Answer:
3
Step-by-step explanation:
Given:
Team heights (inches):
61, 57, 63, 62, 60, 64, 60, 62, 63
To find: IQRs (interquartile ranges) of the heights for the team
Solution:
A quartile divides the number of terms in the data into four more or less equal parts that is quarters.
For a set of data, a number for which 25% of the data is less than that number is known as the first quartile [tex](Q_1)[/tex]
For a set of data, a number for which 75% of the data is less than that number is known as the third quartile [tex](Q_3)[/tex]
Terms in arranged in ascending order:
[tex]57,60,60,61,62,62,63,63,64[/tex]
Number of terms = 9
As number of terms is odd, exclude the middle term that is 62.
[tex]Q_1[/tex] is median of terms [tex]57,60,60,61[/tex]
Number of terms (n) = 4
Median = [tex]\frac{(\frac{n}{2})^{th} +(\frac{n}{2}+1)^{th} }{2} =\frac{2^{nd}+3^{rd}}{2} =\frac{60+60}{2}=\frac{120}{2}=60[/tex]
So, [tex]Q_1=60[/tex]
So, 25% of the heights of a team is less than 60 inches
[tex]Q_3[/tex] is the median of terms [tex]62,63,63,64[/tex]
Median = [tex]\frac{(\frac{n}{2})^{th} +(\frac{n}{2}+1)^{th} }{2} =\frac{2^{nd}+3^{rd}}{2} =\frac{63+63}{2}=\frac{126}{2}=63[/tex]
So, [tex]Q_3=63[/tex]
So, 75% of the heights of a team is less than 63 inches
Interquartile range = [tex]Q_3-Q_1=63-60=3[/tex]
The interquartile range is a measure of variability on dividing a data set into quartiles.
The interquartile range is the range of the middle 50% of the terms in the data.
So, 3 is the range of the middle 50% of the heights of the students.
Score data from a statewide exam for 10th-graders follows a normal distribution, has a mean of 77, and has a standard deviation of 6.5. According to the Empirical Rule, 34% of test scores fall into what range? Select all that apply.
Given Information:
Mean test score = μ = 77
Standard deviation of test score = σ = 6.5 seconds
Answer:
The lower limit represents those 34% test scores which are below the mean test score.
The range of test scores will be (70.5 to 77)
The upper limit represents those 34% test scores which are above the mean test score.
The range of test scores will be (77 to 83.5)
Step-by-step explanation:
Normal Distribution:
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
The Empirical Rule:
The empirical rule states that approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.
68% of all the data lie within 1 standard deviation from the mean, so that means 34% (half of 68%) of the test scores will be below the mean test score and remaining 34% of the test scores will be above the mean test score.
The confidence interval is given by
[tex]CI = \mu \pm 1 \cdot \sigma \\\\CI = 77 \pm 1 \cdot (6.5) \\\\CI = 77 \pm 6.5 \\\\Lower \: limit = 77 - 6.5 = 70.5 \\\\Upper \: limit = 77 + 6.5 = 83.5 \\\\[/tex]
The lower limit represents those 34% test scores which are below the mean test score.
So the range of test scores will be (70.5 to 77)
The upper limit represents those 34% test scores which are above the mean test score.
So the range of test scores will be (77 to 83.5)
HELPPP PLEASEEEEE!!!!!!!!!
Answer:20
Step-by-step explanation:
Since it is a right angled triangle we can use Pythagoras principle to get the missing length
Let the missing length be h
h=√(16^2+12^2)
h=√(16x16+12x12)
h=√(256+144)
h=√(400)
h=20
Please help ASAP! I will mark BRAINLIEST!! Please answer correctly! No guessing!
Answer:
exponential decay...................
Answer:
exponential decay
Step-by-step explanation:
If the amount is 1/2 every half hour, it is getting smaller, so it is decreasing, leaving choices a and b
We start with 100 items
100, 50 ,25, 12.5
this is not linear so it must be exponential decay
Which best describes the solution set for the inequality below?
3x + 7 ≤ 4x – 8 or –2x + 3 ≥ 1
Answer: The answer is A.
Step-by-step explanation:
x < 1 or x > 15
The solution set of the inequalities are,
1) x ∈ [15, ∞)
2) x ∈ (- ∞, 1]
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequalities are,
1) 3x + 7 ≤ 4x - 8
2) - 2x + 3 ≥ 1
Now, Simplify the inequality as;
1) 3x + 7 ≤ 4x - 8
⇒ 3x + 7 ≤ 4x - 8
⇒ 7 + 8 ≤ 4x - 3x
⇒ 15 ≤ x
⇒ x ∈ [15, ∞)
2) - 2x + 3 ≥ 1
⇒ - 2x + 3 ≥ 1
⇒ 3 - 1 ≥ 2x
⇒ 2 ≥ 2x
⇒ 1 ≥ x
⇒ x ∈ (- ∞, 1]
Learn more about the inequality visit:
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Q2:
The figure below is the net of a three-dimensional figure.
