Find the value of x in the figure below.

Find The Value Of X In The Figure Below.

Answers

Answer 1

Answer:

x = 63° and y =153°

Step-by-step explanation:

a streght line measure 180° so in the given we sum up

90° + x + 27°=180° then solve x

and for y u will sum up 90° and x then u will get by vertical opposite angle


Related Questions

A car uses 1 2/3 gallons of gasoline to travel 50 3/4 how far can the car travel on 1 gallon of gasoline ?
a. 4/125
b. 8/15
c. 36 1/4
d. 71 1/20

Answers

The distance that the car travelled on 1 gallon of gasoline is 71 1/20. (option d).

Let's start by finding how far the car can travel on 1/3 gallon of gasoline. We can do this by dividing 50 3/4 by 1 2/3. To divide fractions, we invert the divisor and multiply. So we have:

50 3/4 ÷ 1 2/3 = 50 3/4 × 3/5 = 153/4

This means that the car can travel 153/4 miles on 1 2/3 gallons of gasoline.

Now, we can use the unitary method to find how far the car can travel on 1 gallon of gasoline. We know that the car can travel 153/4 miles on 1 2/3 gallons of gasoline, so we can set up a proportion:

1 2/3 gallons ÷ 153/4 miles = 1 gallon ÷ x miles

To solve for x, we can cross-multiply:

1 2/3 × x = 1 × 153/4

We can simplify the left side by converting 1 2/3 to an improper fraction:

5/3 × x = 153/4

To solve for x, we can cross-multiply again:

5/3x = 153/4 × 3/5

Simplifying both sides, we have:

x = 153/4 × 3/5 ÷ 5/3 = 229/20

So the car can travel 229/20 miles on 1 gallon of gasoline.

To check our answer, we can use the unitary method again to find how far the car can travel on 1 2/3 gallons of gasoline using our answer for how far the car can travel on 1 gallon of gasoline. We have:

1 gallon ÷ 229/20 miles = 1 2/3 gallons ÷ y miles

Simplifying both sides, we have:

20/229y = 3/5

Solving for y, we have:

y = 3/5 × 229/20 ÷ 20/229 = 71 1/20

Therefore, the answer to the question is (d) 71 1/20.

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HELP FAST PLEASE

Simplify: m5 p8 m6 p10

1) mp¹3. mp¹6
2) m11 p18
3)m18.p11
4)(m. p)29

Answers

Answer:

the answer is 2) m11 p18.

Step-by-step explanation:

m5 p8 m6 p10 = (m5 m6) (p8 p10) = m11 p80

Therefore, the answer is 2) m11 p18.

Answer Immeditely Please

Answers

The ratio of the lengths of the corresponding sides of the similar right triangles indicates that the length of the segment [tex]\overline{BD}[/tex] = 8 units

What are similar triangles?

Similar triangles are triangles that have the same shape, and therefore, the interior angles of each triangle are congruent to the three angles in the similar triangle, however, the sizes of the triangles may be different.

The similar triangles are; ΔABD, ΔBCD, ΔACB

∠ABD ≅ ∠BCD ≅ ∠ACB (Corresponding angles in similar triangles are congruent)

[tex]\overline{AD}[/tex]/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/[tex]\overline{DC}[/tex]

4/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/16

4 × 16 = 64 = [tex]\overline{BD}[/tex]²

[tex]\overline{BD}[/tex] = √(64) = 8

The length of the segment [tex]\overline{BD}[/tex] = 8 units

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Mr ade plans to spend his monthly salary as fellow
food-20%
children-25%
parents-20%
car-10%
entertainment-10%
saving-2½
miscellenceous-2½
if the amount of saving kept for saving is Ghc 250.00. calculate his
a) monthly salary
b) total amount spent on his parent​

Answers

a) His monthly salary is, 555.6

b) Total amount spent on his parent​ is, 111.1

Given that;

Mr. Ade plans to spend his monthly salary as follows

food-20%

children-25%

parents-20%

car-10%

entertainment-10%

saving-2½

miscellenceous-2½

And, the amount of saving kept for saving is Ghc 250.00.

