Answer:
the standard error of data set is 2.628
Step-by-step explanation:
Given the data in the question;
set;
x = 9, 13, 21, 30, 31, 31, 34, 25, 28, 20
To get the standard of Error for this data set, we use the formual
S.E = s / √n
First we determine the mean average;
Mean x' = ∑x / n = ( 9 + 13 + 21 + 30 + 31 + 31 + 34 + 25 + 28 + 20 ) / 10
x' = 242 / 10
Mean x' = 24.2
Next we find the standard deviation s:
x (x-x')²
9 231.04
13 125.44
21 10.24
30 33.64
31 46.24
31 46.24
34 96.04
25 0.64
28 14.44
20 17.64
Total ∑(x-x')² = 621.6
so Variance = ∑(x-x')² / (n-1) = 621.6 / ( 10 - 1 ) = 621.6 / 9
Variance = 69.0667
Standard deviation S = √Variance
Standard deviation S = √69.0667
Standard deviation S = 8.3106
So we substitute into our formula to get the standard of error;
S.E = 8.3106 / √10
S.E = 2.628
Therefore, the standard error of data set is 2.628
Answer:
2.63
Step-by-step explanation:
HELP
use the graph below to fill the blank with the correct number:
f(1)=
Answer:
-2
Step-by-step explanation:
f(1) is the value of y when x = 1.
Thus, from the graph, we see that when x = 1 on the x-axis, on the y-axis, we have a corresponding y value of -2.
This means y = -2 when x = 1.
Therefore:
f(1) = -2
The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that a is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees weights is less than 200 lb. Find:
a. Null Hypothesis.
b. Alternative Hypothesis
c. Test Statistic
d. P-value
The answers to all parts shown below.
What is Standard Deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
a) [tex]H_o[/tex]:[tex]\mu[/tex]≥ 200
[tex]H_a[/tex]: [tex]\mu[/tex]< 200
b) Mean = 183.9 and sample standard deviation = 121.2
c) Test statistic:
= (183.9-200)/[121.2/√(54)]
= -0.97611
d) Now,
= ([tex]t[/tex]<-0.97611 with degree of freedom = 53)
= (-10,-1,5036,53)
= 0.168968
Conclusion: Since the [tex]p-value[/tex] is less than 10% [tex]reject[/tex] [tex]H_0[/tex].
The test results support the claim.
Learn more about standard deviation here:
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A coffee pot holds 5 1/2 quarts of coffee. How much is this in cups?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
22 cups
Step-by-step explanation:
1 quart is 4 cups. So therfore 5 1/2 * 4 =22
Hope this helped :)
geometry: HELPPPP PLSS!!
Answer:
A, C and G
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
θ = 25°O = aA = bH = cSubstitute the values into the trigonometric ratios:
[tex]\implies \sf \sin(25^{\circ})=\dfrac{a}{c}[/tex]
[tex]\implies \sf \cos(25^{\circ})=\dfrac{b}{c}[/tex]
[tex]\implies \sf \tan(25^{\circ})=\dfrac{a}{b}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric values} \\\\$\sin(90^{\circ}- \theta)=\cos \theta$\\$\cos(90^{\circ}- \theta)=\sin \theta$\\$\tan(90^{\circ}- \theta)=\cot \theta$\\\end{minipage}}[/tex]
Using trigonometric values and the calculated trigonometric ratios:
