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Proving the Parallelogram Side Theorem
Given: ABCD is a parallelogram.
Prove: AB CD and BC = DA
A
□
Hint
Angles Segments Triangles Statements Reasons
ASA
CPCTC
reflexive property
given
Statements
✓ 3. BC || DA
4. draw AC
✔✓ 5. AC AC
SE
6. BCA and DAC
are alt. interior angles
7. DAC
✓8. ZDCA and are alt. interior angles/
DCA
✓9. Reasons
3. def. of parallelogram
4. unique line postulate
5. reflexive property
6. def. of alt. interior angles
7. alternate interior angles theorem
8. def. of alt. interior angles
9. alternate interior angles theorem

Answer:

2x + 3y - 7

Step-by-step explanation:

3x − 2y − 7 + 5y − x =

2x - 2y - 7 + 5y =

2x + 3y - 7

By combining like terms 3x−2y−7+5y−x is x(3 - 1) +y(5 -2) -7.

In mathematics like terms are those terms which has same variable and they must have exactly same exponent like we can not combine x and x² by addition and subtraction reason is although they are a same variable in x but their power is not same.

We can of course multiply x and x² which is x³.

According to the given data

3x−2y−7+5y−x  we have combine by like terms so,

3x−2y−7+5y−x can be written as

3x - x +5y - 2y - 7

x(3 - 1) +y(5 -2) -7.

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Answer:

Value of ending inventory = $97,650

Step-by-step explanation:

Full costing is a costing method that consider all the costs including all variable and fixed costs in determining the cost of producing products or services.

From the question, we have the following:

Total variable manufacturing costs per unit = $11.00

Fixed manufacturing overhead per year = $233,550

Number of snow shovels produced during the year = 51,900

Number of snow shovels sold during the year = 46,500

Therefore, we have:

Total variable manufacturing costs incurred during the year = Total variable manufacturing costs per unit * Number of shovels produced during the year = $11.00 * 51,900 = $570,900

Based on full costing, we have:

Total cost of producing snow shovel during the year = Fixed manufacturing overhead per year + Total variable manufacturing costs incurred during the year = $233,550 + $570,900 = $804,450

Production cost per unit = Total cost of producing snow shovel during the year / Number of snow shovels produced during the year = $804,450 / 51,900 = $15.50

Number of ending inventory = Number of snow shovels produced during the year - Number of snow shovels sold during the year = 51,900 - 46,500 = 6,300

Value of ending inventory = Number of ending inventory * Production cost per unit = 6,300 * $15.50 = $97,650

Answer: False

Step-by-step explanation: The two lines do not overlap so they do not intercept.

Problem 11

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

Work Shown:

The surface area of a 3D sphere is 4pi*r^2. So a hemisphere has surface area 2pi*r^2 since we cut the surface area in half.

Plug in r = 6 (half of the diameter 12) and we get 2pi*r^2 = 2pi*6^2 = 72pi

Now consider the circle with radius r = 6. Its area is pi*r^2 = pi*6^2 = 36pi

Add the two areas and we get 72pi+36pi = 108pi

Lastly, use your calculator to get 108pi = 108*3.1415926535898 = 339.292006587699 which rounds to 339

======================================

Problem 12

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

Explanation:

Look at where the "0" in the bottom sliding portion lines up with the number scale above. That "0" is between 19 and 20 mm. So you could argue that 19.2 and 19.5 are both valid answers, but I think 19.5 is the better answer since the tickmark seems to be right in the middle (more or less).

Step-by-step explanation:

surface area of hemisphere =3πr²

=3*3.14(6)²

=339.12m²

diameter of pipe= 19.5mm

Answer:

I am so sorry to say that you are the one who made the miatake. Better luck next time!

Step-by-step explanation:

A. 3x+4/2 = 9.5

3x + 4/2 = 9.5........criss cross

3x+4= 9.5×2

3x = 19-4

3x = 15

x=5 ..........divide both sides by 3

B. 7+ 2x/3= 5.......criss cross

7+2x = 5 × 3

7 + 2x = 15

2x = 15-7

2x = 8......divide both sides by 2

x = 4

Answer:

The number of questions answered.

Step-by-step explanation:

Number of questions answered minus 5 questions she got wrong equals her final score.

When x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.