Hence, We get;

Monthly salary is,

Since, We have;

Percent of savings = 100% - 20% - 10% - 10% - 12.5% - 2.5%

                             = 45%

Hence, We get;

45% of salary = 250

45/100 x salary = 250

Monthly salary = 25000 / 45

Monthly salary = 555.6

And, Money spent on parents;

20% of 555.6

20/100 x 555.6

111.1

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please help i don’t understand and need to find d

Answers

Answer:

10 inches

Step-by-step explanation:

The rule for a 45-45-90 triangle is if the two legs equal x then the hypotenuse is x√2.

So if the hypotenuse is 10√2 then the length of the leg d is 10

wo-thirds of the juniors at a local high school volunteer in their community. Of the juniors who volunteer, 45% volunteer at least twice a week. What is the probability that a randomly chosen junior volunteers in the community at least twice a week?

Answers

The probability that a randomly chosen junior who volunteers in their community volunteers at least twice a week is approximately 0.4444, or 44.44%

Explain the term probability

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is used in various fields, including mathematics, statistics, and science, to analyze and predict the outcomes of experiments, games of chance, and real-world events.

According to the given information

Using Bayes' theorem, we can write:

P(T|V) = P(V|T) * P(T) / P(V)

We know that two-thirds of the juniors volunteer in their community, so P(V) = 2/3.

We also know that 45% of the juniors who volunteer do so at least twice a week, so P(T) = 0.45.

To find P(V|T), we can use the conditional probability formula:

P(V|T) = P(V and T) / P(T)

We can interpret P(V and T) as the probability of junior volunteering at least twice a week AND volunteering in their community. We don't have that information directly, but we can use the fact that P(T|V) = 0.45 to estimate it:

P(T|V) = P(V and T) / P(V)

0.45 = P(V and T) / (2/3)

P(V and T) = 0.45 * (2/3) = 0.3

Now we can substitute all these values into the original Bayes' theorem formula:

P(T|V) = P(V|T) * P(T) / P(V)

P(T|V) = (P(V and T) / P(T)) * P(T) / P(V)

P(T|V) = 0.3 / (0.45 * (2/3))

P(T|V) = 0.4444...

Therefore, the probability that a randomly chosen junior who volunteers in their community volunteers at least twice a week is approximately 0.4444, or 44.44%

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Antonio uses a scale drawing of the kitchen floor to determine how many square feet of flooring he will need to buy
5 3/4 in
8 1/2 in
If the floor drawn with a scale of 1in =2ft what is the actual area of the kitchen floor ?

Answers

Answer:

195.5 sq. ft.

Step-by-step explanation:

If you ever wondered how to find the area of your kitchen floor using a scale drawing, you're in luck! I'm going to show you how to do it in a few easy steps. First, you need to know the scale factor, which is the ratio of the scale drawing to the actual floor. In this case, the scale factor is 1 in = 2 ft, which means that one inch on the paper is equal to two feet on the ground. Pretty neat, huh?

Next, you need to multiply the scale drawing dimensions by the scale factor to get the actual floor dimensions. For example, if the scale drawing is 5 3/4 inches long and 8 1/2 inches wide, you multiply those numbers by 2 to get 11 1/2 feet long and 17 feet wide. That's how big your kitchen floor really is!

Finally, you need to multiply the actual floor dimensions to get the area of the floor. This is where it gets tricky, because you have to deal with fractions and decimals. But don't worry, I'll walk you through it. You can use the distributive property to multiply two numbers with fractions. For example, (11 1/2) x (17) = (11 x 17) + (1/2 x 17) = 187 + 8.5 = 195.5. That's the answer! Your kitchen floor has an area of 195.5 square feet. Congratulations, you just learned how to use a scale drawing to find the area of your kitchen floor!

I hope you enjoyed this lesson and found it funny. If not, maybe you should try a different scale factor or a different kitchen. Just kidding!

Please help me
Find x. Complete the explanation.

Answers

Thus, the value of x for the given bottom isosceles triangle is found to be x = 88°.

Explain about the supplementary angles:

Additional angles are two angles that add up to 180 degrees. The situation when they happen to be on the identical side of a straight line is a typical one.

