Answers
Answer:
Please check if the answer is a = 4 or not
Related Questions
Please show step by step working out of stationary points and points of inflection with the y coordinates (and sketch graph) for the equation y=x^4-36x^2
Answers
Answer:
See picture attached
Step-by-step explanation:
What are the expressions for length, width, and height?
Volume = length width height
V = _____ _____ _____
For odyyseyware
Answers
Answer:
[tex]\boxed{V=lwh}[/tex]
Step-by-step explanation:
The formula for volume of a cuboid is:
[tex]V=lwh[/tex]
[tex]volume = length \times width \times height[/tex]
Answer:
V = l w h
Step-by-step explanation:
Volume of a Cuboid = Length × Width × Height
Where l = length, w = width and h = height
pls help me help me
Answers
Answer:
A
Step-by-step explanation:
For an inequality to have a shaded area above the graph, the variable has to be on the left side of a greater than sign, or a greater than or equal to sign.
A is the only option with one of these signs, so it is the correct answer.
For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the new equation, find x if the point P(x, 4) lies on the new line. y=3x-1 y=1/4 x+2
Answers
Answer:
The answer is below
Step-by-step explanation:
a) y=3x-1
The standard equation of a line is given by:
y = mx + c
Where m is the slope of the line and c is the intercept on the y axis.
Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:
3 × d = -1
d = -1/3
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]
b) y=1/4 x+2
Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:
1/4 × f = -1
f = -4
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and standard deviation 7 ml. The fill
volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL?
1.0000
0.8810
0.8413
0.9987
Answers
Answer:
0.8413
Step-by-step explanation:
Find the z score.
z = (x − μ) / σ
z = (992 − 999) / 7
z = -1
Use a chart or calculator to find the probability.
P(Z > -1)
= 1 − P(Z < -1)
= 1 − 0.1587
= 0.8413
The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct
Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined
Probability can be defined as the ratio of favorable outcomes to the total number of events.
We use Z-statistic to find out the probability,
z = (x − μ) / σ
x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1
P-value from Z-Table:
P(x<992) = 0.15866
P(x>992) = 1 - P(x<992) = 0.84134
Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134
Learn more about probability here:
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What are the solutions of the quadratic equation (x – 8)2 - 13(x - 8) + 30 = 0? Use u substitution to solve.
Ox=-11 and x = -18
x= -2 and x = 5
x= 2 and x = -5
x= 11 and x = 18
Answers
Answer:
Its D
Step-by-step explanation:
x=11 and x=18
A tech company is curious about marketing their new drones for home security. Let the proportion of houses that have home security be p. If the tech company would like to know if the proportion of houses that have home security is different than 45%, what are the null and alternative hypotheses
Answers
Answer:
Step-by-step explanation:
The null hypothesis is described as the default hypothesis while the alternative hypothesis us always tested against this null ie the opposite of the null hypothesis.
In this case study, Let the proportion of houses that have home security be p
Thus, the null hypothesis is proportion of houses that have home security is 45% : p = 45%
The alternative hypothesis is proportion of houses that have home security is different than 45%: p =/ 45%
What the answer fast now
Answers
Answer:
45°
Step-by-step explanation:
This is a special 6 - 6 - 6√2 right triangle with angle measures 45° - 45° - 90°
Answer: m∠R = 45°
Step-by-step explanation:
[tex]6^{2}\ +\ 6^{2} = 72[/tex]
[tex]\frac{\left(6\right)}{\sqrt{72}}=0.7071067812[/tex]
[tex]\sin^{-1}\left(\frac{\left(6\right)}{\sqrt{72}}\right)= 45[/tex]
need help with this question
Answers
Answer:
[tex] - 2 {x}^{5} {y}^{7} [/tex]Last option is correct.
Step-by-step explanation:
[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]
Multiply the terms with the same base by adding their exponents
[tex] - 2 {x}^{3 + 2} {y}^{4 + 3} [/tex]
Add the numbers
[tex] - 2 {x}^{5} {y}^{7} [/tex]
Hope this helps..
Best regards!
[tex] - 2 {x}^{5} {y}^{7} [/tex]
Solution:
[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]
[tex] = 2 {x}^{(3 + 2)} {y}^{(4 + 3)} [/tex]
[tex] = - 2 {x}^{5} {y}^{7} [/tex]
[tex]{\boxed{\blue{\textsf{Some Important Laws of Indices}}}}[/tex]
[tex]{a}^{n}.{a}^{m}={a}^{(n + m)} [/tex]
[tex]{a}^{-1}=\dfrac{1}{a}[/tex]
[tex]\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}[/tex]
[tex]{({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}[/tex]
[tex] {a}^{\frac{1}{x}}=\sqrt[x]{a}[/tex]
[tex]a^0 = 1[/tex]
[tex][\text{Where all variables are real and greater than 0}][/tex]
2/3x + 5 = 3 plz helppppppp
Answers
Answer:
2 /3 +5 = 3
5.666667≠3
False
Step-by-step explanation:
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Lets do this step by step.
