A 40. 0-kg ice-skater glides with a speed of 2. 0 m/s toward a 10. 0-kg sled at rest on the ice. The ice-skater reaches the sled and holds on to it. The ice-skater and the sled then continue sliding in the same direction in which the ice-skater was originally skating. What is the speed of the ice-skater and the sled after they collide?

Answer:

r=0

Step-by-step explanation:

28=4r+28

Subtract 28 from both sides, you get

4r=0

so, 0/4 is 0, and r=0

Answer:

r is 7

Step-by-step explanation:

because if you do the math you will see r is 7

The measurement closest to the volume of the bowling ball is 5277 cubic centimeters.

The length of a straight line drawn through the center of a body or figure, most notably a circle or sphere, is the diameter of a circle or sphere.

The radius of the sphere is half of the diameter, so it is 10.8 centimeters.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.

Substituting the value of r, we get:

V = (4/3)π(10.8)³

V ≈ 5276.66928645 cubic centimeters

Rounded to the nearest cubic centimeter, 5277 cubic centimeters is the measurement that most closely resembles the bowling ball's volume.

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Answer:

the queen, the workers, and the drones. :)

Applying the knowledge of quotient and fractions, we have:

The number of soda each person will drink is: \(1\frac{2}{3} \) glasses.

The fraction of sugar to be used per cupcake is: \(1\frac{3}{5} \)

Problem 1:

The expression that matches the situation is: 7 ÷ 3 (quotient of 7 and 3)

7/3 = \(1\frac{2}{3} \)

The number of soda each person will drink is: \(1\frac{2}{3} \) glasses.

Problem 2:

The expression that matches the situation is: 8 ÷ 5 (quotient of 8 and 5)

8/5 = \(1\frac{3}{5} \)

The fraction of sugar to be used per cupcake is: \(1\frac{3}{5} \)

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Answer:

C

Step-by-step explanation:

Given:

Dividing a number by 2 always results in a smaller number.

To find:

The counterexample to the given claim.

Solution:

If 0 is divided by is divided by any non-zero real number \(a\), then

\(\dfrac{0}{a}=0\)

Let us consider the unknown number be 0. Then dividing a number by 2, we get

\(\dfrac{0}{2}=0\)

Here, the result is not a smaller number because \(0=0\).

Therefore, the counterexample to the given claim is "Dividing 0 by 2".

Answer:

-1

Step-by-step explanation:

Juan has enough lumber to make five shelves and he has 2.2 feet of lumber left.

The piece of lumber is 18 feet long that Juan bought.

Now, we know each shelf is 2.5 feet long.

Then, the number of shelves x that can be made will be:

18 = 2.5(x)

x = 18 / 2.5

x = 7.2 feet

(a) Therefore, Juan has enough lumber to make five shelves.

After creating five shelves, the leftover lumber will be:

= 7.2 feet - 5 feet = 2.2 feet of lumber.

(b) One way to find, if Juan can make 5 shelves is by dividing the piece of lumber he bought by the length of lumber required to create one shelf.

Another way to know if Juan has enough lumber to make five shelves is by adding the amount need to create a shelf 5 times. Then check if Juan has enough lumber or not.

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The actual perimeter of the triangular face will be B. 18 1/2 feet.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

PQ + QR + PR

= 12 + 15 + 10

= 37 inches

Therefore, the actual perimeter of the triangular face will be:

= 37 / 2

= 18.5

The correct option is B.

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Answer:

10, 80 and 90 degrees.

Step-by-step explanation:

The third angle will  90 - 10 = 80 degrees.

The probability of selecting three balls of the same color without replacement is 0.0545, and with replacement is 0.0393. The probability of selecting three balls of different colors without replacement is 0.4591, and with replacement is 0.4968.

(a) To select a set of 3 balls that are all of the same color, we need to choose one of the three colors (red, blue, or green), and then select 3 balls of that color from the urn. There are three ways to choose the color of the balls. For each color, the number of ways to select 3 balls of that color is given by the number of combinations of 3 balls from the set of balls of that color. Thus, the total number of ways to select a set of 3 balls that are all of the same color is:

Number of ways to select 3 red balls + number of ways to select 3 blue balls + number of ways to select 3 green balls

= (5 choose 3) + (6 choose 3) + (8 choose 3)

= 10 + 20 + 56

= 86

The total number of ways to select any set of 3 balls from the urn is given by the number of combinations of 3 balls from the set of 19 balls in the urn:

Total number of ways to select any set of 3 balls = (19 choose 3) = 969

Therefore, the probability that each of the balls will be of the same color is:

P(each ball of the same color) = (number of ways to select 3 balls of the same color) / (total number of ways to select any set of 3 balls)

= 86 / 969

= 0.089

So the probability that each of the balls will be of the same color is approximately 0.089 or 8.9%.

