Answer:
[tex]\huge\boxed{IQR = 21}[/tex]
Step-by-step explanation:
The data set given is:
57,63,44,29,36,62,48,50,42,34
Arrange in ascending order:
29,34,36,42,44,48,50,57,62,63
Place parenthesis around the number making two equal sets.
(29,34,36,42,44) | (48,50,57,62,63)
↑ ↑
Q1 Q3
Q1 = 36 , Q3 = 57
So, IQR = Q3-Q1
IQR = 57-36
IQR = 21
Answer:
[tex]\huge \boxed{\sf A. \ 21}[/tex]
Step-by-step explanation:
The data set is given,
[tex]\sf 57 \ 63 \ 44 \ 29 \ 36 \ 62 \ 48 \ 50 \ 42 \ 34[/tex]
Arrange the data set in ascending order.
[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ 48 \ 50 \ 57 \ 62 \ 63[/tex]
Split the data set into two equal sets.
[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ \ \ 48 \ 50 \ 57 \ 62 \ 63[/tex]
Find the median of the lower half and upper half.
[tex]\sf Median \ of \ lower \ half = 36[/tex]
[tex]\sf Median \ of \ upper \ half = 57[/tex]
Interquartile range = median of upper half - median of lower half
[tex]\sf IQR = 57 - 36[/tex]
[tex]\sf IQR = 21[/tex]
The interquartile range for the number of points scored at ten basketball games is 21.
7. The General Society Survey asked a sample of 1200 people how much time they spent watching TV each day. The mean number of hours was 3.0 with a standard deviation of 2.87. A sociologist claims that people watch a mean of 4 hours of TV per day. Do the data provide sufficient evidence to disprove the claim? Use α = .05 to test the hypothesis. a. What are your null and alternative hypotheses? b. What test is appropriate here? Why? c. What is your test statistic? d. What is your critical value? e. What is your final decision: do you reject the null or fail to reject the null?
Answer:
a) and b) Look step by step explanation
c) z(s) = - 12,07
d) z(c) = - 1,64
e) Final decision: Reject H₀
Step-by-step explanation:
We assume Normal Distribution
Data:
Sample population n = 1200
Sample mean μ = 3
Sample Standard deviation 2,87
Claim mean μ₀ = 4
α = 0,05 then from z-table we find z(c) = 1,64 ( critical value )
We need to develop a one tail-test to the left
Test Hypothesis
The General Society developed a survey ( in all cases that is an indication of a sample)
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ < μ₀
To calculate the z(s)
z(s) = ( μ - μ₀ )/ 2,87/√n
z(s) = ( 3 - 4 )/ 2,87/√1200
z(s) = -1 * 34,64 / 2,87
z(s) = - 12,07
To compare z(s) and z(c)
z(s) < z(c) - 12,07 < - 1,64
z(s) is in the rejection region (quite far away) we reject H₀
Data provide enough evidence to disprove the claim
Cancel the common factor of the numerator and the denominator and write specified expression
Step-by-step explanation:
Hello,
I hope you mean to cancel the common factor that exists in numerator and denominator,right.
so, Let's look for the common factor,
here, the expression is,
=4(x-2)/ (x+5)(x-2)
so, here we find the common factor is (x-2)
now, we have to cancel it. And after cancelling we get,
=4/(x+5)
Note:{ we cancel the common factor if the common factors are in multiply form.}
Hope it helps
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 15 HCF of water is 32.84, and the cost for using 43 HCF is 79.04. What is the cost for using 36 HCF of water?
Answer:
67.49
Step-by-step explanation:
Let the number of HCF be x.
Let the cost be y.
You are given 2 points of a line: (15, 32.84) and (43, 79.04).
Now we find the equation of the line that passes through those points.
y - y1 = m(x - x1)
y - 32.84 = [(79.04 - 32.84)/(43 - 15)](x - 15)
y - 32.84 = (46.2/28)(x - 15)
y - 32.84 = 1.65(x - 15)
y = 1.65x - 24.75 + 32.84
y = 1.65x + 8.09
Now we let x = 36 and solve for y.
y = 1.65(36) + 8.09
y = 67.49
solve the following equations for x (3x-6)=18
Answer:
x = 8
Step-by-step explanation:
Hello!
What we do to one side of the equation we have to do to the other side.
