Answer:
4.25
Step-by-step explanation:
The number is bigger in absolute form
Given the set of test scores: 71, 75, 80, 81, 81, 84, 89, 93. If a score of 50 is added to the data set, which statement is true? Select all that apply. Choose all that apply:
The mean decreases.
The median decreases.
The standard deviation increases.
The range increases.
Answer:
The standard deviation increases, it's mean, medium and mode, if you put them in order and then go through and get your middle number it'll be 81.
If a score of 50 is added to the data set,
The standard deviation increases.
The range increases.
What is mean?"It is the average of all elements of the data set."
What is median?"It is the middle number in a sorted list of numbers."
Formula to calculate the standard deviation:[tex]SD=\sqrt{\frac{\sum{(x-M)^{2}} }{N} }[/tex]
where, SD is the population standard deviation
N : the size of the population
x : each value from the data
M : the mean of the data
Formula to calculate the range of the data:range = maximum value - minimum value
For given situation,
Consider the original set of test scores: 71, 75, 80, 81, 81, 84, 89, 93
N = 8
range R = 93 - 71
⇒ R = 22
Mean M = (71 + 75 + 80 + 81 + 81 + 84 + 89 + 93)/8
⇒ M = 654/8
⇒ M = 81.75
Now, we find the median K
First we sort given data set: 71, 75, 80, 81, 81, 84, 89, 93
The middle numbers are 81 and 81
So, the median is the average of 81, 81
So, K = 81
Now, we calculate the standard deviation.
[tex]SD=\sqrt{\frac{[(71-81.75)^{2}+(75-81.75)^{2}+...+(89-81.75)^{2}+(93-81.75)^{2}] }{8} }[/tex]
⇒ SD = 6.61
Consider, the set of test scores with 50 added to the data set.
N = 9
range R = 93 - 50
⇒ R = 43
Mean M = (71 + 75 + 80 + 81 + 50 + 81 + 84 + 89 + 93)/9
⇒ M = 704/9
⇒ M = 78.22
Now, we find the median K
First we sort given data set: 50, 71, 75, 80, 81, 81, 84, 89, 93
The middle number is 81.
So, the median is K = 81
Now, we calculate the standard deviation.
[tex]SD=\sqrt{\frac{[(71-81.75)^{2}+(75-81.75)^{2}+...+(50-81.75)^{2}+(93-81.75)^{2}] }{9} }[/tex]
⇒ SD = 11.76
So, we can observe that if a score of 50 is added to the data set, the correct statements are:
The standard deviation increases.
The range increases.
Learn more about mean, standard deviation, median, range here:
https://brainly.com/question/17998130
#SPJ2
If a card is picked at random from a standard 52-card deck, what is the probability of getting a spade or a 8
Answer:
1/4, 25%, or 0.25
Step-by-step explanation:
Therefore, as each suit contains 13 cards, and the deck is split up into 4 suits, that leaves us with a 13/52 chance to pick a spade.
That fraction is equivalent to 1/4, so that leaves us with a probability of picking a spade at:
1/4, 25%, or 0.25
There are 30 chickens at a farm that are white. This number represents 12% of the total number of chickens at a farm. How many total chickens are at this farm?
Answer:
3.6
Step-by-step explanation:
30 of 12% =3.6
hope this helped
Answer:
3.6
Step-by-step explanation:
Annalise is selling stickers and buys them for $2 each. If she wants to markup the price by 25% how much does she need to sell each sticker for?
Find the area of the shaded region in the figure below, if the diameter of the circle is 8 and the height of the rectangle is 10.
Use 3.14 for pi and round to the nearest hundredth.
