Homework 2: Special Right Triangles Questions 16-24


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Substituting the given variable cost per book for Method 1 (which is not specified), we can calculate the value of 'x' that makes the costs equal for the two methods.

Let's assume the number of books produced is denoted by 'x'. We need to find the value of 'x' for which the costs from the two methods are the same.

For the first method, the total cost is the sum of the one-time fixed cost and the variable cost per book:

Total cost for Method 1 = 44,907 + (variable cost per book) * x

For the second method, the total cost is the sum of the one-time fixed cost and the variable cost per book:

Total cost for Method 2 = 22,907 + (23.25 * x)

To find the number of books produced when the costs from the two methods are equal, we set the total costs equal to each other and solve for 'x':

44,907 + (variable cost per book) * x = 22,907 + (23.25 * x)

Subtracting (23.25 * x) from both sides and rearranging the equation:

21,000 = 23.25 * x - (variable cost per book) * x

21,000 = x * (23.25 - (variable cost per book))

Dividing both sides by (23.25 - (variable cost per book)):

x = 21,000 / (23.25 - (variable cost per book))

Substituting the given variable cost per book for Method 1 (which is not specified), we can calculate the value of 'x' that makes the costs equal for the two methods.

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The Wendy spent $27.78 on a silver necklace online.To calculate the total cost of the silver necklace, we need to add the cost of the necklace to the shipping and handling charges.

The cost of the necklace is given as $23.15.

Wendy bought a silver necklace online. It cost $23.15 plus 20% shipping and handling.

What was the total cost?When purchasing a silver necklace online, Wendy spent $23.15, but she had to pay for shipping and handling as well, which cost 20% of the total price of the item.

To find the total cost of the necklace, follow these steps:

1. Determine the cost of shipping and handling: $23.15 × 0.20 = $4.632

Add the cost of shipping and handling to the cost of the necklace:$23.15 + $4.63 = $27.78

The total cost of the necklace is $27.78.

It's important to consider the additional charges such as shipping and handling when calculating the total cost of an online purchase to have an accurate understanding of the amount spent.

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Answer:

x = 4

Step-by-step explanation:

since the triangle is equilateral then the vertex angles are congruent, each 60°

using the sine ratio in the right triangle with x as its hypotenuse and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{\sqrt{12} }{x}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

x × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{12}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

x = [tex]\frac{2\sqrt{12} }{\sqrt{3} }[/tex] = 2 × [tex]\sqrt{\frac{12}{3} }[/tex] = 2 × [tex]\sqrt{4}[/tex] = 2 × 2 = 4

Answer:

Both students scored in the top 10% of their classes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Top 10% = Above the 100 - 10 = 90th percentile.

The 90th percentile of scores is X when Z has a pvalue of 0.9, that is, Z = 1.28.

So, the student who had a z-score above 1.28 scored in the 90th percentile of their class.

In student A's class the mean was 78 and the standard deviation of 5. He scored 87.

We have that [tex]\mu = 78, \sigma = 5, X = 87[/tex]

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{87 - 78}{5}[/tex]

[tex]Z = 1.8[/tex]

1.8 > 1.28, so student A scored in the top 10% of his/her class.

Student B's class the mean was 76 with a standard deviation of 4. Scored 87.

We have that [tex]\mu = 76, \sigma = 4, X = 87[/tex]

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{87 - 76}{4}[/tex]

[tex]Z = 2.75[/tex]

2.75 > 1.28, so student B also scored in the top 10% of his/her class.

Both students scored in the top 10% of their classes.

Answer:

D. 11

Step-by-step explanation:

Midsegment theorem:

The length of the midsegment of a triangle is half the length of it's third side.

In this question:

Third side: 3x - 5

Midsegment: 14m

So

[tex]\frac{3x - 5}{2} = 14[/tex]

[tex]3x - 5 = 28[/tex]

[tex]3x = 33[/tex]

[tex]x = \frac{33}{3}[/tex]

[tex]x = 11[/tex]

The correct answer is given by option D.

Answer:

139284 238

Step-by-step explanation:

Answer:478.85 in2

Step-by-step explanation:

Just divide LOL

Answer:

6. (a-4)(a+9)

7. (3p+4)(p-2)

8. Will explain below.

9. (5b+4)(5b-4)

Step-by-step explanation:

HELLOOO IM BACK

6. -4*9 = -36 (the variable), 9-4 = 5 (a) , so a^2 +5a - 36 is fulfilled.

