1. two-column proof
Given: AB ≅ XY, AC ≅ XZ, BC ≅ YZ
Prove: ∆ABC ≅ ∆XYZ

Answer:

Bethan = 34

Jack = 30

Ruben = 33

Answer:

16.49 feets

Step-by-step explanation:

Using Pythagoras rule, we could find, h the height of the wall ;

Using the relation :

a² = b² + c²

36² = h² + 32²

1296 = h² + 1024

h² = 1296 - 1024

h² = 272

h = √272

h = 16.49 feets

Answer:

A=6

YZ=38

I tried so if I’m wrong srry

The value of n is 4 and the measure of the line segment YZ is 1 if Y is between X and Y and XY = 4n + 3. YZ = 2n-7, XZ = 20.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Y is between X and Z.

XY = 4n + 3. YZ = 2n-7, XZ = 20

From the question:

XZ = XY + YZ

20 = (4n + 3) + (2n - 7)

20 = 6n - 4

6n = 24

n = 24/6

n = 4

YZ = 2n - 7 = 2(4) - 7

Plug n = 4 in the above expression:

YZ = 8 - 7

YZ = 1

Thus, the value of n is 4 and the measure of the line segment YZ is 1 if Y is between X and Y and XY = 4n + 3. YZ = 2n-7, XZ = 20.

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Answer:

2y=3x=-4

Step-by-step explanation:

grouping like terms

y+ly =4x-x=-4

2y=3x=-4

A: The probability of cantaloupe having dia. more than 127 is 0.12167.

B: Cantaloupe selected at random from the warehouse, then the probability that has a diameter of more than 127 mm is 0.3782.

C: The probability that the cantaloupe will be from warehouse B given randomly selected cantaloupe's diameter is greater than 127 mm, is 0.8069.

The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability is a measure of the likelihood of an event occurring.  Also, the favorable number of outcomes cannot be negative.

Given two warehouses, A and B

mean for warehouse A = μ = 120 mm

The standard deviation for warehouse A = σ = 6mm

A:  a cantaloupe selected at random from Warehouse A

to find the probability of cantaloupe having a diameter greater than      127 mm = P(x > 127)

P(x > 127) = 1 - P(x ≤ 127)

P(x ≤ 127) = P((x - μ)/σ)

P(x ≤ 127) = P((127 - 120)/6)

P(x ≤ 127) = P(z ≤ 1.66)

P(x ≤ 127) = 0.87833

P(x > 127) = 1 - P(x ≤ 127)

P(x > 127) = 1 - P(x < 127) = 0.12167

probability of cantaloupe having dia. more than 127 is 0.12167.

B: Let event A for distributor A and  let event B for distributor B

and event C for a diameter greater than 127 mm.

and given A randomly selected cantaloupe from Warehouse B has a probability of 0.763 that it will have a diameter greater than 127 mm,

and the percentage of cantaloupe provided by B is 40%

rest 60% for A,

therefore, for cantaloupe selected at random, the probability of having a diameter greater than 127 mm is

P(C) = P(C|A)P(A) + P(C|B)P(B)

=  0.12167(0.6) + 0.763(0.4)

= 0.073 + 0.3052

P(C) = 0.3782

cantaloupe selected at random from the warehouse, then the probability that has a diameter of more than 127 mm is 0.3782.

C:   the probability the cantaloupe came from Warehouse B, given that the randomly selected cantaloupe's diameter is greater than 127 mm,

P(B|C) = P(B ∩ C)/P(C)

P(B|C) = (P(C|B)P(B))/P(C)

substitute values

P(B|C) = ((0.763)(0.4))/0.3782

P(B|C) = 0.3052/0.3782

P(B|C) = 0.8069

The probability that the cantaloupe will be from warehouse B given randomly selected cantaloupe's diameter is greater than 127 mm, is 0.8069.

Hence the probabilities are,

A;  0.12167

B; 0.3782

C; 0.8069.

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Answer:

1250 g

Step-by-step explanation:

12.5% of 10 kg

12.5% of 10000 g

.125 of 10000 g

.125 * 10000 g

1250 g

Answer:

Step-by-step explanation:

\( \frac{12.5}{100} \times 10kg = x \: grams\)

\(1.25kg = 1250 \: grams\)

Answer:

The answer is "\(\bold{\frac{9}{13}}\)"

Step-by-step explanation:

In this question, the image file is missing, which is defined in the attached file. please find it.

