Part III: The Olympic triangle (22 points)
Draw a sketch of the short course triangle below, labeling the points A, B, and C. Don’t draw it on your master map yet! (3 points)

Answer:

Option 4

Step-by-step explanation:

Both the quadrilaterals are similar,

ABCD ~ WXYZ

Therefore, ratio of the corresponding sides will be constant in other words ratio of the corresponding sides will be common.

Scale factor = \(\frac{AD}{WZ}\)

                    = \(\frac{15}{6}\)

                    = \(\frac{5}{2}\)

Therefore, option (4) will be the correct option.

answer:

speed= 72 km - per • hour

Answer:

Speed of car = 72 km per hour

Answer:

LB=7701 3

degrees

Answer:

26, 40  and 6 is not a possible triangle

Step-by-step explanation:

Answer:

I'm pretty sure it should be 34

Step-by-step explanation:

4(x + 6) - 5y

4(5 + 6) - 5(2)

20 + 24 - 10

44 - 10

34

4(5 + 6) - 5(2)

4(11) -10

44 - 10 =

answer; 34

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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Answer: It’s 18+0.15x divided by x so it’s B

Step-by-step explanation:

The expressions that represent average cost A(x) are B) A(x) = (18 + 0.15x)/x

and F)  A(x) = 18/x + 0.15.

When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.

To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.

Given, A local office supply store charges $18 to set up their business card printing machine with the design and $0.15 in materials per business card to print.

The expression that represents average cost A(x) = (set up cost + cost per business card×no of cards) divided by no. of cards.

A(x) = (18 + 0.15x)/x.

Also A(x) = 18/x + 0.15.

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In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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The perimeter of the rectangle WXYZ that has vertices at W(−6, 1) , X(−1, 6) , Y(2, 3) , and Z(−3, −2) is 22.62 units.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

We have a rectangle WXYZ has vertices at W(−6, 1) , X(−1, 6) , Y(2, 3) , and Z(−3, −2) .

Using the distance formula:

\(\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Calculate the distance WX between (-6,1) and (-1,6)

WX = 7.07

The distance XY between (-1,6) and (2,3)

XY = 4.24

The distance YZ between (2,3) and (-3,-2)

YZ = 7.0

The distance ZW between (-6,1) and (-3,-2)

ZW = 4.24

Perimeter of the rectangle =   7.07+ 4.24 + 7.07 + 4.24 = 22.62 units

Thus, the perimeter of the rectangle WXYZ that has vertices at W(−6, 1) , X(−1, 6) , Y(2, 3) , and Z(−3, −2) is 22.62 units.

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If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.

To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.

First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:

9 feet = 9 * 12 = 108 inches

0 1/2 inch = 0.5 inch

Total height = 108 + 0.5 = 108.5 inches

Next, we divide the total height by the number of risers (14) to find the height of each riser:

Height of each riser = Total height / Number of risers

Height of each riser = 108.5 inches / 14

Using a calculator, we can compute:

Height of each riser ≈ 7.75 inches

Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.

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Answer: I have to make one up In geometry, a branch of mathematics, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°).

Step-by-step explanation:

The maximum temperature during summer in that year was 34°C.

It's not possible for the maximum temperature in Gulmarg, Kashmir to rise by 44°C during the summer.

A temperature rise of that magnitude would be extremely unusual and potentially dangerous.

However, assuming that the question meant to ask about the difference between the minimum temperature in January and the maximum temperature in summer, we can proceed with the calculation.

The minimum temperature in January was -10°C, and if we add 44°C to it, we get:

-10°C + 44°C = 34°C

Therefore, the maximum temperature during summer in that year was 34°C.

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Answer:

8 footballs

18 basketballs

36 baseballs

24 softballs

Step-by-step explanation:

Let f = footballs

f = 8

Let b = basketballs

b = 2+2f = 2 +2(8) = 2 +16 = 18

Let B = baseballs

B = 5f -4 = 5(8) -4 = 40-4 = 36

Let s = softballs

s = 6+1/2B = 6+1/2(36) = 6+18 = 24

The total is 86

f+b+B +s = 86

8+18+36+24 = 86

86=86

There are 8 footballs.

Two more than twice the number of footballs are basketballs:

2f + 2 = b

f = number of footballs

b = number of basketballs

In the first statement, there are 8 footballs. So, f = 8

2(8) + 2 = b

16 + 2 = b

18 = b

Therefore, there are 18 basketballs.

Four less than 5 times the number of footballs are baseballs:

5f - 4 = a

f = number of footballs

a = number of baseballs

In the first statement, there are 8 footballs. So, f = 8

5(8) - 4 = a

40 - 4 = a

36 = a

Therefore, there are 36 baseballs.