7. 4*-2 = -8, 4-2 = 2, so 3p^2 - 2p - 8 is fulfilled.

9. 25b^2 = (5b)^2

16 = 4^2

Using the difference of squares formula, a^2-b^2= (a+b)(a-b)

Answer:

x=48°

Step-by-step explanation:

We two lines cross over each other, making four angles, the angles opposite each other are equal. They're called vertically opposite angles.

(a) √2 · √8. The simplified surd expression is 4.

(b) √80. The simplified surd expression is  4√5.

(c) √5/√20. The simplified surd expression is  1/2.

(d) √20. The simplified surd expression is  2√5.

The given surd expression is simplified as follows;

(a) √2 · √8

we can simplify it as;

√2 · √8 = √(2 x 8) = √16 = 4

(b) √80

we can simplify it as;

√80 = √ (16 x 5) = √16  x √5 = 4√5

(c) √5/√20

we can simplify it as;

√5/√20  x  √20 / √20

= (√5  x √20 ) /(20)

= √100 / 20

= 10/20

= 1/2

(d) √20

we can simplify it as;

√20 = √4  x √5 = 2√5

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The percentage of debit shoppers has increased.

21% (2006) < 40% (2009)

In 2006, the percentage of debit shoppers is 21%.

In 2009, the percentage of debit shoppers is 40%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

In 2006:

A sample of 200 in-store shoppers showed that 42 paid by debit card.

The percentage of debit shoppers in 2006.

= 42/200 x 100

= 42/2

= 21%

In 2009:

A sample of the same size showed that 80 were paid by debit card.

The percentage of debit shoppers in 2009.

= 80/200 x 100

= 40%

Thus,

The percentage of debit shoppers has increased.

21% (2006) < 40% (2009)

In 2006, the percentage of debit shoppers is 21%.

In 2009, the percentage of debit shoppers is 40%.

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Answer:

4/x = [tex]\frac{\pi }{6}[/tex], 5 [tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

Sorry if I am wrong

The average rate of change of the function in the given interval [0, π] is [tex]\dfrac{2}{\pi }[/tex].

The average Rate of Change of the function f(x) can be calculated as;

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]

The given function is f(x) = 2sin(1/2)x on the interval [0, π]

Here a = 0

b = π

f(a) = 2sin(1/2)a

f(0) = 0

f(b) = 2sin(1/2)π = 2

Step 2: Find Average

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\f(x) = \dfrac{2- 0}{\pi }\\\\f(x) = \dfrac{2}{\pi }\\[/tex]

Therefore, the average rate of change of the function in the given interval [0, π] is [tex]\dfrac{2}{\pi }[/tex].

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Answer:

Volume uses cubic ___  

A mile or kilometer is to big

So an cubic centimeter is about right

C

Using the context surrounding the word trough in line 9 of "Concrete Mixers," explain what a trough looks like and what it does on a concrete mixer. .

sorry I can't delete it this not answer your question

Answer:

28. 0.2461 or 24.61%.

29. 0.00058275 or 0.058275%.

Step-by-step explanation:

Question 28:

we can use the binomial probability formula to calculate the probability:

[tex]\boxed{\bold{P(X = k) = (nCk) * p^k * (1 - p)^(n - k)}}[/tex]

Where:

In this case, we have n = 9 babies, and each baby has a 50% chance of being a girl (p = 0.5). We want to find the probability that exactly 4 of them are girls (k = 4).

Using the formula, we can calculate the probability as follows:

[tex]\bold{P(X = 4) = (9C4) * (0.5)^4 * (1 - 0.5)^(9 - 4)}[/tex]

Calculating the values:

Now, we can substitute these values into the formula:

P(X = 4) = 126 * 0.0625 * 0.03125 = 0.2461 or 24.61%

Therefore, the probability that exactly 4 out of 9 babies are girls is approximately 0.2461 or 24.61%.

Question 29:

We need to calculate the number of possible outcomes to calculate this probability, where the gambler correctly predicts the top 3 finishers in order and divides it by the total number of possible outcomes.