\(\to raise= y_2-y_1\)

             \(=-1-(-10)\\\\=-1+10\\\\=9\)

\(\to run= x_2-x_1\)

          \(=9-(-4)\\\\=9+4\\\\=13\)

\(\to \text{formula for slope} =\frac{rise}{run} =\frac{9}{13}\)

The number of students in the telescope club by $x$ and the number of students in the math club by $y$.

$y=2x$Now, suppose there are $z$ students who are members of both clubs. Then the total number of students who are in the math club or the telescope club (or both) is given by:$x + y - z$ Substituting $y=2x$ in the above expression, we get:$x + 2x - z=3x - z$ Hence, the expression for the total number of students who are in the math club or the telescope club (or both) is $3x - z$.b)The number of students who are in the math club but not in the telescope club is given by:$y-z$ And the number of students who are in the telescope club but not in the math club is given by:$x-z$ Adding these two expressions, we get the total number of students who are in the math club or the telescope club but not both:$ y-z+x-z $.

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Answer:

312

Step-by-step explanation:

120x0.4=48

48x3=144

120x0.7=84

84x2=168

168+144=312

Answer:

Nia

Step-by-step explanation: Everybody had 60% except Nia who had 65%

Answer:

nia

Step-by-step explanation:

The image point of (6, 4) after the transformation T<1, 5> R90° is  (-6, -11).

What is a transformation?

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The transformation shifts a point up by 5 units on the y-axis. The transformation is a point 90 degrees counterclockwise.

So, to find the image point of (6, 4) after the transformation, we first apply the rotation R90° :

(6, 4)  → (-4, -6)

Next, we apply the translation T<1, 5> :

(-4, -6)  → (-4, -11)

Hence, the image point of (6, 4) after the transformation R90° is (-6, -11).

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According to the given statement While spring training records can provide some insight, they should not be the sole basis for predicting a team's success during the regular season.

There is a correlation between a major league baseball team's record during spring training and its performance during the regular season. Over a six-year period, the correlation coefficient between a team's winning percentage in spring training and its winning percentage in the regular season is .

However, it's important to note that this correlation does not imply causation. While a strong performance in spring training may suggest a team's potential success, it does not guarantee it. Factors such as injuries, roster changes, and overall team strategy can also significantly impact a team's performance during the regular season.

Therefore, while spring training records can provide some insight, they should not be the sole basis for predicting a team's success during the regular season.

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Answer:

Nathan will make $20

Jackson will make $29

hope you like it

Considering the expression of a line, the slope of the line that contains the pair of points (6,2) and (-8,1) is \(\frac{1}{14}\).

Equation of a line having 2 points

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

\(m=\frac{y2-y1}{x2-x1}\)

m=(y2-y1)÷ (x2-x1)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, being (x1,y1)= (6,2) and (x2,y2)= (-8,1), the slope m can be calculated as:

m=(1-2)÷ (-8-6)

Solving:

m= (-1)÷ (-14)

m= \(\frac{1}{14}\)

Finally, the slope of the line that contains the pair of points (6,2) and (-8,1) is \(\frac{1}{14}\).

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Answer:

ok im  not good at math but les see how this goes errr

Step-by-step explanation:welp i think it s35 beAZcausee im smART   :))))

your welcome

you can thank me later :))\

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

Explanation:

Let y be the unmarked angle to the right of (x+85). Since angle (x+85) and angle y form a straight angle, we know that (x+85)+y = 180.

We also know that y = 60 since line a is parallel to line b, and corresponding angles are congruent when we have parallel lines.

So (x+85)+y = 180 updates to (x+85)+60 = 180

-------

Let's solve for x

(x+85)+60 = 180

x+85+60 = 180

x+145 = 180

x = 180-145

x = 35

D. The project timeline not including holidays which the team members plan to take off does not represent a constraint described in Dempster's triangle.

The constraints described in Dempster's triangle are related to project scope, time, and resources, and typically include limitations on budget, technology, staffing, and other factors that may impact project success. While holidays may impact project scheduling, they are not typically considered a constraint in the same sense as other Dempster's triangle that directly impact project deliverables.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The average stopping distance when driving at 55 mph on dry, level pavement can vary depending on several factors such as vehicle condition, road conditions, and driver reaction time.

Therefore, it is not possible to provide an exact average stopping distance without more specific information.

However, as a general guideline, it is commonly recommended to use the "3-second rule" for following distance. This means that you should maintain a distance from the vehicle in front of you that would allow you to come to a complete stop within three seconds. At higher speeds like 55 mph, the stopping distance will be longer compared to lower speeds.

