what is the measure of an angle if it is 130 less than three times its own complement

Answers

Answer 1

The measure of the angle is 35 degrees.

What are complementary angles?

Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.... For example, a 50-degree angle and a 40-degree angle are complementary; a 60-degree angle and a 120-degree angle are supplementary.

Let's assume that x is the measure of the angle in question.

The complement of x is the angle that, when added to x, forms a right angle (90 degrees). Therefore, the complement of x can be represented as 90 - x.

According to the problem, the measure of the angle is 130 less than three times its own complement. We can write this information as an equation:

x = 3(90 - x) - 130

Simplifying and solving for x, we get:

x = 270 - 3x - 130

4x = 140

x = 35

Therefore, the measure of the angle is 35 degrees.

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Related Questions

En una ciudad de 5000 habitantes, la tasa diaria
de infección con un virus de la gripe varia directamente con el producto de
personas infectadas y el número de personas no infectadas. Cuando se han
infectado 1000 personas, la gripe se esparce a razón de 40 nuevos casos por día.
¿Para qué número de personas infectadas, la tasa diaria de infección es la
máxima?

Answers

According to the information, the maximum infection rate is:  k * 2500 * (5000 - 2500) = 6250k = 40

How to calculate for what number of infected people, the daily infection rate is the maximum?

To address this problem, we can use the law of the infection rate, which states that the infection rate is directly proportional to the product of the number of people infected and the number of people not infected. Therefore, we can write:

infection rate = k * (infected people) * (uninfected people)

where "k" is a constant of proportionality. Since we want to find the number of people infected that produces the maximum infection rate, we can consider the infection rate as a function of the variable "x" representing the number of people infected. Therefore, we can write:

infection rate = k * x * (5000 - x)

To find the value of "x" that maximizes the infection rate, we can derive this function and set the derivative equal to zero:

d(infection rate)/dx = k * (5000 - 2x) = 0

This implies that 5000 - 2x = 0, and therefore:

x = 2500

Therefore, the number of infected people that produces the maximum daily rate of infection is 2,500.

However, we must verify that this result is consistent with the information given in the problem. We know that when there are 1,000 people infected, the flu spreads at the rate of 40 new cases per day. Therefore, if we add 1,500 more infected people (for a total of 2,500), the infection rate would be:

infection rate = k * 2500 * (5000 - 2500) = 6250k

If the infection rate is 40 new cases per day, we have:

40 = 6250k

which implies that:

k = 0.0064

Therefore, the maximum infection rate is:

maximum infection rate = k * 2500 * (5000 - 2500) = 6250k = 40

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What is the product? 1/2 . [12 64 78 30 ]

Answers

Answer:

[tex]\left[\begin{array}{c c c c}6 & 32 & 39 & 15\end{array}\right][/tex]

Step-by-step explanation:

When multiplying a constant by a matrix, we have to multiply each element by the constant.

[tex]\dfrac{1}{2} \cdot \left[\begin{array}{c c c c}12 & 64 & 78 & 30\end{array}\right][/tex]

[tex]= \left[\begin{array}{c c c c} \dfrac{12}{2} & \dfrac{64}{2} & \dfrac{78}{2} & \dfrac{30}{2}\end{array}\right][/tex]

[tex]= \left[\begin{array}{c c c c}6 & 32 & 39 & 15\end{array}\right][/tex]

Mr. Johnson was paid $190 for a job that required 40 hours of work. At this rate, how much should he be paid for a job requiring 60 hours of work?

Answers

Answer:

Mr. Johnson should be paid $285 for a job requiring 60 hours of work.

Step-by-step explanation:

If Mr. Johnson was paid $190 for 40 hours of work, then we can write:

190/40 = x/60

Where x is the amount he should be paid for 60 hours of work.

To solve for x, we can cross-multiply and simplify:

190 * 60 = 40 * x

11,400 = 40x

x = 11,400/40

x = 285

Therefore, Mr. Johnson should be paid $285 for a job requiring 60 hours of work at the same rate.