If the net is folded along the dashed lines, what three-dimensional figures would it form?
A
rectangular prism
B
cube
C
triangular prism
D
rectangular pyramid
Answer: rectangular prism
Step-by-step explanation:
The article “Heavy Drinking and Polydrug Use Among
College Students” (J. of Drug Issues, 2008: 445–466) stated
that 51 of the 462 college students in a sample had a lifetime
abstinence from alcohol. Does this provide strong evidence
for concluding that more than 10% of the population sam-
pled had completely abstained from alcohol use? Test the
appropriate hypotheses using the P-value method. [Note:
The article used more advanced statistical methods to study
the use of various drugs among students characterized as
light, moderate, and heavy drinkers.]
Answer:
Yes it does provide strong evidence
Step-by-step explanation:
Which number line correctly shows 0.8 + 0.3?
Answer:
the second answer
Step-by-step explanation:
cause 0+0.8 is 0.8 and 0.8+0.3 is 1.1
Answer:
A
Step-by-step explanation:
Difference between-9°C and -21°C
Answer:
12
Step-by-step explanation:
21-9=12 hope this helps :)
The cost of 900 shares of stock selling for 57 5/8 is
Answer:
$51,862.50
Step-by-step explanation:
... the product of the number of shares and the price:
(900)($57 5/8) = $51,862.50
Answer:
51 862.5
Step-by-step explanation:
If the share cost 57 5/8 per share
It means 900 share would cost
900 * 57 5/8
900 * 461/8 = 51 862.5
The net price equivalent rate of 3/7/13 is:
The sum of 5 consecutive integers is 70 what are the numbers
Answer:
12, 13, 14, 15, 16
Step-by-step explanation:
Let the five consecutive integers be (x - 2), (x - 1), x, (x + 1) & (x + 2)
According to the given condition:
[tex](x - 2) + (x - 1) + x + (x + 1) + (x + 2) = 70 \\ 5x = 70 \\ x = \frac{70}{5} \\ x = 14 \\ \implies \\ (x - 2) = (14 - 2) = 12 \\ (x - 1) = (14 - 1) = 13 \\ x = 14 \\ (x + 1) = (14 + 1) = 15 \\ (x + 2) = (14 + 2) = 16\\ [/tex]
Two solutions of salt water contain 0.04% and 0.2% salt respectively. A lab technician wants to make 1 liter of solution which contains 0.12% salt. How much of each solution should she use?
x = amount (in L) of 0.04% solution
y = amount (in L) of 0.2% solution
x + y = 1
Each liter of p% salt solution contributes 0.01*p L of salt to the mixture. In the new solution, the lab tech wants to end up with a concentration of 0.12%, which comes out to 0.0012 * (1 L) = 0.0012 L of salt:
0.0004x + 0.002y = 0.0012
Solve for y in the first equation:
y = 1 - x
Substitute this into the other equation and solve for x, then y:
0.0004x + 0.002(1 - x) = 0.0012
0.0008 = 0.0016x
x = 0.5 L
y = 1 - 0.5 = 0.5 L
A little kid running a lemonade stand sells small and large beverages. Each small beverage sells for $2 and each large beverage sells for $5. Small beverages require 4 lemons and 6 tablespoons of sugar each. Large beverages require 5 lemons and 10 tablespoons of sugar each. She has 100 lemons and 180 tablespoons of sugar. How many of each beverage should she sell to maximize her earnings?
Answer:
No. of Small Beverage = x = 10
No. of Large Beverage = y = 12
Step-by-step explanation:
Analyzing the given situation, we can form two algebraic equations.
Since, she has 100 lemons and 4 lemons are required for small beverage, while 5 lemons are required for large beverage. So, we can form the equation:
4x + 5y = 100 --------- eqn (1)
where,
x = No. of small beverages sold
y = No. of large beverages sold
Similarly, she has 180 table spoons of sugar and 6 table spoons are required for small beverage, while 10 table spoons are required for large beverage. So, we can form the equation:
6x + 10y = 180 -------- eqn (2)
From eqn (1):
x = (100 - 5y)/4 ------- eqn (3)
Substituting this value of x in eqn (2)
(6)(100 - 5y)/4 + 10y = 180
10 y - 7.5 y= 180 - 150
2.5 y = 30
y = 30/2.5
y = 12
Using this value of y in eqn (3)
x = [100 - (5)(12)]/4
x = 10
Therefore, in order to maximize the earnings the kid should sell following number of each beverage:
No. of Small Beverage = x = 10
No. of Large Beverage = y = 12
CAN SOMEONE HELP ME WITH THIS ONE QUESTION PLEASE AND THANK YOU :D
Answer:
number of wanted outcomes/ amount of different outcomes in total
number of winners/total amount of contestants
Step-by-step explanation:
You might need:
Calculator
Skill Sum
Aliaa and Zhang Li are tennis-playing robots capable of placing shots with superhuman precision
thagore
Aliaa is about to hit its next shot to the far corner of the court. It (Aliaa) knows that the distance between
itself and Zhang Li is 520 cm, and it knows that the angle between Zhang Li and the far corner is 53°
Similarly, Zhang Li knows that the angle between Aliaa and the far corner is 100°.