In the given question, we have to find what is remainder when x^3+2x^2+x+1 is divided by (x+1).

To find the remainder there are two ways. First we divide the x^3+2x^2+x+1 by (x+1). Second we find the value of from (x+1) by equating (x+1) equal to zero. The put the value of x in the expression x^3+2x^2+x+1.

In this we ca easily find the remainder.

Now we firstly find the value of x;

(x+1) = 0

Subtract 1 on both side we get;

x= −1

Now put x= -1 in the expression x^3+2x^2+x+1.

x^3+2x^2+x+1 = (−1)^3+2(−1)^2+(−1)+1

x^3+2x^2+x+1 = −1+2−1+1

x^3+2x^2+x+1 = 1

Hence, when x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.

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The right question is:

What is remainder when x^3+2x^2+x+1 is divided by (x+1)?

have a good day :)

:)

:)

:)

:)

Answer:

i think its 64

Step-by-step explanation:

There are 3 mangoes left behind after making 39 trays of 9 mangoes each

To find out how many trays can be made from 354 mangoes, we divide the total number of mangoes by the number of mangoes per tray.

Number of mangoes per tray = 9

Number of trays = 354 mangoes / 9 mangoes per tray

Number of trays = 39 trays

So, 39 trays can be made from 354 mangoes.

To determine how many mangoes are left behind, we subtract the number of mangoes used for the trays from the total number of mangoes.

Number of mangoes left behind = Total number of mangoes - Number of mangoes used for trays

Number of mangoes left behind = 354 mangoes - (39 trays * 9 mangoes per tray)

Number of mangoes left behind = 354 mangoes - 351 mangoes

Number of mangoes left behind = 3 mangoes

Therefore, there are 3 mangoes left behind after making 39 trays of 9 mangoes each

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Answer:

The range of f(x) is  { 6 , 7 , 8 }

Step-by-step explanation:

Given a function y=f(x), the domain of f(x) is the set of values that x can take and the range of f(x) is the set of values that f gets when x is in the domain.

We have the function:

f(x)=1/2x+5

And the domain is

(2,4,6)

Compute the range by assigning each value of x:

For x=2:

f(2) = (1/2)2 + 5 = 1 + 5 = 6

For x=4:

f(2) = (1/2)4 + 5 = 2 + 5 = 7

For x=6:

f(2) = (1/2)6 + 5 = 3 + 5 = 6=8

The range of f(x) is:  { 6 , 7 , 8 }

Now that we have added up all three alternatives ("or" = sum), we have the general option of choosing two different colors. = 0.7316

There must be some mistakes in this. But I make an effort to address the appropriate topics.

Nothing is underneath (a). I have nothing to say in response.

(a) Her purse contains 20 candies. If all 20 are yellow, then 9.

As a result, the probability is the proportion of desirable possibilities to all possible outcomes.

Hence, ta da! 9/20

That is the likelihood that Samira will choose a yellow candy.

Again, 20 candies are the starting point [1](i).

Six are green.

When she chooses the first option, her likelihood of selecting a green option is 6/20 = 3/10 = 0.3.

She chooses another candy now, assuming that her prediction came true.

Only 19 were left this time, and 5 of them are green.

Therefore, the likelihood is 5/19.

For the situation we are describing, both occurrences are now required. No overlapping, no ifs, ands, or buts exist. It is simply the sum of the two probabilities.

3/10 × 5/19 = 15/190 = 3/38

That's what I believe the description calls for.

(ii) The likelihood is that the first choice is red and the second is not, plus the first choice is green and the second is not, plus the first choice is yellow and the second is not.

so,

red and not red

5/20 = 1/4 red

15/19 not red (there are still 15 sweets of other colors in the bag, but again now only 19 total).

red and not red = 1/4 × 15/19 = 15/76 = 0.1974

green and not green

6/20 = 3/10 = green

14/19 = not green

green and not green = 3/10 × 14/19 = 52/190 = 26/95 =

= 0.2737

yellow and not yellow

9/20 = yellow

11/19 = not yellow

yellow and not yellow = 9/20 × 11/19 = 99/380 = 0.2606

Now that we have added up all three alternatives ("or" = sum), we have the general option of choosing two different colors.

