Answer: Split it in half to turn it into a triangle! The hypotenuse if the triangle will give you the diagonal length of the suitcase, because it’s a rectangle. Hope this helps :D
Step-by-step explanation:
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?
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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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
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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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?
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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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?
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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help help help urgenttt.. i need this done today by 11:59 pmm
The one less likely to be picked is the one with less & (Vice Versa).
To find the probability: (#of paper clips/total amount of items)
Consider the probability that at most 46 out of 319 DVDs will malfunction.
Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
Answer
2 Points
Keypad
Tables
Area to the right of 45. 5
Area to the right of 46. 5
Area to the left of 45. 5
Area to the left of 46. 5
Area between 45. 5 and 46. 5
The best description of the area under the normal curve that would be used to approximate binomial probability is 'Area to the left of 46.5'.
To approximate the binomial probability, we can use the normal distribution as an approximation for the binomial distribution when the sample size is large enough, and the probability of success is not too close to 0 or 1. The mean of the normal distribution is equal to the mean of the binomial distribution, which is np, and the standard deviation of the normal distribution is equal to the square root of npq, where q is the probability of failure.
In this case, the number of DVDs that may malfunction follows a binomial distribution with parameters n = 319 and p = 1/100, where 1/100 is the probability of a DVD malfunctioning. Therefore, the mean of the binomial distribution is np = 3.19, and the standard deviation is [tex]\sqrt{npq}[/tex] = [tex]\sqrt{3.19*0.99}[/tex] ≈ 1.77.
To find the probability that at most 46 out of 319 DVDs will malfunction, we need to find the area under the normal curve to the left of 46.5 (since we are interested in the probability of at most 46 malfunctions, which includes 46.5 as well). Therefore, the answer is 'Area to the left of 46.5'.
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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.
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? --
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
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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Which of the following is equivalent to Log7(a) • logb(7)
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]
please help i don’t understand and need to find d
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
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.
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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 write a division expression for each 2. 5/6,3. 9/15,4. 10/25,5. 16/31
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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estimate 15.58 - 7.237 by first rounding each number to the nearest tenth
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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Bottom of a flower pot has a diameter of 7 cm. How much space will the flower pot take up
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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What happens if the red lines are NOT parallel. Which angle types are still congruent? (Please help...thanks)
Answer:
When the red lines in a geometric figure are not parallel, the congruency of angles may vary. Vertical angles formed by the intersection of non-parallel lines are always congruent, while corresponding angles and alternate interior angles may or may not be congruent. The congruency of angles depends on the specific relationship between the angles and the lines in the figure, and further analysis of the figure would be necessary to determine which angles are congruent.
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
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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What is the media, mean, mode, and range for 92, 63, 22, 80, 63, 71, 44,35
Answer:
Answers down below!
Step-by-step explanation:
Mean: 58.75
Median: 63
Range: 70
Mode: 63
Hope this helps!
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
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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John travels north 36 miles and then east 48 miles. o that he is 0 miles from his original starting point. Which equation could NOT be used to determine if these measurements form a right triangle?
The incorrect measurements of the right triangle is 36² + 60² = 48²
Given data ,
Let the triangle be represented as ABC
Now , let the height of the triangle be AB = 36 miles north
Let the base of the triangle be BC = 48 miles east
Now , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , 36² + 48² = 60²
So , the incorrect option from the data is 36² + 60² = 48²
Hence , the triangle is formed
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Answer Immeditely Please
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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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
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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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
m²
3
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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What is the value of x in the right triangle below?
Show your work and round your answer to the nearest hundredth
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.
What is the coordinate of R
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:
HELP FAST PLEASE
Simplify: m5 p8 m6 p10
1) mp¹3. mp¹6
2) m11 p18
3)m18.p11
4)(m. p)29
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.
!!PLEASE HELLPPP MEEEE!!
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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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
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).
RIGHT ANSWER GETS BRAINLIEST POINTS AND 15 POINTS. Fill in the blanks with greater or less
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.
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
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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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)
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. EquationsThe 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. SolutionWe 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 practiceIf 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.)
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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