Trapezoid WXYZ is isosceles. Angle WZY measures (8x – 3) and angle XYZ measures (7x + 2). Find the measure of angle WZY.

By using the concept of permutation, it can be calculated that

Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]

                                                                                          = [tex]\frac{2}{7}[/tex]

What is permutation?

Permutation is the arrangement technique that determines how many possible arrangement that can be made in a set where the order of arrangement matters.

Here, concept of permutation is used

Number of 7 number combinations that can be formed using the number 3795523 = [tex]\frac{7!}{2! \times 2!}[/tex] = 1260

The two 3's are always together

Number of 7 digit numbers formed = [tex]\frac{6!}{2!}[/tex] = 360

Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]

                                                                                          = [tex]\frac{2}{7}[/tex]

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The total miles of the trip are 521.68 miles.

Addition in maths, a process of combining two or more numbers.

Given that, Rosie drives 317.88 miles before lunch and then  [tex]203\frac{4}{5}[/tex] miles before break,

Total miles = 317.88 +  [tex]203\frac{4}{5}[/tex] miles = 521.68 miles

Hence, The total miles of the trip are 521.68 miles.

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Answer:

Step-by-step explanation: 10.75

The value of m and n from the obtained probability is equal to 3 and 14 respectively.

As given in the question,

Nine tiles numbered 1, 2, .....9

Number of odd numbered tiles are 1,3,5,7,9 = 5

Number of even numbered tiles are 2,4,6,8 = 4

Number of players =3

Possibility to choose 3 tiles by first player out of 9 tiles = ⁹C₃

                                                                                            = 84 ways

Possibility to choose 3 tiles by second player out of 6 tiles = ⁶C₃

                                                                                                 =20 ways

Possibility to choose 3 tiles by third player out of 3 tiles = ³C₃

                                                                                             = 1 way

Total number of ways = 84× 20 ×1

                                     = 1680

To have a sum of 3 tiles is odd number at least one tile should be odd.

Chances of first player all the 3 tiles are 0dd out of 5 = ⁵C₃

Next two players must 2 even tiles and 1 odd tile.= ²C₁

One player can be selected in ³C₁ way

Remaining 4 even tiles distributed equally = (4!)(2!)/ (2!)² ( 2!)

Number of favourable outcomes =  ⁵C₃ × ²C₁ ׳C₁  × (4!)(2!)/ (2!)² ( 2!)

                                                       = 10 × 2 × 3 × 6

                                                       = 360

Probability (m/n) =  360 /1680

                            = 3/14

m = 3 and n = 14.

Therefore, from the probability that all three players obtain an odd sum is m/n , the value m = 3 and n = 14.

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Answer:2.25 gallons

Step-by-step explanation:

By using the concept of probability, it can be calculated that

Probability that the flight arrives on time =  [tex]\frac{399}{500}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Total number of flights = 1000

Number of flights arriving on time = 798

Probability that the flight arrives on time = [tex]\frac{798}{1000}[/tex]

                                                                   = [tex]\frac{399}{500}[/tex]

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Because it diverges using a comparison test, the correct answer is an option (E).

The comparison test, also known as the direct comparison test to distinguish it from other closely related tests, offers a method for determining whether an infinite series or an improper integral will converge or diverge.

The test is effective in both situations by contrasting the given series or integral with one whose convergence characteristics are known.

So, refer to the image attached below.

According to the image which has the reason for convergence and divergence, we know that the correct answer would be option (E).

The reason is the comparison test.

Therefore, because it diverges using a comparison test, the correct answer is an option (E).

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The output firm will get maximum profits when the quantity is 4 units and the company will charge a price of $15 for maximum profit.

The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3

Demand for the product that the firm produces is given by P = 27- 3Q.

The total cost is calculated by adding fixed cost and variable cost.

TC = FC + VC

Average total cost = total cost / quantity

Quantity  price (37 - 3Q) fixed cost variable cost  total cost average cost

1                27 - 3(1) = 24      24            3 (1)                 27             27

2               27 - 3(2) = 21      24            3(2) = 6           30            15

3                27 - 3(3) = 18      24            3(3) = 9           33            11

4               27 - 3(4) = 15       24           3(4) = 12          36             9

5               27 - 3(5) = 12       24           3(5) = 15          39            7.8

Upon analysing the table we can say that

B) the number of output units is 4

C) Maximum profit is when price is $15

Therefore, the maximum profit is when the output units is 4 and the company will charge a price of $15 for maximum profit.