= 0.7316

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Answer:Blue whale

Step-by-step explanation:

The blue whale goes  an extra kilometer faster

The Mako shark faster at top cruising speed and by 20km/h.

Given that,

Based on the above information, the calculation is as follows:

We know that

\(Speed = \frac{Distance}{Time}\)

For Mako shark,

\(= \frac{4}{\frac{1}{10} }\)

= 40 km/h

For Blue whales

\(= \frac{5}{\frac{1}{4} }\)

= 20 km/h

Based on the above calculations we can say that the Mako shark should be faster and by 20 km/h.

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Answer:

Step-by-step explanation:

\(\frac{6}{7}x - 8 - \frac{4}{7}x - 8 = \frac{6}{7}x -\frac{4}{7}x - 8 - 8\\\\=\frac{6-4}{7}x - 16\\\\=\frac{2}{7}x - 16\\\)

When selecting a single score from a population with a mean of 100 and a standard deviation of 20, we can expect, on average, the selected score to be approximately 20 units away from the population mean.

The population mean (μ) is a measure of the average or central tendency of the population, while the population standard deviation (σ) is a measure of the variability or spread of the scores in the population. In this case, the population mean is 100 and the population standard deviation is 20.

When we select a single score from the population, we can expect it to be, on average, close to the population mean. This is because the population mean represents the center or average value of the population.

The standard deviation provides us with a measure of the dispersion or spread of scores around the mean. A standard deviation of 20 indicates that the scores in the population tend to deviate from the mean by an average of 20 units.

Considering that the standard deviation represents the average distance between individual scores and the mean, we can conclude that, on average, a single score selected from the population would be approximately 20 units away from the population mean.

However, it is important to note that this is a probabilistic statement. While the average distance between individual scores and the mean is expected to be 20 units, there will be some scores that are closer to the mean and others that are further away.

The distribution of scores in the population follows a bell-shaped curve (assuming a normal distribution), and the majority of scores will fall within a few standard deviations from the mean.

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Note the full question is A population has μ = 100 and σ = 20. If you select a single score from this population, on the average, how close would it be to the population mean? Explain your answer.

Answer:

B. Negative

Step-by-step explanation:

A slope of zero would cause the red line (the slope) to be horizontal/sideways

A negative slope goes down

A positive slope goes up

An undefined slope is vertical/up and down

Hope this helps!

Answer:

Hi there!

The answer is:

B. Negative

Step-by-step explanation:

Slopes that increase to the left and decrease to the right are negative! Think about is as rise/run (which determines slope). It rises 4 for every -2 units (or units to the left!)

Hope this makes sense!

Most likely I have scored 375 3-point darts.

The expected (mean) value of the total points is as follows, with a 50% chance of scoring 1-point darts and the same for 3-point darts:50 percent of the 500-point darts score and 50 percent of the 500-point darts score. The anticipated number of points is 1 point multiplied by 1/2 (500) times 3 points yielding 1000 points.

The equality of distribution between the 1-point and 3-point scoring indicates that you scored 1500/1000, or 1.5 times the means, assuming that you actually scored 1500 points in total. That indicates that 1500 points are equal to 1.5 (.5) 500 (1 point) plus 1.5 (.5) 500 (3 points). Therefore, you scored 1.5 (.5) 375 3-point dart hits.

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As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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Answer:

Wow, thanks :)

Step-by-step explanation:

You are just too kind :D

Answer:

MEEEEEEE

Step-by-step explanation:

I WAS ON THE TOLITE IN  CLASS AND MY CAM TURNED ON THEN MY MOM CAME IN...

2?

An alpha value of 0.2 will cause exponential smoothing to react more slowly to a sudden drop in demand compared to an alpha value of 0.4.

The statement is incorrect. An alpha (α) value of 0.2 in exponential smoothing will actually cause the forecast to react more slowly to a sudden drop in demand compared to an alpha value of 0.4.

Exponential smoothing is a forecasting technique that assigns weights to past observations, and the alpha value determines the weight given to the most recent observation. A smaller alpha value means less weight is given to recent observations, resulting in a smoother and slower reaction to changes in the data.

When the alpha value is 0.2, the forecast will be more influenced by historical data and less responsive to sudden changes in demand. On the other hand, with an alpha value of 0.4, the forecast will be more influenced by recent data and react more quickly to sudden drops or increases in demand.

