Hey there! I'm happy to help!
The IQR is how far apart the first and third quartiles are, which are the middle numbers of the first and second halves of a data set. Let's find some random numbers that are 17 apart. We will use 3 and 20.
Now, we have to create a data set where 3 is the middle number of the first half and 20 is the middle number of the second half. Let's have one with six numbers because that's a good amount I guess. Remember that the data has to be going from least to greatest.
In our first half we will have one number that is smaller than 3 and one bigger than three so that 3 is in the middle. Here's an example of what our first half should look like:
2,3,5
Now, for our second half, we need a number smaller than 20 and one greater than 20 so 20 is the the middle. Here's the second half I've made for you.
16,20,100
So, the data set I've created for you is 2,3,5,16,20,100. However, there are many other possibilities as you've seen.
My answers for your question 1 and 2 are in the explanation I've done, and here's the math that shows that the interquartile range is 17.
You split the data in half.
2,3,5, 16,20,100
Q1 is the middle number of the first, which is 3. Q3 is the middle of the second, which is 20.
You find how far apart they are by subtracting 3 from 20.
20-3=17.
The IQR is 17.
Have a wonderful day! :D
Please I need help!
Write the equation of the line that passes through the points (7, -4) and ( 1, 3), first in point-slope form, and then in
slope intercept form
The slope of the line is
When the point (7, -4) is used, the point-stope form of the line is
The slope intercept form of the line is
Answer:
1)
[tex]\text{ Slope = -3}[/tex]
2)
[tex]y+4=-\frac{7}{8}(x-7)[/tex]
3)
[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]
Step-by-step explanation:
We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.
1)
First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:
[tex]m=\frac{3-(-4)}{-1-7}[/tex]
Subtract. So, our slope is:
[tex]m=\frac{7}{-8}=-7/8[/tex]
2)
Now, let's use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:
[tex]y-(-4)=-\frac{7}{8}(x-7)[/tex]
Simplify. So, our point-slope equation is:
[tex]y+4=-\frac{7}{8}(x-7)[/tex]
3)
Finally, we want to convert this into slope-intercept form. So, let's solve for our y.
On the right, distribute:
[tex]y+4=-\frac{7}{8}x+\frac{49}{8}[/tex]
Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:
[tex]y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}[/tex]
Subtract. So, our slope-intercept equation is:
[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]
And we're done!
Answer: Shown Below
Step-by-step explanation:
1. -7/8
2. y+4= (-7/8)(x-7)
3. y=(-7/8)x+ (17/8)
Just did it
From the set {6, 16, 24}, use substitution to determine which value of x makes the inequality true. 4 + x < 20 A. 16 B. 6 C. none of these D. 24
================================================
Explanation:
In math, the term "substitution" basically means "replace". Keep in mind that x is a placeholder for a number. Think of it as a box we place a number inside.
We have the items {6, 16, 24} to use as replacements for x. We only do one number at a time
Let's try x = 6
4 + x < 20
4 + 6 < 20 ... replace x with 6
10 < 20 ... this is a true statement as 10 is less than 20
So x = 6 is a solution
Let's try x = 16
4+x < 20
4+16 < 20
20 < 20 ... this is false because we can't have a number smaller than itself
Lastly, let's try x = 24
4+x < 20
4+24 < 20
28 < 20 ... also false; 28 is not smaller than 20
We've shown that x = 16 and x = 24 are not solutions. Only x = 6 is a solution from the set {6,16,24}. This is why the answer is choice B.
-----------------
Alternative method:
4+x is the same as x+4. We can add two numbers in any order we want.
x+4 < 20 solves to x < 16 after subtracting 4 from both sides. So the set of solutions is anything smaller than 16. Looking at {6,16,24} we see that the only allowed answer is x = 6.
x = 16 is not a solution because x < 16 would turn into 16 < 16, but again we can't have a number smaller than itself.