There are figures on the territory of a country in 2021 as follows:
Government spending on goods and services
Income from export factor 400
Import factor income 250
Export​850
Imported ​490
Net Investment: ​350
Depreciation:​520
Profit: ​780
Salary:​1700
Profit: ​320
Household Consumption:​2100
Indirect Tax 240
Rent​530
Price index in 2021 is 135 and 2020 is 120
a. Calculate nominal GDP at market prices using the methods
b. Calculate GNP at market price and at factor cost
c. Calculate real GDP, real GNP and inflation rate in 2021
d. Calculate the economic growth rate in 2021 knowing the nominal GDP in 2020 is 3500.

Answers

a. To calculate nominal GDP at market prices, we need to add up the total value of all final goods and services produced within the country in 2021. This can be done using the expenditure approach:

Nominal GDP = C + I + G + (X - M)

where C is household consumption, I is net investment, G is government spending on goods and services, X is income from exports, and M is income from imports.

Substituting the given values, we get:

Nominal GDP = 2100 + 350 + (1700 + 240 + 530) + (850 - 490) = $4,280 billion

Alternatively, we can use the income approach to calculate nominal GDP:

Nominal GDP = compensation of employees + rent + interest + profit + indirect taxes - subsidies

Substituting the given values, we get:

Nominal GDP = 1700 + 530 + 0 + 780 + 240 - 0 = $3,250 billion

b. To calculate GNP at market price, we need to add up the total income earned by all resident entities in the country, including income earned abroad and deducting income earned by foreign entities within the country. We can use the formula:

GNP at market price = GDP + net factor income from abroad

Substituting the given values, we get:

GNP at market price = $4,280 + 400 - 250 = $4,430 billion

To calculate GNP at factor cost, we need to deduct indirect taxes and add subsidies from GNP at market price. Since no subsidies are given, we only need to subtract indirect taxes:

GNP at factor cost = GNP at market price - indirect taxes = $4,430 - 240 = $4,190 billion

c. To calculate real GDP and real GNP, we need to adjust nominal GDP and GNP for changes in price levels between 2020 and 2021 using a price index. The real GDP and GNP formulas are:

Real GDP = Nominal GDP / Price index in 2021 x 100

Real GNP = Nominal GNP / Price index in 2021 x 100

Substituting the given values, we get:

Real GDP = $4,280 / 135 x 100 = $3,174.07 billion

Real GNP = $4,430 / 135 x 100 = $3,281.48 billion

The inflation rate in 2021 can be calculated as the percentage increase in the price index between 2020 and 2021:

Inflation rate = (Price index in 2021 - Price index in 2020) / Price index in 2020 x 100

Substituting the given values, we get:

Inflation rate = (135 - 120) / 120 x 100 = 12.5%

d. To calculate the economic growth rate in 2021, we can use the formula:

Economic growth rate = (Nominal GDP in 2021 - Nominal GDP in 2020) / Nominal GDP in 2020 x 100

Substituting the given values, we get:

Economic growth rate = ($4,280 - $3,500) / $3,500 x 100 = 22.29%

la quinta parte de la diferencia entre el doble de un numero y su mitad es 24. Cual es el numero?

Answers

The number in the given expression is 160.

We have,

Let's call the number "x".

The difference between twice a number and its half is:

2x - (1/2)x = (3/2)x

One-fifth of this difference is 24, so we can set up the equation:

(1/5)(3/2)x = 24

Multiplying both sides by 10 to eliminate the fraction, we get:

3x = 480

Dividing both sides by 3, we get:

x = 160

Therefore,

The number in the given expression is 160.

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The complete question.

One fifth of the difference between twice a number and its half is 24. What is the number.

Choose the inequality that represents this graph. Open circle at -5 open circle at 4, and shaded between -5 and 4

Answers

Answer:

The inequality is -5 < x < 4.

Hillary was told that based on the price of her home, her approximated closing costs would range from $11,600 to $40,600. How much was the price of her home?

Answers

We need more information about the property and the specific services required to determine the price of Hillary's home.

Answer:

Unfortunately, without additional information, it is impossible to determine the price of Hillary's home. The range of closing costs provided does not provide enough information to calculate the price of the home.

To determine the price of the home, we would need to know either the exact amount of the closing costs or additional information about the home's value, such as its appraised value or sale price.