(b) To select a set of 3 balls that are of different colors, we need to choose one ball of each color from the urn. The number of ways to select one ball of each color is given by the product of the number of balls of each color:

Number of ways to select 1 ball of each color = 5 x 6 x 8 = 240

The total number of ways to select any set of 3 balls from the urn is still 969.

Therefore, the probability that each of the balls will be of different colors is:

P(each ball of different color) = (number of ways to select 1 ball of each color) / (total number of ways to select any set of 3 balls)

= 240 / 969

= 0.248

So the probability that each of the balls will be of different colors is approximately 0.248 or 24.8%.

When the balls are selected with replacement, the probabilities remain the same because the probabilities of selecting each ball are unchanged on each draw.

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We will have the following:

Using the data provided and applying linear regression we will have that the lines of best fit will be:

Now, that is using 1984 as the starting point (0 years) now, we determine the value at 2010 (26 years after):

So, the prediction using the best fit would be approximately 107 students enrolled in 2010.

Answer:

Mean: 34.8

median:34

Mode: 13,34

Range:65

Step-by-step explanation:

The value of Mean is 34.4

The value of Median is 34 (middle term)

The value of Mode is 13 and 34.

The value of Range is 56.

Here,

The data set is,

53, 13, 34, 41, 26, 61, 34, 13, 69

We have to find the value of Mean , Median , Mode and Range.

What is Range of the data set?

To find Range of the data set we have to find the difference of highest and lowest number of the set.

Now,

The data set is,

53, 13, 34, 41, 26, 61, 34, 13, 69

Firstly we arranged in the ascending order we get;

13, 13, 26, 34, 34, 41, 53, 61, 69

The Mean of data set is calculated as;

Mean = \(\frac{13+13+ 26+ 34+ 34+41+ 53+61+ 69}{9} = \frac{310}{9} = 34.4\)

Hence, The value of Mean is 34.4

And, The Median is calculated as,

There are nine numbers (odd) in the data set, so the median is the middle value of given data set after arranging in ascending order.

Hence, The value of Median = 34 (middle term)

Now, The Mode is the number that appears most often within a data set.

In the data set,

13, 13, 26, 34, 34, 41, 53, 61, 69

Number 13 and 34 repeat two times.

So, The value of Mode = 13 and 34

Now, To find Range of the data set we have to find the difference of highest and lowest number of the set.

Here, In the data set;

The highest number = 69

The lowest number = 13

Hence, Range = 69 - 13 = 56

Therefore,

The value of Mean is 34.4

The value of Median is 34 (middle term)

The value of Mode is 13 and 34

The value of Range is 56

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Answer:

The answer is (C.

Step-by-step explanation:

Answer:

C. x≤−6

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

q²-10q+16

Step-by-step explanation:

FOIL stands for:

First -> (q-2)(q-8)

Outer -> (q-2)(q-8)

Inner -> (q-2)(q-8)

Last -> (q-2)(x-8)

Following FOIL, we get:

(q-2)(q-8)

(q)(q)+(q)(-8)+(-2)(q)+(-2)(-8)

q²-8q-2q+16

q²-10q+16

Therefore, the expanded form is q²-10q+16

The questions doesn't really specify much here is as much I can say.

Since 50 is the slope we can say that this is the hourly cost of a car repair (as stated in the question).

20 represents the y-intercept so this could represent the cost for the technician to look at whats wrong with the car.

Best of Luck!

The general solution is the sum of the particular solution and the complementary function: y((x) = (3/4)x + 1/2 + (C1 + C2x)e⁻²ˣ, where C1 and C2 are arbitrary constants.

To solve the given differential equation using the method of undetermined coefficients, assume a particular solution of the form:

y_p(x) = Ax + B

where A and B are constants to be determined.

First, let's find the derivatives of y_p(x):

y'_p(x) = A

y''_p(x) = 0

Now, substitute these derivatives into the original differential equation:

0 + 4(A) + 4(Ax + B) = 3x + 5

Simplifying this equation:

4Ax + 4B + 4A = 3x + 5

Now, equate the coefficients of like terms on both sides of the equation:

4A = 3         (coefficient of x on the right-hand side)

4B + 4A = 5    (constant term on the right-hand side)

Solving these equations simultaneously:

4A = 3

4B + 4A = 5

From the first equation, we find A = 3/4. Substituting this value into the second equation:

4B + 4(3/4) = 5

4B + 3 = 5

4B = 2

B = 1/2

Therefore, the particular solution is:

y_p(x) = (3/4)x + 1/2

To find the general solution, we also need the complementary function. The characteristic equation for the homogeneous equation y'' + 4y' + 4y = 0 is:

r² + 4r + 4 = 0

Factoring this equation, we have:

(r + 2)² = 0

The characteristic equation has a repeated root of -2. Therefore, the complementary function is:

y_c(x) = (C1 + C2x)e⁻²ˣ

where C1 and C2 are constants to be determined.