Six more than half of the baseballs are softballs:

a/2 + 6 = s

a = number of baseballs

s = number of softballs

In the third statement, there are 36 baseballs. So, a = 36

(36)/2 + 6 = s

18 + 6 = s

24 = s

Therefore, there are 24 softballs.

Best of Luck!

Answer:

Step-by-step explanation:

Answer:

Mean: 94.5.

Median: 99.5

Standard deviation: 33.1

We can tell the owner that the applicants don't have a score significantly below from 100.

Step-by-step explanation:

First, we analize the sample and calculate the statistics (mean, median and standard deviation).

Mean of the sample:

\(M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(95+105+120+81+90+115+99+100+130+10)\\\\\\M=\dfrac{945}{10}\\\\\\M=94.5\\\\\\\)

The median, as the sample size is an even number, can be calculated as the average between the fifth and sixth value, sort by value:

\(\text{Median}=\dfrac{99+100}{2}=99.5\)

The standard deviation is:

\(s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((95-94.5)^2+(105-94.5)^2+(120-94.5)^2+. . . +(10-94.5)^2)}\\\\\\s=\sqrt{\dfrac{9834.5}{9}}\\\\\\s=\sqrt{1092.7}=33.1\\\\\\\)

To tell if this sample has a value significantly lower than the expected score of 100, we should make a hypothesis test.

The claim is that the mean score is significantly lower than 100.

Then, the null and alternative hypothesis are:

\(H_0: \mu=100\\\\H_a:\mu< 100\)

The significance level is 0.05.

The sample has a size n=10.

The sample mean is M=94.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.1.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{33.1}{\sqrt{10}}=10.467\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{94.5-100}{10.467}=\dfrac{-5.5}{10.467}=-0.53\)

The degrees of freedom for this sample size are:

\(df=n-1=10-1=9\)

This test is a left-tailed test, with 9 degrees of freedom and t=-0.53, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t<-0.53)=0.306\)

As the P-value (0.306) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean score is significantly lower than 100.

Answer:

y=-3x-1

Step-by-step explanation:

hope it helps.

Answer:

A

Step-by-step explanation:

surface area = length x width x depth

so 5x5x7=175.

The mean is 0.477514 (rounded to 6 decimal places).

The standard deviation is 0.288919 (rounded to 6 decimal places).

To calculate the mean and standard deviation, we will use the following formulas:

Mean = (sum of all values) / (number of values)

Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]

Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:

Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514

Therefore, the mean is 0.477514 (rounded to 6 decimal places).

Now we will calculate the standard deviation:

Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919

Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).

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Answer:

b is the answer

Step-by-step explanation:

b is the answer

Answer: x = 24

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

Step 1: Remove parentheses.

12 (2 − 2) + 32 = \(x\) + 6 + 2

Step 2: Simplify 2 − 2 to 0.

12 × 0 + 32 = \(x\)  + 6 + 2

Step 3: Simplify 12 × 0 to 0.

0 + 32 = \(x\) +  6 + 2

Step 4: Simplify 0 + 32 to 32.

32 = \(x\) + 6 + 2

Step 5: \(x\) + 6 + 2 to \(x\) + 8.

32 = \(x\) + 8

Step 6: Subtract 8 from both sides.

32 − 8 = \(x\)

Step 7: Simplify 32 − 8 to 24.

24 = \(x\)

Step 8: Switch sides.

\(x\) = 24

~I hope I helped you! :)~

Hi! I'm Carriyana!! Glad to help you today! :)

Cole needs to work 28 hrs!!

My steps:

First I did 500/20 and got 25

Then I did 700/25

And ended up with 28

So the answer should be...

Answer:

28 hours

Step-by-step explanation:

To calculate how many hours Cole must work to earn $700, we must first calculate how much he makes per hour.

This can be done by taking the total amount he earned and dividing by the number of hours:

$500 / 20 hours = $25 an hour

Since we now know how much he makes an hour, we can determine how many hours it takes to earn $700 by using a similar equation to the one above:

Total Money / Total Hours = $ an hour

$700 / Total Hours = $25 an hour

It can be represented algebraically as:

700 / x = 25

Then, solve for x:

(700 / x) * x = (25) * x

700 = 25x

(700) / 25 = (25x) / 25

28 = x

28 hours

Answer: x=0, 13/2......