~~~~~~~~~~~~~~~~~~~~
Multiply both sides of the equation by [tex]\frac{3}{2}[/tex] .
[tex]\frac{3}{2} . \frac{2}{3} . x = \frac{3}{2} . 5[/tex]
Simplify both sides of the equation.
~~~~
Simplify [tex]\frac{3}{2} . \frac{2}{3} . x .[/tex]
[tex]x = \frac{3}{2} . 5[/tex]
Multiply [tex]\frac{3}{2} . 5[/tex]
[tex]x = \frac{15}{2}[/tex]
The result can be shown in multiple forms.
Exact Form: [tex]x = \frac{15}{2}[/tex]
Decimal Form: [tex]x = 7.5[/tex]
Mixed Number Form: [tex]x = 7\frac{1}{5}[/tex]
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●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Evaluate the series
Answers
Answer:
the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
C) 59
Step-by-step explanation:
Recall that;
[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]
Therefore, we can evaluate the series;
[tex]\sum_{k=1}^{6}(25-k^2)[/tex]
by summing the values of the series within that interval.
the values of the series are evaluated by substituting the corresponding values of k into the equation.
[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]
So, the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
At 2:00 PM a car's speedometer reads 30 mi/h. At 2:15 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:15 the acceleration is exactly 80 mi/h^2. Let v(f) be the velocity of the car t hours after 2:00 PM._________ Then By the Mean Value Theorem, there is a number c such that 0 Since v'(t) is the acceleration at time t.______ the acceleration c hours after 2:00 PM is exactly 80 mi/h^2.
Answers
Here is the correct format for the question
At 2:00 PM a car's speedometer reads 30 mi/h. At 2:15 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:15 the acceleration is exactly 80 mi/h².Let v(f) be the velocity of the car t hours after 2:00 PM.Then [tex]\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box[/tex]. By the Mean Value Theorem, there is a number c such that 0 < c < [tex]\Box[/tex] with v'(c) = [tex]\Box[/tex]. Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly 80 mi/h^2.
Answer:
Step-by-step explanation:
From the information given :
At 2:00 PM ;
a car's speedometer v(0) = 30 mi/h
At 2:15 PM;
a car's speedometer v(1/4) = 50 mi/h
Given that:
v(f) should be the velocity of the car t hours after 2:00 PM
Then [tex]\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box[/tex] will be:
[tex]= \dfrac{50-30}{1/4 -0}[/tex]
[tex]= \dfrac{20}{1/4 }[/tex]
= 20 × 4/1
= 80 mi/h²
By the Mean value theorem; there is a number c such that :
[tex]\mathbf{0 < c< \dfrac{1}{4}}[/tex] with [tex]\mathbf{v'(c) = \dfrac{v(1/4)-v(0)}{1/4 -0}} \mathbf{ = 80 \ mi/h^2}[/tex]
By the mean value, theorem a number [tex]C[/tex] is [tex]0 < C < \frac{1}{4}[/tex].
The velocity of the car is [tex]80 \ mi/h^{2}[/tex].
Speed:Speed is defined as The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
Given that,
at 2:00 pm [tex]v(0)=30 \ mi/h[/tex]
at 2:15 pm [tex]v(1/4)=50 \ mi/h[/tex]
Then,
[tex]=\frac{v(1/4)-v(0)}{1/4-0} \\=\frac{50-30}{1/4} \\=20\times4\\=80 \ mi/h^{2}[/tex]
By the mean value theorem a number [tex]C[/tex] such that express as,
[tex]0 < C < \frac{1}{4}[/tex].
Now with,
[tex]{v}'(c)=\frac{v\left ( \frac{1}{4} \right )-v\left ( 0 \right )}{\frac{1}{4}-0} \\ =80 \ mi/h^{2}[/tex]
Learn more about the topic Speed: https://brainly.com/question/26417650
Given that r = ( 7, 3, 9) and v = ( 3, 7, -9), evaluate r + v
a. (-21,-21,81)
b. (10,10,0)
c. (21,21,-81)
d. (-10,-10,0)
Answers
Answer:
b. (10,10,0)
Step-by-step explanation:
r+v can be evaluated if the vectors/matrices have the same dimensions.