For the top isosceles triangle:

Base angle = ?

Using the property of supplementary angles:

base angle + 113 = 180

base angle = 180 - 113

base angle = 67

Now, using the Triangle sum Theorem:

Vertex angle = ?

Vertex angle + 67 + 67 = 180

Vertex angle = 180 - 134

Vertex angle = 46

For the bottom isosceles triangle:

base angle  = Vertex angle of top triangle (vertically opposite angles)

base angle  = 46

Now,

For the values of x, use Triangle sum Theorem:

x + 46 + 46 = 180

x = 180 - 92

x = 88

Thus, the value of x for the given bottom isosceles triangle is found to be x = 88°.

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What is the value of x in the right triangle below?
Show your work and round your answer to the nearest hundredth

Answers

Answer:

9

Step-by-step explanation:

Based on the Pythagorean theorem, A equals the square root of C squared minus B squared. By plugging in these numbers, you get 9.

the lifetimes of batteries created by a company are normally distributed with a mean of 105 hours and a standard deviation of 12 hours. what percentage of these batteries will last between 90.6 and 109.8 hours? state your answer as a percent rounded to the nearest hundredth, but do not include a % symbol in your answer.

Answers

Around 21.13% of the batteries will final(last) between 90.6 and 109.8 hours. 

To unravel this issue, ready to utilize the standard typical conveyance by standardizing the values utilizing the equation:

z = (x - μ) / σ

where

x is the esteem we need to discover the likelihood

μ is cruel(mean), and σ is the standard deviation.

So, for the lower conclusion of the extent, we have:

z1 = (90.6 - 105) / 12 ≈ -1.20

z1 = -1.20

And for the upper conclusion of the extension, we have the:

z2 = (109.8 - 105) / 12 ≈ 0.45

z2 =  0.45

We need to discover the rate of batteries that will final(last) between these two values, which compares to the area under the typical bend between z1 and z2.

Able to utilize a standard ordinary conveyance table or calculator to discover this zone, or we will utilize the properties of the typical conveyance to inexact it.

Since the typical conveyance is symmetric around the cruel, we know that the zone between z1 and z2 is the same as the range between -z2 and -z1 (i.e., the comparing values on the other side of the mean).

So, ready to discover the range between -z2 and -z1, which compares to the rate of batteries that will final between 90.6 and 109.8 hours:

P(-z2 < z < -z1) ≈ P(z < -z1) - P(z < -z2)

Employing a standard typical dissemination table or calculator, we discover:

P(z < -1.20) ≈ 0.1151

P(z < -0.45) ≈ 0.3264

So, the rate of batteries that will final between 90.6 and 109.8 hours is rough:

P(-z2 < z < -z1) ≈ 0.3264 - 0.1151 ≈ 0.2113

Increasing by 100%, we get:

0.2113 * 100% ≈ 21.13D

44 Subsequently, roughly 21.13% of the batteries will final between 90.6 and 109.8 hours. 

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A nursery school playground is 160 m long and 80 m
wide. In it, an 80 m by 80 m section is kept for the
swings, and in the remaining portion, there are 1.5
m wide paths parallel to the width and length. The
remaining area is covered by grass. Find the area
covered by grass.
1.5 m
1.5 m
80 m
Swings
-80 m-
Grass area =
80 m

3

Answers

The area covered by grass in the nursery school playground is 5760 square meters.

How can we find the area ?

To find the area covered by grass in the nursery school playground, we first need to calculate the total area of the playground, and then subtract the areas of the swings and the paths.

Given:

Length of playground = 160 m

Width of playground = 80 m

Width of swings = 80 m

Width of paths = 1.5 m

Total area of the playground = Length × Width = 160 m × 80 m = 12800 m²

Area of the swings = Width of swings × Width of swings = 80 m × 80 m = 6400 m²

Since there are two sides of the swings that are parallel to the length of the playground, we need to subtract the area of the paths along those two sides. The total width of the paths is 1.5 m + 1.5 m = 3 m.

Area of the paths along the length = Length of playground × Width of paths = 160 m × 3 m = 480 m²

Similarly, since there are two sides of the swings that are parallel to the width of the playground, we need to subtract the area of the paths along those two sides.