The total number of possible outcomes is the number of permutations of 13 horses taken 3 at a time.

This can be calculated as:

[tex]13P3 = \frac{13! }{(13 - 3)! }= \frac{13! }{ 10! }=\frac{13*12*11*10! }{ 10! }= 13 * 12 * 11 = 1,716[/tex]

Now,

To calculate the number of favorable outcomes where the gambler predicts the top 3 finishers correctly, we need to consider that there is only one correct order for the horses to finish.

Therefore, there is only one favorable outcome.

The probability of the gambler winning his bet is given by:

[tex]\boxed{\bold{P\:(winning) = \frac{Number\: of \:favorable\: outcomes }{ Total \:number \:of \:outcomes}}}[/tex]

[tex]P(winning) = \frac{1 }{1,716}=0,00058275 \: or\:0.058275%[/tex]

Therefore, the probability that the gambler will win his bet is approximately 0.00058275 or 0.058275%.

Answer:

28)  0.246 = 24.6%

29)  1/286 = 0.350%

Step-by-step explanation:

We can model the given scenario as a binomial distribution.

[tex]X \sim \text{B}(n,p)[/tex]

where:

Given the probability that a baby is born a girl is 0.5, and the number of babies is 9:

[tex]\boxed{X \sim \text{B}(9,0.5)}[/tex]

where the random variable X represents the number of babies who are girls.

To find the probability that at exactly 4 babies are girls, we need to find P(X = 4).

To do this, we can use the binomial distribution formula:

[tex]\boxed{\displaystyle \text{P}(X=x)=\binom{n}{x} \cdot p^x \cdot (1-p)^{n-x}}[/tex]

Substitute the values of n = 9, p = 0.5 and x = 4 into the formula:

[tex]\begin{aligned}\displaystyle \text{P}(X=4)&=\binom{9}{4} \cdot 0.5^4 \cdot (1-0.5)^{9-4}\\\\&=\dfrac{9!}{4!\:(9-4)!} \cdot 0.5^4 \cdot 0.5^{5}\\\\&=126 \cdot 0.0625 \cdot 0.03125\\\\& = 0.24609375\end{aligned}[/tex]

Therefore, the probability that 4 babies from a sample of 9 babies are girls is 0.246 (3 s.f.) or 24.6%.

We can also use the binomial probability density function of a calculator to calculate P(X = 4).

Inputting the values of n = 9, p = 0.5 and x = 4 into the binomial pdf:

[tex]\text{P}(X=4)=0.24609375[/tex]

Therefore, this confirms that the probability that 4 babies from a sample of 9 babies are girls is 0.246 (3 s.f.) or 24.6%.

[tex]\hrulefill[/tex]

To calculate the probability that the gambler will win his bet, we need to determine the number of favorable outcomes (winning combinations) and the total number of possible outcomes.

The gambler wins if he picks the top three horses in any order. There are 6 ways for the three winners to be arranged in the top three.

There are a total of 13 horses in the race.

Therefore, the total number of possible outcomes is:

[tex]13 \times 12 \times 11 = 1716[/tex]

Therefore, the probability that the gambler will win his bet is:

[tex]\begin{aligned} \sf Probability &=\sf \dfrac{Favorable \;outcomes}{Total\;outcomes}\\\\&=\dfrac{6}{1716}\\\\&=\dfrac{1}{286}\\\\ & \approx0.350\%\; \sf (3\;d.p.)\end{aligned}[/tex]

The quadratic equation from the given root is 4x² - 41x + 45 = 0

From the question, we have the following parameters that can be used in our computation:

Roots = 5/x and 4

The equation of the function can be calculated as

(x - root) * (x - root) = 0

using the above as a guide, we have the following:

(x - 5/4) * (x - 9) = 0

When expanded, we have

(4x - 5)(x - 9)/4 = 0

This gives

4x² - 5x - 36x + 45 = 4 * 0

So, we have

4x² - 41x + 45 = 0

Hence, the quadratic equation from the given root is 4x² - 41x + 45 = 0

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The simplified exponential function is determined as x⁴.