Therefore, we cannot determine the price of Hillary's home based on the given information.

Step-by-step explanation:

We only know that the estimated closing costs for her home range from $11,600 to $40,600. Closing costs can vary based on a variety of factors, such as the location of the home, the type of mortgage, and the specific fees charged by the lender and other parties involved in the transaction.

To determine the price of Hillary's home, we would need additional information, such as the appraised value of the home, the amount of the down payment, and the specific closing costs that were incurred.

A proportional relationship is represented by the equation 4y = 24x. If y = kx, where k is the constant of proportionality what is the value of k? Show your work.

Please provide answer with explanation!!

Answers

Answer:   k=6

Step-by-step explanation:

4y=24x           Divide both sides by 4

y=6x

y=kx           you can see k=6

but if they want you to actually prove

substitue y=6x into y=kx

you get

6x=kx     divide both sides by x

6=k

What's the height of the pyramid? slant height is 60. 22 is the base.

Answers

The height of the square pyramid is 58.95 units.

To find the height of the square pyramid, we can use the Pythagorean theorem. Let's call the height "h".

The slant height is the hypotenuse of a right triangle with legs equal to half the length of one side of the square base and the height of the pyramid. The length of one side of the square base is given as 22, so the length of half a side is 11. Using the Pythagorean theorem, we get:

[tex]h^{2}[/tex] + [tex]11^{2}[/tex] = [tex]60^{2}[/tex]

Simplifying, we have:

[tex]h^{2}[/tex]  + 121 = 3600

Subtracting 121 from both sides, we get:

[tex]h^{2}[/tex]  = 3479

Taking the square root of both sides, we get:

h ≈ 58.95

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The graph of a function g is shown below. Find g(1).

Answers

Check the picture below.

pls solve
-2n+1<5

pls explain solution

Answers

Answer:

n > -2

Step-by-step explanation:

[tex]-2n+1 < 5[/tex]

This is a two-step equation, so the first thing you would do is subtract 1 from both sides of the equation.

[tex]-2n+1-1 < 5-1\\-2n < 4[/tex]

Then, divide -2 from both sides of the equation.

[tex]\frac{-2n}{-2} < \frac{4}{-2} \\[/tex]

The less than symbol will become a greater than symbol because you divided by a negative number.

So the solution is:

[tex]n > -2[/tex]

Match each point in polar coordinates with either​ A, B,​ C, or D on the graph.

Answers

A.= [tex]$\left( -4,\frac{5\pi}{4}\right)\,\, \left( 4,\frac{-7\pi}{4}\right)[/tex],  B = [tex]$\left( 4,\frac{3\pi}{4}\right)\,\, \left( -4,\frac{-\pi}{4}\right)[/tex],

C=[tex]$\left( -4,\frac{\pi}{4}\right)\,\, \left( 4,\frac{5\pi}{4}\right)[/tex],  D = [tex]$\left( -4,\frac{3\pi}{4}\right)\,\, \left( 4,\frac{7\pi}{4}\right)[/tex]

[tex]$\left( -4,\frac{5\pi}{4}\right) = \left( 4,\frac{5\pi}{4}+\pi = 2\pi + \pi/4\right )\,\,, \left( 4,\frac{-7\pi}{4}\right) =\left( 4,\frac{-7\pi}{4}+2\pi = \pi/4\right)[/tex]

[tex]$\left( 4,\frac{3\pi}{4}\right)\,\, , \,\left( -4,\frac{-\pi}{4}\right) = \left(4,\frac{-\pi}{4}+\pi = 3\pi/4\right)[/tex]

[tex]$\left( -4,\frac{\pi}{4}\right)=\left( 4,\frac{\pi}{4}+\pi = 5\pi/4\right)\,\, ,\,\left( 4,\frac{5\pi}{4}\right)[/tex]

[tex]$\left( -4,\frac{3\pi}{4}\right)=\left ( 4,\frac{3\pi}{4}+\pi = 7\pi/4 \right)\,,\, \left( 4,\frac{7\pi}{4}\right)[/tex]

How to convert any given polar coordinates into standard polar coordinates.