Area of the paths along the width = Width of playground × Width of paths = 80 m × 3 m = 240 m²

Now, we can calculate the remaining area covered by grass by subtracting the area of the swings and the areas of the paths from the total area of the playground:

Area covered by grass = Total area of playground - Area of swings - Area of paths along length - Area of paths along width

Area covered by grass = 12800 m² - 6400 m² - 480 m² - 240 m²

Area covered by grass = 5760 m²

So, the area covered by grass in the nursery school playground is 5760 square meters.

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RIGHT ANSWER GETS BRAINLIEST POINTS AND 15 POINTS. Fill in the blanks with greater or less

Answers

Answer:  The mean of data set K is greater than the mean of data set L.

The median of data set K is greater than the median of data set L

Step-by-step explanation:

we need to calculate the mean (average) of each data set and compare them.

Mean of data set K = (28 + 145 + 112 + 57 + 130) / 5 = 112.4

Mean of data set L = (141 + 171 + 68 + 124 + 43) / 5 = 109.4

'Arranging the values in data set K in ascending order, we get:

28, 57, 112, 130, 145

The median of data set K is the middle value, which is 112.

The mean of data set L is 109.4.

   

Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours.

The equation 3t = 5(3 – t) can be used to find the time it took Stu to hike one way.

How long did it take Stu to hike the trail one way?


hours

How long is the trail?


miles

What is the total distance Stu traveled?


miles

Answers

To find the time it took Stu to hike the trail one way, we can use the equation given:

3t = 5(3 - t)

Expanding the right side, we get:

3t = 15 - 5t

Adding 5t to both sides, we get:

8t = 15

Dividing both sides by 8, we get:

t = 15/8 = 1.875 hours

Therefore, it took Stu 1.875 hours to hike the trail one way.

To find the length of the trail, we can use the formula:

distance = rate x time

When hiking, Stu traveled at a rate of 3 miles per hour, so the distance he covered in one way is:

distance = 3 x 1.875 = 5.625 miles

Since Stu hiked the trail one way and then ran back on the same trail, the total length of the trail is twice the distance he covered in one way:

total distance = 2 x 5.625 = 11.25 miles

Therefore, the trail is 11.25 miles long.

To find the total distance Stu traveled, we can add the distance he covered while hiking to the distance he covered while running back:

total distance = 5.625 + 5.625 = 11.25 miles

Therefore, Stu traveled a total distance of 11.25 miles.

What is the coordinate of R

Answers

Answer:

if you go into your reading lessone on one of the sentences in page 2 or 4 there is the answer hope this helped

Step-by-step explanation:

5. Carrie Burnside is single, earns $350. 15 weekly, and claims 1 allowance.

6. Ray Barbee, a radio announcer, is single, earns $300. 74 weekly, and

claims 2 allowances.

7. Stephen Jensen, a pharmacist, is married, earns $369. 23 weekly, and

claims 2 allowances.

8. Lisa Steamer is married, earns $290. 34 weekly as a receptionist, and

claims no allowances.

9. Catherine Hall, a restaurant hostess, earns $208. 35 a week. She is single

and claims 2 allowances.

10. Veterinarian Ike Stone earns $925. 32 a week. He is single and claims

1 allowance.

11. Doug Smalley, a meteorologist, is married and earns $1,304. 30 a week.

He claims 2 allowances.

12. Kristen Martinez, a dentist, is married, earns $1,352. 75 a week, and

claims 1 allowance.

Answers

Carrie will have $15,481.24 after taxes for a year assuming she works 52 weeks.

First, let's calculate the total taxes she pays each week:

Federal income tax rate = 10% of $350.15 = $35.02

State income tax rate = 5% of $350.15 = $17.51

Total taxes per week = $35.02 + $17.51 = $52.53

Now, we can calculate the total amount of taxes she pays for a year:

Total taxes for a year = $52.53 x 52 weeks = $2,731.56

Amount Carrie will have after taxes for a year:

Annual income before taxes = $350.15 x 52 weeks = $18,212.80

Net income after taxes = Annual income before taxes - Total taxes for a year

Net income after taxes = $18,212.80 - $2,731.56 = $15,481.24

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--The complete Question is, Carrie Burnside is single, earns $350.15 weekly, and claims 1 allowance. If the federal income tax rate is 10% plus an additional 5% state income tax rate, how much will Carrie have after taxes for a year assuming she works 52 weeks? --

Convert the angle -4 radians to degrees, rounding to the nearest 10th.

