Find each difference. If you get stuck, consider drawing a number line diagram. HELP ASAP



1. 9 - 4
2. 4 - (-9)
3. 50 - 400
4. -50 - (-200)
5. -120 - 400
6. 0 - (-200)
7. 2 + 3
8. (-11) + 2
9. (-6) - (-3)
10. 2 - (-11)

Answer:

m = -5 / 10 = -1 / 2 = -0.5

Step-by-step explanation:

Answer:

The value of x is 108

Step-by-step explanation:

This is because the A and B lines are parallel meaning that the point where the line passes through one will be at the same degree as the other one

Answer:

1. 24 different 4-digit numbers can be formed.

Step-by-step explanation:

2. The probability that the number 3 will be the first or third digit is 1:1, which is equal to 1/2 and 50%

3. The probability is 3:1, 3/4, or 75%

4.  What is the probability that the first digit will be the number 3 and the second digit will be the number 7? Answer: 1/12

The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.

To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.

Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.

The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).

Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:

yz + λ = 0

xz + 3λ = 0

x*y + 4λ = 0

x + 3y + 4z - 9 = 0

Solving these equations simultaneously, we get:

x = 1.5, y = 1, z = 2.25, and λ = -0.5625

Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.

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Since a triangle's two sides have the same ratio as the two sides of another triangle. Because the angles are equal, the triangles are similar.

Similar triangles are those that resemble one another but may not be precisely the same size. When two objects have the same shape but different sizes, they can be said to be comparable. This indicates that comparable shapes superimpose one another when amplified or demagnified. This feature of similar shapes is referred to as "similarity."

As listed below, there are three main categories of similarity rules.

Angle-Angle Similarity Theory, abbreviated AA (or AAA),

Side-Angle-Side Similarity Theory, or SAS

Side-Side-Side Similarity Theory, or SSS

In the example question, two triangles are said to be similar if the ratio of one triangle's two sides to those of another triangle is the same, and the angles that each triangle's two sides inscribe are equal.

Thus, if ∠WUV = ∠SUT

and UV/UW = UT/US

then ΔWUV ~ΔSUT.

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Answer:

w = 11.25

Step-by-step explanation:

To solve this problem, we are going to move all of the terms containing the variable w to the left side of the equation and all of the constant terms (ones with numbers only) to the right side of the equation.

w - 24 = -3w + 21

To do this, we should first add 24 to both sides of the equation.

w - 24 + 24 = -3w +21 + 24

If we simplify, we get:

w =  -3w + 45

Next, we should add 3w to both sides of the equation.

w + 3w = -3w + 3w + 45

4w = 45

Finally, we can divide both sides by 4.

4w/4 = 45/4

w = 11.25

Hope this helps!

Answer:

36 cubic meters

Step-by-step explanation:

Formula for volume of a prism:

length * width * height = 6 * 2 * 3 = 36

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Answer:

1/6 +√6 = 2.6162

Step-by-step explanation:

Answer:

B:2.6161564...

Step-by-step explanation:

edge2020

There are 210 distinct sets of inputs for the given logical circuit where the sum of the Boolean random variables equals 4.

Since x1, x2, ..., x10 are distinct Boolean random variables, they can only take the values 0 or 1. In order to satisfy the given condition, we need to find the number of distinct sets of inputs such that exactly four of the variables are 1 and the rest are 0.

This can be viewed as selecting 4 variables out of 10 to be equal to 1. The number of distinct sets can be determined by calculating the combinations: C(10,4) = 10! / (4! * 6!) = 210. Therefore, there are 210 distinct sets of inputs that satisfy the given condition.

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Answer: 56%

Probably that it will rain and she goes + probably that it will be sunny and she goes

=     0.4 * 0.2     +           0.6*0.8

=          0.08      +              0.48

=   0.56

56% chance

The radius of the cone whose volume is 3π is approximately 2.121 as per the concept of cone.

To find the radius of a cone whose volume is 3π, we can equate the given volume to the volume formula of a cone and solve for the radius.

The volume formula of a cone is given as:

\(V = \frac{1}{3} \pi}r^{2}h\)

Given:

V = 3π

h = 2

Substituting these values into the volume formula, we have:

\(3\pi = \frac{1}{3} \pi}r^2(2)\)

Simplifying the equation, we get:

\(3 = \frac{1}{3} r^2(2)\)

Multiplying both sides by 3 to eliminate the fraction, we have:

\(9 = 2r^2\)

Dividing both sides by 2, we get:

\(4.5 = r^2\)

Taking the square root of both sides, we have:

r = √4.5

Using a calculator to evaluate the square root of 4.5, we find:

r ≈ 2.121

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The complete question:

The volume of a cone of height 2 and radius r is \(V = \frac{3}{2} \pi}r^{2}h\). What is the radius of such a cone whose volume is 3π ? r= help (numbers)

Answer:

7.5

Step-by-step explanation:

Just do 6/(4/5)

Which turns into 6*5/4 which is 30/4

which equals 7.5

The recurrence relation that describes the sequence A(n) = n² - n is A(n) = A(n-1) + 2n - 1, for n > 1, with the initial condition A(1) = 0.