When [tex]r\geq 0[/tex] and [tex]0\leq \theta < 2\pi[/tex], we call the polar coordinates [tex](r,\theta)[/tex] standard polar coordinates. To convert any given coordinates to standard coordinates 1. if r<0 then replace r with |r| and [tex]\theta[/tex] with [tex]\theta + \pi[/tex]. 2. Now if [tex]\theta < 0 \textrm{ or }\theta\geq 2\pi[/tex], we add a suitable multiple of [tex]2\pi \textrm{ to }\theta[/tex] to bring it inside [0,[tex]2\pi[/tex]) interval.

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URGENT which expression is equivalent?

Answers

The equivalent expression to the given one is the second option:

[tex]log_2( y^4*z^4/x^2)[/tex]

Which expression is equivalent?

Here you need to remember two logarithmic rules, these are:

[tex]log(x^n) = n*log(x)[/tex]

[tex]log(x) + log(y) = log(x*y)[/tex]

And these work for any base of the logarithm.

Here we start with the expression:

[tex]-2log_2(x) + 4log_2(y)+ 4log_2(z)[/tex]

Using the first one:

[tex]-log_2(x^2) + log_2(y^4) + log_2(z^4)[/tex]

Using the second one:

[tex]log_2( y^4*z^4/x^2)[/tex]

That is the equivalent expression, the second option.

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Tanya's garden measures 18 feet by 20 feet and has a perimeter of


76 feet. Marely's garden measures 12 feet by 33 feet.



How much longer is the perimeter of Marely's garden than Tanya's?

Answers

Answer:

I'm pretty sure the answer is 14 feet. hope this helps!

3B. Table 2 shows the time it takes the boys to walk different distances. Examine Table 2 carefully then complete the blank spaces with the appropriate distance and/or time. Table 2- Time Taken to Walk Different Distances Distance 200 m 400 m 600 m m 1000 m m Time Taken 3 minutes 6 minutes 9 minutes. 12 minutes minutes minutes​

Answers

Answer:

Step-by-step explanation:

The missing values in the table are:

Distance 800 m 1200 m

Time Taken _______ _______
The time taken to walk 800m in Table 2 is not provided, so the blank space remains unfilled.

The cost of 3 sweaters and 2 pairs of jeans is $112.48. Two sweaters and one pair of jeans is
$65.10. Find the cost of each.

Answers

Let's assume the cost of one sweater be "s" and the cost of one pair of jeans be "j".

According to the problem, we have two equations:

3s + 2j = 112.48 ...(1)

2s + j = 65.10 ...(2)

Solving equation (2) for j, we get:

j = 65.10 - 2s

Substituting this value of j in equation (1), we get:

3s + 2(65.10 - 2s) = 112.48

Simplifying and solving for s, we get:

s = $20.06

Substituting the value of s in equation (2) and solving for j, we get:

j = $25.98

Therefore, the cost of one sweater is $20.06 and the cost of one pair of jeans is $25.98

My watch gains 2 minutes in every 24 hours. If I put it right at 10 a.m. on Monday, what time will it show at 10 p.m. the same night? What time will it show at 10 a.m. on Tuesday? What time will it show at 10 a.m. on Wednesday? What time will it show at 10 a.m. on the following Monday?​

Answers

The time your watch will show at 10 a.m. on the following Monday is 10:14 a.m.

What time will the watch show?

If your watch gains 2 minutes in every 24 hours, that means it gains 1 minute every 12 hours.

At 10 a.m. on the following Monday (7 days after 10 a.m. on Monday):

7 days = 168 hours

12 hours = 1 minute

168 hours = ?

= 168/12

= 14 minutes

Your watch would show 10:14 a.m. on the following Monday, as it gains 1 minute every 12 hours and there are 7 days (168 hours) between Monday 10 a.m. and the following Monday 10 a.m.

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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36

Answers

x² + (y - 3)² = 36; x² + (y + 8)² =36 represent the circles that have a diameter of 12 units and a center that lies on the Y axis.

We know that the abscissa of coordinates of a point on Y axis is 0.

So the equation of a circle center at (0, k) and radius 'r' is given by,

x² + (y - k)² = r²

Here given that the diameter of the circle must be = 12 units

So the radius of the circle = 12/2 = 6 units.