A tiling company completes two jobs. The first job has $1200 in labor expenses for 40 hours worked, while the second job has $1560 in labor expenses for 52 hours worked. The relationship between the labor expenses and the hours worked is linear. Which equation can be used to calculate the y-intercept of the linear equation? 1200 = 40 (40) + b 1560 = 30 (40) + b 1560 = 30 (52) + b 1200 = 52 (30) + b
The slope (change in y/change in x) of the line is (1560 - 1200)/(52 - 40), which is equal to 30. We can plug this into the equation y = mx + b using either the point (40, 1200) or (52, 1560). The slope is represented by m and the y - intercept by b. Therefore, the two possible equations you could use are:
1200 = 30(40) + b
or 1560 = 30(52) + b
Using either equation, you'll get that b is equal to 0, which makes sense in the context of the problem, since it's reasonable to expect that the labor expenses would be 0 for 0 hours worked.
Answer:
im pretty sure its C
Step-by-step explanation:
Hope this helped! :) Oh and I took the test on edge and got a good grade, but i didnt know if i got this right or wrong bc i couldnt look back at it
Can someone help me please
Answer:
No more than ≥
Not under ≤
No less than ≤
maximum ≥
Greater than or equal to ≥
Less than or equal to ≤
Does not exceed ≥
At most ≥
At least ≤
Minimum ≤
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. 23 and 44
Answer:
21 < x < 67 answer
Range is between 21 and 67 where 21 and 67 are not included in the range.
Step-by-step explanation:
we will use the concept of triangle
1. sum of two sides of triangles is always greater than the third side
2. difference of trow sides of triangle is always less than the third side.
Given two sides
23 and 44
let the third side b x
using first concept
sum of to sides = 23+44 = 67
thus,
x <67
using second concept
Difference of to sides = 44 - 23 = 21
thus,
x > 21
Combining
x <67 and x > 21
21 < x < 67 answer
Range is between 21 and 67 where 21 and 67 are not included in the range.
Are the arcs below congruent?
A. No, because the ares do not have the same measure.
B. There is not enough information to determine.
C. No because the ares are not oriented the same
D. Yes because the ares have the same measure.
Answer:
A
Step-by-step explanation:
Answer:
B
You do not have enough information to solve the question.
A train travels 60km in y minutes.If this average speed is 400km per hour,find the value of y
Answer:
9
Step-by-step explanation:
Speed of the train is:
60 km / y minAnd average speed is:
400 km / h = replacing 1 h with 60 min400 km/ 60 min = 20 km /3 min = 60 km / 9 minComparing the two above, we see y= 9
help me plz i want help
Answer:
2/9
Step-by-step explanation:
We want blue green in any order. That means BG or GB
There are 9 possibilities
P ( BG or GB ) = number of BG or GB's / total
= 2/9
Question below. Please answer it, its math.