3x - 6 = 18
Add 6 to both sides
3x = 24
Divide both sides by 3
x = 8
The answer is 8
Hope this helps!
Answer:
x=8
Step-by-step explanation:
(3x-6)=18
Add 6 to each side
(3x-6+6)=18+6
3x= 24
Divide by 3
3x/3 = 24/3
x = 8
How many solutions does the following system have x+y=3, 2x+2y-5
Answer:
Step-by-step explanation:
x + y = 3
2x + 2y = 5
-2x - 2y = -6
2x + 2y = 5
0 not equal to -1
no solution
Plz answer quickkkk help will give 5 star rate if answer is right nd will say thx
Answer:
To find the x-intercept, substitute in 0 for y and solve for x.
To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s):
(−6,0)
y-intercept(s):
(0,3)
So I would say -6 and 0 and 2 are in domain
Answer:
-6, 0 ,2 are in the domain
Step-by-step explanation:
The domain is what values that x can take
There are no restrictions on the values that x can take
All real numbers are in the domain
-6, 0 ,2 are in the domain
Andrea is buying fruit for a fruit salad. Strawberries cost $2 a pound, and blueberries cost $6 a pound. She plans to buy at least 5 pounds of berries and spend no more than $30. Which of the following is a possible combination for the number of pounds of berries she can buy?
6 pounds of strawberries and 1 pound of blueberries
I did the quiz
Select the correct answer from each drop-down menu.
A cross section is the intersection of a
Solid or point and a plane or plane. Helpp
Answer:
solid, plane
Step-by-step explanation:
A cross section is the intersection of a solid and a plane.
Answer:
A cross section is the intersection of a solid and a plane.
Step-by-step explanation:
Got this right on plato, hope it helps :P
4. Identify the means and the extremes in each of the following proportions.
a. 4 : 24 = 2 : 12
b. 24/6 = 164
c. 4:8 = 8:16
d. 650 = 3/25
Answer:
a) Means: 24 and 2; Extremes: 4 and 12
b) Means: 6 and 16; Extremes: 24 and 4
c) Means: 8 and 8; Extremes: 4 and 16
d) Means: 50 and 3; Extremes: 6 and 25
Step-by-step explanation:
The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:
a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.
The Means are the values that appear in the middle of the one line expression, that is: b and c.
Recall as well that the proportion can also be written with fractions:
a : b = c : d is the same as: a / b = c / d
so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.
13,226 divided by 29
13226/29= 456.068965517
y=mx+6 , solve for m
Answer:
m = [tex]\frac{y-6}{x}[/tex]
Step-by-step explanation:
Given
y = mx + 6 ( subtract 6 from both sides )
y - 6 = mx ( divide both sides by x )
[tex]\frac{y-6}{x}[/tex] = m
Compute the least-squares regression line for the given data set. Use a TI-84 calculator. Round final answers to four decimal places, as needed.
x 5 7 6 2 1
y 4 3 2 5 1
Regression line equation: ŷ = _______ + _______ x.
Answer:
Y = 2.843+ 0.037 X
Step-by-step explanation:
Let the equation of the straight line to be fitted to the data , be Y = a+b X where a and b are to be evaluated. The normal equations fro determining a and b are
∑Y = na +b ∑X
∑XY = a∑X + b∑X²
We now calculate ∑X, ∑Y , ∑X², and ∑XY
X Y XY X²
5 4 20 25
7 3 21 49
6 2 12 36
2 5 10 4
1 1 1 1
21 15 64 115
Thus the normal equation becomes
5a + 21b =15
21a +115b = 64
Solving these two equations simultaneously we get
105 a + 441b = 315
105a + 575b = 320
134b= 5
b= 0.037 , a= 2.843
Hence the equation for the required straight line is
Y = 2.843+ 0.037 X
Beginning 177 miles directly north of the city of Morristown, a van travels due west. If the van is travelling at a speed of 31 miles per hour, determine the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles. (Do not include units in your answer, and round to the nearest hundredth.)
Answer:
Step-by-step explanation:
From the given information;
let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c
SO, using the Pythagoras theorem
a² = c² + 177²
By taking the differentiation of both sides with respect to time t , we have
[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]
[tex]a = \sqrt{ 5041+31329}[/tex]
[tex]a = \sqrt{ 36370}[/tex]
a = 190.71
SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]
Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]
[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]
[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex] to the nearest hundredth.
