Answer:
184 cm³
Step-by-step explanation:
Volume= base*height
V= 20 cm²*9.2 cm= 184 cm³
Answer:184 cm³
Step-by-step explanation: I took the test a while ago
vlumber company is making boards that are 2944.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 25 is made, and it is found that they have a mean of 2941.0 millimeters with a standard deviation of 12.0. A level of significance of 0.1 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2941-2944}{\frac{12}{\sqrt{25}}}=-1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{24}<-1.250)=0.223[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2944 mm
Step-by-step explanation:
Information provided
[tex]\bar X=2941[/tex] represent the sample mean
[tex]s=12[/tex] represent the standard deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =2944[/tex] represent the value to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean for this case is equal to 2944 mm, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2944[/tex]
Alternative hypothesis:[tex]\mu \neq 2944[/tex]
The statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{2941-2944}{\frac{12}{\sqrt{25}}}=-1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{24}<-1.250)=0.223[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2944 mm
Let X equal the number of pounds of butterfat produced by a Holstein cow during the 305-day milking period following the birth of a calf. We shall test the null hypothesis 22 22 H0 : σ = 140 against the alternative hypothesis H1 : σ > 140 at α = 0.05, based on given data: n = 25, and a sample standard deviation of s = 150.1. What is the type of the test?A) Right-tailedB) Left-tailedC) Two-tailed2. Calculate Observed Test Statistic3. Find the Critical Value of Critical Region of the Test4. Draw Your Conclusion of the Test at α = 0.05A) Fail to Reject H0B) Reject H0
Answer:
Step-by-step explanation:
Given that:
[tex]\mathbf{H_o : \sigma = 140} \\ \\\mathbf{H_i : \sigma > 140} \\ \\ \mathbf{ \alpha = 0.05 \ \ \ \ n = 25 \ \ \ \ S = 150}[/tex]
1. This type of test is right tailed since the alternative hypothesis is right tailed
2. The Observed test statistic is calculated as follows:
[tex]X^2 = \dfrac{(n-1)s^2}{\sigma^2} \\ \\ X^2 = \dfrac{(25-1)150^2}{140^2} \\ \\ X^2 = \dfrac{(24)22500}{19,600} \\ \\ X^2 =27.55[/tex]
3. Critical Value
where ∝ = 0.05 and the test statistic is right tailed ;
By using [tex]X^2[/tex] table
[tex]X^2 _{\alpha/2 , n-1}= 36.415[/tex]
4. Conclusion:
∝ = 0.05
where
X² = 36.415
Therefore ; we reject [tex]\mathbf{H_o}[/tex]
please answer this correctly
Answer:
Step-by-step explanation:
Brazil : 12,500,000 = 5,000,000 + 5,000,000 + 2,500,000
= full cat + full cat + half cat
The Senator of Azenator State, is worried about the rising numbers in high blood pressure related deaths in his Jurisdiction and wants an end to this canker. A reputable medical research officer has claimed that, the situation is probably as a result of the ageing population of his State. The blood pressures, Y (mmHg), and Ages, X (years) of 10 hospital patients were sampled from Azenator State and summarized below. Patient A B C D E F G H I J Age (X) in Years 20 25 50 30 45 60 10 15 35 70 BP(Y) in (mmHg) 80 85 125 90 100 135 80 70 100 140 NB: Approximate to 2 decimal places Use the table to answer the questions that follow; i) Calculate the product moment correlation coefficient for the data and interpret your result. (3 Marks) ii) If the Senator decides to purchase and distribute Norvasc (a medicine that reduces blood pressure), based on your results in (i), which age group (youth or old adults) should be given priority? Briefly explain your answer. (3 Marks) iii) Give a reason to support fitting a regression model of the form = + + , where (a) is the y-intercept or constant, (b) is the slope of the function, (y) is the blood pressure of a patient, (X) is the age of a patient and is the error term. (3 Marks) iv) From the model specified in (iii), estimate the values of (a) and (b) and interpret the values (4 Marks) v) What is the blood pressure of an infant at birth? (2 Marks) vi) Predict the blood pressure of a patient who is 90 years old. (2 Marks) vii) Estimate the coefficient of determination and interpret your result.