Answers

The angle -4 radians is equal to -229.0 degrees when rounded to the nearest 10th.

To convert from radians to degrees, we need to multiply the angle by 180/π. Therefore, to convert -4 radians to degrees, we have:

-4 radians x 180/π ≈ -229.2 degrees

Rounding this to the nearest 10th gives us:

-229.2 degrees ≈ -229.0 degrees

Therefore, the angle -4 radians is equal to -229.0 degrees when rounded to the nearest 10th.

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A brick layer has 20 stacks with an equal number of bricks on them. If the total weight of all the bricks is 3,264 pounds, how much does each stack of bricks weigh?
A.
162.1 pounds
B.
164.1 pounds
C.
162.2 pounds
D.
163.2 pounds

Answers

each stack of bricks weighs 163.2 pounds. So the answer is D) 163.2 pounds. we need to form equation to solve this

what is equation  ?

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), that are separated by an equal sign (=). An equation tells us that the expressions on both sides have the same value or are equivalent.

In the given question,

If there are 20 stacks with an equal number of bricks on them, let's call the number of bricks on each stack "x". Then the total number of bricks is:

total number of bricks = 20 stacks × x bricks/stack = 20x bricks

We are also told that the total weight of all the bricks is 3,264 pounds. Let's call the weight of each brick "w". Then the total weight is:

total weight = number of bricks × weight per brick = (20x) bricks × w pounds/brick

We want to find the weight of each stack of bricks, which is equal to the weight of a certain number of bricks. Let's call this weight "s". Then we have:

s pounds/stack = x bricks/stack × w pounds/brick

We can solve for "s" by using the two equations above:

total weight = (20x) bricks × w pounds/brick = 3,264 pounds

s pounds/stack = x bricks/stack × w pounds/brick

Dividing the first equation by 20x, we get:

w pounds/brick = 3,264 pounds ÷ (20x) bricks/stack = 163.2 pounds/stack

Substituting this into the second equation, we get:

s pounds/stack = x bricks/stack × 163.2 pounds/stack

Dividing both sides by x, we get:

s pounds/stack ÷ x bricks/stack = 163.2 pounds/stack

Simplifying, we get:

s pounds/brick = 163.2 pounds/stack

Therefore, each stack of bricks weighs 163.2 pounds.

So the answer is D) 163.2 pounds.

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!!PLEASE HELLPPP MEEEE!!

Answers

It will take approximately 25 years for $7,000 to double in an account that pays 2.8% simple interest.

How long it take for $7,000 to double with 2.8% S.I?

The 70 rule is a helpful shortcut for calculating the number of years it will take an investment to double in value using simple interest. The formula is 70 divided by the interest rate.

In this case, we have an interest rate of 2.8%, so we can calculate that it will take approximately 70/2.8 = 25 years for $7,000 to double in value. It's important to note that this rule assumes the interest rate remains constant over the entire period, which may not always be the case in real-world investments.

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Which of the following is equivalent to Log7(a) • logb(7)

Answers

Answer:

[tex] log_{7}(a) \times log_{b}(7) [/tex]

[tex] \frac{ log(a) }{ log(7) } \times \frac{ log(7) }{ log(b) } = \frac{ log(a) }{ log(b) } = log_{b}(a) [/tex]

Suppose 15% of x equals 20% of y. What percentage of x is y?


A 5

B 35

C 75

D 133 1/3

E 300

Answers

If 15% of "x" is 20% of "y", then "y" is 75 percent of "x", the correct option is (c).

The "Percentage" is defined as a way to express the proportions or rates in terms of a "relative-scale" out of 100,

We know that, 15% of "x" equals 20% of "y".