Hence, the general solution is the sum of the particular solution and the complementary function: y(x) = (3/4)x + 1/2 + (C1 + C2x)e⁻²ˣ , where C1 and C2 are arbitrary constants.

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Answer:

-4/20, -1/20, 0, 3/20 and 7/20

Step-by-step explanation:

Rewrite -1/4 and 1/4 as -5/20 and 5/20.  Then -4/20, -1/20, 0, 3/20 and 7/20 are definitely between -1/4 and 1/4.  These fractions are not unique; there are many others between -1/4 and 1/4.

Answer:

When multiplying whole numbers by 10, simply add a 0 to the end of the number

When dividing by 10 remove a 0 from the end of the number.

Step-by-step explanation:

Multiplication:

10 x 2 = 20

10 x 6970 = 69750

Division

20 / 10 = 2

6970 / 10 = 697

Hope this helps! :)

ఊhe directional derivative of f at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j is 2√2.

To find the directional derivative of the function f(x, y, z) = 2z^2x + y^3 at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j, we can use the formula for the directional derivative:

D_v(f) = ∇f · v

where ∇f is the gradient of f.

Taking the partial derivatives of f with respect to each variable, we have:

∂f/∂x = 2z^2

∂f/∂y = 3y^2

∂f/∂z = 4xz

Evaluating these partial derivatives at the point (1, 2, 2), we get:

∂f/∂x = 2(2)^2 = 8

∂f/∂y = 3(2)^2 = 12

∂f/∂z = 4(1)(2) = 8

Therefore, the gradient ∇f at (1, 2, 2) is given by ∇f = 8i + 12j + 8k.

Substituting the values into the directional derivative formula, we have:

D_v(f) = ∇f · v = (8i + 12j + 8k) · (1/5√2)i + (1/5√2)j

= 8(1/5√2) + 12(1/5√2) + 8(0)

= (8/5√2) + (12/5√2)

= (8 + 12)/(5√2)

= 20/(5√2)

= 4/√2

= 4√2/2

= 2√2

Hence, the directional derivative of f at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j is 2√2.

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Answer:

D)

Step-by-step explanation:

If the variable attractiveness increases while the variable weight remains constant, the correlation is said to be a positive correlation. A positive correlation means that as one variable increases, the other variable also tends to increase.

For example, let's consider a study examining the relationship between the attractiveness of a person and their weight. If the study finds that as attractiveness increases, weight also tends to increase while keeping other factors constant, then we can say there is a positive correlation between attractiveness and weight.

In this case, the variable attractiveness is increasing while the variable weight remains constant. This means that as attractiveness increases, weight also tends to increase, indicating a positive correlation.

It's important to note that correlation does not imply causation. Just because two variables are correlated does not necessarily mean that one variable causes the other to change. Correlation simply measures the strength and direction of the relationship between two variables.

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Answer:

AC and YX are corresponding sides.

AB and YZ are corresponding sides.

BC and ZX are corresponding sides.

Step-by-step explanation:

Hope this helps and have a nice day

Answer: m=-14

Step-by-step explanation: Use the slope-intercept form y=mx+b to find the slope m.

Graph down below.

I hope this helps you out. If not, I am so sorry.

The arc measure of the arc BC is 155°.

A complete circle has an arc, that is, a central angle of 360°. whose sum of angles is shown below:

AD + AB + BC + CD = 360°

Where AD = 155°

Since the four angles are generated by two diameters, then we find that AD = BC and AB = CD. Hence:

2 · AD + 2 · AB = 360                          Given

AD + AB = 180                                     Compatibility with multiplication / Existence of the multiplicative inverse / Modulative property

AB = 180 - AD                                      Compatibility with addition / Existence of the additive inverse / Modulative property

AB = 180 - 155                                     Given

AB = 25                                                Definition of subtraction / Result

Then, the arc measure of the arc BC is 155°.

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1.

60² + 30² = 4500²

Opposite corner = 67.08 ft.

//

2.

6² + 8² = 100²

The wire must be 10 ft.

//

3.

7² + 14² = 245²

The rope is 15.65 ft.

//

4.

180² + 300² = 122400²

He ran 349.85 ft.

//

I'm not too sure about question 3.