Answer:
Step-by-step explanation:
Hello!
Given the variables:
Y: Blood pressure of a hospital patient (mmHg)
X: Age of a patients (years)
You have to analyze the claim that the rising numbers in high blood pressure related deaths is associated with the aging of the State's population.
i)
[tex]r= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{\sqrt{[sumX^2\frac{(sumX)^2}{n} ]+[sumY^2-\frac{(sumY)^2}{n}] } }[/tex]
To calculate the correlation coefficient you need to do several additional calculations.
n= 10
∑Y= 1005 mm Hg; ∑Y²= 106475 mmHg²
∑X= 360 years; ∑X²= 16500 years²
∑XY= 40425 years*mmHg
[tex]r= \frac{40425-\frac{360*1005}{10} }{\sqrt{[16500\frac{(360)^2}{10} ]+[106475-\frac{(1005)^2}{10}] } }= 0.96[/tex]
The coefficient of correlation is close to 1 and positive, this means that there is a strong positive correlation between these two variables. This means the blood pressure increases as age does.
ii)
If blood pressure increases with age and so does the risk of dying due to a high blood pressure, then the most logical decision to take is to give priority to the old adults.
iii)
The estimated regression is ^Y= a + bXi + ei
a= y-intercept: is the estimated average blood pressure of the patients when age is 0 years.
b= slope: in the modification of the estimated average blood pressure of the patients when age increases 1 year.
ei= residues
The estimated regression model will allow you to analyze and predict the values of blood pressure of patients within the determined range of age.
iv)
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{40425-\frac{360*1005}{10} }{16500-\frac{(360)^2}{10} } = 1.20 \frac{mmHg}{years}[/tex]
X[bar]= 36 years
Y[bar]= 100.50 mmHg
[tex]a= Y[bar] - bX[bar]= 100.50-1.20*36= 57.33 mmHg[/tex]
The estimated regression equation is ^Y= 57.33 + 1.20Xi
57.33mmHg in the estimated average blood pressure of a patient age zero.
1.20 mmHg/years is the modification on the estimated average blood pressure when the age of the patients increases one year.
v)
At birth an infant is zero years old, so according to the regression model, it's blood pressure will be 57.33 mmHg
According to medical parameters 64.41 mmHg is the average blood pressure of a newborn child, as you can see this model is a little off the average but still within acceptable parameters.
vi)
Using the estimated regression equation you can predict the value of blood pressure for a determined age by replacing the value of X in it:
^Y= 57.33 + 1.20*90= 165.33 mmHg
It is predicted that a 90-year-old patient will have a blood pressure of mmHg.
vii)
[tex]R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{sumY^2-\frac{(sumY)^2}{n} } = \frac{1.20^2[16500-\frac{(360)^2}{n} ]}{[106475-\frac{(1005)^2}{10} ]} = 0.93[/tex]
93% of the variability of the patients blood pressure is explained by their age under the model: ^Y= 57.33 + 1.20Xi
I hope this helps!
the given equation has been solved on the table
Answer:
A. Step 2
Step by step explanation:
It was applied in Step 2 where 9 was added to both sides of the equation.
An employer uses the linear regression equation y = 0.18 x + 320.22 to predict the weekly salary, y, of an employee who sells x dollars worth of merchandise. Last week, Joaquin sold $1500 worth of merchandise. The same week, Alex earned $650. Using the regression equation, which is an accurate comparison? Alex sold merchandise worth about $60 more than what Joaquin sold. Joaquin sold merchandise worth about $60 more than what Joaquin sold. Alex earned about $60 more than Joaquin did. Joaquin earned about $60 more than Alex did.
Answer:
Option C is correct.
Alex earned about $60 more than Joaquin did.
Step-by-step explanation:
The linear regression equation
y = 0.18 x + 320.22
is used to predict the weekly salary, y, of an employee who sells x dollars worth of merchandise.
Joaquin sold $1500 worth of goods. Meaning that x for that week for Joaquin is 1500.