Mathematically, this can be expressed as,

0.15x = 0.20y,           ...because 15% = 0.15 and 20% = 0.20;

To find what percentage of x is y, we need to express "y" as a percentage of "x".
On solving further,

We get,

⇒ 0.15x = 0.20y,

⇒ y = (0.15x)/0.20,

⇒ y = 0.75x

It is read as "y" is read as 75% of "x".

Therefore, "y" is 0.75 times "x", or 75% of "x", Option(c) is correct.

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George had 660 points in a reward program he used 35% of the points to redeem a voucher how many points were left in his reward program ?
In percentage and the explanation

Answers

Answer: the point that were left are 429

Step-by-step explanation:

i got this by multiplying 660 and 35% or .35 and got 429 and the amount left is 65% and to get that you would subtract 100% and 35% which gets you 65%.

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in this experiment, you are asked to repeat the time measurements for each height a few times. why do we want to repeat these measurements? to reduce the statistical errors to reduce the systematic errors

Answers

In this experiment, we want to repeat the time measurements for each height a few times.
By repeating the measurements, we can reduce the statistical errors associated with random fluctuations in the measurement process. These fluctuations can be caused by factors such as variations in the environmental conditions or in the way the measurements are taken. By taking multiple measurements and calculating the average, we can reduce the impact of these random errors.
By reducing statistical errors, repeating the measurements can also help to reduce systematic errors, which are caused by consistent biases or inaccuracies in the measurement process. By taking multiple measurements and analyzing their differences, we can identify and correct for any systematic errors.
Hence, repeating the time measurements for each height a few times helps to increase the accuracy of the results by reducing both statistical and systematic errors.

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the mass of substance A decreases at the rate of 20% every 6 hours. 500 grams of substance A is put in a dish. work out the mass of substance A in the fish at the end of 12 hours

Answers

Answer: We can use the formula for exponential decay to find the mass of substance A in the dish after 12 hours:

A = A0 * e^(-kt)

where:

A0 = initial mass of substance A (500 grams)

A = mass of substance A after time t

k = decay constant

t = time (in hours)

Since the mass of substance A decreases at the rate of 20% every 6 hours, we can find the decay constant as follows:

20% = 0.2 = e^(-k*6)

Taking the natural logarithm of both sides, we get:

ln(0.2) = -k*6

k = -ln(0.2)/6

k ≈ 0.1155

Substituting the values of A0, k, and t into the formula for exponential decay, we get:

A = 500 * e^(-0.1155*12)

A ≈ 169.2 grams

Therefore, the mass of substance A in the dish at the end of 12 hours is approximately 169.2 grams.

Step-by-step explanation:

The mass of substance A in the dish at the end of 12 hours would be 320 grams.

To solve this problem

The mass of substance A decreases at a rate of 20% every 6 hours. After 6 hours, the mass of substance A remaining in the dish would be:

500 - (20/100) * 500

500 - 100

400 grams

After another 6 hours (i.e. at 12 hours), the remaining mass of substance A would be:

400 - (20/100) * 400

400 - 80

320 grams

Therefore, the mass of substance A in the dish at the end of 12 hours would be 320 grams.

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the scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 10. what test score is 0.6 standard deviations above the mean?

Answers

The test score that is 0.6 standard deviations above the mean is 111.

We can use the formula for z-score to find the test score that is 0.6 standard deviations above the mean:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.

In this case, we want to find x when z = 0.6, μ = 105, and σ = 10:

0.6 = (x - 105) / 10

Multiplying both sides by 10, we get:

6 = x - 105

Adding 105 to both sides, we get:

x = 111

Therefore, the test score that is 0.6 standard deviations above the mean is 111.

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The test score that is 0.6 standard deviations above the mean is 111.

To find the test score that is 0.6 standard deviations above the mean, we can use the formula

z = (x - μ) / σ

where z is the number of standard deviations from the mean,

x is the test score we want to find,

μ is the mean of the distribution (105), and

σ is the standard deviation of the distribution (10).

We know that the desired test score is 0.6 standard deviations above the mean,

so we can set z = 0.6 and solve for x:

0.6 = (x - 105) / 10

Multiplying both sides by 10, we get:

6 = x - 105

Adding 105 to both sides, we get:

x = 111

Therefore, the test score that is 0.6 standard deviations above the mean is 111.