Which expression is equivalent to (jk)l? A. (j + k) + l B. j(kl) C. (2jk)l D. (j + k)l
Answer:
B. j(kl)
Step-by-step explanation:
(jk)l
We can change the order we multiply and still get the same result
j(kl)
Answer:
Step-by-step explanation:
its B i did it
2000 2yrs at 2% How much interest is owed
Answer:
Rs. 80 is owed.
Step-by-step explanation:
Principle (P) = 2000
Time (T) = 2 years
Rate (R) = 2%
Interest (I) = ?
Here,
I = (P×T×R) / 100
= (2000×2×2) / 100
= (8000) / 100
= Rs. 80
Answer:
P= 2000
T= 2
R=2÷100
I = PTR
= 2000×2×2÷100
2÷100=0.02
2000×2×0.02= 80
So i is 80
Find the length of a square with a perimeter of 48cmeter
Answer:
12
Step-by-step explanation:
Perimeter of a square:
4(L)
L = Length
=> 4(L) = 48
=> 4L = 48
=> 4L/4 = 48/4
=> L = 12
The length of the square is 12 cm.
Answer:
12
Step-by-step explanation:
Since the lengths of the sides of a square are equal, divide the perimeter by 4
Two cards are dealt at random from a standard 52 card deck (without replacement). (Ace, King, Queen, Jack are face cards.)
Required:
a. Find the probability that the first card is a face card and the second is NOT a face card.
b. Find the probability that they are both face cards.
c. Find the probability that the second is a face card given the first is NOT a face card.
Answer:
The answer is below
Step-by-step explanation:
There are 52 cards in a deck, 12 of these cards are face cards (4 kings, 4 queens and 4 jacks) and 40 are not face cards
a. Find the probability that the first card is a face card and the second is NOT a face card.
There are 12 first card, the probability that the first card is a face card is 12/52.
Since there are no replacement, after picking 1 face card the number of cards remaining is 51, the probability of the second card not being a face card = 40/51. Therefore:
The probability that the first card is a face card and the second is NOT a face card = P(first is face card) × P(second is not face card) = 12/52 × 40/51 = 40/221
b) Find the probability that they are both face cards.
The probability that the first card is a face card is 12/52.
Since there are no replacement, after picking 1 face card the number of cards remaining is 51 and the number of face card remaining is 11, the probability of the second card is a face card = 11/51. Therefore:
The probability that they are both face cards = P(first is face card) × P(second is face card) = 12/52 × 11/51 = 11/221
c) Find the probability that the second is a face card given the first is NOT a face card.
The probability that the first card is not a face card = 40/52
Since there are no replacement, after picking the first card the number of cards remaining is, the probability of the second card is a face card = 12/51. Therefore:
The probability that the second is a face card given the first is NOT a face card = P(first is not a face card) × P(second is face card) = 40/52 × 12/51 = 40/221
PLEASE HELP FOR 70 POINTS!!!!!! Maria and Jackson like in adjacent neighborhoods. If they superimpose a coordinate grid on the map of their neighborhoods, Maria lives at (–9, 1) and Jackson lives at (5, –4). Each unit on the grid is equal to approximately 0.132 mile. 8. How far apart do Maria and Jackson live to the nearest thousandth? 9. If April lives equidistant to both Maria and Jackson, at what coordinate on the grid would she live? 10. How far apart would Maria and April live to the nearest thousandth?
Answer:
8) 1.962 miles
9) (-2, -1.5)
10) 0.515 miles
Step-by-step explanation:
√(-9 - 5)² + (1 - -4)² = 14.866
14.866 x .132 = 1.962
(-9+5)/2, (1 + -4)/2
-4/2, -3/2
-2, -3/2
√(-2 - 1)² + (-3/2 - -4)² = 3.905
3.905 x .132 = 0.515 miles
BRAINLIST AND A THANK YOU AND 5 stars WILL BE REWARDED PLS ANSER
Answer:
The first picture's answer would be (6, 21)
Step-by-step explanation:
You have to find the points on the 8th and the 9th day, and then you would add them together, and then divide by two finding the average, which would be 24 and 18, so when added, you get 42, divided by 2 you get 21. You look on the graph for the point with 21, and you find it is on 6.