Answer:
- 0.8
Step-by-step explanation:
The first thing we want to do here is simplify the expression -
[tex]\frac{3}{5}[/tex]( 2x + 5 ) - 2x, Distribute the " [tex]\frac{3}{5}[/tex] " to elements within the parenthesis
= [tex]\frac{3}{5}[/tex] [tex]*[/tex] 2x + [tex]\frac{3}{5}[/tex] [tex]*[/tex] 5 - 2x, Focus on simplifying the expression " [tex]\frac{3}{5}[/tex] [tex]*[/tex] 2x + [tex]\frac{3}{5}[/tex] [tex]*[/tex] 5 "
= [tex]2\cdot \frac{3}{5}x+5\cdot \frac{3}{5}[/tex] - 2x
= [tex]\frac{6x}{5}+3[/tex] - 2x, Combine fractions
= [tex]-\frac{4x}{5}[/tex] + 3
= [tex]-\frac{4}{5}[/tex]x + 3
So we have our simplified expression " [tex]-\frac{4}{5}[/tex]x + 3, " with [tex]-\frac{4}{5}[/tex] being the coefficient of x. Our requirements are that this fraction should be expressed as a decimal, so we can simply divide the numerator by the denominator to figure that out,
- 4 / 5 = - 0.8,
Solution = - 0.8
Students in a school were asked to collect old bottles as part of a recycling drive. Some of the data recorded at the drive is shown in the histogram below: A histogram is shown with title Recycle Drive Collection. On the horizontal axis the title is Number of bottles. The title on the vertical axis is Students. The range on the horizontal axis is 0 to 5, 6 to 11, and 12 to 17. The values on the vertical axis are from 0 to 10 at intervals of 1. The bar for the first range is till 3, the bar for the second range is till 6, the bar for the third range is till 1. Help 50 points :0 Which information is not provided in the histogram? A : The total number of students who collected bottles B : The number of students who collected 6 or more bottles C :The number of students who collected exactly 4 bottles D :The total number of students who collected 12 or more bottles
Answer:
A) C
B) 47 inches
Step-by-step explanation:
A) The range on the horizontal axis is 0 to 5, we cannot tell how many students collected the exact number of bottles.
The correct option would be the number of students who collected exactly 4 bottles.
B) The mean of a data set is written as:
[tex]mean = \frac{sum \: of \: terms}{number \: of \: terms}[/tex]
[tex]mean=\frac{45+48+49+40+53}{5}[/tex]
[tex]mean=\frac{235}{5}[/tex]
[tex]mean=47[/tex]
The average height of the students is 47 inches.
Answer:
A & B
Step-by-step explanation:
Draw a picture to help you find the answers.
When Andrew got in his car to drive home from work, be saw that his fuel gauge
indicated that the tank was1/2 full. When he pulled into his driveway, the fuel gauge
showed that he used 1/3 of the fuel that was in the tank before he started his trip home.
3) How full was the tank when Andrew arrived home?
4) If the fuel tank had 4 gallons of gasoline left when he got home, how many
gallons of gasoline can the fuel tank hold?
Answer:
2/6 (1/3)
12 gallons
Step-by-step explanation:
3) 1/2x1/3=1/6, so he'd used 1/6 of a tank.
1/2-1/6=
3/6-1/6=2/6. So the tank was 2/6 full, or 1/3 full when he got home.
4) If it's 1/3 full and has 4 gallons, it can hold 12 gallons. (4x3)
Which is the best approximation for the solution of the system of equations? y = A system of equations. y equals negative StartFraction 2 over 5 EndFraction x plus 1. y equals 3 x minus 2.x + 1 y = 3x – 2 A coordinate grid with 2 lines. The first line passes through (0, 1) and (5, negative 2). The second line passes through (0, negative 2) and (1, 1). the lines appear the intersect at a point that is almost to 1 and almost to 1. (0.45, 0.88) (0.88, 0.65) (0.88, 1.1) (1.3, 0.88)
Answer:
(0.88, 0.65)
Step-by-step explanation:
Given that the two equations of the line are:
y =( -2/5)x + 1 and y = 3x – 2. To find the solution, we have to solve the equations simultaneously.
y =( -2/5)x + 1 . . . 1)
y = 3x – 2 . . . 2)
Subtracting equation 1 from equation 2:
3.4x -3 = 0
3.4x = 3
Dividing through by 3.4
3.4x/3.4 = 3/3.4
x = 0.88
To find y, substitute x = 0.88 in equation 2:
y = 3(0.88) - 2
y = 2.65 - 2
y = 0.65
This means that the solution to the system of equations is the point of intersection of the two lines which is at (0.88, 0.65)
Answer:
(0.88, 0.65)
Step-by-step explanation:
i just took the test
3. What is the degree of the polynomial 3x^4 + 2x^2 + 5x? *
Answer:
the degree of that polynomial is 4
May someone please explain what a central tendency is I do not understand what it exactly means
4. A local orchard packages apples in bags. When full, the bags weigh 5 pounds
each and contain a whole number of apples. The weights are normally distributed
with a mean of 5 pounds and a standard deviation of 0.25 pound. An inspector
weighs each bag and rejects all bags that weigh less than 4.75 pounds. What
percentage of bags will the inspector reject? *
Your answer
Answer: The percentage of bags will the inspector reject = 15.87%
Step-by-step explanation:
Given, The weights of apple bags are normally distributed with a mean of 5 pounds and a standard deviation of 0.25 pound.