To determine the recurrence relation for the given sequence A(n) = n² - n, we need to find a formula that relates A(n) to the previous term A(n-1).

Let's consider the formula for A(n):

A(n) = n² - n.

Now, let's substitute n with (n-1) in the formula to find A(n-1):

A(n-1) = (n-1)² - (n-1) = n² - 3n + 2.

To find the recurrence relation, we subtract A(n-1) from A(n):

A(n) - A(n-1) = (n²- n) - (n² - 3n + 2) = 2n - 1.

We observe that the difference between consecutive terms is always 2n - 1. Therefore, the recurrence relation for the sequence A(n) = n^2 - n can be expressed as A(n) = A(n-1) + 2n - 1, for n > 1.

In addition, we have the initial condition A(1) = 0, which represents the base case for the recurrence relation.

By utilizing this recurrence relation and the initial condition, we can generate the sequence A(n) = n²- n for any value of n.

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Answer:

2) 2/3x - 5 = 14

Step-by-step explanation:

2x-15=42

2x=57

X=28.5

Expert Answer:

Since the numbers are in the ratio 3:4 then let the numbers be 3x and 4x.

Thus the H.C.F. of the two numbers = x.

But the H.C.F is given as 4.

So, x = 4.

So, the numbers are,I

3x = 3 x 4 =12

And

4x = 4 x 4 = 16

We know,

H.C.F x L.C.M = Product of the two numbers

4 x L.C.M = 12 x 16

L.C.M = 48

Thus, the L.C.M of 12 and 16 , 48

To find out how far a car will travel (in feet) before a driver reacts to an obstacle, given that the car is moving at 34 miles per hour in a residential neighborhood, we need to convert the speed of the car from miles per hour to feet per second. This can be done using the conversion factor that 1 mile per hour is equal to 1.46667 feet per second. Therefore, 34 miles per hour is equal to 34 x 1.46667 = 49.86678 feet per second.

We know that the average reaction time of the driver is 1.2 seconds, and we can use the following formula to calculate the distance traveled by the car before the driver reacts to the obstacle:

d = v x t

where d is the distance, v is the velocity, and t is the time taken. Using the formula above, we can calculate the distance traveled by the car before the driver reacts to the obstacle as:

d = 49.86678 x 1.2 = 59.84014 feet

Therefore, the car will travel 59.84014 feet before a driver reacts to an obstacle.

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The model is a representation of the polynomial factors using algebraic

tiles.

The equation represented by the model is the option;

Reasons:

The parameters of the model of the polynomial and the factors of the

polynomial are;

The number of factors of the polynomial = 2

1 of the four tiles is labelled x

3 of the four tiles is labelled -ve

Therefore;

A factor of the polynomial is x-tile, -tile, -tile, -tile = (x tile - 3 tiles) = (x - 3)

1 of the two tiles is labelled x

1 of the two tiles is labelled -ve

Which gives;

A factor of the polynomial is x, -tile = (x-tile - 1 tile) = (x - 1)

The 8 tiles are as follows;

1 of the 8 tiles is labelled x²

4 of the 8 tiles are labelled -x

3 of the 8 tiles are labelled +

Which gives;

The product of the polynomial is; (x²-tile - 4·x-tiles + 3-tiles) = (x² - 4·x + 3)

Multiplying the factors gives;

(x - 3) × (x - 1) = x² - 3·x - x + 4 = x² - 4·x + 3

The correct option is therefore;

The question options are;

x² - 2·x - 3 = (x - 3)·(x + 1)

x² - 4·x + 3 = (x - 3)·(x - 1)

x² + 2·x + 3 = (x + 3)·(x - 1)

x² + 4·x - 3 = (x + 3)·(x + 1)

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Answer:

The translation corresponds to a translation of 13 units to the right

Step-by-step explanation:

Translation of a Graph

If the graph of

y=f(x) is translated a units horizontally, then the equation of the translated graph is

y =f(x - a)

The value of a is considered positive for translations to the right.

The parent function is

y = x

and the given function is

y = x - 13

The translation corresponds to a translation of 13 units to the right

Answer:

Step-by-step explanation:

Answer:

all

Step-by-step explanation:

2x3=6 3x3=9 so 6:9

2x4=8 3x4=12 so 8:12

2x2=4 3x2=6 so 4:6

The volume of the crystals is x³ - 9x² + 27x - 27

The volume of a cube can be found as follows:

volume of a cube = l³

where

Therefore,

length of the cubic crystal salt = (x - 3) cm

Hence,

volume of the crystal = (x - 3)³

volume of the crystal = (x - 3)(x - 3)(x - 3)

volume of the crystal = (x² - 3x - 3x + 9)(x - 3)

volume of the crystal =(x² - 6x + 9)(x - 3)

volume of the crystal = x³ - 3x² - 6x² + 18x + 9x - 27

volume of the crystal = x³ - 9x² + 27x - 27

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The following a probability model? what do we call the outcome No, the provided information is not sufficient to determine if it is a probability model. The outcome "red" is typically referred to as an event.