(Algebra) HELP ME ASAP PLZ
Answer:
no solution because the answer will be p=2
10 - [ 8p + 3 ] = 9 [ 2p - 5 ]
10 - 8p - 3 = [ 2p - 5 ]
-8p + 10 - 3 = [ 2p - 5 ]
p = 2 We need to get rid of expression parentheses.
If there is a negative sign in front of it, each term within the expression changes sign.
Otherwise, the expression remains unchanged.
In our example, the following 2 terms will change sign:
8p, 3
Step-by-step explanation:
1. What happened when you had a negative plus a negative, (-a) + (-b)?
I
2. What happened when you had a positive plus a negative, a + (-b)?
***Is this the same as a positive minus a positive, a - b?
3. What happened when you had a positive minus a negative, a - (-b)?
4. What happened when you had a negative minus a negative, (-a) - (-b)?
Answer:
See Explanation
Step-by-step explanation:
1.
What happens when negative adds to negative; e.g (-a) + (-b)
First, we need to simplify the expression
[tex](-a) + (-b)[/tex]
Open the brackets
[tex]-a - b[/tex]
Factorize
[tex]-(a+b)[/tex]
So, what happens is that: the two numbers are added together and the result is negated;
E.g.
[tex](-5) + (-3) = -(5 + 3) = -8[/tex]
2.
What happens when positive is added to negative; e.g. a + (-b)
First, we need to simplify the expression
[tex]a + (-b)[/tex]
Open the brackets
[tex]a - b[/tex]
So, what happens is that: the negative number is subtracted from the positive number
And Yes; [tex]a + (-b)[/tex] is the same as [tex]a - b[/tex] (As shown above)
E.g.
[tex]5 + (-3) = 5 - 3 =2[/tex]
3.
What happens when to positive minus a negative; e.g. a - (-b)
First, we need to simplify the expression
[tex]a - (-b)[/tex]
Open the brackets
[tex]a + b[/tex]
So, what happens is that; the two numbers are added together.
E.g.
[tex]5 - (-3) = 5 + 3 = 8[/tex]
4.
What happens when negative minus a negative; e.g. (-a) - (-b)
First, we need to simplify the expression
[tex](-a) - (-b)[/tex]
Open the brackets
[tex]-a + b[/tex]
Reorder
[tex]b - a[/tex]
So, what happens is that; the first number is subtracted from the second.
E.g.
[tex](-5) - (-3) = 3-5 = -2[/tex]
as part of a group exercise, four students each randomly selected 3 cards with angle measures written on them. The table shows the results.
Answer:
Option (A)
Step-by-step explanation:
As we know sum of interior angles of a triangle = 180°
If the sum of angles written on 3 cards is equal to 180°, will make a triangle.
Total of Alisha's cards = 100° + 90° + 170°
= 360°
Total of Aella's cards = 60° + 25° + 95°
= 180°
Total of Andrew's cards = 35° + 35° + 35°
= 105°
Total of Ah Lam's cards = 90° + 60° + 35°
= 185°
Since total of Aella's cards is 180°, triangle is possible with the angles given on the cards of Aella only.
Therefore, Option (A) will be the answer.
What is the missing statement in step 10 of the proof?
Answer:
c/sin C = b/sin C
Step-by-step explanation:
Look at the statement in the previous step and the reason in this step.
c sin B = b sin C
Divide both sides by sin B sin C:
(c sin B)/(sin B sin C) = (b sin C)/(sin B sin C)
c/sin C = b/sin B
Find the sum of the even numbers between 199 to 1999
[tex]S_n=\dfrac{n(a_1+a_n)}{2}\\a_1=200\\a_n=1998\\n=?\\\\a_n=a_1+(n-1)d\\d=2\\1998=200+(n-1)\cdot2\\2n-2=1798\\2n=1800\\n=900\\\\S_{900}=\dfrac{900\cdot(200+1998)}{2}=450\cdot 2198=989100[/tex]
The Sum is 989100.
what is sum of Even numbers?The sum of even numbers formula is determined by using the formula to find the arithmetic progression. The sum of even numbers goes on until infinity. The sum of even numbers formula can also be evaluated using the sum of natural numbers formula. We need to obtain the formula for 2 + 4+ 6+ 8+ 10 +...... 2n.