Therefore, an alpha value of 0.4 will cause an exponential smoothing forecast to react more quickly to a sudden drop in demand compared to an alpha value of 0.2.

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a) In standard form, Maximize: 3A + 2B, Subject to: A + B + S₁ = 4, 3A + 4B - S₂ = 24 , A - S₃ = 2, A - B + S₄ = 0. b) The optimal solution is A = 2, B = 2, and the maximum value is 10. c) The values of S₁ = 0, S₂ = 14, S₃ = 0, and S₄ = 0.

a. To write the linear program in standard form, we need to introduce slack and surplus variables to convert all inequalities into equalities.

The given linear program in its original form is:

Maximize: 3A + 2B

Subject to:

A + B ≥ 4

3A + 4B ≤ 24

A ≥ 2

A - B ≤ 0

A, B ≥ 0

To convert the inequalities into equalities, we introduce slack and surplus variables as follows:

Maximize: 3A + 2B

Subject to:

A + B + S₁ = 4 (introducing slack variable S₁)

3A + 4B - S₂ = 24 (introducing slack variable S₂)

A - S₃ = 2 (introducing slack variable S₃)

A - B + S₄ = 0 (introducing surplus variable S₄)

A, B, S₁, S₂, S₃, S₄ ≥ 0

Now the linear program is in standard form.

b. To solve the linear program, we can use the simplex method. However, since this is a small problem, we can also solve it directly by substituting the constraints.

Using the constraint A + B ≥ 4, we have A ≥ 4 - B.

Using the constraint A - B ≤ 0, we have A ≤ B.

Substituting A ≤ B into A ≥ 4 - B, we get B ≥ 4 - B, which simplifies to 2B ≥ 4. This implies B ≥ 2.

Since A ≤ B and A ≥ 4 - B, the possible range for A is 2 ≤ A ≤ B.

Considering the constraint A ≥ 2, we have 2 ≤ A ≤ B. Therefore, A = 2 and B = 2 is a feasible solution.

Plugging the values of A = 2 and B = 2 into the objective function, we get:

3A + 2B = 3(2) + 2(2) = 10.

Thus, the optimal solution is A = 2, B = 2, and the maximum value is 10.

c. To determine the values of the slack and surplus variables at the optimal solution, we substitute the optimal values of A = 2 and B = 2 back into the constraints:

A + B + S₁ = 4:

2 + 2 + S₁ = 4,

S₁ = 0.

3A + 4B - S₂ = 24:

3(2) + 4(2) - S₂ = 24,

S₂ = 14.

A - S₃ = 2:

2 - S₃ = 2,

S₃ = 0.

A - B + S₄ = 0:

2 - 2 + S₄ = 0,

S₄ = 0.

Therefore, the values of the slack variables at the optimal solution are S₁ = 0, S₂ = 14, S₃ = 0, and the value of the surplus variable is S₄ = 0.

Correct Question :

Consider the linear program below and answer the following questions. LO  2, 4 , 6, 7

Max 3A + 2B

s.t.

A+B ≥ 4

3A+4B ≤ 24

A ≥ 2

A-B ≤ 0

A,B ≥ 0

a. Write the problem in standard form.

b. Solve the problem.

c. What are the values of the slack and surplus variables at the optimal solution?

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The standard deviation of the data set will increase by a factor of 10. This is because standard deviation measures how much variation or dispersion exists from the mean of a data set. Adding 10 to every value of the data set will increase the overall spread of the data and thus increase the standard deviation.  

To prove this mathematically, let's consider a data set A with mean M and standard deviation SD. Let's add 10 to every value of the data set to get a new data set B. The mean of set B is M+10 and the standard deviation of set B is SD'.   The formula for SD' is:  

SD':\(\sqrt{(x_{1} -(M+10))^{2} +(x_{2} -(M+10))^2+ (x_{3}-(M+10))^2 +...+ (x_{n}-(M+10))^2)/n }\) We can simplify this by substituting the values for the xi:

 SD' =\(\sqrt{(((x_{1}-M-10)^2 + (x_{2}-M-10)^2 + (x_{3}-M-10)^2 +...+ (x_{n}-M-10)^2)/n) }\)  Now let's consider the original data set A and its standard deviation SD:

 SD =\(\sqrt{(((x_{1}-M)^2 + (x_{2}-M)^2 + (x_{3}-M)^2 +...+ (x_{n}-M)^2)/n) }\) ,We can substitute the values for xi in this formula as well:  

SD= \(\sqrt{ (((x_{1}-M-10)^2 + (x_{2}-M-10)^2 + (x_{3}-M-10)^2 +...+ (x_{n}-M-10)^2)/n)}\)  If we compare SD and SD', we can see that they are identical, except that the value of M has been replaced with M+10. This means that when we add 10 to every value of the data set, the standard deviation increases by a factor of 10.