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a group of 155 students at a private university were asked if they are full-time or part-time and if they have gym memberships. the results are shown in the table below. given that a randomly selected survey participant is part-time, what is the probability that this student has a gym membership?

Answers

the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

How to solve the question?

To calculate the probability that a randomly selected part-time student has a gym membership, we need to use conditional probability. Specifically, we need to use Bayes' theorem:

P(Gym Membership | Part-Time) = P(Part-Time | Gym Membership) * P(Gym Membership) / P(Part-Time)

Where:

P(Gym Membership | Part-Time) is the probability that a student has a gym membership given that they are part-time.

P(Part-Time | Gym Membership) is the probability that a student is part-time given that they have a gym membership.

P(Gym Membership) is the overall probability of a student having a gym membership (regardless of whether they are full-time or part-time).

P(Part-Time) is the overall probability of a student being part-time (regardless of whether they have a gym membership).

Let's start by filling in the values we know from the table:

P(Part-Time) = (40 + 25) / 155 = 0.5484

P(Gym Membership) = (30 + 25) / 155 = 0.3226

P(Part-Time | Gym Membership) = 25 / (30 + 25) = 0.4545

To find P(Gym Membership | Part-Time), we need to calculate P(Part-Time and Gym Membership). We can use the formula:

P(Part-Time and Gym Membership) = P(Part-Time | Gym Membership) * P(Gym Membership)

Plugging in the values we know, we get:

P(Part-Time and Gym Membership) = 0.4545 * 0.3226 = 0.1463

Now we can use this value, along with P(Part-Time) and P(Gym Membership), to calculate P(Gym Membership | Part-Time):

P(Gym Membership | Part-Time) = 0.1463 / 0.5484 ≈ 0.2667

Therefore, the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

It's worth noting that this result is based on the assumption that the sample of 155 students is representative of the larger population of the university. If there are any biases or other factors that make this sample unrepresentative, then our calculated probability may not be accurate. Additionally, the results could be affected by other factors, such as the cost of gym membership or the availability of on-campus fitness facilities.

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 write a division expression for each 2. 5/6,3. 9/15,4. 10/25,5. 16/31

Answers

The division expressions are given below.

Given are divisions, we need to write their division expressions,

5/6 = 5÷6

9/15 = 9÷15 = 3÷5

10/25 = 10÷25 = 2÷5

16/31 = 16÷31

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Bottom of a flower pot has a diameter of 7 cm. How much space will the flower pot take up

Answers

The amount of space that the flower pot will take up is: 38.47 cm²

How to find the area of a circle?

We are given that the bottom of the given flower pot has a diameter of 7 cm.

Now, the space that the flower pot will cover is simply the area the the circle base.

Formula for the area of a circle is:

A = πr²

where:

A is area

r is radius

We have d = 7 cm

Thus: r = 7/2 = 3.5 cm

A =  π * 3.5²

A = 3.14 * 3.5²

A = 38.47 cm²

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Need help ASAP!!!

Jordyn likes to practice dancing while preparing for a math tournament. She spends 60 minutes every day practicing dance and math. To help her concentrate better, she dances for 20 minutes longer than she works on math.


Part A: Write a pair of linear equations to show the relationship between the number of minutes Jordyn practices math every day (x) and the number of minutes she dances every day (y). (5 points)


Part B: How much time does Jordyn spend practicing math every day? Show your work. (3 points)


Part C: Is it possible for Jordyn to have spent 60 minutes practicing dance if she practices for a total of exactly 80 minutes and dances for 20 minutes longer than she works on her math? Explain your reasoning. (2 points)

Answers

Answer:

  A: x +y = 60; y = x +20

  B: 20 minutes on math

  C: no

Step-by-step explanation:

You have some relations and some questions about dance times and math practice times with dance times longer than math practice by 20 minutes.