The sum of even numbers = 2(1 + 2+ 3+ .....n). This implies 2(sum of n natural numbers) = 2[n(n+1)]/2 = n(n+1)
Given:
a1 = 200
an= 1998
So, using formula
S= n(a1 + an)/2
now,
d=2
an= a1+(n-1)d
1998= 200 + (n-1) 2
1998-200= (n-1)2
1798/2=n-1
n= 900
S900= 900( 200 + 1998)/2
=450*2198
= 989100
Hence, the sum is 989100.
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Find the radius of the circle with equation x^2 + y^2 - 10x - 16y + 53 = 0.
Answer:
radius = 10.5 unitsStep-by-step explanation:
Equation of a circle is given by
x² + y² + 2gx + 2fy + c = 0
To find the radius of the circle we use the formula
[tex]r = \sqrt{ {g}^{2} + {f}^{2} - c } [/tex]
where g and f is the center of the circle
From the question
x² + y² - 10x - 16y + 53 = 0
Comparing with the general equation above we have
2g = - 10 2f = - 16
g = - 5 f = - 8
c = 53
Substitute the values into the above formula
That's
[tex]r = \sqrt{ ({ - 10})^{2} + ( { - 8})^{2} - 53 } [/tex]
[tex]r = \sqrt{100 + 64 - 53} [/tex]
[tex]r = \sqrt{111} [/tex]
We have the final answer as
radius = 10.5 unitsHope this helps you
In a triangle ABC,AB=9 and BC =12 which of the following Cannot be the length of AC.
Step-by-step explanation:
mark it as the brainliest
Answer:
i need help with this too
Step-by-step explanation:
Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.
plzzzzzzzzz someone help
Answer: 4
Step-by-step explanation:
Since this inequality gives us a list, we want to choose the greatest number shown because x≤?. Because x has to be less than or equal to a number, it makes the most sense to put the greatest number there. In the list, 4 is the greatest number.
A car enters a turnpike 22 miles north of a town. The car teavels north at an average speed of 64 miles per hour. How far is the car from the town after 4 hours? Explain how you can use linear function to solve this problem. Then, solve the problem.
Answer:
distance traveled can be modeled by a linear functionthe car is 260 miles north of townStep-by-step explanation:
a) When the speed is constant, the distance traveled is proportional to the travel time, a linear relationship. The distance traveled can be added to the initial distance to obtain the total distance (from town). This relation is a linear function. It can be modeled by the equation ...
d(t) = 4 + 64t . . . where t is travel time in hours, d(t) is the distance in miles
b) After 4 hours, the distance north of town is ...
d(4) = 4 +64(4) = 260
The car is 260 miles from the town after 4 hours.
Answer: Distance is a function of time. The constant rate of change is 64. Write the equation y = 64x + 22. Substitute 4 in for x to get 278 miles.
Step-by-step explanation:
Given that the sum of squares for error is 60 and the sum of squares for regression is 140, then the coefficient of determination is:
Answer:
0.7Step-by-step explanation:
The coefficient of determination which is also known as the R² value is expressed as shown;
[tex]R^{2} = \frac{sum\ of \ squares \ of \ regression}{sum\ of \ squares \ of total}[/tex]
Sum of square of total (SST)= sum of square of error (SSE )+ sum of square of regression (SSR)
Given SSE = 60 and SSR = 140
SST = 60 + 140
SST = 200
Since R² = SSR/SST
R² = 140/200
R² = 0.7
Hence, the coefficient of determination is 0.7. Note that the coefficient of determination always lies between 0 and 1.
The coefficient of determination of the dataset is 0.7
The given parameters are:
[tex]SSE = 60[/tex] --- sum of squared error
[tex]SSR = 140[/tex] --- sum of squared regression
Start by calculating the sum of squared total (SST)
This is calculated using
[tex]SST =SSE + SSR[/tex]
So, we have:
[tex]SST =60 +140[/tex]
[tex]SST =200[/tex]
The coefficient of determination (R^2) is then calculated using
[tex]R^2 = \frac{SSR}{SST}[/tex]
So, we have:
[tex]R^2 = \frac{140}{200}[/tex]
Divide
[tex]R^2 = 0.7[/tex]
Hence, the coefficient of determination is 0.7
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