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The answer to following questions are as follows:-A)experiment

B)meaning “statistically non significant” C)explained below

A wave is a dynamic disturbance that propagates over one or more quantities in the domains of physics, mathematics, and allied sciences. When waves are periodic, those parameters repeatedly oscillate around an equilibrium value at a certain frequency.

The answers are: a) It is an experiment since some claims are not supported by evidence.

b) When the analysis reveals that there are substantial variations between the observed, "not statistically significant" refers to "statistically non significant." And we are unable to analyse any of the statistics' results.

c) The fact that Motorola, a cell phone company, funded this research reveals to us that this claim is untrue because Motorola conducts this research to boost their sales.

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The year becomes 1993, when the newspaper circulation is closest to the average circulation.

Part a:

The function is n(x)=0.00792x^3−0.37x^2+3.557x+51.588

The formula for the average of the function is 1b−a∫baf(x)dx

The year 1986 corresponds to 6 and 2000 corresponds to 20 as x is the number of years since 1980.

Obtain the average:

1b−a∫baf(x)dx==≈1/20−6∫20-6[0.00792x^3−0.37x^2+3.557x+51.588]dx

1/14[0.00792x^4/4−0.37x^3/3+3.557x^2/2+51.588x]20-6

51.70094

Therefore, the average newspaper circulation from 1986 to 2000 was 51.70094.

Part b:

Now, the equation is obtained as

0.00792x^3−0.37x^2+3.557x+51.588=51.70094

0.00792x^3−0.37x^2+3.557x−0.11294=0

Obtain the value of x using an online graphing calculator as follows:

Thus, the value of x becomes 13.481

Hence, 1993 is the year of the closest average circulation

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Answer:

R= 2sqrt(13) = about 7.2

Step-by-step explanation:

D^2= 12^2 + 8^2

 = 144+64=208

D=4sqrt(13)

R= D/2= 2sqrt(13)

Given that the dividend is 15a²-a-28 and the divisor is 3a+4, the quotient will be 5a-7 and the remainder will be 0.

A multi-term algebraic statement is referred to as a polynomial. It contains exponents, coefficients, variables, constants, and arithmetic operators. It uses a polynomial long division algorithm to divide the polynomials. It is the long division technique in a more generalized form. In this method, a polynomial is divided by other polynomials of the same degree or lower. Synthetic division method is a simple and quick technique that is occasionally employed as well.

Here,

dividend=15a²-a-28

divisor=3a+4

remainder=0

15a²-a-28=(3a+4)(5a-7)

quotient=5a-7

The quotient will be 5a-7 and remainder will be 0 as dividend is 15a²-a-28 and divisor is 3a+4.

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Answer: I think it's 2/5, it is closest to the answer I came up with

Answer: 270 I think

Step-by-step explanation:

try it you can get this right

Answer: 70%

Step-by-step explanation:

The resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]

A term's multiplicative history can be determined by an index, which is a discrete number. Indexes is the plural of index.

The exponentiation operator is the caret (). It is important to distinguish the exponent operator from the base-10 exponent sign. In a numeric literal, a base-10 exponent sign (scientific notation) can be represented by either an uppercase "E" or a lowercase "e."

[tex](125x^{7/3})^{-1/3}[/tex]

Using the indices law that states;

[tex](a^n)^m = a^{mn}[/tex]

Given,

[tex](125x^{7/3})^{-1/3}[/tex]

Since, [tex](125x^{7/3})^{-1/3}[/tex]= [tex][((5x)^3)^{7/3}]^{-1/3}[/tex]

= [tex][(5x)^7]^{-1/3}[/tex]

= [tex]5x^{-7/3}[/tex]

= [tex]\frac{1}{5x^{7/3}}[/tex]

Hence the resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]

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The first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.

Given, A Tomato juice 46 oz. Cans cost $2. 53

B Tomato juice 6-pack of 10 oz. Cans costs $4. 50

we have to find the best buy between the given two.