i.e. [tex]\mu=5[/tex] and [tex]\sigma=0.25[/tex]
Let X be the weight of any random apple bag.
Since an inspector weighs each bag and rejects all bags that weigh less than 4.75 pounds.
Then, the probability of bags will be rejected = probability that bags weigh less than 4.75 pounds.
[tex]=P(X<4.75)\\\\=P(\dfrac{X-\mu}{\sigma}<\dfrac{4.75-5}{0.25})\\\\=P(z<-1)\ \ \ [z=\dfrac{X-\mu}{\sigma}][/tex]
[tex]=1-P(z<1)\\\\=1-0.8413\ \ \ [\text{By z-value table}]\\\\=0.1587=15.87\%[/tex]
Hence, the percentage of bags will the inspector reject = 15.87%
Please help soon! Will give 5 starts, thanks, and brainliest! Thank you! The hypotenuse of a right triangle measures 6sqrt(2) inches and one angle is 45 degrees. What is the number of square inches in the area of the triangle?
Answer:
Area = 18 sq. inches
Step-by-step explanation:
Hypotenuse = 6√2
as it is a right angled triangle and one of the angles is 45°,
=> the other angle is also 45°.
According to 45°-45°-90° theorem,
the side is 1/√2 times the hypotenuse.
Therefore, side = 6√2 × 1/√2
=6 inches.
Area of triangle = 1/2 × base × height
= 1/2 × 6 × 6
= 1/2 × 36
=18 sq. inches
Does anyone know this
Answer:
I believe it's 220 in.
Step-by-step explanation:
area = base 1 + base 2 divided by 2 times the height
FIRST GETS BRAINLLEST If you spin the spinner below 150 times, which of the following outcomes are reasonable? Select all that apply. A) Lands on blue 60 times B) Lands on red 120 times C) Lands on yellow 90 times D) Lands on yellow 44 times
Answer:
Step-by-step explanation:
Spinner pointing to red, blue or yellow is equally likely:
P(blue) = P(yellow) = P(red) = 1/3.
In a perfect world, the spinner would land on blue (1/3)(150) = 50 times; on red 50 times and on yellow 50 times.
If in real life the spinner lands on yellow 44 times (C) is most reasonable, as that is closest to the ideal 50 times.
A) Lands on blue 60 times - Reasonable outcome.
B) Lands on red 120 times - Not reasonable.
C) Lands on yellow 90 times - Not reasonable.
D) Lands on yellow 44 times - Reasonable.
If the spinner has three colors (red, yellow, and blue) with equal areas, and we spin it 150 times, the reasonable outcomes would be:
A) Lands on blue 60 times - Reasonable since there is an equal chance of landing on each color, and 60 is a fraction of 150 that falls within the expected range.
B) Lands on red 120 times - Not reasonable since the expected number of times for each color is 150 / 3 = 50, and 120 is significantly higher than this expected value.
C) Lands on yellow 90 times - Not reasonable since the expected number of times for each color is 150 / 3 = 50, and 90 is significantly higher than this expected value.
D) Lands on yellow 44 times - Reasonable since there is an equal chance of landing on each color, and 44 is a fraction of 150 that falls within the expected range.
Therefore, the reasonable outcomes would be A) Lands on blue 60 times and D) Lands on yellow 44 times.