Answer:
73.72 units²
Step-by-step explanation:
Area of the shaded region = Area if the rectangle - area of the semicircle
Area of the rectangle = length*width
Length = 10 units
Width = 8 units
Area of rectangle = 10*8 = 80 units²
Area of semicircle = ½(πr²)
radius (r) = 8/2 = 4 units
π = 3.14
Area of semicircle = ½(3.14*4) = 3.14*2 = 6.28 units²
Area of the shaded region = 80 - 6.28 = 73.72 units²
Answer: 54.88
Step-by-step explanation:
The shape shown is a circle that overlaps a rectangle. The shaded region is a rectangle with half a circle cut out. To find the area of the shaded region, we can find the area of the rectangle and the area of the overlapping semi-circle and subtract them. The rectangle has a height of 10. The width of the rectangle is the diameter of the circle, 8. First, find the area of the rectangle:
AAA=length×width=10⋅8=80
To find the area of the circle, we need to find the radius. The radius is one half the diameter, therefore r=4. Use the value of r to solve for the area:
AAA=πr2=3.14⋅(42)=50.24
Now we can subtract half the area of the circle from the area of the rectangle:
Area of rectangle−Area of half circle=Area shaded region
80−50.242
A=54.88
So the area of the shaded region is 54.88.
For which equation does x = 2?
Answer:
what are the equations
Step-by-step explanation:
Is 0 a real rational irrational integer whole natural number?
Answer:
0 is a rational, whole, integer and real number. Some definitions include it as a natural number and some don't (starting at 1 instead).
Answer:
0 is a rational, whole, integer and real number.
Consider the equation a(3-x)=-2x+b What values of a and b make the solution of the equation x=-2? Write a number from the box onto each blank to complete the answer.
Answer:
4x-7
Step-by-step explanation:
What is the sum of 8x^2-x+4 and x-5 is
Answer:
8x^2-1
Step-by-step explanation:
8x^2-x+4+x-5=8x^2-x+x+4-5=8x^2+4-5=8x^2-1
PLEASE ANSWER ASAPPP!!!! REALLY EASY
Chloe and Kiera both wrote numbers, shown below. Chloe: 634,915 Kiera: 369,451 Which statement below is true about Chloe’s and Kiera’s numbers?
The value of the 6 in Kiera's number is 10x greater than the 6 in Chloe's number
Who ever gets it right gets a Brainliest
Answer:
im pretty sure thats a trench ;_;
Step-by-step explanation:
In a group of 20 students, there are 7 boys.
What is the ratio of girls to boys?
O 13:20
O 13:7
07:20
07:13
Answer:
13:7
Step-by-step explanation:
20 - 7 = 13 girls
Girls Boys
13 7
Answer:
it would be 7:20 im pretty sure
Step-by-step explanation:
kelly flies a distance of 2,100 miles. The trip takes 4 2/3 hours.
What is the airplane's unit rate of speed in miles per hour?
Answer:
450 miles per hour
Step-by-step explanation:
Kelly flies at a distance of 2,100 miles
The time taken for the trip is 4 2/3 hours
Therefore the rate of speed can be calculated as follows
= 2,100 ÷ 4 2/3
= 2,100 ÷ 14/3
= 2100 × 3/14
= 150 × 3
= 450 miles per hour
Answer:
450
Step-by-step explanation:
Which function describes the arithmetic sequence shown?
The sequence is : -1, 1, 3, 5, 7, 9, 11, 13
Answer:
The function [tex]a_n=2n-3[/tex] describes the arithmetic sequence.
Step-by-step explanation:
Given the sequence
-1, 1, 3, 5, 7, 9, 11, 13
An arithmetic sequence has a constant difference 'd' is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
Compute the differences between all the adjacent terms:
[tex]1-\left(-1\right)=2,\:\quad \:3-1=2,\:\quad \:5-3=2,\:\quad \:7-5=2,\:\quad \:9-7=2,\:\quad \:11-9=2,\:\quad \:13-11=2[/tex]
As the difference between all of the adjacent terms is the same and equal to
[tex]d=2[/tex]
As the first element is
[tex]a_1=-1[/tex]
so the term will be:
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=2\left(n-1\right)-1[/tex]
[tex]a_n=2n-3[/tex]
So, the function [tex]a_n=2n-3[/tex] describes the arithmetic sequence.
A random sample of 5 homes in Newberry, Florida had a mean of $169,900 and a standard deviation of $21,756. Construct a 95% confidence interval for the average home of this size in Newberry.
A. (144885.25, 194914.75).
B. (150440.842, 189359.16).
C. (150830, 188969.98).
D. (142886, 196914).
Answer:
D. (142886, 196914).
Step-by-step explanation:
To solve for this question, we would use t score instead of z score. The reason is because, our sample size is small.
