Answer: The mean increases by 2.1
Step-by-step explanation:
According to the given description (dots are denoting the frequency for each value), the given data is :-
50 , 72, 72 , 74, 76 , 78 , 79 , 79 , 79 80, 81, 82, 82, 82
[Note - We take 79 as the value between 78 and 80, 81 as between 80 and 82 ]
Mean = [tex]\overline{x}_1=\dfrac{\text{Sum of observations}}{\text{No. of observations}}[/tex] (1)
[tex]=\dfrac{1066}{14}=76.1428571429\approx76.1[/tex]
First Quartile: [tex]Q_1=[/tex] Median of the lower half ( 50 , 72, 72 , 74, 76 , 78 , 79 )
= 74
Third Quartile: [tex]Q_3=[/tex] Median of the upper half ( 79 , 79 80, 81, 82, 82, 82 )
= 81
Interquartile range (IQR)=[tex]Q_3-Q_1=81-74=7[/tex]
According to the IQR rule,
Upper limit = [tex]1.5\times IQR+Q_3=1.5\times7+81=91.5[/tex]
Lower limit = [tex]Q_1-1.5\times IQR=74-1.5\times7=63.5[/tex]
Since 50 < 63.2 , so 50 is outlier .
When 50 is removed from the data , the new data will be 72, 72 , 74, 76 , 78 , 79 , 79 , 79 80, 81, 82, 82, 82
Mean = [tex]\overline{x}_2=\dfrac{\text{Sum of observations}}{\text{No. of observations}}[/tex]
[tex]=\dfrac{1016}{13}=78.1538461538\approx78.2[/tex] (2)
Change in mean from (1) and (2)
[tex]\overline{x}_2-\overline{x}_1\\\\=78.2-76.1=2.1[/tex]
Hence, the mean increases by 2.1.
Answer:
2.4
Step-by-step
Evaluate the expression x + 9, if x = 8.
If x is 8, then plug 8 into the expression:
x+9
= (8)+9
= 17
I'm pretty sure this is correct!
Answer: 17 hope it helps (⌐■-■)
Step-by-step explanation:
3z-2=13
Solve each equation
What is the decimal equivalent of 32/9
Answer:
3.55555555556
Step-by-step explanation:
You measure the shadow cast by a certain tall building and find that it is 105 feet long. Then you measure the shadow by a three foot post and find that is 4 inches long. Determine the buildings height
The height of the building is 315 feet because the ratio of the building's height to the post's height is equal to the ratio of the building's shadow length to the post's shadow length.
How to find height?This problem can be solved using the concept of proportionality.
The height of the building is proportional to the length of its shadow, and the height of the post is proportional to the length of its shadow.
Express this mathematically as follows:
Building height / Post height = Shadow length / Post shadow length
Substituting the known values:
Building height / 3 feet = 105 feet / 4 inches
Convert 105 feet to inches first. 105 feet is equal to 105 × 12 = 1260 inches.
Rewrite the equation as follows:
Building height / 3 feet = 1260 inches / 4 inches
The units cancel out, and are left with:
Building height = 1260 / 4 = 315 feet
Therefore, the height of the building is 315 feet.
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Final answer:
To calculate the building's height, we set up a proportion using similar triangles. With the shadow of the building being 105 feet and the shadow of a 3-foot post being 4 inches (1/3 feet), we solve the proportion to find that the building is 315 feet tall.
Explanation:
To determine the height of the building, we can use similar triangles. The method involves setting up a proportion based on the principle that similar triangles have corresponding sides that are in the same ratio. Given the length of the building's shadow and the length of the shadow cast by a known post, we can find the building's height.
Let's define the following variables: B for the height of the building, Sb for the length of the building's shadow, P for the height of the post, and Sp for the length of the post's shadow. From the problem, Sb = 105 feet, P = 3 feet, and Sp = 4 inches, which is 1/3 feet since there are 12 inches in a foot.