Factorize the numerator and denominator, then simplify:

10/45 = (2×5)/(9×5) = 2/9

Now,

1/9 = 1/10 + 1/90

1/90 = 1/10 × 1/9 = 1/10 × (1/10 + 1/90) = 1/100 + 1/900

1/900 = 1/100 × 1/9 = 1/100 × (1/10 + 1/90) = 1/1000 + 1/9000

and so on, which is to say

1/9 = 1/10 + 1/100 + 1/1000 + …

or

1/9 = 0.111…

so that multiplying both sides by 2 gives

2/9 = 0.222…

Answer:

a. Angel has a greater flat fee

b. Difference = $130

Step-by-step explanation:

Given

Rose:

\(Flat\ Fee = \$50\)

\(Rate = \$12\)

Angel

Guests --- Charges

10 -------- $180

15 -------- $255

25 -------- $405

30 -------- $480

Solving (a): Who charges the greater flat fee?

We have that the flat fee of Rose is:

\(Flat\ Fee = \$50\)

For Angel, we need to determine the equation of the given table

Start by calculating the slope (m) of the table

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where x and y represent any two corresponding values of the guests and the charges.

\((x_1,y_1) = (10, 180)\)

\((x_2,y_2) = (30, 480)\)

So: \(m = \frac{y_2 - y_1}{x_2 - x_1}\) becomes

\(m = \frac{480 - 180}{30 - 10}\)

\(m = \frac{300}{20}\)

\(m = 15\)

Next, we calculate the equation using:

\(y - y_1 = m(x - x_1)\)

Where

\(m = 15\)

\((x_1,y_1) = (10, 180)\)

\(y - 180 = 15(x - 10)\)

\(y - 180 = 15x - 150\)

Add 180 to both sides

\(y - 180 + 180 = 15x - 150 + 180\)

\(y= 15x + 30\)

From the equation above:

The slope = 15 --- This represents the hourly rate

and

y intercept = 30 --- This represents the flat fee

This is better represented as:

Angel

\(Flat\ Fee = \$30\)

\(Rate = \$15\)

and

Rose:

\(Flat\ Fee = \$50\)

\(Rate = \$12\)

By comparison, Angel has a greater flat fee

Solving (b): Difference between total charges of 50 guests for both caterers.

For angel, the equation is:

\(y= 15x + 30\)

and x = 50.

So:

\(y = 15 * 50 + 30\)

\(y = 750 + 30\)

\(y = 780\)

For Rose,

First, we need to determine the equation.

\(Flat\ Fee = \$50\)

\(Rate = \$12\)

The equation is:

\(y = Flat\ Fee + Rate * x\)

\(y = 50 + 12 * x\)

So, the total charges for 50 guests is:

\(y = 50 + 12 * 50\)

\(y = 50 + 600\)

\(y = 650\)

The difference is then calculates as:

\(Difference = 780 - 650\)

\(Difference = \$130\)

Answer:

$0.25

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The correct name for point T in the triangle is known as point of concurrency.

A point of concurrency in a triangle is a point where three lines, each passing through one vertex of the triangle and the opposite side's midpoint, intersect.

There are several such points of concurrency in a triangle, such as;

For the given figure or diagram, we can see clearly that the lines from point D, point F all intersect at point T, so we call this point of intersection a point of concurrency.

The marks on point T is known as a point of concurrency.

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Answer:

the simplified expression is 192h + 176

Step-by-step explanation:

To simplify the expression 16(12h +11), we can use the distributive property of multiplication over addition, which states that:

a(b+c) = ab + ac

Using this property, we can distribute the 16 to both terms inside the parentheses as follows:

16(12h +11) = 1612h + 1611

Multiplying 16 by 12h and 11, we get:

1612h = 192h

1611 = 176

Substituting these values back into the expression, we have:

16(12h +11) = 192h + 176

Therefore, the simplified expression is 192h + 176.

Answer:

These are all quadratics, where the x/y/a/b coefficient has been cancelled out. So it's like factorising a quadratic. What i mean by the x/y/a/b coefficient being cancelled out is for example y^2 - 1, becomes (y - 1)(y + 1). This is equal to y^2 - y + y - 1. You can see that - y + y = 0, to therefore it's not visible in the final equation, but it's there.

c) y^2 - 1 = (y - 1)(y + 1)

d) x^2 - 64 = (x - 8)(x + 8)

g) a^2 - 81 = (a - 9)(a + 9)

h) x^2 - y^2 = (x - y)(x + y)

k) 25 - x^2 = (5 - x)(5 + x)

l) 1 - b^2 = (1 - b)(1 + b)

o) x^2 - 400 = (x - 20)(x + 20)

p) 900 - y^2 = (30 - y)(30 + y)

I hope this makes sense :))

Answer:

Step-by-step explanation:

What is an angle that is adjacent to BEC?

two angles that have the same vertex and a side in common

so

angle BEA