So the equation of the required circle looks like

x² + (y - k)² = 6², where k is an real number.

x² + (y - k)² = 36

So we can see that the equations x² + (y - 3)² = 36; x² + (y + 8)² =36 can be the equation of the required circle.

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Use the vertical line test to determine which graph does not represent a function. 0 Graph A M 10000 6 of 10 Graph B 0 Done​

Answers

The graph that does not represent a function is graph b

Determine which graph does not represent a function

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

Graphs A to C

As a general rule of the vertical line test

For a graph to represent a function, a line drawn from the x-axis must intersect with the graph at most once

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

The graph b would intersect with a line from the x-axis twice

Hence, the graph is b

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Question 3 of 10
What is the center of the circle shown below?
S
M
Ο A. A
B. AS
C. M
D. S
SUBMIT

Answers

The center of the circle shown is point S

Identfying the center of the circle shown?

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

The circle

By definition, the center of a circle is the point that is equidistant to all points on the circumference of the cirlce

In the given circle, the point that satisfies the above definition is the point S

This means that the circle can also be called the circle S

Hence, the center of the circle shown is S

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- Ava spent 15% of her paycheck at the mall, 35% she saved and 45% was spent on bills. The
remaining amount was donated to charity. If Ava spent $48 at the mall, how much was donated to
charity?

Answers

Let X be the total amount of Ava's paycheck.

According to the problem, Ava spent 15% of X at the mall, so:

0.15X = $48

Solving for X, we get:

X = $48 / 0.15

X = $320

Now, we know that 35% of X was saved, so:

0.35X = 0.35 * $320

0.35X = $112

And we also know that 45% of X was spent on bills, so:

0.45X = 0.45 * $320

0.45X = $144

Finally, we can calculate the amount donated to charity by subtracting the amounts spent on bills, saved, and spent at the mall from the total paycheck:

Amount donated to charity = X - (0.15X + 0.35X + 0.45X)

Amount donated to charity = $320 - ($48 + $112 + $144)

Amount donated to charity = $16

Therefore, Ava donated $16 to charity.

Giving a test to a group of students, the grades and gender are summarized below

Grades and Gender
A B C Total
Male 14 20 2 36
Female 15 19 18 52
Total 29 39 20 88

If one student is chosen at random, find the probability that the student was male AND got a "C". Round your answer to 4 decimal places.

Answers

The probability that the student chosen at random is male AND got a "C" is 0.0227.

What is Conditional Probability:

Conditional probability is the probability of an event (A) occurring given that another event (B) has already occurred. It is denoted by P(A | B) and is read as "the probability of A given B".

The formula for conditional probability is:

P(A | B) = P(A and B) / P(B)

Where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

Here we have

The total number of students is 88

Out of these 88 students, 36 are male

Number of males that got grade C =  2

P(male AND C) =  number of males who got C / total number of students

= 2/88 = 0.02272727272  

Rounding this to 4 decimal places, we get:

P(male AND C) = 0.0227

Therefore

The probability that the student chosen at random is male AND got a "C" is 0.0227.

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A call center claims that the mean wait time for a customer to connect with a customer care executive is at most 2 minutes. A random sample of 20 calls at the call center yielded a test statistic of 1.75. Assuming that the wait time is normally distributed, what is the corresponding p-value? Round your answer to three decimal places.

Answers

Answer:

To find the p-value, we need to first find the corresponding area in the normal distribution table for the test statistic of 1.75.

Since the sample size (n) is greater than 30 and the population standard deviation is unknown, we use the t-distribution to calculate the p-value.

The degrees of freedom (df) for the t-distribution is n - 1 = 20 - 1 = 19.

Using a t-table or calculator, we can find that the area to the right of 1.75 (with df=19) is approximately 0.049.

Since this is a one-tailed test (the alternative hypothesis is that the mean wait time is greater than 2 minutes), the p-value is equal to the area to the right of the test statistic, which is 0.049.

Therefore, the corresponding p-value is 0.049 (rounded to three decimal places).