The formula for Confidence Interval =
C.I = Mean ± t score × standard deviation/√n
n = 5 samples
Degrees of freedom = n - 1 = 5 - 1 = 4
The t score for a 95% confidence interval with degrees of freedom 5 is : 2.776
Hence,
Confidence Interval =
169,900 ± 2.776 × 21,756/√5
169,900 ± 2.776 × 9.7295789837
169, 900 ± 27009.311259
Confidence Interval
169,900 - 27009
= 142886
169, 900 + 27009.311259
= 196914
Hence, the confidence interval = (142886, 196914)
Option D is the correct answer
Using the t-distribution, it is found that the 95% confidence interval for the average price of a home of this size in Newberry is of (142886, 196914), given by option D.
In this problem, we have the standard deviation for the sample, thus, the t-distribution is used to solve this question.
The sample mean is [tex]\overline{x} = 169900[/tex].The sample standard deviation is [tex]s = 21756[/tex].The sample size is [tex]n = 5[/tex]First, we find the number of degrees of freedom, which is the sample size subtracted by 1, so df = 5 - 1 = 4.
Then, we find the critical value for the 95% confidence interval with 4 df, which looking at the t-table or using a calculator is given by t = 2.7765.
The margin of error is:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
In this case:
[tex]M = 2.7765\frac{21756}{\sqrt{5}} = 27014[/tex]
The confidence interval is:
[tex]\overline{x} \pm M[/tex]
Then
[tex]\overline{x} - M = 169900 - 27014 = 142,886[/tex].
[tex]\overline{x} + M = 169900 + 27014 = 196,914[/tex].
Thus, the correct option is D. (142886, 196914).
A similar problem is given at https://brainly.com/question/15180581
Fihd the area of the triangle.
6
8
square units
Answer:
area of triangle is
[tex]\frac{1}{2} * b*h\\\\\frac{1}{2} *6*8\\\\6*4=24[/tex]
What will answer the question 2+2?
Answer: 4.
Step-by-step explanation: 2 + 2 is 4.
An ice cream shop ordered a box of 700 cones. When they opened the box, they noticed 164 of the cones were broken. How many cones do they have left? *
Answer:
The answer would be 536 cones.
Step-by-step explanation:
You have to subtract 164 from 700.
700-164=536.
Helpppp I need it before 11:15
Answer: 3x + 2
P(x) = 6x³ + kx² - x+ 6
= 6x³ - 6x² + (k + 6)x² - (k+ 6)x + (k+5)x - (k + 5) + k + 11
= 6x²(x - 1) + (k + 6)x(x - 1) + (k+5)(x -1) + k + 11
= (6x² + (k + 6)x + k + 5)(x - 1) + k + 11
because when P(x) is divided by x - 1, the remainder is 0
=> k + 11 = 0
⇔ k = -11
with k = -11 => P(x) = (6x² - 5x - 6)(x - 1)
⇔ P(x) = (2x - 3)(3x + 2)(x - 1)
Step-by-step explanation:
Noah and Andre are 15 miles apart on a bike path when they start biking toward each other. Noah rides at a constant speed of 4 miles per hour, and Andre rides at a constant speed of 2 miles per hour. How long does it take until Noah and Andre meet?
Answer:
2.5 hours
Step-by-step explanation:
Noah Andre
4 2 =6 1hr
8 4 =12 2hr
12 6 =18 3hr
10 5 =15 2.5hr
What's the slope and y-intercept?
Help please!!!
Answer:
slope of fig 1st(m)= 1/4
y-intercept of 1st fig=-1
slope of fig 2= -1
y-intercept of 2nd fig=2
Step-by-step explanation:
The speed of a boat in still water is 10 km/hr. If it can travel 78 km downstream and 42 km upstream in the same time, the speed of the stream is?
Answer:
umm let me look at this one more time then I will answer:)
Show all work to factor x^4 − 17x^2 + 16 completely.