In first case,

46 cans cost $2.53

46 cans = $2.53

1 can = 2.53/46

1 can costs $0.055

In second case,

60 cans cost $4.50

60 cans = $4.50

1 can = 4.50/60

1 can costs $0.075

So, it is clear that first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.

Hence, the first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.

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Answer:

y = 2x - 9

Step-by-step explanation:

The slope is the change in y over the change in x.  From the 2 points, the y's are 7 and 5.  The x's are 8 and 7.

[tex]\frac{7-5}{8-7}[/tex] = [tex]\frac{2}{1}[/tex] = 2

2 is the slope.

Now we need to find the y intercept (b).  Use one of the points on the line.  It does not matter which one.  I am going to use (8,7)

slope (m) = 2

x = 8

y = 7

y=mx + b

7 = 2(8) + b  Plug in what we know and solve for b

7 = 16 + b  Subtract 16 from both sides

-9 = b

The y intercept (b) is -9

y = mx + b

y = 2x -9

We want to finish each statement by analyzing the graph provided.

The function's y-intercept is y =2.

y = 3x+2 is the equation.

The line connects (0, 2) and (2, 6).

The earliest known attempt to the concept of function may be traced back to the works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity. The position of a planet, for example, is a function of time.

So, first, we need to find the y-intercept. We know that the y-intercept is the y-value at which the function intersects the y-axis, and we can see from the graph that the y-intercept is y = 2.

Then we'd like to see the line's equation.

Remember that y = ax + b is a generic line.

Where a denotes the slope and b the y-intercept, we may deduce:

y = ax + 2

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a=(y₂-y₁)/(x₂-x₁)

Given that the line passes through (0, 2) and (-2/3, 0), the slope is as follows:

a=(-2/3)/(-2)

a=1/3

The equation of the line is:

y =3x+2

And using that equation, we can show that the line does indeed pass through the points (0, 2) and (2, 6)

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Answer:

  4/39

Step-by-step explanation:

You want to know the fraction of 39 students represented by the 4 that have blue eyes.

The fraction is the ratio of the part of interest to the whole.

  (students with blue eyes)/(total number of students) = 4/39

If a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.

Two or more expressions with an Equal sign is called as Equation.

A cyclist rides at an average speed of 18 miles per hour.

We have to find the number of miles she ride in seven hours

Assume x be the number of miles she ride

Let us form a proportional equation

18/1 = x/7

Apply cross multiplication

18×7=x

126=x

Hence, if a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.

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Answer: -10

Step-by-step explanation:

Substitute the numbers in for the variables.

np + n = (2)(-6) + 2

-12 + 2

-10

Answer: 84

Step-by-step explanation: so 7:8 increased by some number is 180 degrees. add 7 and 8 to get 15. 180/15 is 12 so x = 12 7*12 is 84.

The true proportion of adults is in the interval 0.4026< P< 0.4594.

Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.

Data provided:

selected (x) = 329

Total(n) = 763

Sample proportion (p') = x/n

                                       = 329/ 763

                                       = 0.431

Critical z-value = 1.59

margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]

                             = 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]

                             = 1.59 × 0.0179

                             = 0.0284

88% confidence interval is:

(p' ± E) = ( 0.431 ± 0.0284)

          = 0.4594 and 0.4026

Therefore the estimate is 0.4026< P< 0.4594.

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The equations represent the given situation is:

2x - y = -6

3x - y = -5

where, x is the smaller number and y is the larger number.

Let the smaller number be x.

We have been given a number, y, is equal to twice the sum of a smaller number and 3

So, we get an equation,

y = 2(x + 3)

y = 2x + 6                        

2x - y = -6

The larger number is also equal to 5 more than 3 times the smaller number.

So, we get an equation,

y = 5 + 3x                        

3x - y = -5

Therefore, the equations represent the situation:

2x - y = -6

3x - y = -5

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Answer

$1,580.54

1215.80×(1+0.3)= 1580.54

Answer: 315 children and 15 adults

Step-by-step explanation:

15 x 21 = 315
315 + 15 = 330
c = 315
a = 15