These do. They are both 1 by 3 vectors.
Just add first to first in each.
Just add second to second in each.
Just add third to third in each.
Example:
(5,-5,6)+(1,2,3)
=(5+1,-5+2,6+3)
=(6,-3,9)
Done!
In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).
r+v
=(7,3,9)+(3,7,-9)
=(7+3,3+7,9+-9)
=(10,10,0)
Done!
Find the indicated binomial probability. A multiple choice test has 30 questions, and each has four possible answers, of which one is correct. If a student guesses on every question, find the probability of getting exactly 12 correct.
Answers
Answer:
0.02906
Step-by-step explanation:
number of questions =30
getting exactly right : 12
30C12 the number of possibilities
probability to get it right (1/4)^12
probability of failure =1-1/4=(3/4)^18 ( 18 = 30 questions -12 right )
P(12)=30C12*(1/4)^12*(3/4)^18=0.02906
hope it helps
Professor Easy's final examination has 9 true-false questions followed by 3 multiple-choice questions. In each of the multiple-choice questions, you must select the correct answer from a list of five. How many answer sheets are possible? choices
Answers
Answer: 2⁹5³ = 64,000
Step-by-step explanation:
There are 9 questions with 2 options (true or false) = 2⁹
There are 3 multiple questions with 5 options = 5³
true/false questions AND multiple choice questions
2⁹ x 5³ = 2⁹5³
We draw a random sample of size 25 from a normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?
Answers
Answer:
11.2≤[tex]\mu[/tex]12.8Step-by-step explanation:
Confidence interval for the population mean is expressed by the formula;
CI = xbar ± Z(S/√n) where;
xbar is the sample mean = 12.5
Z is the z score at 99% confidence = 2.576
S is the standard deviation = √variance
S = √2.4 = 1.5492
n is the sample size = 25
Substituting the given values into the formula given above,
CI = 12.5 ± 2.576(1.5492/√25)
CI = 12.5 ± 2.576(0.30984)
CI = 12.5 ± 0.7981
CI = (12.5-0.7981, 12.5+0.7981)
CI = (11.2019, 12.7981)
Hence the 99% confidence interval for the population mean is 11.2≤[tex]\mu[/tex]12.8 (to 1 decimal place)
A 99% confidence interval for the population mean will be "11.2 [tex]\leq[/tex] 12.8".
StatisticsAccording to the question,
Sample mean, [tex]\bar x[/tex] = 12.5
Z score at 99%, Z = 2.576
Standard deviation, S = √Variance
= √2.4
= 1.5492
Sample size, n = 25
We know the formula,
Confidence interval, CI = [tex]\bar x \ \pm[/tex] Z ([tex]\frac{S}{\sqrt{n} }[/tex])
By substituting the given values, we get
= 12.5 [tex]\pm[/tex] 2.576 ([tex]\frac{1.5492}{\sqrt{25} }[/tex])
= 12.5 [tex]\pm[/tex] 2.576 (0.30984)
= 12.5 [tex]\pm[/tex] 0.7981
Now,
Cl = (12.5 - 0.7981, 12.5 + 0.7981)
= (11.2019, 12.7981) or,
= (11.2, 12.8)
Thus the above answer is appropriate.
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All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?
Answers
Answer:
Perimeter= 40 units
Step-by-step explanation:
Ok
We are asked to look for the perimeter.
We have some clue given.
All at right angle and some sides are given it's full length.
We have the bae to be 11 unit
The height to be 7 unit.
What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.
Let's go for the other side of the height.
Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.
So we have 7+7+11
But it's not complete yet.
We are given a dimension 2.
And the 2 is in two places so it's total 2*2= 4
The two is for a small base .
The base is actually an extra to the 11 of the other base.
So summing up
We have 2*11 + 2*7 + 2*2
Perimeter= 22+14+4
Perimeter= 40 units
Identify the percent, amount, and base in this problem What is 15% of 60?
Answers
Answer:
9
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
helppp i will give stars,thanks and also bralienst
Answers
Answer:
21.30 dollarsis the answerStep-by-step explanation:
Total money/ number of people
63.90/3 = 21.30
If you divide by 3 then the 3 friends will get the equal amount of money.
Answer:
Step-by-step explanation:
The total amount of money is $63.90. Also, there are 3 friends.