Joaquin' s salary for that week is then given as
y = 0.18x + 320.22
y = 0.18(1500) + 320.22 = 590.22
Hence, Joaquin's salary for that week = $590.22
Alex earns $650 that week. Meaning that y for Alex in that week = 650
y = 0.18x + 320.22
650 = 0.18x + 320.22
0.18x = 650 - 320.22 = 329.78
x = (329.78/0.18) = 1832.1
Hence, Alex sold goods worth $1832.1 that week.
Joaquin sold goods worth $1500
Joaquin earned $590.22
Alex sold goods worth $1832.1
Alex earned $650
From this calculation, it is evident that 'Alex earned about $60 more than Joaquin did' is the correct option as $650 is about $60 more than $590.22
Hope this Helps!!!
Answer:
the answer is C :)
Step-by-step explanation:
surface area, will mark brainliest.
Answer: 30 in^2
Step-by-step explanation:
x2 + y2 =400 has center coordinates ____ and a radius equal to ___
Answer:
Answers are below
Step-by-step explanation:
The center coordinates of the circle are at (0,0).
The radius of the circle is 20
I graphed the circle on the graph below to show you how I got my answers.
The center of the equation x² + y² = 400 is, (0, 0).
And, The radius is 20.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
The equation is,
⇒ x² + y² = 400
Now, We know that;
The standard for of the equation of circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h, k) is the center of the circle and 'r' is the radius of the circle.
Hence, By comparing we get;
⇒ x² + y² = 400
⇒ (x - 0)² + (y - 0)² = 20²
The center of the equation x² + y² = 400 is, (0, 0).
And, The radius is 20.
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16
To get to Amala's house, Tara walks 4 blocks west (left), then 3 blocks north (up), and
then 2 blocks west. Amala's house has coordinates (9,9). What are the coordinates of
Tara's starting point?
A
B.
C
D
(2,0)
(2,6)
(15,6)
(12, 2)
Answer:
Correct answer is C. (15,6)
Step-by-step explanation:
Let us think of the [tex]xy[/tex] co-ordinates plane. We can move in four directions.
1. North (i.e. upwards) If we move north or upwards the value of y-coordinate will increase.
2. South (i.e. downwards) If we move south or downwards the value of y-coordinate will decrease.
3. West (i.e. left) If we move west or left the value of x-coordinate will decrease.
4. East (i.e. right) If we move east or right the value of x-coordinate will increase.
Let us imagine, the starting coordinate of Tara be [tex](x,y)[/tex]
Let us apply the above 4 directions and the properties in the question statement.
Step 1: Tara walks 4 blocks west (left), x coordinate will decrease by 4.
New coordinates will be [tex](x-4,y)[/tex].
Step 2: Tara walks 3 blocks north (up), y coordinate will increase by 3.
New coordinates will be [tex](x-4,y+3)[/tex].
Step 3: Tara walks 2 blocks west (left), x coordinate will decrease by 2.
New coordinates will be [tex](x-4-2,y+3) \Rightarrow (x-6,y+3)[/tex].
Now Tara is at (9,9)
Comparing the x and y coordinates:
[tex]x-6=9\\\Rightarrow x = 15[/tex]
[tex]y+3=9\\\Rightarrow y = 6[/tex]
So, Tara's starting point is (15,6) hence, option C is correct.
In a survey, 376 out of 1,078 US adults said they drink at least 4 cups of coffee a day. Find a point estimate (P) for the population proportion of US adults who drink at least 4 cups of coffee a day, then construct a 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day.
Answer:
The point estimate is 0.3488.
The 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day is (0.3114, 0.3862).
Step-by-step explanation:
In a sample with a number n of people surveyed with a point estimate of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1078, \pi = \frac{376}{1078} = 0.3488[/tex]
The point estimate is 0.3488.
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3488 - 2.575\sqrt{\frac{0.3488*0.6512}{1078}} = 0.3114[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3488 + 2.575\sqrt{\frac{0.3488*0.6512}{1078}} = 0.3862[/tex]
The 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day is (0.3114, 0.3862).
What type of polynomial is P(x) = 7x3 + 2x2 – 3x4?
Answer:
quartic
Step-by-step explanation:
p(x) = 7 x^3 + 2 x^2 - 3 x^4
The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 3, 2, and 4.