Step-by-step explanation:

gg

You are writing a program to help compare two sports teams. A sample member of the list scores is [2.5] where
your team scored 2 and the opponent team scored 5. This part of the program is counting the wins and losses.
What is the missing line of code?
for item in scores:
sum sum + item[1]
if item[0]> item[1]:
Mark this and return
Save and Exit
TIVE REMAINS
59:11
Next
Submit answer

Answers

Here is   the missing line of code is    

if item[0]   > item[1]:

   wins += 1

else:

   losses += 1

What is the complete code?

The comlete code should look like this:


  scores = [[2, 5], [3, 1], [4, 4], [1, 0], [2,  3] ]

wins = 0

losses = 0

for item in scores:

   if item [0] > item[1] :

       wins += 1

   else:

       losses += 1

print("Number of wins:", wins)

print("Number of losses:", losses)

This code examines the scores of the two teams for each game, and if the home team's score ( item  [0]) is higher than the opponent team's score (item[1  ]), it counts as a victory, and the "wins" variable is increased by one.

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For this problem you need to determine the correct height of a flagpole large enough to support the Star Spangled Banner flag that flies over Fort McHenry. This flag is 30 by 42 feet in size. (We know that the ratio of the height of a flagpole to the width of any flag is 4 to 1.)
a. How tall will the flagpole need to be to support the Star Spangled Banner?
b. You have a model of Ft. McHenry that you need to add a flagpole to that would be proportional to the real pole at the fort. The ratio of the model is 1 inch to 10 feet.
c. You are given a model flagpole that is 8 inches tall; is this the correct size? If not, how tall does it need to be?
d. You have a model flag that is 5 by 6.3 inches. Are the model flag and original flag similar figures? If not, what would the model flag dimensions need to be? What is the scale factor?
e. Refer to the model in part c. What is the ratio of the perimeter of the model flag in comparison to the original flag?
f. Refer to the model in part d. What is the ratio of the area of the model flag in comparison to the original flag?
g. What is the relationship between the ratios of perimeter and area?

Answers

After considering all the given data we conclude that the generated answers to the sub questions are

a) 120 feet

b) 1200 inches

c) 120 inches tall

d) 72

e) 1

f) 1

g) proportional

a. To evaluate the height of the flagpole needed to support a 30 by 42 feet flag, we can apply the ratio of the height of a flagpole to the width of any flag which is 4 to 1.

This projects that the height of the flagpole is be four times the width of the flag. The width of the flag is 30 feet, so the height of the flagpole should be 4 × 30 feet = 120 feet.

b. If the individual have a model of Ft. McHenry that you need to add a flagpole to that will be proportional to the real pole at the fort and the ratio of the model is 1 inch to 10 feet, then you can apply this ratio to determine how tall the individuals model flagpole should be.

The real pole at Fort McHenry is 120 feet tall (as determined in part a), so you can multiply this by 10

10 × 120 = 1200

to get 1200 inches. This means that your model flagpole should be 1200 inches tall.

c. It is given that a model flagpole that is 8 inches tall; this is not the correct size. To evaluate how tall it needs to be, we can use the same ratio as in part b.

The real pole at Fort McHenry is 120 feet tall (as determined in part a), so you can multiply this by 10 to get 1200 inches.

This means that your model flagpole should be 1200/10 = 120 inches tall.

d. To evaluate if the model flag and original flag are similar figures, we can compare their corresponding sides.

The original flag has dimensions of 30 by 42 feet, which is equivalent to 360 by 504 inches. The model flag has dimensions of 5 by 6.3 inches. To determine if they are similar figures, we can compare their corresponding sides using ratios.

The ratio of the length of corresponding sides must be equal for two figures to be similar. The length of corresponding sides for these two flags are:

- Original Flag: Length = 360 inches; Width = 504 inches

- Model Flag: Length = 5 inches; Width = 6.3 inches

To compare these lengths, we can divide each length by its corresponding length on the other figure:

- Length Ratio: (360 / 5) = 72

- Width Ratio: (504 / 6.3) = 80

Since these ratios are not equal, these two flags are not similar figures.