I think I have to use completing the square or something but i don't know how
Answer:
[tex]x^{4}-17x^{2} +16[/tex] = (x -1)(x + 1)(x - 4)(x + 4)
Step-by-step explanation:
At first, let us find the first two factors of [tex]x^{4}-17x^{2} +16[/tex]
∵ The sign of the last term is positive
∴ The middle signs of the two factors are the same
∵ The sign of the middle term is negative
∴ The middle signs of the two factors are negative
∵ [tex]x^{4}[/tex] = x² × x² ⇒ first terms of the two factors
∵ 16 = -1 × -16 ⇒ second terms of the two factors
∵ x²(-1) + x²(-16) = -x² + -16x² = -17x² ⇒ the value of the middle term
∴ (x² - 1) and (x² - 16) are the factors of [tex]x^{4}-17x^{2} +16[/tex]
Now let us factorize each factor
→ The factors of the binomial a² - b² (difference of two squares) are
(a - b) and (a + b)
∵ x² - 1 is the difference of two squares
∴ Its factors are (x - 1) and (x + 1)
∵ x² - 16 is the difference of two squares
∴ Its factors are (x - 4) and (x + 4)
∵ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of (x² - 1) and (x² - 16)
∵ (x² - 1) and (x² - 16) are the factors of [tex]x^{4}-17x^{2} +16[/tex]
∴ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of [tex]x^{4}-17x^{2} +16[/tex]
∴ [tex]x^{4}-17x^{2} +16[/tex] = (x -1)(x + 1)(x - 4)(x + 4)
Factoring an expression involves rewriting the expression in simpler forms
The factorized expression is (x - 4)(x + 4)(x - 1)(x + 1)
The expression is given as:
[tex]\mathbf{x^4 - 17x^2 + 16}[/tex]
Express 17 as 1 + 16
[tex]\mathbf{x^4 - 17x^2 + 16 = x^4 - x^2 - 16x^2 + 16}[/tex]
Factorize
[tex]\mathbf{x^4 - 17x^2 + 16 = x^2(x^2 - 1) - 16(x^2 - 1)}[/tex]
Factor out x^2 - 1
[tex]\mathbf{x^4 - 17x^2 + 16 =(x^2 - 16)(x^2 - 1)}[/tex]
Express 16 as 4^2, and 1 as 1^2
[tex]\mathbf{x^4 - 17x^2 + 16 =(x^2 - 4^2)(x^2 - 1^2)}[/tex]
Apply difference of two squares
[tex]\mathbf{x^4 - 17x^2 + 16 =(x - 4)(x + 4)(x - 1)(x + 1)}[/tex]
Hence, the factorized expression is (x - 4)(x + 4)(x - 1)(x + 1)
Read more about factoring expressions at:
https://brainly.com/question/19386208
What are the y- coordinates of b
What is the solution to -4|-2x + 6| = -24?
x = 0
x= 0 or x = -6
x = 0 or x = 6
no solution
I can't help solve my friends problems,I got too much to do help him out please
Answer:
the ask a question about the question isnt working
Step-by-step explanation:
but can you zoom in its really glitchy and blurred from far away
Yeah I would also need it zoomed in please.
Nine hundred light bulbs are packaged and shipped to a retail store. Thirteen percent of the light bulbs arrive broken. Which equation can be used to find the number of light bulbs that were broken? StartFraction 13 times 9 Over 100 times 9 EndFraction = StartFraction 117 Over 900 EndFraction StartFraction 13 times 9 Over 900 times 9 EndFraction = StartFraction 117 Over 8100 EndFraction StartFraction 100 divided by 9 Over 900 divided by 9 EndFraction = StartFraction 11.1 Over 100 EndFraction StartFraction 900 divided by 9 Over 13 divided by 9 EndFraction = StartFraction 100 Over 1.4 EndFraction
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Help and please do not report I got an practice thing from my tutor, so it's not a quiz.
Answer:
The answer is D. II 1 > -2 and III -2< 1 Hopefully this is helpful!
Step-by-step explanation:
How many cups are in 3 gallons? 1 gallon = 16 cups
Label your answer in cups.
Answer:
48 cups
Step-by-step explanation:
Answer: 48
Step-by-step explanation:
Usually, I would do the four cups in one gallon thing. This time, I don't need to because we already know how many cups there are in one gallon. Just multiply 16 by 3 to find how many cups.
= 16 x 3
= 48
Need help ASAP please This is actually confusing
Answer:
the first one is false and
the second one is false
Answer:
i think it is true fals true ture fals
Step-by-step explanation:
but if it is not dont be mad im not good ate math but i still like to try to help pepole when they need it like they woud do for me