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Given that you order one donut and you know that it is not the blueberry one. We need to determine the probability that it is the chocolate one.

Say we have 3 flavors of donuts such as Blueberry, Chocolate and Glazed. There are a total of 3 possibilities for the first choice. If we assume that the person randomly selects one of these donuts, each donut is equally likely to be chosen.

Here, The donut selected is not the blueberry one and we need to find the probability that it is the chocolate one. Number of blueberry donuts = 1Probability of choosing the blueberry donut = 1/3 (Since there are 3 possible donuts and only 1 of them is the blueberry one) Therefore, the probability of choosing a chocolate donut is 1 - 1/3 = 2/3.

Similarly, the probability of choosing a glazed donut is also 2/3. Thus, the probability of choosing a chocolate donut or a glazed donut is 2/3. Answer: 2/3.

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Answer: 0.0000203%

Step-by-step explanation:

The total number of people struck by lightning includes both those who died and those who were injured:

= 39 + 24

= 63 people

Probability of being struck is:

= People struck / U.S. Population

= 63 / 310,000,000

= 0.0000203%

The amounts of each substance are given as follows:

The graphic solution of a system of equations is given by the point of intersection of the equations that compose the system.

The variables that define the system in this problem are given as follows:

Yaritza sold a total of 75 pounds of peaches and grapes, hence:

x + y = 75.

Each pound of peaches sell for $2.50 and each pound of grapes sells for $3.75, and she made $225, hence:

2.5x + 3.75y = 225.

As given by the image at the end of the answer, the intersection of these two equations in the graph is given as follows:

(45, 30).

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The students are expected to make $85 in week 8 if the trend continues.

To determine the earnings for week 8, we need to analyze the given data and look for a pattern or trend. Since the table shows the earnings for the first 6 weeks, we can use this information to make a prediction for week 8.

Week | Earnings

-----|---------

1    | $50

2    | $55

3    | $60

4    | $65

5    | $70

6    | $75

From the given data, we can observe that the earnings increase by $5 each week. This indicates a constant weekly increment in earnings. To predict the earnings for week 8, we can apply the same pattern and add $5 to the earnings of week 6.

Earnings for week 6: $75

Increment: $5

Earnings for week 8 = Earnings for week 6 + (Increment * Number of additional weeks)

Number of additional weeks = 8 - 6 = 2

Earnings for week 8 = $75 + ($5 * 2) = $75 + $10 = $85

According to the pattern observed in the given data, the students are expected to make $85 in week 8 if the trend continues.

However, it's important to note that this prediction assumes the pattern remains consistent throughout the 6-month period. In reality, there might be variations or changes in the earning pattern due to various factors.

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Answer:

a = 1

Step-by-step explanation:

\(\frac{2}{3} (9x - 3) = 2(3x - a)\)

One must simplify this expression, by distributing. In order to find a solution, where x has infinite solutions, one must make this equation an identity. That means that the equation will hold true, no matter what value of x is plugged in.

\(\frac{2}{3} (9x - 3) = 2(3x - a)\)

Distribute;

6x - 2 = 6x - 2a

Inverse operations;

6x - 2 = 6x - 2a

-6x        -6x

-2 = -2a

1 = a

For this equation to be true no matter what, a must equal 1.

Answer:

1

Step-by-step explanation:

Answer: $16

Step-by-step explanation:

reduce by 20% means cutting from 100% and leftover with 80% of original

                                            100%-20%=80%

original price: $20×100%=$20

after reduction: $20×(100%-20%)=$16

Answer:

16

Step-by-step explanation:

First find the discount

20 * 20%

20 * .20

4

Subtract this from the price

20 -4

16

The new price is 16