Answer:
a) The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.
b) 0.0078.
Step-by-step explanation:
Question a:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting.
At the null hypothesis, it is tested if the mean is of 421, that is:
[tex]H_0: \mu = 421[/tex]
It is believed that the machine is underfilling the bags.
At the alternative hypothesis, it is tested if the mean is of less than 421, that is:
[tex]H_a: \mu < 421[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
421 is tested at the null hypothesis:
This means that [tex]\mu = 421[/tex]
A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.
This means that [tex]n = 43, X = 414, \sigma = 19[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{414 - 421}{\frac{19}{\sqrt{43}}}[/tex]
[tex]z = -2.42[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean below 414, which is the p-value of z = -2.42.
Looking at the z-table, z = -2.42 has a p-value of 0.0078.
The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.
b. Find the P-value of the test statistic.
As found above, the p-value of the test statistic is 0.0078.
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
9514 1404 393
Answer:
$562,500 per hour
Step-by-step explanation:
The cost will be a minimum where C'(x) = 0.
C'(x) = 0.56x -0.7 = 0
x = 0.7/0.56 = 1.25
The cost at that production point is ...
C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625
The minimum production cost is $562,500 per hour for production of 1250 items per hour.
_____
Additional comment
This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.
y
Ау
What is the pre-image of vertex A' if the image shown
on the graph was created by a reflection across the y-
axis?
(-8. -6)
4-6. 8)
(8.6)
06. -
4
BY
-
Answer:
(- 6, 8 )
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
A' (6, 8 ) → A (- 6, 8 )
Then the pre-image of A' is A (- 6, 8 )
The pre-image of vertex A' would be (-8, 6) on the graph was created by a reflection across the y- axis
The pre-image of vertex A' after a reflection across the y-axis can be found by taking the corresponding point on the other side of the y-axis.
If the image is shown on the graph, and vertex A' is located at (8, 6), then the pre-image of vertex A' would be the point on the opposite side of the y-axis, which has the same x-coordinate but the opposite sign for the y-coordinate.
So, the pre-image of vertex A' would be (-8, 6).
To know more about vertex , here
https://brainly.com/question/21191648
#SPJ2
*REVERSE PROPORTION*
9514 1404 393
Answer:
33.3%
Step-by-step explanation:
The selling price of £42 is (1 +40%) times the total purchase price.
1.40 × purchase price = £42
purchase price = £42/1.40 = £30
The total profit is 40% of this, so is ...
£30 × 40% = £12
The purchase price of the skirt is ...
total cost - glove cost = skirt cost = £30 -3 = £27
The profit on the skirt is ...
total profit - glove profit = skirt profit = £12 -100% × £3 = £9
Then the percentage profit on the skirt is ...
skirt profit % = skirt profit / skirt cost × 100% = £9/£27 × 100% = 33.3%
The percentage profit on the cost of the skirt was 33.3%.
in a group of boys the number of arrangments of boys 4 boys is 12 times the number of arrangment of 2 boys the number of boys in the group is
Answer:
4*12*2
Step-by-step explanation:
it will be the right answer
Answer:
There are 6 boys in group.
Step-by-step explanation:
Since we have given that
Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.
So, Let the number of boys in the group be 'x'.
So, Number of boys in the group will be
\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}
x=
4
12×2
x=
4
24
x=6
Hence, there are 6 boys in the group.
hope it helps you a follow would be appreciated
PLEASE HELP ME ASAP (72 POINTS)
Answer:
d=10.45t
Step-by-step explanation:
The last one is the answer.
Hope this helps!
--Applepi101
Answer:
D) d=10.45t
Step-by-step explanation:
His distance(d) was 100. And his time(t) was 9.58 seconds.
So 100=9.58x
x≈10.44
The answer is D, because 10.45 is greater than 10.44.
I hope this helps!
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is with a standard deviation of days. Assume the data to be approximately bell-shaped.
Required:
a. Between what two values will approximately 68% of the numbers of days be?
b. Estimate the percentage of customer accounts for which the number of days is between 18 and 46.
c. Estimate the percentage of customer accounts for which the number of days is between 11 and 53.
(2/3)x-1=27/8,find x
Answer:
x = 105/16
Step-by-step explanation:
2/3x - 1 = 27/8
Add 1 to each side
2/3x - 1+1 = 27/8+1
2/3x = 27/8 + 8/8
2/3x = 35/8
Multiply each side by 3/2
3/2 * 2/3x = 35/8 *3/2
x = 105/16
I have 1/3 of my garden is parsely, I want to take 4/5 for lettuce. How much of my garden will be lettuce
Which of the following functions is graphed below?
20
15
10
-8-84
-2
42
-5
-10
-15
-20
9514 1404 393
Answer:
D.