The degree of the polynomial is the highest degree of any of the terms; in this case, it is 4.
The time spent driving (which depends on the number of miles needed to
travel) is 2 hours.
Please answer this multiple choice question !! Thank u !! Will give brainliest!!
Answer:
B: 3/2x - 7 + 3 = 0
Step-by-step explanation:
Answer: C
Step-by-step explanation:
General form is in Ax+By+C. To do this, you move everything onto one side.
[tex]\frac{3}{2}x -y+3=0[/tex]
This should be the general form, but this is not correct in these answer choices! Let's try this another way to get Ax+By+C by making Ax not a fraction.
[tex]y=\frac{3}{2} x-3[/tex]
[tex]y+3=\frac{3}{2} x[/tex]
[tex]2(y+3)=3x[/tex]
[tex]2y+6=3x[/tex]
[tex]3x-2y-6=0[/tex]
This may seem incorrect, but we can always check our answer by plugging in numbers.
In our slope intercept form, let's say x=2. What would be our y?
[tex]y=\frac{3}{2} (2)-3[/tex]
[tex]y=3-3[/tex]
[tex]y=0[/tex]
Now we know our coordinates should be (2, 0). When we rewrite the slope-intercept form, we should still get 0 when we plug in x=2 and y=0. Let's check on all answer choices to see which one works.
A. Correct
-3(2)+2(0)+6
-6-6=0
0=0
B. Incorrect
3/2(2)-(0)+3
3+3=6
6≠0
C. Correct
3(2)-2(0)-6
6-6=0
0=0
D. Incorrect; not general form
2(0)=3(2)-6
0=6-6
Now, you can see that A and C are both correct, but the main difference, is that you want to make A positive. The only option where A is positive is in answer C.
PLEASE HELP NO ONE IS HELPING
Answer:
-7 goes in the box
Step-by-step explanation:
x^ -3 = x^4 * x^n
We know that a^b * a^c = a^ (b+c)
x^-3 = x^(4+n)
When the bases are the same the exponents are the same
-3 = 4+n
Subtract 4 from each side
-3 -4 = 4+n-4
-7 = n
PLZZZ I need URGENT help with problems 1 and 2! I'm so confused. Thx!
Answer:Y=x3
2nd answer: Just add it all up and divide by how many things you had to add. For an example: (2+2+2+2)/4.
Step-by-step explanation:
What are the factors of x2 + 4x + 3?
A X3 - 1
B
4x2 + 3
C (x - 3)(x + 1)
D (x+3)(x + 1)
Answer:
D. (X + 3 ) ( X +1 )
process:
x² + 4x + 3
= x² + (3 + 1)x +3
= x² + 3x + x + 3
= X (x+3) + 1 (X+3)
= (X + 3 ) ( X +1 )
What’s the correct answer for this question?
Answer:
C:
Step-by-step explanation:
In the attached file
Compare 7/8 with 14/16 using ( <, >, =).
A. 7/8= 14/16
B.7/8< 14/16
c.7/8>1446
D. none of the above
Answer:
A
Step-by-step explanation:
multiply 7/8 by 2/2 to get 14/16. they are equal
Find the time required for an investment of 5000 dollars to grow to 6100 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Answer:
The time (t) = 2.6 years
Step-by-step explanation:
To calculate the time for earning a compound interest, compounded on a certain amount of present value (PV), compounded periodically, the following formula is used:
[tex]FV=PV(1+\frac{i}{n} )^{n*t}[/tex]
where:
FV = future value = $6,100
PV = present value = $5,000
i = interest rate in decimal = 7.5% = 0.075
n = number of compounding periods per year = quarterly = 4 (4 quarters a year)
t = time of compounding in years = ???