Using these variables, the proportion can be set up as follows:
B/Sb = P/SpPlugging in the known values, we get:
B/105 = 3/(1/3)By solving this proportion for B, we find that:
B = (3 × 105) × 3B = 315 feetTherefore, the height of the building is 315 feet.
what is the value of the rational expression below when x is equal to 6? x-2/x-5
a. 3
b. 2/5
c. 8
d. 4
given
[tex] \frac{x - 2}{x - 5} [/tex]
put x = 6 into equation
[tex] \frac{6 - 2}{6 - 5} [/tex]
[tex] = \frac{4}{1} [/tex]
[tex] = 4[/tex]
Final answer:
The value of the rational expression (x-2)/(x-5) when x is 6 is 4.
Explanation:
To find the value of the rational expression x-2/x-5 when x is equal to 6, simply substitute the value of x into the expression:
((6-2)/(6-5) = 4/1 = 4)
So, the value of the expression when x is 6 is 4.
Sandra says that 4/7 - 1/3 = 3/4 because all you have to do is subtract the numerators and subtract the denominators. Convince Sandra that she is wrong. You may draw a rectangular fraction model to support your thinking.
Answer:
She is wrong and the correct answer is [tex]\frac{5}{21}[/tex].
Step-by-step explanation:
The given expression is
[tex]\frac{4}{7}-\frac{1}{3}[/tex]
Sandra says that [tex]\frac{4}{7}-\frac{1}{3}=\frac{3}{4}[/tex] because all you have to do is subtract the numerators and subtract the denominators.
She is wrong. The correct method is shown below.
Make the denominator common.
[tex]\frac{4\times 3}{7\times 3}-\frac{1\times 7}{3\times 7}[/tex]
[tex]\frac{12}{21}-\frac{7}{21}[/tex]
On further simplification we get
[tex]\frac{12-7}{21}[/tex]
[tex]\frac{5}{21}[/tex]
Therefore, the correct answer is [tex]\frac{5}{21}[/tex].
how much greater than n-11 is n+3
Answer:
14 units greater.
Step-by-step explanation:
Subtracting:
n + 3 - (n - 11)
= n - n + 3 + 11
= 14.
If we subtract n-11 from n+3 then we found n+3 is greater from n-11 by 14.
What is difference?
In mathematics difference means the difference in values means which value is how much greater than or less than from other.
How to find difference?We have to find how much is n+3 greater than n-11.
We have just subtract n-11 from n+3
=n+3-(n-11)
=n+3-n+11
=14
Hence n+3 is 14 number greater than n-11.
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Find the derivative from the first principle y=×3
The equation below can be best described as an example of which of the following properties?
a + b = b + a
A. Reflexive Property
B. Associative Property
C. Distributive Property
D. Commutative Property
twice a number is less than or equal to the sum of a number and 15
Answer:
10+5
Step-by-step explanation:
It is the answer In my views
3 people have 2 bananas to share how much banana does each person get
Answer:
1.5 bananas.
Step-by-step explanation:
1.5 x 2 = 3
Answer:
1.5
Step-by-step explanation:
3 divided by 2 is 1.5
if a basketball court is the shape of a rectangle and is 50 feet wide and 94 feet long what is the area
Answer:
4700
Step-by-step explanation:
Area for rectangle is length times width (lw) so it is 50*94 = 4700
Is 86.7% a rational number
Answer:
yes
Step-by-step explanation:
The number 86.7 is a rational number. It is possible to obtain the number 86.7 by dividing the integer 867 by the integer 10, as in 867/10. Because 86.7 is a quotient that results when two integers are divided, we say that 86.7 is a rational number.
At a company that markets televisions, marketers learn that many of the consumers who are willing to pay for high-quality televisions are sports fans. Which of the following would be the best way for the marketers to apply their knowledge of consumer behavior?
A.Charge a price that all customers can afford
B.Associate their brand with a reference group of star athletes
C.Run ads to change consumers' attitudes about sports
D.Try to shorten the consumer decision-making process
Answer:
B.Associate their brand with a reference group of star athletes
Step-by-step explanation:
At a company that markets televisions, marketers learn that many of the consumers who are willing to pay for high-quality televisions are sports fans.
B.Associate their brand with a reference group of star athletes.