To know more about outcome, refer here:
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ten times a number increased by eighty four equals 194. what is the number
Answer: x = 11
Step-by-step explanation:
10x+84=194
10x = "10 times a number"
+84 = "increased by eighty four"
=194 = "equals 194"
10x+84=194
Subtract 84
10x = 110
Divide by 10
x = 11
Hope it helps <3
Answer:
The number is 11
Step-by-step explanation:
Represent the number by n.
Then: 10n + 84 = 194.
Subtracting 84 from both sides, we get: 10n = 110, and so:
n = 110/10 = 11
PLS HELP ASAP!!!Which phrase describes the algebraic expression 8t + 7? the product of 8 and 7 more than a number the quotient of 8 and 7 8 times the sum of a number and 7 8 times a number plus 7
Answer:
8 times a number plus 7
Step-by-step explanation:
if helps please mark brainliest!! Thanks!
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is D.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression 8t+7 can be best described as 8 times a number plus 7.
Learn more about Expression:
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2) Which of the following could be the equation
of the graph shown below?
Answer:
D
Step-by-step explanation:
From the graph, the solutions are x = -2 and x = 3, therefore, the equation must be (x - (-2)) * (x - 3) = (x + 2)(x - 3).
A dress is on sale for 20% off.
Including the discount and 9%
tax, the sales price of the dress
is $74.12. What is the price of
the dress before the discount
and tax?

Answer:
Step-by-step explanation:
let's say the price of the dress in the beginning is 100x
the on sale price decreases 80x
80x = 74.12
100 x = 92.75
Write an algebraic equation to match each graph. (These graphs are not drawn to scale!)
Answer:
y=|x+1|
Step-by-step explanation:
The y value appears to be 1 more than the x value, so we need to add one to the x to make them even. (x+1)
But the y value doesn’t go below zero, so we need to add the absolute value brackets |x+1|
So y=|x+1|
The graph represents the equation : g(x) = |x + 1|
We have a graph given to us.
We have to write the algebraic expression depicting this graph.
What is Modulus of the function y = f(x) = x ?The modulus of the function y = f(x) = x is given by -
y = |x| = [tex]\left \{ {{x\;\;for\;x > 0} \atop {-x\;\;for\;x < 0}} \right.[/tex]
Using the above property, we can find out the number of solutions of any modulus equation.
The algebraic equation for the graph can be written as -
g(x) = [tex]\left \{ {{x+1;\;for\;x \geq 0} \atop {-x-1\;for\;x < 0}} \right.[/tex]
In the form of modulus function, we can write the above equation as -
g(x) = |x + 1|
Hence, the graph represents the equation : g(x) = |x + 1|
To solve more questions on modulus function, visit the following link -
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The time it takes to drive from Orangeville to the Vaughan Mills Mall is normally distributed with a mean of 52 minutes and standard deviation of 5 minutes. What intervals could you estimate, using the knowledge from this activity that do not include the mean as a max or min? For example, is an interval we could estimate? However, it includes the mean as the maximum of the interval. Another example is as an example of a probability interval that we know from this activity, but it includes the mean as the minimum.
Given:
Mean of 52 minutes and a standard deviation of 5 minutes.
Solution:
According to the empirical rule: For the normal distribution, all of the data will fall within three standard deviations of the mean.
1: 68% of the data will fall within the first standard deviation from the mean.
2: 95% of the data fall within two standard deviations.
3: 99.7% of the data fall within three standard deviations.
[tex]3SD =99.7\%=\mu\pm3\sigma\\[/tex]
Therefore, the 7 intervals and their probabilities are:
1. [tex]1SD=0.68=P(47<x<57)[/tex]
2. [tex]0.95=P(42<x<62)[/tex]
3. [tex]0.997=P(37<x<67)[/tex]
4.[tex]13.5\%=P(42<x<47)[/tex]
5.[tex]13.5\%=P(57<x<62)[/tex]
6. [tex]2.35\%=P(37<x<42)[/tex]
7.[tex]2.35\%=P(62<x<67)[/tex]
If y varies inversely with x and y= 17
when z = 11
when y = 11
find y when x=19
.