Therefore the time is calculated thus:
[tex]6100=5000(1+\frac{0.075}{4} )^{4*t}[/tex]
[tex]6100=5000(1+0.01875 )^{4t}[/tex]
[tex]6100=5000(1.01875 )^{4t}[/tex]
Next, let us divide both sides of the equation by 5000
[tex]\frac{6100}{5000} = \frac{5000(1.01875)^{4t} }{5000}[/tex]
1.22 = [tex](1.01875)^{4t}[/tex]
Taking natural logarithm of both sides
㏑(1.22) = ㏑[tex](1.01875)^{4t}[/tex]
㏑(1.22) = 4t × ㏑(1.01875)
0.1989 = 4t × 0.01858
4t = [tex]\frac{0.1989}{0.01858} = 10.71[/tex]
∴ 4t = 10.71
t = 10.71 ÷ 4 = 2.6 years
IXL RELATED PLEASE HELP
In ΔDEF, the measure of ∠F=90°, DE = 82 feet, and EF = 55 feet. Find the measure of ∠E to the nearest tenth of a degree.
Answer:
To the nearest tenth of a degree
∠E= 47.9°
Step-by-step explanation:
ΔDEF , let's recognize that it's a right angle triangle because of the presence of ∠F=90°.
Other important measurements are
DE = 82 feet, and EF = 55 feet.
We are to find ∠E
Let's find the missing side first
Side DF
DF² = DE² - EF²
DF²= 82²_55²
DF²=6724-3025
DF²= 3699
DF= 60.82 feet
Let's use the sine formula to look for the angle.
DF/sin ∠E= DE/sin 90
Sin 90= 1
DE= 82
DF= 60.82
Sin ∠E= DF/DE
Sin ∠E= 60.82/82
Sin ∠E= 0.7417
∠E= sin^-1 (0.7417)
∠E= 47.8764
To the nearest tenth of a degree
= 47.9°
(1 1 6 − 7 18 )÷2.8 0.5+ 1 18
Step-by-step explanation:
(116-718) /(2.805+118) [as, there cannot be two decimals in one numbers
=-602/120.805
=0.498
A paint tin is leaking, a circular
puddle is formed and the radius of the
circle increases at a constant rate.
a) If the circumference of the circle
is increasing at a rate of 12cm/s, find
the rate at which the radius is increasing.
Answer:
The rate at which the radius is increasing
dr/dt = 1.91 cm/s
Step-by-step explanation:
The circumference C of a circle can be written as;
C = 2πr .....1
Where;
r = radius
The rate at which the circumference of the circle
is increasing can be written as dC/dt;
Differentiating equation 1, we have;
dC/dt = 2π dr/dt
Making dr/dt the subject of formula;
dr/dt = (dC/dt)/2π
Given;
dC/dt = 12cm/s
Substituting the value of dC/dt;
dr/dt = 12/2π
dr/dt = 1.909859317102 = 1.91 cm/s
The rate at which the radius is increasing dr/dt is 1.91 cm/s
A laptop computer consumes about 20 watts of electricity per hour when operating. At 10 cents per kilowatt-hour, how much does a laptop cost to operate for 5 hours?
Step 1:
Convert the electricity per hour in kilowatts,
Electricity per hour = 20 watts
=20/1000 kilo,watts
Step 2:
The electricity consumes in 5 hour is ,
Electricity in 5 hour = 5x 20/1000 kilo watts.
Obtain the cost as,
=5x20/1000x10
=1 Cent
Answer: =1 Cent
Please mark brainliest
Hope this helps.
The cost of the energy consumed by the laptop for the 5 hours period is 5 cents.
Given:
rate of energy consumption of the laptop, R = 20 Watts per hour
time of operation of the laptop, t = 5 hours
cost of energy consumption, c = 10 cent per kWh
To find:
the cost of the energy consumed by the laptop for the 5 hours periodThe energy consumed by the laptop in kWh is calculated as;
[tex]Energy = Power \times time \\\\Energy = (\frac{20 \ W}{hr} \times 5 \ hr) \times 5\ hr\\\\Energy = (100 \ W) \times ( 5 \ hr)\\\\Energy = (0.1 \ kW) \times (5 \ hr)\\\\Energy = 0.5 \ kWh[/tex]
The cost of consuming 0.5 kWh is calculated as;
[tex]Cost = energy \ rate \ \times \ energy \ consumed \\\\Cost= \frac{10 \ cent}{kWh} \times 0.5 \ kWh\\\\Cost = 5 \ cents[/tex]
Thus, the cost of the energy consumed by the laptop for the 5 hours period is 5 cents.