This seems the most appropriate answer. When a brand is associated with someone we like, it is very likely that we use the same products like that person.
on the first day of the clothing drive 11 rain jackets were collected at the end of the drive 10 times that number of rain jackets were collected how many rain jackets were collected
Answer:
There were 121 rain jacket were collected
Step-by-step explanation:
* Lets explain how to solve the problem
- On the first day of the clothing drive, 11 rain jackets were collected
- At the end of the drive 10 times that number of rain jackets were
collected
- We want to find how many rain jackets were collected
∵ There were 11 rain jacket were collected on the first day
∵ Ten times that number were collected at the end of the drive
- Ten times means we will multiply the number of rain jacket in
the first day of the clothing drive by 10
∴ The number of rain jacket at the end of the drive = 10 × 11 = 110
∴ There were at the end of the drive 110 jackets
- To find the number of the rain jacket were collected is the sum
of the number of rain jacket at the first day and at the end of
the drive
∴ The number of rain jacket = 110 + 11 = 121
* There were 121 rain jacket were collected
Find the solution of the system of equations.
–8x + 15y = –28
2x + 5y = -28
Step-by-step explanation:
To solve this system of equations, you can use either substitution or elimination. Let's use the elimination method.
First, multiply the second equation by 4 to make the coefficients of \( x \) in both equations opposites:
\( (2x + 5y) \times 4 = -28 \times 4 \)
This gives us:
\( 8x + 20y = -112 \)
Now, we'll subtract the first equation from this modified second equation:
\( (8x + 20y) - (-8x + 15y) = -112 - (-28) \)
Simplify:
\( 8x + 20y + 8x - 15y = -112 + 28 \)
\( 16x + 5y = -84 \)
Now we have a new equation:
\( 16x + 5y = -84 \)
And the first equation remains the same:
\( -8x + 15y = -28 \)
Now, we can solve this system of equations by elimination or substitution. Let's continue with elimination. Multiply the first equation by 2:
\( -16x + 30y = -56 \)
Now, add this equation to the second modified equation:
\( (-16x + 30y) + (16x + 5y) = -56 - 84 \)
\( 30y + 5y = -140 \)
\( 35y = -140 \)
Divide both sides by 35:
\( y = -4 \)
Now, substitute \( y = -4 \) into one of the original equations to solve for \( x \). Let's use the first equation:
\( -8x + 15(-4) = -28 \)
\( -8x - 60 = -28 \)
Add 60 to both sides:
\( -8x = -28 + 60 \)
\( -8x = 32 \)
Divide both sides by -8:
\( x = -4 \)
So, the solution to the system of equations is \( x = -4 \) and \( y = -4 \).
How do you solvs q/r-6=q for r?
Answer:
r = q -6
Step-by-step explanation:
q= [tex]\frac{q}{r} -6[/tex]
[tex]\frac{\frac{q}{r} -6}{r}[/tex]
You do kcf (keep it, change it, flip it)
[tex]\frac{q}{r} -6 times \frac{r}{1}[/tex]
To solve the equation q/r - 6 = q for r, you need to isolate the variable r on one side of the equation.
Explanation:To solve the equation q/r - 6 = q for r, we need to isolate the variable r on one side of the equation. First, we'll get rid of the fraction by multiplying both sides of the equation by r. This gives us r(q/r) - 6r = qr. Simplifying further, we have q - 6r = qr. Next, we'll move all the terms involving r to one side by subtracting qr from both sides of the equation. This gives us q - qr - 6r = 0. Factoring out the common factor of r from the last two terms, we have q - r(q + 6) = 0. Finally, we solve for r by dividing both sides of the equation by q + 6. So, the solution to the equation is r = q/(q + 6).
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100 POINTS please answer! ill give you brainliest but i rlly need help! (the circled ones!)
Hi there! I will try my best to help you. If the answers I give you are wrong, I am so sorry.
Answer:
1. <
2. <
3. >
7. Apricot sulphur, large orange sulphur, white-angled sulfur, great white
9. 8 (with the sign), 7/2 (with the sign), 2
10. pi, 12 (with the sign), 3.5
11. -20, 26 (with the sign), 35 (with the sign), 13.5
12. -5.25, 3/2, 6 (with the sign), 5
Answer:
lol this is a lot
Step-by-step explanation:
A cat adoption facility takes in an average of 4 cats per day. The facility has to keep their cat occupancy below 200. Currently, the facility has 172 cats.