To estimate the average stopping distance, you can consider the total stopping distance, which is the sum of the perception distance, reaction distance, and braking distance. The perception distance is the distance your vehicle travels while you recognize a need to stop, the reaction distance is the distance traveled during your reaction time, and the braking distance is the distance covered while your vehicle comes to a stop after applying the brakes.

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Option (a) it is the same as the gross pay. is true statement about a person who is claiming 5 exemptions and biweekly salary of $ 840.

Yοur incοme is referred tο be yοur grοss pay if it is unaffected by taxes and οther withhοldings.

When referring tο yοur yearly grοss incοme, the phrase "annual pay" is frequently used. Net pay is the amοunt that remains after deductiοns like sοcial security and incοme tax have been made.

the persοn want mοre exemptiοns, it means that persοn thinks that, his οr her salary is less than οthers when cοmpared with οther emplοyee having mοre expenditure, and he οr she dοes nοt want tο pay tax οr will pay minimum amοunt οf tax tο the Gοvernment.

Sο, tο dο this he want exemptiοns.

As,persοn earns a grοss biweekly salary οf $840 and claims 5 exemptiοns.

→it means he οr she want tο reduce his tοtal tax tο minimum amοunt.

→it means he οr she dοes nοt have enοugh mοney in his οr her pοcket thrοughοut the year.

→ there will be nο tax deductiοn οn persοn net pay.And if he fοund caught cheating , he will have tο pay Penality.

Sο, οptiοn (a)  it is the same as the grοss pay. is true statement abοut a persοn whο is claiming 5 exemptiοns and biweekly salary οf $ 840.

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After finding out the value of ln (52) and rounding value it to the nearest ten thousandth, we have the value as 3.9512.

Given logarithm function is ln (52).

We have to find out the value of the logarithm by rounding it to the nearest ten thousandth.

The easiest way to do this is to make use of a calculator where we can put the value of natural log.

After putting ln (52) in the calculator, we have

ln (52) = 3.951243719

In order to round the answer of ln (52) to the nearest ten thousandth, we have to first check if the number after the ten thousandth one is greater than 5 or if it is not.

Here, the ten thousandth number is 2. The number after the ten thousandth one is 4 which is less than 5. So, there will be no increase in the ten thousandth number.

Therefore, rounding the value of ln (52) to the nearest ten thousandth, we have the value as 3.9512.

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The argument is valid. If a number is not prime, it does not imply that the number is odd.

The given argument is invalid. The argument's structure follows the form of denying the consequent (modus tollens). However, the argument itself contains a logical flaw. While it is true that all prime numbers greater than 2 are odd, it does not follow that a number being not prime implies it is not odd.

The argument assumes that the negation of being prime automatically leads to not being odd, which is not necessarily true. There exist non-prime numbers that are odd, such as 9, 15, and 21. Therefore, the fact that a number is not prime does not guarantee that it is not odd.

To establish the conclusion that a number is not odd based on it not being prime, additional information or reasoning is needed. Hence, the argument is invalid.

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Divide the numerator by the denominator.

When a letter like a, b, x or y pops up in a mathematical expression, it's called a variable, but really it's a placeholder that represents a number of unknown value. You can perform all the same mathematical operations on a variable that you'd perform on a known number. That fact comes in handy if the variable pops up in a fraction, where you'll need tools like multiplication, division and canceling of common factors to simplify the fraction.

Combine like terms in both the numerator and the denominator of the fraction. When you first start handling fractions with variable, this may be done for you. But later on, you might encounter "messier" fractions like the following:

(a + a) / (2_a_ - a)

When you combine like terms, you end up with a much more civilized fraction:

2_a_/a

Factor the variable out of both numerator and denominator of the fraction if you can. If the variable is a factor in both places, you can then cancel it. Consider the simplified fraction just given:

2_a_/a

As a quick aside, any time you see a variable by itself, it's understood to have a coefficient of 1. So this could also be written as:

2_a_/1_a_

Which makes it more obvious that when you cancel the common factor a from both the numerator and denominator of the fraction, you're left with the following:

2/1

Which, in turn, simplifies to the whole number 2.

What if you have a fraction like 3_a_/2? You can't factor a out of both the numerator and the denominator of the fraction, but because it's in the numerator, you can treat it as a whole number. To make sense of this, first write the fraction out thusly:

3_a_/2(1)

You can insert the 1 in the denominator thanks to the multiplicative identity property, which states that when you multiply any number by 1, the result will be the original number you started with. So you haven't changed the value of the fraction at all; you've just written it a little differently.