Richie and his brother have a paper route. Together they can deliver all of the papers in 40 minutes, and Richie can do it alone in 90 minutes. Richie’s brother slept in one day, leaving Richie to deliver alone for 30 minutes. How long must the two of them work together to finish delivering the newspapers?
Answer
30 minutes
Step-by-step explanation:
Answer: approximately 26.66667 minutes
This converts to 26 minutes, 40 seconds
=================================================
Explanation:
Let's say there are 360 newspapers that need to be delivered.
The two brothers can get the job done in 40 minutes if they work together. Their rate is 360/40 = 9 newspapers per minute.
Richie can do the full job alone in 90 minutes. So his rate would be 360/90 = 4 newspapers per minute. In 30 minutes, he delivers 30*4 = 120 newspapers. This leaves 360 - 120 = 240 left over.
Divide this over the rate of 9 papers per minute to get 240/9 = 26.66667 approximately. It takes about 26.66667 minutes to finish up delivering the 240 remaining newspapers if the brothers work together.
The portion 0.66667 multiplies with 60 to get 0.66667*60 = 40.0002 which rounds to 40 (we have rounding error going on). This means
26.66667 minutes = 26 minutes, 40 seconds
Compare 6 ⋅ 108 to 3 ⋅ 106. 6 ⋅ 108 is 2,000 times larger than 3 ⋅ 106. 6 ⋅ 108 is 200 times larger than 3 ⋅ 106. 6 ⋅ 108 is 20 times larger than 3 ⋅ 106. 6 ⋅ 108 is 2 times larger than 3 ⋅ 106.
Answer:
[tex]\boxed{Option \ 2}[/tex]
Step-by-step explanation:
[tex]6*10^8\\=> 600000000[/tex]
[tex]3*10^6\\=> 3000000[/tex]
Dividing both
=> 600000000 ÷ 3000000
=> 200
So,
[tex]6*10^8[/tex] is 200 times larger than [tex]3* 10^6[/tex]
Answer:
[tex]\boxed{\mathrm{Option \: 2}}[/tex]
Step-by-step explanation:
[tex]6 \times 10^8 = 600000000[/tex]
[tex]3 \times 10^6 =3000000[/tex]
[tex]\frac{600000000}{3000000} =200[/tex]
6 × 10⁸ is 200 times larger than 3 × 10⁶.
What is the product
(-2d^2+x)(5d^-6x)
Answer:
-10a4 + 17d4s2 - 6s2
Step-by-step explanation:
On Edgenuity
(06.01 MC)What is the value of the expression 2 + 3^2 ⋅ (3 − 1)?
Answer:
Step-by-step explanation:
2 + 3² * ( 3 -1) = 2 + 9 * 2
= 2 + 18
= 20
Answer:
20
Step-by-step explanation:
2 + 3² · (3 - 1)
= 2 + 3² · 2 -- (3 - 1 = 2)
= 2 + 9 · 2 -- (3² = 9)
= 2 + 18 -- (2 · 9 = 18)
= 20
[tex]if \sqrt{p ^{2} } +1= \frac{5}{4} .Find the postive value of p[/tex]
Answer:
Positive value of p = 1/2
Step-by-step explanation:
Given:
[tex]\sqrt{p^2}+1=\frac{5}{4}[/tex]
Find:
Positive value of p
Computation:
[tex]\sqrt{p^2}+1=\frac{5}{4}\\\\\sqrt{p^2}=\frac{5}{4}-1\\\\\sqrt{p^2}=\frac{5-4}{4}\\\\\sqrt{p^2}=\frac{1}{4}\\\\p = \frac{1}{2}[/tex]
Positive value of p = 1/2