In order to pay equally, divide $63.90 and 3 friends, so the answer would be dollars per friend
$63.90/3 friends = $21.3/friend
So the items you would drag would be:
2 $10 bills
1 $1 bill
3 $0.10 dimes
The formula to convert Fahrenheit to Celsius is C=5/9(F-32). Convert 30c to Fahrenheit. Round to the nearest degree
Answers
Answer:
86 degrees farenheit
Step-by-step explanation:
First, we plug 30 in for C.
Next, solve for F
Multiplying both sides by 9/5 gives us 54=F-32
Add 32 to both sides 86=F
What is the total of 49 1/4+3 3/8
Answers
Answer:
52 5/8
Step-by-step explanation:
To add fractions, you have to make sure both fractions have a common denominator.
As you can see, the fractions have different denominators, so to make both denominators 8, we have to multiply 1/4 by two, which gives us 2/8.
Then, we just add like normal!
49 2/8+ 3 3/8 = 52 5/8!
Hope this helped! :)
The radius of a nitrogen atom is 5.6 × 10-11 meters, and the radius of a beryllium atom is 1.12 × 10-10 meters. Which atom has a larger radius, and by how many times is it larger than the other?
Answers
Answer:
The beryllium atom; 1.99 times larger.
Step-by-step explanation:
The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.
(1.12 * 10^-10) / (5.6 * 10^-11)
= (1.112 / 5.6) * (10^-10 + 11)
= 0.1985714286 * 10
= 1.985714286 * 10^0
So, the beryllium atom is about 1.99 times larger than the other.
Hope this helps!
A manufacturer claims that its rechargeable batteries are good for an average of more than 1.000 charges. A random sample of 100 batteries has a mean life of 1002 charges and a standard deviation of 14. Is there enough evidence to support this claim at a significance level of 0.01?
a. State the hypotheses.
b. State the test statistie information
c. State either the p-value or the critical information d. State your conclusion and explain your reasoning
Answers
It's 1000 charges and not 1.000 charges
Answer:
A)Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = 1.4286
C) p-value = 0.15628
D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges
Step-by-step explanation:
We are given;
x = 1002 charges
s = 14
μ = 1000 charges
n = 100
degree of freedom = n - 1 = 100 - 1 = 99
A) The hypotheses are;
Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = (x - μ)/(s/√n)
(1002 - 1000)/(14/√100) = 1.4286
C) From the t-score calculator results attached, the p-value is approximately 0.15628
D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.
An entertainment company specifies that its employees must weigh between 40 kgs - 50 kgs. If X is the random variable denoting the weights of employees, X is a __________ random variable.
Answers
Answer: Continuous
If X is the random variable denoting the weights of employees, X is a continuous random variable.
Step-by-step explanation:
Given: An entertainment company specifies that its employees must weigh between 40 kgs - 50 kgs.
here weights of the employees vary.
Also, weight is measured not counted , that means weight is a continuous variable.
If X is the random variable denoting the weights of employees, X is a continuous random variable.
The weights of employees, X, is a: continuous random variable.
Facts about Random Continuous VariableA continuous variable is obtained simply through measuring.Examples of continuous variable are: weight of students, distance travelled.A continuous random variable are values given for an interval of numbers.Therefore, the weights of employees, X, is a: continuous random variable.
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If ABC=DEC B=48 and E=C+4
x=?
Answers
Answer:44
Step-by-step explanation:the two triangles are congruent , so we deduce from that the angle B=angle E =48
So, x+4=48 , x=44 degree
conditional probability. please help!
Answers
Answer:
a. 0.06
b. 0.2
Step-by-step explanation:
a. P(B given A) = P(A and B) / P(A)
0.1 = P(A and B) / 0.6
P(A and B) = 0.06
b. P(A given B) = P(A and B) / P(B)
P(A given B) = 0.06 / 0.3
P(A given B) = 0.2
Currently Shawn pays $550 per month to rent his apartment. Next year his rent will increase by 13.5% from what he currently pays . a) find the amount that shawn's rent will increase . b) what will be shawn's new monthly rent?. c) If you divide your answer from (b) by shawn's original rent of $550, what is the decimal result? do you see any connection to part (a)?
Answers
a) Simply do 0.135(13.5%)*550 to get that his rent increases by $74.25.
b) Simply do 550+74.25 to get that his new rent is $624.25.
c) 624.25/550 = 1.135, or 100%+13.5%, the amount his rent increased.
Hope it helps <3
Answer:
A. $74.25
B. $624.25
C. 1.135, and this is a connection to part a because it's what we multiplied 550 by to get our new rent.
Step-by-step explanation:
If Shawn pays $550 per month for rent, and he has a 13.5% increase, we can multiply 550 by [tex]1+\frac{13.5}{100}[/tex] to get our new number.