A probability model is a mathematical representation of a random experiment, where the sample space is defined, and probabilities are assigned to all possible outcomes. To determine if the given information is a probability model, we would need to know the complete list of possible outcomes, their corresponding probabilities, and ensure that the probabilities meet the necessary conditions (sum up to 1 and are non-negative).

Based on the limited information provided, we cannot determine if it is a probability model. The outcome "red" is called an event in the context of probability.

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We are given the dot-plots of sixth-grade test scores and seventh-grade test scores.

Let us first find the median of the two test scores.

Recall that the median is the value that divides the distribution into two equal halves.

Sixth Grade Geograph Test Scores:

From the dot-plot, we see that 11 is the median test score since it divides the distribution into two equal halves.

Median = 11

Seventh Grade Geograph Test Scores:

From the dot-plot we see that 13 is the median test score since it divides the distribution into two equal halves.

Median = 13

Therefore, the median score of the seventh-grade class is 2 points greater than the median score of the sixth-grade class.

Now let us find the interquartile range which is given by

Seventh Grade Geograph Test Scores:

The upper quartile is given by

At the 10th position, we have a test score of 13

The lower quartile is given by

At the 3rd position, we have a test score of 11

So, the interquartile range is

Sixth Grade Geograph Test Scores

The upper quartile is given by

At the 9th position, we have a test score of 10

The lower quartile is given by

At the 3rd position, we have a test score of 8

So, the interquartile range is

So, the IQR is the same as the difference between medians.

Therefore, the median score of the seventh-grade class is 2 points greater than the median score of the sixth-grade class. The difference is the same as the IQR

Hence, the correct answer is option B

Answer:

y = -2x + 3

Step-by-step explanation:

y2 - y1/ x2 - x1

7 - (-5) / -2 - 4

-2

The slope is -2.

To find the y-intercept, you need to plug the coordinates into the equation.

y = -2x + b

7 = -2(-2) + b

7 = 4 + b

3 = b

y = -2x + 3

Answer:

y=-2x+3

Step-by-step explanation:

To find the equation of the line passing through the points (4, -5) and (-2, 7), we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

where (x₁, y₁) represents one of the given points, and m is the slope of the line.

Let's calculate the slope (m) using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates of the points (4, -5) and (-2, 7) into the formula:

m = (7 - (-5)) / (-2 - 4)

m = 12 / -6

m = -2

Now we have the slope (m = -2), and we can choose one of the given points (4, -5) to substitute into the point-slope form. Let's use (4, -5):

y - (-5) = -2(x - 4)

Simplifying:

y + 5 = -2(x - 4)

y + 5 = -2x + 8

y = -2x + 3

I think its options b c and e

Answer:

Marty's with a slope of 1/3

Step-by-step explanation:

The functions Marty and Ethan wrote are analyzed the find the slope of each of the function

The equation Marty wrote is presented here as follows;

\(y + 3 = \dfrac{1}{3} \cdot\left (x + 9 \right)\)

Marty's equation can be written in slope and intercept form, y = m·x + c, as follows;

\(y = \dfrac{1}{3} \cdot\left (x + 9 \right) - 3\)

\(y = \dfrac{1}{3} \cdot x + \dfrac{9}{3} \right) - 3 = \dfrac{1}{3} \cdot x + 0\)

\(y = \dfrac{1}{3} \cdot x\)

By comparison, the slope of the function, m = 1/3

\(\therefore \ the \ slope \ of \ Marty's \ function, \ y + 3 = \dfrac{1}{3} \cdot\left (x + 9 \right), \ m =\dfrac{1}{3}\)

Marty's function has a slope of m = 1/3

Ethan has the following two column table;

\(\begin{array}{rl}x&y\\-4&9.2\\-2&9.6\\0&10\\2&10.4\end{array}\)

The slope, m, of the data in the above table is given as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Taking any two points, (x₁, y₁) = (-4, 9.2), and (x₂, y₂) = (2, 10.4), we get;

\(Slope, \, m =\dfrac{10.4-9.2}{2-(-4)} = \dfrac{1.2}{6} = \dfrac{1}{5}\)

Ethan's function has a slope of m = 1/5

Therefore;

Marty's slope of 1/3 is larger, given that 1/3 > 1/5.

Answer:

C. Marty’s with a slope of 1/3

Step-by-step explanation:

Did the test and got it correct

Answer:

32

Step-by-step explanation:

Answer:

6577

Step-by-step explanation:

nn