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A stem and leaf plot shows data in _____ order.
alphabetical
numerical
reverse
Solve 25 = 5x − 4.
one half
2
4
6
Answer:
29/5 =x
Step-by-step explanation:
25 = 5x − 4
Add 4 to each side
25+4 = 5x − 4+4
29 = 5x
Divide each side by 5
29/5 = 5x/5
29/5 =x
Answer:
The answer is 6
Step-by-step explanation:
:)
Which expressions have the same solution as
Check all that apply.
-4(6)?
04(-6)
4(-6)
6(-4)
-8(2)
12(-2)
Answer: B C E
Step-by-step explanation:
Which of the following equations is equivalent to S = pi r squared h?
Answer:
B. h=S/πr²
Step-by-step explanation:
The question lacks options. Here is the complete question.
Which of the following equations is equivalent to S = πr²h
a. h=S-πr^2
b. h=S/πR^2
C. h= πr^2/S
D. h=S+ πr^2
To know the equation equivalent to πr²h, we will make h the subject of the formula as shown from the one given in equation.
S = πr²h
To get h, we will divide both sides by the coefficient of h (i.e πr²)
S/πr² = πr²h/πr²
S/πr² = h
h = S/πr²
This shows that h = S/πr² is equivalent to S = πr²h
Data was collected on the heights of boys at 12 and 24 months of age. The data is summarized in the following boxplots. Is there more variation in the boys' heights at 12 months or 24 months? Explain how you can tell from the boxplots.
A. There is more variation in height at 24 months. The whiskers are more symmetric for the 24-month data, indicating greater spread in the data.
B. There is more variation in height at 12 months. The box length is smaller, indicating a smaller interquartile range and greater spread in the data.
C. There is more variation in height at 12 months. The whiskers are less symmetric for the 12-month data, indicating greater spread in the data.
D. There is more variation in height at 24 months. The box length is longer, indicating a larger interquartile range and greater spread in the data
Answer:
D. There is more variation in height at 24 months. The box length is longer, indicating a larger interquartile range and greater spread in the data
Step-by-step explanation:
One easy way we can easily tell about the spread and variation data sets is by considering the length of the box in the box plot.
The length of a box plot represents the interquartile range of a data set. The longer the box length, the more the variation and spread there is in the data.
Therefore, considering the diagram of the box plots attached below, the box length for length of boys at 24months is longer than that of the box length of heights of boys at 12 months.
The longer box lengths for heights of boys at 24 months indicates a larger interquartile range compared to that of heights of boys at 12 months. This larger interquartile range implies that, there is more variation in heights at 24 months.
Therefore, the correct option is "D. There is more variation in height at 24 months. The box length is longer, indicating a larger interquartile range and greater spread in the data."
Based upon extensive data from a national high school educational testing program, the standard deviation of national test scores for mathematics was found to be 121 points. If a sample of 256 students are given the test, what would be the standard error of the mean?
Answer:
The standard error of the mean is 7.56Step-by-step explanation:
The standard error of the mean is defined as the ratio of standard deviation to the square root of the sample size of a data. The standard error of the mean is mathematically expressed as shown below;
[tex]X = \frac{\sigma}{\sqrt{n} }[/tex]
X is the standard error of the mean
[tex]\sigma[/tex] is the standard deviation
n is the sample size.
Given;
[tex]\sigma = 121\\n = 256[/tex]
On substitution into the formula we have;
[tex]X = \frac{121}{\sqrt{256} }[/tex]
[tex]X = \frac{121}{16} }\\[/tex]
X ≈ 7.56
Which equation will solve the following word problem? One small pitcher and one large pitcher can hold 12 cups of water. If the large pitcher is twice the size of the small pitcher, how much does the small pitcher hold? 2S + S = 12 2S = 12/S 2S - S = 12 S = 12/2S
Answer:
Option (1).
Step-by-step explanation:
Amount of water hold by both the pitchers (Large + small) = 12 cups
Let the small pitcher holds the water = S cups
If the water hold by the large pitcher is twice the size of the small pitcher, then the amount of water hold by large pitcher = 2S
Total amount water hold by both = S + 2S
Equation for this situation will be,
S + 2S = 12
Therefore, Option (1) will be the answer.