[tex]1+0.135=1.135[/tex]
[tex]550\cdot1.135=624.25[/tex]
This is the new monthly rent, part B. To find Part A, let's subtract 550 from thi number.
[tex]624.25-550=74.25[/tex]
Now, for part C, let's divide 624.25 by 550.
[tex]624.25\div550 = 1.135[/tex]
If you notice, 1.135 is the same number we multiplied 550 by to get our new cost, and as a percent, 1.135 is 113.5%.
Hope this helped!
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.9 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb.
b. If 39 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb.
c. When redesigning the ejection seat which probability is more relevant?
Answers
Answer:
The answer is below
Step-by-step explanation:
Given that:
mean (μ) = 138 lb, standard deviation (σ) = 34.9 lb
z score is used in statistic to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{150-138}{34.9}=0.34[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{201-138}{34.9}=1.81[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(0.34 < z < 1.81) = P(z < 1.81) - P(z < 0.34) = 0.9649 - 0.6331 = 0.3318 = 33.18%
b) If 39 different pilots are randomly selected i.e. n = 39. For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{150-138}{34.9/\sqrt{39} }=2.15[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{201-138}{34.9/\sqrt{39} }=11.3[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(2.15 < z < 11.3) = P(z < 11.3) - P(z < 2.15) = 1 - 0.9842 = 0.0158 = 1.58%
c) The probability from part C is more important
The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingredient. The manufacturer claims each tablet has at least 200 milligrams of the active ingredient. The consumer Watchdog Bureau assumes the manufacturer claim is correct, but occasionally tests samples of the tablets to ensure they contain enough of the ingredient. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The sample mean content of the active ingredient is 205.7 milligrams, while the sample standard deviation is 21 milligrams. What is the p-value for this test?
Answers
Answer:
The p-value is [tex]p-value = 0.013167[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu[/tex] = 200 milligrams
The sample size is [tex]n = 70[/tex]
The sample mean is [tex]\= x = 205.7[/tex]
The sample standard deviation is [tex]\sigma = 21 \ milligram[/tex]
Generally the Null hypothesis is mathematically represented as
[tex]H_o : \mu = 200[/tex]
The Alternative hypothesis is
[tex]H_a : \mu < 200[/tex]
The test statistics is mathematically represented as
[tex]t_s = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }[/tex]
substituting values
[tex]t_s = \frac{ 205.7 - 200 }{\frac{21}{\sqrt{70} } }[/tex]
[tex]t_s = 2.270[/tex]
Now the p-value is mathematically represented as
[tex]p-value = P(Z \le t_s )[/tex]
substituting values
[tex]p-value = P(Z \le 2.270 )[/tex]
Using the Excel function[=NORMDIST(2.270)] to calculate the p-value we obtain that
[tex]p-value = 0.013167[/tex]
Answer:
A) 0.012
From CollegeBoard
A popular charity used 31% of its donations on expenses. An organizer for a rival charity wanted to quickly provide a donor with evidence that the popular charity has expenses that are higher than other similar charities. The organizer randomly selected 10 similar charities and examined their donations. The percentage of the expenses that those 10 charities spend on expenses is given below. Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether the mean is less than 31% and then draw a conclusion in the context of the problem. Use α=0.05. 26 12 35 19 25 31 18 35 11 26 Select the correct answer below: Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%. Reject the null hypothesis. There is insufficient evidence to conclude that the mean is less than 31%. Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%. Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is less than 31%.
Answers
Answer:
Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%.
Step-by-step explanation:
In this case we need to test whether the popular charity has expenses that are higher than other similar charities.
The hypothesis for the test can be defined as follows:
H₀: The popular charity has expenses that are higher than other similar charities, i.e. μ > 0.31.
Hₐ: The popular charity has expenses that are less than other similar charities, i.e. μ < 0.31.
As the population standard deviation is not known we will use a t-test for single mean.
Compute the sample mean and standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{10}\cdot[0.26+0.12+...+0.26]=0.238\\\\s= \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 0.0674 }{ 10 - 1} } =0.08654\approx 0.087[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{0.238-0.31}{0.087/\sqrt{10}}=-2.62[/tex]
Thus, the test statistic value is -2.62.
Compute the p-value of the test as follows:
[tex]p-value=P(t_{\alpha, (n-1)}<-2.62}[/tex]
[tex]=P(t_{0.05,9}<-2.62)\\=0.014[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.014.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.014 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Thus, concluding that there is sufficient evidence to conclude that the mean is less than 31%.