Next, separate the factors thusly:

a/1 × 3/2

And simplify a/1 to a. This gives you:

a × 3/2

Which can be simply written as the mixed number:

a (3/2)

What if you end up with a messy fraction like the following?

(b2 - 9) / (b + 3)

At first glance there's no easy way to factor b out of both numerator and denominator. Yes, b is present in both places, but you'd have to factor it out of the entire term in both places, which would give you the even messier b(b - 9/b) in the numerator and b(1 + 3/b) in the denominator. That's a dead end.

But if you've been paying attention in your other lessons, you might notice that the numerator can actually be rewritten as (b2 - 32), also known as "the difference of squares," because you're subtracting one squared number from another squared number. And there's a special formula that you can memorize to factor the difference of squares. Using that formula, you can rewrite the numerator as follows:

(b - 3)(b + 3)

Now, take a look at that in the context of the entire fraction:

(b - 3)(b + 3) / (b + 3)

Thanks to that standard formula you either memorized or looked up, you now have the identical factor (b + 3) in both the numerator and the denominator of your fraction. Once you cancel that factor, you're left with the following fraction:

(b - 3) / 1

Which simplifies to just:

(b - 3)

Answer:

Answer is 1

Step-by-step explanation:

Answer:     40

Step-by-step explanation:

5/3    24/?

    divided by 8 =24 divided by 8 =3

                     5 x 8   =40  

Hope this helps :)

Answer:

40 girls

Step-by-step explanation:

Answer: 144 dresses in 1440 minutes.

Step-by-step explanation:

Divide 144 and 12 you get 12. So you multiply 12 and 120 and you get 1440.

The rate is 120min/12dresses. Let's simplify it.

12/120 = 10min/1dress (or just 10)

Lets use this rate for 144 dresses

10 x 144 = 1140

It will take 1440 minutes to sell 144 dresses.

Answer:

g = 6

Step-by-step explanation:

Over 7 years, there would be 49% increase, so 600 (1.49) = 894

$894

Answer:

x = -5

Step-by-step explanation:

Answer:

Hey there!

It can be used because -3-(-6) is equal to -3+6, which is 3.

Let me know if this helps :)

A beverage company has decided to manufacture a new juice with mixed flavors, which is prepared from orange and pineapple. The vitamin contents are 5% of vitamin A and 2% of vitamin C in the orange flavor, while pineapple flavor contains 8% of vitamin C.

The company's policies are to add at least 20 L of orange flavor to the new juice and limit the vitamin C content to no more than 5%. The cost of orange flavor is $1000 per liter, while the cost of pineapple flavor is $400 per liter.To satisfy a minimum demand of 100 L of juice, we must determine the optimal amount of each flavor to use.A) A linear programming model is needed for the company to solve this problem (Minimize production cost of the new juice)B) Use a graphic solution for this problem.The objective function of the optimization problem can be given as:min C = 1000x + 400yThe constraints that the company has are,20x + 0y ≥ 100x + y ≤ 5x ≥ 0 and y ≥ 0The feasible region can be identified by graphing the inequality constraints on a graph paper. Using a graphical method, we can find the feasible region, and by finding the intersection points, we can determine the optimal solution.The graph is shown below; The optimal solution is achieved by 20L of orange flavor and 80L of pineapple flavor, as indicated by the intersection point of the lines. The optimal cost of producing 100 L of juice would be; C = 1000(20) + 400(80) = $36,000.C) If the company decides that the juice should have a vitamin C content of no more than 7%, it would alter the problem's constraints. The new constraint would be:x + y ≤ 7Dividing the equation by 100, we obtain;x/100 + y/100 ≤ 0.07The objective function and the additional constraint are combined to create a new linear programming model, which is solved graphically as follows: The feasible region changes as a result of the addition of the new constraint, and the optimal solution is now achieved by 20L of orange flavor and 60L of pineapple flavor. The optimal cost of producing 100 L of juice is $28,000.

In conclusion, the optimal amount of each flavor that should be used to satisfy a minimum demand of 100 L of juice is 20L of orange flavor and 80L of pineapple flavor with a cost of $36,000. If the company decides that the juice should have a vitamin C content of no more than 7%, the optimal amount of each flavor is 20L of orange flavor and 60L of pineapple flavor, with a cost of $28,000.

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