ythagore
What distance should Aliaa hit the ball so that it lands perfectly in the far corner of the court?
Do not round during your calculations. Round your final answer to the nearest centimeter.
pecialrig
cm
100% 150
Aliaa
TV53°
520 cm
Introductie
100
Zhang Li
Show Calculator
Do 5 problems OOOOO
Answer:
1128cm
Step-by-step explanation:
The diagram of the problem is annotated and attached.
In the diagram, we are required to find the distance between Aliaa and the far corner, b.
In Triangle ABC
[tex]\angle A+\angle B+\angle C=180^\circ\\53^\circ+100^\circ+\angle C=180^\circ\\\angle C=180^\circ-153^\circ\\\angle C=27^\circ[/tex]
Using Law of Sines
[tex]\dfrac{b}{sin B} =\dfrac{c}{sin C} \\\dfrac{b}{sin 100} =\dfrac{520}{sin 27}\\b=(520 X sin 100)\div sin 27\\b=1127.997\\b\approx 1128$ cm (to the nearest centimeter.)[/tex]
Therefore, Aliaa should hit the ball a distance of 1128cm so that it lands perfectly in the far corner of the court.
(-2h+9)(9h-2) in standard form
Answer: -18h^2 + 85h - 18
Step-by-step explanation:
(-2h+9)(9h-2)
Open brackets
(-2h x 9h) + (-2h x -2) + (9 x 9h) + (9 x -2)
-18h^2 + 4h + 81h - 18
Add like terms 4h + 81h
-18h^2 + 85h - 18
Mr.Lipps flips a coin 20 times how many times can he expect heads
Answer:
Mr. Lipps would expect it to land on heads 10 times
Step-by-step explanation:
hope this helps :)
If you flip a coin ten times, how many different sequences of heads and tails are possible? a. 2 Superscript 9 Baseline = 512 b. 10 squared = 100 c. 10 squared = 1024 d. 2 Superscript 10 Baseline = 1024
Answer:
1024
Step-by-step explanation:
I don't know what this superscript is but the answer is above.
Answer:OPTION D: 2^10 = 1024
Step-by-step explanation: I just took the quiz on edge.hope this helps :)
What’s the volume of the solid ?
Answer:
I think its 70in hope it helps
Step-by-step explanation:
he diameter of the circle is 18 m. Eugene incorrectly says that the circumference of the circle is about 113.04 m. What is the circumference of the circle? What mistake did Eugene make? Use 3.14 for pi.
Answer:
The circumference of the circle is [tex]C=56.55 \:m[/tex].
Eugene confused the radius with the diameter to find the circumference of the circle.
Step-by-step explanation:
The circumference of a circle is the distance around the outside of the circle.
The circumference of a circle is found using this formula:
[tex]\begin{matrix} C=\pi \cdot d\\or\\ \, C=2\pi \cdot r \end{matrix}[/tex]
From the information given the diameter of the circle is 18 m. Therefore, the circumference of the circle is
[tex]C=\pi \cdot d\\\\C=3.14 \cdot 18 \approx 56.55 \:m[/tex]
Eugene used the wrong formula to find the circumference of a circle.
[tex]C=2\cdot(3.14)\cdot 18=113.04 \:m[/tex]
He confused the radius with the diameter.
Answer:
Eugene used the wrong formula to find the circumference of a circle.
He confused the radius with the diameter.
Step-by-step explanation:
Which is the same as moving the decimal point 3 places to the right in a decimal number
Answer:
Moving the decimal 3 places to the right in a decimal number is the same as multiplying the number by 1000.
A researcher planned a study in which a crucial step was offering participants a food reward. It was important that three food rewards were equal in appeal. Thus, a pilot study was designed in which participants were asked which of the rewards they preferred. The observed frequencies are as follows:
Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots.
1. The appropriate statistical test for this problem is (be specific): ________.
2. What are the expected frequencies for this question?
3. What is the cutoff on the comparison distribution (step 3)?
4. What is the correct calculation for chi-square (step 4)?
Answer:
Step-by-step explanation:
Hello!
A pilot study was conducted to test if three food rewards are equally appealing to the participants.
