in a quadrilateral = 360°

Given :

▪︎Measure of angle U in quadrilateral RSTU = 80°

We know that corresponding angles in a quadrilateral are equal.

Which means :

▪︎Angle U = Angle y

Thus, the measure of angle y = 80°

Angle T = angle x (corresponding angles of a quadrilateral are equal)

Let us name angle T and angle x together as 2x.

Which means :

\( = \tt 80 + 80 + 2x = 360\)

\( = \tt160 + 2x = 360\)

\( \tt \: \: \: \: = 2x = 360 - 160 \: \ \\ = \tt120\)

\( = \tt \: x = \frac{200}{2} \)

\( \hookrightarrow \color{plum}\tt angle \: x = 100°\)

Thus, the measure of angle x = 100°

Therefore, the correct option is (a) y = 80, x = 100

Answer:

8n - 3 = 25

Step-by-step explanation:

Answer: 165 miles

Step-by-step explanation: In order to figure out the answer, you must do 55 x 3 because he drove for 3 hours at 55 mph so you could break it up and go 50 x 3 to equal 150 and 5 x 3 to equal 15 and add those to get 165.

Answer:

The answer is 165miles

Step-by-step explanation:

\(distance = speed \times time\)

d=55×3

d=165 miles

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

Answer:  \(y= \frac{1}{10}x\)

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

Given: \(\textsf{Slope = 1/10 and goes through (20, 2)}\)

Find: \(\textsf{Slope in slope-intercept form}\)

Solution: First we need to plug into the point slope formula which is \((y - y_1) = m(x - x_1)\).  Let us plug in the values first and then solve for the slope-intercept form.

Plug in the values

Simplify

Answer: Therefore, the final answer in slope-intercept form for the line with a slope of 1/10 that passes through the point (20, 2) is \(y= \frac{1}{10}x\)

Answer:

It will take them 3.5 hours to paint the room.

Step-by-step explanation:

Step 1: Add the number of hours it takes them together

    A. 6 + 8

Step 2: Divide the total number of hours by two (since two people are working together)

    B. 12 / 2 = 7 hours

Step 3: Divide by two again since you now have twice the speed

    C. 7 / 2 = 3.5 hours

Answer:

Hello! answer: y = 60

Step-by-step explanation:

Hope that helps!

Answer:

D) 60°

Step-by-step explanation:

If you look at the triangle, you could see that all the angles and sides are congruent.  Vertical angles, or opposite angles. You could find the value of y, by looking at the other angles and sides and comparing them.

Hope this helps!

Note:

Pls notify me if my answer is incorrect, for the other users that will see this response. Thank you.

-kiniwih426