[tex]\begin{aligned} \sf \sin(90^{\circ}- 25^{\circ})&=\sf \cos (25^{\circ})\\\implies \sf \sin(65^{\circ}) &=\sf \dfrac{b}{c}\end{aligned}[/tex]
[tex]\begin{aligned} \sf \cos(90^{\circ}- 25^{\circ})&= \sf \sin(25^{\circ})\\\implies \sf \cos(65^{\circ}) &=\sf \dfrac{a}{c}\end{aligned}[/tex]
[tex]\begin{aligned}\sf \tan(90^{\circ}- 25^{\circ})&= \sf \cot(25^{\circ})\\\implies \sf \tan(65^{\circ}) &= \sf \dfrac{1}{\tan(25^{\circ})}\\\implies \sf \tan(65^{\circ}) & = \sf \dfrac{b}{a}\end{aligned}[/tex]
Therefore, the true equations are:
[tex]\sf A: \quad \cos(25^{\circ})=\dfrac{b}{c}[/tex]
[tex]\sf C: \quad \sin(65^{\circ})=\dfrac{b}{c}[/tex]
[tex]\sf G: \quad \sin(25^{\circ})=\cos(65^{\circ})[/tex]
estimate and measure liquid volume
Determine the values of the parameter s for which the system has a unique solution, and describe the solution. x 1 - 5 sx 2
Answer:
[tex]s \ne \±2[/tex]
[tex]x_1 = \frac{3s - 2}{3(s^2 -4)}[/tex]
[tex]x_2 = \frac{2(s- 6)}{5(s^2 - 4)}[/tex]
Step-by-step explanation:
Given
[tex]3sx_1 +5x_2 = 3[/tex]
[tex]12x_1 + 5sx_2 =2[/tex]
Required
Determine the value of s
Express the equations as a matrix
[tex]A =\left[\begin{array}{cc}3s&5\\12&5s\end{array}\right][/tex]
Calculate the determinant
[tex]|A|= (3s*5s -5 *12)[/tex]
[tex]|A|= (15s^2 -60)[/tex]
Factorize
[tex]|A|= 15(s^2 -4)[/tex]
Apply difference of two squares
[tex]|A|= 15(s -2)(s + 2)[/tex]
For the system to have a unique solution;
[tex]|A| =0[/tex]
So, we have:
[tex]15(s -2)(s+2) = 0[/tex]
Divide both sides by 15
[tex](s -2)(s+2) = 0[/tex]
Solve for s
[tex]s -2 = 0\ or\ s +2 = 0[/tex]
[tex]s = 2\ or\ s = -2[/tex]
The result can be combined as:
[tex]s =\±2[/tex]
Hence, the system has a unique solution when [tex]s \ne \±2[/tex]
Next, we solve for s using Cramer's rule.
We have:
[tex]mat\ x_1 = \left[\begin{array}{cc}3&5\\2&5s\end{array}\right][/tex]
Calculate the determinant
[tex]|x_1| = (3 * 5s - 5 *2)[/tex]
[tex]|x_1| = 15s - 10[/tex]
So:
[tex]x_1 =\frac{|x_1|}{|A|}[/tex]
[tex]x_1 = \frac{15s - 10}{15(s -2)(s+2)}[/tex]
Factorize
[tex]x_1 = \frac{5(3s - 2)}{15(s -2)(s+2)}[/tex]
Divide by 5
[tex]x_1 = \frac{3s - 2}{3(s -2)(s+2)}[/tex]
[tex]x_1 = \frac{3s - 2}{3(s^2 -4)}[/tex]
Similarly:
[tex]mat\ x_2 =\left[\begin{array}{cc}3s&3\\12&2\end{array}\right][/tex]
Calculate the determinant
[tex]|x_2| = 3s * 2 - 3 * 12[/tex]
[tex]|x_2| = 6s- 36[/tex]
So:
[tex]x_2 =\frac{|x_2|}{|A|}[/tex]
[tex]x_2 = \frac{6s- 36}{15(s -2)(s+2)}[/tex]
Factorize
[tex]x_2 = \frac{6(s- 6)}{15(s -2)(s+2)}[/tex]
Divide by 3
[tex]x_2 = \frac{2(s- 6)}{5(s -2)(s+2)}[/tex]
[tex]x_2 = \frac{2(s- 6)}{5(s^2 - 4)}[/tex]
Find the area of the shaded region.
Answer:
253 cm^2
Step-by-step explanation:
Large rectangle (without the cutout)
A = wl
A = 18*18
A = 325
Small rectangle (cutout)
A = wl
A = 12 * 6
A = 72
Substract 72 from 325
Jen factored x² - 4x - 21 as (x - 3)(x + 7) What did she do wrong?