If none of their cats get adopted, how many more days, x, can the facility continue to take in cats? Select the inequality that includes the largest number of days this facility can continue to take in cats without exceeding its occupancy limit.
A. x < 7
B. x < 28
C. x < 50
D. x < 24
Answer:
A. x<7
Step-by-step explanation:
B. x < 28
C. x < 50
D. x < 24
These answers exceed the cat adoption facilities cat limit.
Rate as Brainliest plz
Answer:
A. x<7
Step-by-step explanation:
We know three things:
The facility takes 4 cats per dayThe facility has to keep the occupancy below 200Currently, the facility has 172 catsNow we want to know how many more days the facility can continue to take in cats if none of their cats get adopted.
First, we want to know how many cats until the facility exceeds the occupancy and to do it we have to subtract the occupancy minus the cats they already have:
200 - 172 = 28
With this answer, we know that if they get 28 more cats they will have 200 cats and the occupancy has to be below 200.
Now we want to know how many days will it take them to get 28 more cats:
We know that every day they get 4 cats, so we are going to divide the number of cats to get 200 by the number of cats they get every day:
28(cats) / 4(cats per day) = 7 days
So in 7 days, they will pass their occupancy, which means that they can only take cats less than 7 days.
The expression will be:
x < 7
Where:
x is how many more days they can take in cats
< means less than
The ramp is 1 ft high. The base of the ramp extends 14ft along the side of a building. How long is the sloped part of the ramp to the nearest hundredth of a foot?
Answer:
Pythagorean theorem:
14.03 ft
Step-by-step explanation:
Indicate whether each of the following numbers is divisible by 3.
Answer yes or no.
a. 27
b. 35
c. 123
d. 402
Answer:
a: yes
b: no
c:yes
D: yes
Step-by-step explanation:
inal answer:
To determine divisibility by 3, the sum of the digits in a number must be divisible by 3. The numbers 27, 123, and 402 are divisible by 3, while 35 is not.
Explanation:
To determine whether a number is divisible by 3, you can use the rule that a number is divisible by 3 if the sum of its digits is divisible by 3. Here are the step-by-step examinations for each of the numbers:
27: The digits add up to 2 + 7 = 9, which is divisible by 3. Yes, 27 is divisible by 3.
35: The digits add up to 3 + 5 = 8, which is not divisible by 3. No, 35 is not divisible by 3.
123: The digits add up to 1 + 2 + 3 = 6, which is divisible by 3. Yes, 123 is divisible by 3.
402: The digits add up to 4 + 0 + 2 = 6, which is divisible by 3. Yes, 402 is divisible by 3.
A company makes cones out of a solid foam. Each cone has a height of 9 inches, and it’s bade has a diameter of 5 inches. How much foam is needed to make 120 cones?
Final answer:
The volume of foam needed to make 120 cones, each with a 9-inch height and a 5-inch diameter base, is approximately 7,068.6 cubic inches.
Explanation:
The question involves finding the volume of a single cone and then calculating the total volume of foam needed for producing 120 cones. To find the volume of one cone, we use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height. Given that the diameter of the base is 5 inches, the radius (r) would be half of that, which is 2.5 inches. The height (h) is given as 9 inches. Therefore, the volume of one cone is:
V = (1/3)π(2.5)²(9)
This simplifies to V ≈ 58.905 cubic inches (using 3.14159 for π). To find the volume for 120 cones, we multiply the volume of one cone by 120:
Total volume = 58.905 in³ × 120 ≈ 7,068.6 cubic inches.
This is the amount of foam needed to make 120 cones.
Does the phrase 20 more than a number indicate multiplication?
Answer:
No, the phrase 20 more indicates addition.
For instance, 20 more than 50 is 70.
If 448 is rounded to 450 and 450 is rounded to 500 does that mean 448 is rounded to 500 too?