To find out what dimensions would make them similar figures, we can use these ratios as scale factors:

Length Scale Factor: (360 / x) = 72

- Width Scale Factor: (504 / y) = 80

Evaluating for x and y gives us:

- x = (360 / 72) = 5

- y = (504 / 80) = 6.3

This means that if we scaled down the original flag by a factor of 72, its dimensions would be equivalent to those of the model flag.

e. To evaluate the ratio of the perimeter of the model flag in comparison to the original flag using the scale factor from part d:

Perimeter Scale Factor: (72 + 80) / 2 = 76

Model Flag Perimeter: (2 * (5 + 6.3)) = 23.6

- Original Flag Perimeter: (2 * (360 + 504)) = 1688

The ratio of these perimeters is:

Perimeter Ratio: (23.6 / (1688 /76)) ≈ 1

This means that the perimeter of the model flag is approximately equal to that of the original flag.

f. To evaluate the ratio of area between these two flags using scale factor from part d:

- Area Scale Factor: (72 × 80) = 5760

- Model Flag Area: (5 × 6.3) ≈ 31.5

- Original Flag Area: (360 × 504) ≈ 181440

The ratio of these areas is:

Area Ratio: (31.5 / (181440 /5760)) ≈ 1

This means that area of model flag is approximately equal to that of original flag.

g. Here relationship between ratios of perimeter and area is that they are both proportional to each other.

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A wedding website states that the average cost of a wedding is $25,549
. One concerned bride hopes that the average is less than reported. To see if her hope is correct, she surveys 60
recently married couples and finds that the average cost of weddings in the sample was $24,342
. Assuming that the population standard deviation is $5054
, is there sufficient evidence to support the bride’s hope at the 0.01
level of significance?
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.

Answers

The value of test statistic is -2.23.

What is test statistic?

In statistics, a test statistic is a value calculated from a sample of data that is used to assess the evidence against a null hypothesis.

We can use a one-sample t-test to test the hypothesis:

Null hypothesis: The true population mean cost of weddings is $25,549

Alternative hypothesis: The true population mean cost of weddings is less than $25,549

The test statistic can be calculated using the formula:

t = ([tex]\bar{x}[/tex] - μ) / (s / √n)

where [tex]\bar{x}[/tex] is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (24,342 - 25,549) / (5054 / √60) = -2.23

Rounding to two decimal places, we get t = -2.23.

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A worker in the UK is paid 22,000 GBP per year as a gross salary. Her pay is increased by 11.5%. What is her new salary? Round your answer to the nearest dollar.

Answers

Answer:

Step-by-step explanation:

First mulitply the current salary by 11.5% to find the increase.

Change 11.5% into a decimal by moving the decimal two places to the left.

11.5% becomes .115.

22000 × .115 = 2530 - the increase

22000 + 2530 = 24530 GBP

The new gross salary.

Find the value of x for the following

Answers

Applying the principle of similar triangles, the value of x is 6 units

What is similar triangles

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

To find the value of x in this problem, we have to apply similar triangle theorem here.

(8 + x) / 2√21 = 2√21 / x

cross multiply both sides

x(8 + x) = (2√21)(2√21)

8x + x² = 84

Rewrite the equation;

x² + 8x - 84 = 0

solving for x

x = 6, x= -14

Taking the positive value, the value of x = 6

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Maurice is traveling to Mexico and needs to exchange $370 into Mexico pesos. If each dollar is worth 12.29 pesos. How many peso will he get for his trip ?

Answers

Answer: 4547.30 pesos

Step-by-step explanation:

You can set up proportion

[tex]\frac{x}{370}=\frac{12.29}{1}[/tex]         as long as you put pesos on top and dollars on bottom to set up proportion

now solve for x

x=12.29(370)= 4547.30 pesos

or

you can think of it as if you have 1 dollar and that is 12.29 pesos then 370 dollars would be 370x12.29

=4547.30

Question 8 of 10
If two cylinders are similar and the ratio between the lengths of their edges is
4:3, what is the ratio of their volumes?
A 4:3
OB. 16.9
OC. 64.27
OD. 16:27

Answers

OD. 16.27

cylinder 4:3 the ratio if their volumes is (4/3)^3, which simplies to 64/27.So the correct answers is D.

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