Answer:
She didn't put the sign's in the proper place, it should be ( x + 3 ) ( x - 7 )
Step-by-step explanation:
( x - 3 ) ( x + 7 ) = x² + 7x - 3x - 21 = x² + 4x - 21
( x + 3 ) ( x - 7 ) = x² - 7x + 3x - 21 = x² - 4x - 21
Are all numbers that are divisible by 2 also divisible by 10
Answer:The Rule for 10: Numbers that are divisible by 10 need to be even and divisible by 5, because the prime factors of 10 are 5 and 2. Basically, this means that for a number to be divisible by 10, the last digit must be a 0. ... So this number is even and divisible by 5. That means that it is also divisible by 10
Step-by-step explanation:
What type of number can be written as a fraction, where p and q are
integers and q is not equal to zero?
A. A rational number
B. All numbers
C. An irrational number
D.n
Answer:
A. rational number can be written p/q form, where q not equal to zero.
Answer:
its A
Step-by-step explanation:
a Car has a 15 gallon gas tank . I f a car gets 32 miles per gallon and travels 384 miles . how much gas will be left in the tank?
Answer:
so you would actually multiply 32 x 15=480 then subtract 480 - 384= it would have 96 miles left. then divide 96/32= 3
so your answer would be 3 gallons left
Step-by-step explanation:
A medical researcher wants to estimate the difference in the proportions of women with high blood pressure for women who use oral contraceptives versus women who do not use oral contraceptives. In an observational study involving a sample of 700 women, the researcher finds that 0.16 (16%) of the 400 women who used oral contraceptives had high blood pressure, whereas only 0.11 (11%) of the 300 women who did not use oral contraceptives had high blood pressure.
Required:
a. What is the research question of interest for this study?
b. What is the population parameter in this study? What is the appropriate statistical notation for this parameter?
c. What is the value of the sample estimate (statistic) in this study?
d. What is the appropriate statistical notation for this estimate?
Answer:
1.) Difference between the proportion of women with high blood pressure who use oral contraceptive and those who don't use oral contraceptive.
2.)
Difference between the Total proportion of women with high blood pressure who use oral contraceptives, P1 and
Total proportion of women with high high blood pressure who don't use oral contraceptive, P2
P1 - P2
3.)
Difference between the proportion of the 700 women with high blood pressure who use oral contraceptives, Phat1 and
those who don't use oral contraceptive, Phat2
4.)
Phat1 - Phat 2
0.16 - 0.11 = 0.05
Step-by-step explanation:
1.
The question the research intends to answer is : " Difference between the proportion of women with high blood pressure who use oral contraceptive and those who don't use oral contraceptive."
Population parameter will be :
Difference between the Total proportion of women with high blood pressure who use oral contraceptives, P1 and
Total proportion of women with high high blood pressure who don't use oral contraceptive, P2
P1 - P2
3.)
Sample statistic:
Difference between the proportion of the 700 women with high blood pressure who use oral contraceptives, Phat1 and
those who don't use oral contraceptive, Phat2
Phat1 - Phat 2
Convert 73% to a decimal *
Answer
0.73
Step-by-step explanation:
73% = 0.73 in decimal form. Percent means 'per 100'. So, 73% means 73 per 100 or simply 73/100.
Answer:
Step-by-step explanation:
73%
=73/100
=0.73
when u divide the percentage with hundred percentage sign will be removed.
4+4 HELP ME RNNNNN zzolzzz
Answer:
8
Step-by-step explanation:
I'm not too sure, I think it might be 8.
Answer:
4+4 = 8
Step-by-step explanation:
On an architects blueprint, 1 inch corresponds to 9 feet. If an exterior wall is 60 feet long, find how long the blueprint measurement should be
Answer:
x = 6.67 inches
Step-by-step explanation:
Set upa s a proportion
x/60 = 1/9
x = 1/9 * 60
x = 6.67 inches
What is the center and radius of the circle with the given equation? (x+6)^2 + (y-1)^2=9
Answer:
center=(-6, 1)
radius=√9= 3
Step-by-step explanation:
(x-h)^2 + (y-k)^2=r^2
You roll a number cube (six sides, #1 - 6). What is the probability of rolling a 5? *
Answer:
The probability of rolling a 5 is 1/6.