Answer:
NO
Step-by-step explanation:
Since you are rounding to a numbers in the 100s you need to find the closest multiple of 100 to 448, this would be 400 since the difference between 448 and 400 is 48 while the difference between 500 and 448 is 52 and 48<52
For which rational expression is -which expression is equivalent to 2x^2+2x-4/2x^2-4x+2
Answer:
[tex]\frac{x+2}{x-1}[/tex]
Step-by-step explanation:
Factorise the numerator and denominator
2x² + 2x - 4 ← factor out 2 from each term
= 2(x² + x - 2)
= 2(x + 2)(x - 1) ← in factored form
2x² - 4x + 2 ← factor out 2 from each term
= 2(x² - 2x + 1)
= 2(x - 1)² ← in factored form
Thus
[tex]\frac{2x^2+2x-4}{2x^2-4x+2}[/tex]
= [tex]\frac{2(x+2)(x-1)}{2(x-1)^2}[/tex]
Cancel 2 and factor (x - 1) on numerator/ denominator, leaving
= [tex]\frac{x+2}{x-1}[/tex]
What are rational exponents
Answer: A rational number is any number that can be written as a fraction where the numerator and denominator are counting numbers.
Hope this helps
Step-by-step explanation:
What is m<2 + m<3? Explain.
Answer:
[tex]\large\boxed{m<1\to m\in(-\infty,\ 1)}[/tex]
Step-by-step explanation:
[tex]m<2+m<3\to m<2+m\ and\ 2+m<3\\\\m<2+m\qquad\text{subtract}\ m\ \text{from both sides}\\m-m<2+m-m\\0<2\qquad\bold{TRUE}\to m\in\mathbb{R}\ (all\ real\ numbers)\\\\2+m<3\qquad\text{subtract 2 from both sides}\\2-2+m<3-2\\m<1\\\\m\ \text{is any real number and}\ m<1.\\\\\text{Therefore}\ m<1\to m\in(-\infty,\ 1)[/tex]
Which equation is quadratic in form?
© 2(x + 5)2 + 8x + 5+6 = 0
x6 + 6x +8=0
7x6 + 36x3 + 5 = 0
4x9 + 20x2 + 25 = 0
Answer: 2(x+5)2+ 8x + 5+6=0
Step-by-step explanation:
2(x + 5)2 + 8x + 5 + 6=0
2(x+5)(x+5) + 8x + 11=0
2(x^2+ 10x + 25) + 8x + 11=0
2x^2 +20x + 50 + 8x + 11=0
2x^2 +28x +66=0
This is a second-degree equation, the greatest power is two. Hence it is a quadratic equation.
None of the given equations are purely quadratic in form; they include terms of higher degrees or additional constant terms. Therefore, none of them fit the criteria.
To determine which equation is quadratic in form, we need to look for equations that can be written in the form [tex]\(ax^2 + bx + c = 0\)[/tex], where [tex]\(a\), \(b\), and \(c\) are constants and \(x\)[/tex] is the variable.
Let's analyze each given equation:
[tex]1. \(2(x + 5)^2 + 8x + 5 + 6 = 0\)[/tex]
This equation involves a quadratic term [tex]\((x + 5)^2\)[/tex], but it also includes linear and constant terms. Therefore, it is not purely quadratic in form.
2. [tex]\(x^6 + 6x + 8 = 0\)[/tex]
This equation contains a sixth-degree term [tex]\(x^6\)[/tex], making it a polynomial of degree 6. It is not quadratic in form.
[tex]3. \(7x^6 + 36x^3 + 5 = 0\)[/tex]
Similar to the previous equation, this equation contains a sixth-degree term [tex]\(x^6\)[/tex] and a third-degree term [tex]\(x^3\)[/tex].
It is not quadratic in form.
[tex]4. \(4x^9 + 20x^2 + 25 = 0\)[/tex]
This equation contains a ninth-degree term [tex]\(x^9\)[/tex] and a quadratic term[tex]\(20x^2\).[/tex]
However, it also contains a constant term. Therefore, it is not purely quadratic in form.
None of the given equations are purely quadratic in form.
Name the sets of numbers to which each number belongs. 192.0005
you should add me on snap connorpike2
Answer:
0.029
Step-by-step explanation:
"To write 29/1000 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 29 by 1000 what we write down as 29/1000 and we get 0.029"
-Solutions easy
Diana earns $8.50 an hour working as a life guard. Write a function to find Diana’s money earned m for any number of hours h. How much does she make in 9 hours ?
Answer:
76.5$
Step-by-step explanation:
8.5 x 9 = 76.5