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

To simplify an exponential function, we will apply the rules of exponent as shown below;

The given exponential function;

= (∛ x² )⁶

The given expression is simplified as follows;

= [tex](x^2) ^{\frac{1}{3} \times 6}[/tex]

= ( x² )²

= x⁴

Thus, the simplified exponential function is determined by applying the rules of multiplication of powers.

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Printer A has the better rate of cost per page because the approximate rate of Printer A, $0.24 per page, is greater than the approximate rate of Printer B, $0.23 per page.

Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Printer A prints 100 pages for $23.99. The rate is:

[tex]\sf = \dfrac{\$23.99}{100}[/tex]

[tex]\sf = 0.2399\thickapprox\$0.24 \ per \ page[/tex]

Printer B prints 275 sheets for $63.99. The rate is:

[tex]\sf = \dfrac{\$63.99}{275}[/tex]

[tex]\sf = 0.2327\thickapprox\$0.23 \ per \ page[/tex]

Therefore, based on the above calculations, we can see that Printer A has the better rate of cost per page because the approximate rate of Printer A, $0.24 per page, is greater than the approximate rate of Printer B, $0.23 per page.

So option (A) is correct.

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Answer:

0.79

Step-by-step explanation:

Answer:

equal

alternate exterior angles

Step-by-step explanation:

The measure of given angles are equal to each other because they are alternate exterior angles,

Answer:

3 for vowles and two for number

Step-by-step explanation:

I also need help on this one just need points

Answer:

15, 14, 13, 12, 11 and so on

Step-by-step explanation:

Answer:

2/5 or 0.4

Step-by-step explanation:

convert -14/5 / (-7)

divide 14/5 / 7  ( two negatives equal a positive)

equals 2/5 or 0.4 in decimal

The value of angle k is determined as  60⁰.

The value of angle m is determined as 120⁰.

The measure of angle m and k is calculated by applying the following theorem as follows;

The value of angle k is calculated as;

60 + 2k = 180 (opposite angles of a cyclic quadrilateral are supplementary)

60 + 2k = 180

2k = 180 - 60

2k = 120

k = 120/2

k = 60⁰

The value of angle m is calculated as;

m + 60 = 180  (opposite angles of a cyclic quadrilateral are supplementary)

m = 180 - 60

m = 120⁰

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Answer:

64 m²

Step-by-step explanation:

Area of the trapezoid = ½(a + b)h

Where,

a = 6 m

b = 10 m

h = 8 m

Plug in the values

Area = ½(6 + 10)*8

Area = ½(16)*8

Area = 8*8

Area = 64 m²

Answer:

42°

Step-by-step explanation:

According to Exterior Angle Theorem,

an exterior angle of a ∆ is equal to the sum of the opposite interior angles.

So,

h+96°=138°

h=138°-96°

h=42°

Answer:

40 square units

Step-by-step explanation:

This is a rhombus, so you multiply the two diagonals and divide by 2.

8x10÷2=40

Answer:

For [tex]x = -2[/tex]

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

[tex]f(x) = x^2 - 2x[/tex]

[tex]g(x) = 6x + 4[/tex]

[tex]f(x) + g(x) = (f+g)(x)  = x^2 - 2x + 6x + 4 = x^2 + 4x + 4[/tex]

Which is a value of x does (f+g)(x) =0

[tex]x^2 + 4x + 4[/tex]

Quadratic equation with [tex]a = 1, b = 4, c = 4[/tex]

So

[tex]\Delta = 4^{2} - 4*1*4 = 0[/tex]

[tex]x_{1} = \frac{-4 + \sqrt{0}}{2} = -2[/tex]

[tex]x_{2} = \frac{-4 - \sqrt{0}}{2} = -2[/tex]

For [tex]x = -2[/tex]

Answer:

They are all correct.

Step-by-step explanation:

1.

1/2(b)(h)

1/2(4)(6)

1/2(24)

12

2. l x w

7 x 5

35

3. (b)(h)

(8)(4)

32

134 degrees is equivalent to the measure of arc RS

In order to determine the measure of the arc RS, we will use the theorem below:

The measure of the angle at the vertex is half that of its intercepted arc. Based on the theorem, we can set up the equation:

arcRS = 2m<Q
arcRS = 2(67)
arcRS = 134 degrees

Hence the measure of the arc RS from the given circle is equivalent to 134 degrees

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