Step-by-step explanation:
There is only one 5 out of the 6 sides, therefor you can only get it once, so the probability of rolling a 5 would be 1/6.
7) Suppose that the amount of time it takes to process insurance claims is normally distributed with a mean of 12 weeks and a variance of 9 weeks. What is the probability that the next claim will be processed within
This question is incomplete, the complete question is;
Suppose that the amount of time it takes to process insurance claims is normally distributed with a mean of 12 weeks and a variance of 9 weeks. What is the probability that the next claim will be processed within; a) 10 weeks, b) 11 weeks, c) 12 weeks.
Answer:
a) the probability that the next claim will be processed within 10 weeks is 25.14%
b) the probability that the next claim will be processed within 11 weeks is 37.07%
c) the probability that the next claim will be processed within 12 weeks is 50.00%
Step-by-step explanation:
Given the data in the question;
mean 12 weeks
Variance = 9 weeks
Standard deviation SD = √Variance = √ 9 = 3 weeks.
Since, the amount of time it takes to process insurance claims is normally distributed.
z = ( x - mean ) / SD
where x is weeks of next claim.
a) 10 weeks
z = ( x - mean ) / SD
we substitute
z = ( 10 - 12 ) / 3
z = -2/3
z = -0.67
{ from standard normal distribution table }
value of z is 0.2514
Therefore, the probability that the next claim will be processed within 10 weeks is 25.14%
b) 11 weeks
z = ( x - mean ) / SD
we substitute
z = ( 11 - 12 ) / 3
z = -1/3
z = -0.33
{ from standard normal distribution table }
value of z is 0.3707
Therefore, the probability that the next claim will be processed within 11 weeks is 37.07%
c) 12 weeks
z = ( x - mean ) / SD
we substitute
z = ( 12 - 12 ) / 3
z = 0/3
z = 0.00
{ from standard normal distribution table }
value of z is 0.5000
Therefore, the probability that the next claim will be processed within 12 weeks is 50.00%
d + 5.5 = 10. Solve for d.
Answer:
d=4.5
Step-by-step explanation:
d+5.5=10
d=10-5.5
d=4.5
Hope this is helpful
Celia simplified the expression Negative 4 x (1 minus 3) minus (2 x + 2). She checked her work by letting x = 5 in both expressions. Her work for the original expression is shown below.
Negative 4 x (1 minus 3) minus (2 x + 2) = negative 4 (5) (1 minus 3) minus (2 (5) + 2) = negative 20 (negative 2) minus 12 = 40 minus 12 = 28.
Celia knows that the simplified expression should also equal 28 when x = 5. Which shows Celia’s simpllifed expression?
Answer:
-4x (1-3) - (2x + 2)
-4(5)(1-3) - (2(5) + 2)
-20(1-3) - (10 + 2)
-20(-2) - (12)
40 - (12)
28
Step-by-step explanation:
Decide whether 4 is a solution of 9x - 6 = 7x
No, 4 is not a solution of [tex]9x - 6 = 7x[/tex].
Here's why:-
[tex]9x - 6 = 7x \\ ⇢ 9x - 7x = 6 \\ ⇢ 2x = 6 \\ ⇢ x = \frac{6}{2} \\ ⇢ x = 3[/tex]
Clearly, the value of [tex]x[/tex] is 3.
[tex]{ \bf{ \underbrace{To\:verify:}}}[/tex]
[tex]9x - 6 = 7x \\ ⇢ 9 \times 3 - 6 = 7 \times 3 \\ ⇢ 27 - 6 = 21 \\ ⇢ 21 = 21 \\ ⇢ L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
Write the quadratic equation whose roots are 1 and -1, and whose leading coefficient is 4
Answer:
y = 4x² - 4
Step-by-step explanation:
y = a(x - x₁ )(x - x₂)
Plug in the knowns
y = 4(x - 1)(x + 1)
expand
y = 4(x² - 1)
y = 4x² - 4
Wilson and Brian are practicing for a swim meet. Last week, Wilson swam 400 meters on each day for three days. Brian swam 0.8 kilometers total for two days. Which boy swam farther last week and by how much?