A. Equations

The given relations can be written as two equations:

  x + y = 60 . . . . . total time is 60 minutes

  y = x + 20 . . . . . dance time is 20 minutes longer than math time

B. Solution

We want the value of x. We can find that by using the second equation to substitute for y in the first equation:

  x + (x +20) = 60

  2x = 40 . . . . . . . . . subtract 20

  x = 20 . . . . . . . . divide by 2

Jordyn practices math 20 minutes every day.

C. More practice

If Jordyn dances for 60 minutes, then she will practice math for 60 -20 = 40 minutes. That brings her total practice time to 60 +40 = 100, which is more than 80.

It is not possible to spend 80 minutes total if she spends 60 minutes dancing.

(She could spend 50 minutes dancing, 30 minutes on math, and have a total practice time of 80 minutes.)

Final answer:

Jordyn spends 20 minutes each day practicing math. However, if her total practice time is 80 minutes, it would not be possible for her to spend 60 minutes practicing dance.

Explanation:

The total time Jordyn spends practicing both dancing and math is 60 minutes. If we establish the time she spends on math as 'x' and the time she spends dancing as 'y', we can establish the following and equations:

y = x + 20: This equation represents the fact that Jordyn dances 20 minutes longer than she works on math. x + y = 60: This equation represents the total time Jordyn spends on dancing and math combined.

To solve for 'x', substitute the first equation into the second to get x + (x + 20) = 60. Simplify to get 2x + 20 = 60. Subtract 20 from each side to get 2x = 40, and finally divide by 2 to get x = 20. Therefore Jordyn spends 20 minutes practicing math each day.

To answer Part C, if Jordyn practices for a total of exactly 80 minutes and dances 20 minutes longer than she does math, it would not be possible for her to spend 60 minutes practicing dance. The most amount of time she could spend dancing is 50 minutes (80 total minutes- 30 minutes for math).

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estimate 15.58 - 7.237 by first rounding each number to the nearest tenth

Answers

After rounding , The calculated result of 15.58 - 7.237 is therefore around  8.4

What does rounding mean?

When a number is rounded, it is approximated by using a smaller, more straightforward number that is near to the original value. For instance, 3.141 is the result of rounding 3.14159 to two decimal points.

We can round 15.58 to 15.6 and 7.237 to 7.2 to estimate 15.58 - 7.237 by first rounding each number to the nearest tenth

. After that, we may take 7.2 away from 15.6 to get:

15.6 - 7.2 = 8.4

The calculated result of 15.58 - 7.237 is therefore around  8.4

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Can someone please help me ASAP? It’s due tomorrow!! I will give brainliest if it’s all correct

Please do step a, b, and c

Answers

Answer:

Step A: The third quartile is 9.5, choice d.

Step B: The median of the data set is 6.5.

Step C: The IQR of the data set is 6, and we found this value by subtracting the first quartile from the third quartile (9.5 - 3.5 = 6).

Step-by-step explanation:

First, let's analyze the data set.

1 2 3 4 5 6 7 8 9 10 11 12

Since this data set is already sorted in numerical order, we can determine the median by finding the middle value that divides the data set in half. With 12 values in the data set, the median would be between the 6th and 7th numbers, so we can find this by using the calculation (6+7)/2 = 6.5.

                 6.5

{1 2 3 4 5 6} | {7 8 9 10 11 12}

With this median, we split our data set into two halves. Now, we can find the first quartile, or the 25th percentile, by finding the median of the first half. This would be the value between 3 and 4, so (3+4)/2 = 3.5.

       3.5        6.5

{1 2 3} | {4 5 6} | {7 8 9 10 11 12}

We can repeat this step in the second half in order to find the third quartile or the 75th percentile. The median of the second half would be between 9 and 10, so (9+10)/2 = 9.5.

       3.5         6.5        9.5

{1 2 3} | {4 5 6} | {7 8 9} | {10 11 12}

Now we know Q1 (first quartile) and Q3 (third quartile), we can find the IQR which is Q3 - Q1, so Q3 - Q1 = 9.5 - 3.5 = 6.

So now we can answer the question:

Step A: The third quartile is 9.5, choice d.

Step B: The median of the data set is 6.5.

Step C: The IQR of the data set is 6, and we found this value by subtracting the first quartile from the third quartile (9.5 - 3.5 = 6).

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