Of 60 participants surveyed:
16 preferred cupcakes (CC)
26 preferred candy bars (CB)
18 preferred dried apricots (DA)
If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3
1.
The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. [tex]X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex] Where k= number of categories of the variable.
For this example the statistical hypotheses are:
H₀: P(CC)=P(CB)=P(DA)= 1/3
H₁: At least one of the proportions isn't equal to the others.
2.
To calculate the expected frequencies for each category you have to use the formula: [tex]E_i= n* P_i[/tex] where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.
[tex]E_{CC}= n* P(CC)= 60*1/3= 20[/tex]
[tex]E_{CB}= n*P(CB)= 60*1/3= 20[/tex]
[tex]E_{DA}= n* P(DA)= 60* 1/3= 20[/tex]
3.
The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:
Assuming α: 0.05
[tex]X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378[/tex]
The rejection region is then X²₂ ≥ 7.378
4.
[tex]X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8[/tex]
I hope this helps!
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! Show your work!
Answer:
All positive real numbers i think
Answer:
B
Step-by-step explanation:
4^x can never be 0 or negative, the graph has a horizontal asymptote at y = 0
So the range only includes positive values
Do you remember the difference between a row and a column
in Math?
Answer:
Rows are the steps - they go left to right and are numbered 1,2,3,... Columns are the columns - they go up and down and are lettered A,B,C,... Cells are defined by the row and column they are in.
Step-by-step explanation:
20 POINTS What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
_____ ft²
Answer:
46.1
Step-by-step explanation:
Mark BRAINLIEST
Answer:
Hello! The correct answer is 2.95 [tex]ft^{2}[/tex]
Given tan A = − 12/35 and that angle A is in Quadrant IV, find the exact value of sinA in simplest radical form using a rational denominator.
Answer:
Sin A= − 12/37
Step-by-step explanation:
tan A = − 12/35
Reason for minus sign is because of it's in the fourth quadrant.
12 = opposite
35 = adjacent
? = Hypotenuse
12² + 35² = hypotenuse ²
1369 = hypotenuse ²
hypotenuse = √1369
hypotenuse= 37
Sin = -12/37
Reason for minus sign is because of it's in the fourth quadrant.
What times what gives you 1,000,000
Evaluate the related
series of each sequence
19, 28, 37, 46, 55
Answer: You add 9 each time
Step-by-step explanation:
19 + 9 = 28 + 9 = 37 + 9 = 46 + 9 = 55
hope this helps mark me brainliest if it did
On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).
What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J?
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
(40, 96)
(85, 105)
(80, 104)
(96, 72)
Answer:
the answer is (40,96)
Step-by-step explanation:
Point P on the directed line segment from K to J has x and y coordinates that are three-fifths of the length of the line segment from K to J
(85, 105).
What are coordinates?The coordinates point to any point can be found by using the following formula.
X = [m/(m + n)](x₂ - x₁) + x₁
Y = [m/(m + n)](y₂ - y₁) + y₁
Given, On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).
The x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is;
X = [m/(m + n)](x₂ - x₁) + x₁
X = [3/(3 + 5)](- 40 - 160) + 160.
X = - 75 + 160.
X = 85.
Y = [m/(m + n)](y₂ - y₁) + y₁
Y = [3/(3 + 5)](80 - 120) + 120.
Y = - 15 + 120.
Y = 105
As a result, point P's x and y coordinates are such that P is three-fifths the length of the directed line segment from K to J (85, 105).
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Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The table displays the starting positions for the winners of 240 competitions. Calculate the chi-square test statistic X2 used to test the claim that the probability of winning is the same regardless of starting position.
Starting Position 1 2 3 4 5 6
Number of Wins 33 44 32 36 45 50
a.12.592
b.15.541
c.9.326
d.6.750
Answer:
d) 6.750
The chi - square value = 6.750
Step-by-step explanation:
Given data
Starting Position 1 2 3 4 5 6
Number of Wins (O) 33 44 32 36 45 50
Step(i) :-
mean = [tex]\frac{33+44+32+36+45+50}{6} = \frac{240}{6} =40[/tex]
Expected frequency = 40
Number of Wins (O) : 33 44 32 36 45 50
Expected frequency(E) : 40 40 40 40 40 40
(O - E ) : -7 4 -8 -4 5 10
(O-E)² : 49 16 64 16 25 100
[tex]\frac{(O-E)^2}{E}[/tex] : 1.225 0.4 1.6 0.4 0.625 2.5
Step(ii):-
The χ² test
χ² = ∑ [tex]\frac{(O-E)^2}{E}[/tex]
χ² = 1.225 + 0.4 + 1.6 + 0.4 +0.625 +2.5 = 6.75
The chi - square value = 6.750
Final answer:-
The chi - square value = 6.750