Answer:
wilson swam farther by 0.4 km
Step-by-step explanation:
wilson swam 1.2km
brian swam 0.8km
1.2 - 0.8 = 0.4
What is the answer to this??
Answer:
C
Step-by-step explanation:
Arianna has a coin collection. She keeps 4 of the coins in her box, which is 10% of the
collection. How many total coins are in her collection?
Answer: 40 coins. Doesn't your profile say college?
2x + 3 ≥ 6 illustrat in number line
Answer:
2x + 3 ≥ 6
2x + 3 - 3 ≥ 6 - 3
2x ≥ 3
2x ÷ 2 ≥ 3 ÷ 2
x ≥ 1.5
If the two angles are complementary, find the measure of each of angle.
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\text{D) } 40 \text{ and }50[/tex]
»»————- ★ ————-««
Here’s why:
Complementary Angles have a sum of 90°.⸻⸻⸻⸻
[tex]\boxed{\text{Setting up an equation...}}}\\\\ \text{We know that complementary angles add up to 90 degrees.}\\\text{Therefore, the sum of the two angles is 90 degrees.}\\\\\rightarrow 4r + 5r = 90[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'r'...}}\\\\4r + 5r = 90\\---------------\\\rightarrow 9r = 90\\\\\rightarrow \frac{9r=90}{9}\\\\\boxed{r = 10}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Evaluating the expressions given...}}\\\\4r \text{ and } 5r\\----------------\\\boxed{4r}\\\\\rightarrow 4(10)\\\\\rightarrow 4 * 10\\\\\rightarrow\boxed{40}\\----------------\\\boxed{5r}\\\\\rightarrow 5(10)\\\\\rightarrow 5 * 10\\\\\rightarrow \boxed{50}[/tex]
⸻⸻⸻⸻
The correct answer should be D.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
D 40 degree and 50 degree
Step-by-step explanation:
* We can work in units when dealing with tens as 4 + 5 = 9
* As the angle ASD is a Right Angle 4r : 5r = 9r
* 2 angles we see within add up to 90 degree 90 = 9r
ASM + MSO = 90 degree
* 5r = ASM and 4r = MSO = 50 = ASM and 40 = MSO
Therefore ASO - MSO = ASM = 90 - 50 = 40
90 - 50 = 40 and 90 - 5r = 4r
4r = 40 degree and 5r = 50 degree
So just list a few of the above and show that
4r + 5r = 90
9r = 90/9
r = 10
Rounding to zero angles = 40 + 50 = 90 as r = 10
* Answer is D 40 degree and 50 degree
Write an equation for the line graphed below: y=??
Answer: y=-2x-1
Step-by-step explanation:
First let's find the slope by using the formula [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]\frac{-3--1}{1-0} \\\frac{-2}{1} \\-2[/tex]
The equation for slope intercept form is y=mx+b where m is the slope and b is the y-intercept
The y-intercept is -1 giving us the equation
y=-2x-1
Given f(x) = 4x + 2, find f(x + 3).
O f(x + 3) = x + 5
O f(x + 3) = 4x2 + 14x + 6
O f(x + 3) = 4x + 14
O f(x + 3) = 4x + 5
Answer:
f(x+3) = 4x + 14
Step-by-step explanation:
f(x+3) = 4(x+3) + 2
f(x+3) = 4x + 12 + 2
f(x+3) = 4x + 14
hope this helps!
Answer:
f(x)=4x+2
f(x+3) means substitute x as (x+3)
f(x+3)=4(x+3) +2
= 4x + 12 + 2
=4x+14.
OPTION C IS LEGIT
Let : → be the quadratic function defined by () = 2
2 + 6 − 8. Find
(i) the vertex (ii) the range
(iii) the axis of symmetry (iv) x-intercepts
(v) the graph of the function f
please answer step by step
Step-by-step explanation:
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