Step-by-step explanation:
The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.
In the context of the Pearson r correlation coefficient, the absolute size of r is the:_____.
a. coefficient that indicates the measurement scale that applies to two variables.
b. direction of the relationship between two variables.
c. strength of the relationship between two variables.
d. curvilinear relationship between two variables.
Answer:
strength of the relationship between two variables.
Step-by-step explanation:
The Pearson r correlation Coefficient used to measure the relationship or association between two variables. The correlation Coefficient, R ranges between - 1 and 1. As it provides information on both the strength and type of the relationship. The type of relationship could be positive or negative.
The absolute size of r measures Tha strength of the relationship as it ignores the sign. As the Pearson r value moves closer to 1, the higher the strength of the relationship.
The side lengths of a triangle are 5,10, and 13. Is this a right Triangle?
No because 5^2 +10^2 is not equavalent to 13^2
by using the pythagoras' theorem
PLEASE CORRECT BEFORE ANSWERING I AM HAVING TROUBLE GETTING THINNGS RIGHT SO PLEASE HELP
9514 1404 393
Answer:
3
Step-by-step explanation:
AB is 1 unit long.
A'B' is 3 units long.
The scale factor is the ratio of these lengths:
scale factor = A'B'/AB = 3/1 = 3
ABC is dilated by a factor of 3 to get A'B'C'.
When a < 0 in the quadratic function y = ax2 + bx + C, the graph of the quadratic function opens _____?
Answer:
downwards
Step-by-step explanation:
Given the quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 )
• If a > 0 then the graph opens upwards
• If a < 0 then the graph opens downwards
Find the height of a cone with a diameter of 12 m whose volume is 226m Use 3.14 for pi and round your answer to the nearest meter
Answer:
6m
Step-by-step explanation:
h=3(/V πr^2)=3(226/ π·6^2)≈5.99484
round to 6
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 16.3 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23.
Answer:
Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=30[/tex]
Variance [tex]\sigma= 16.8[/tex]
Significance Level [tex]\alpha=0.05[/tex]
[tex]\sigma = 23[/tex]
Genet=rally the Hypothesis are as follows
Null [tex]H_0=\sigma^2=23[/tex]
Alternative [tex]H_a=\sigma^2 \neq 23[/tex]
Generally the equation for Chi distribution t is mathematically given by
t test statistics
[tex]X^2=\frac{(n-1)\sigma}{\sigma^2}[/tex]
[tex]X^2=\frac{(30-1)16.8^2}{23}[/tex]
[tex]X^2=355.86[/tex]
Therefore
Critical Value
[tex]P_{\alpha,df}[/tex]
Where
[tex]df=29[/tex]
[tex]P_{\alpha,df}=16.0471 and 45.7223[/tex]
[tex]X^2=45.7223[/tex]
Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23
ALEKS questions driving me insane
Answer:
3000
growth
3.4
Step-by-step explanation:
Answer:
k bestie here we go again...
Initial price: $3200
Function represents growth
Price increases by 4.1% every year
yo so ill give you a trick
the very first number in the equation is ALWAYS the initial price for exponential functions
if the decimal in the parantheses has a 1 in front of it (e.g. 1.041) it's ALWAYS going to be growth
To find how much it increases move the decimal forward by 2 places
If land the domain of the following peicewise function f(x)={x^2 +2 if -6
Answer:
? what is this question asking
Step-by-step explanation:
Robin will choose a movie from the Red Box when all movies are in stock. If she
randomly chooses a Romance, Comedy, or Action, what is the probability she will
choose a Romance?
x -3,4,11,18 y -3,1,5,9
Is the relationship linear, exponential, or neither?
Choose 1 answer:
9514 1404 393
Answer:
linear
Step-by-step explanation:
The points all lie on a straight line. The relationship is linear.
One number is 2 less than a second number.
Twice the second number is 16 more than 4 times
the first. Find the two numbers.
Answer:
x = one number
y = second number
Where,
x = y - 3
2y = 4x - 16
Multiply the first equation by 2 and substitute the second equation into it.
2(x=y-3) : 2x = 2y - 6
2x = (4x - 16) - 6
Combine like terms
2x = 4x - 22
2x - 2x + 22 = 4x - 2x -22 + 22
22 = 2x
22/2 = 2x/2
11 = x
Step-by-step explanation:
simplify. can someone help i am lost
9514 1404 393
Answer:
[tex](S)\cdot(H)\cdot(E)\cdot(e)\cdot(\theta)\cdot(\epsilon+1+1)\cdot(\xi)\cdot(s)\cdot(h)[/tex]
Step-by-step explanation:
The inverse function of fun(x) is indicated using a -1 exponent. That is ...
[tex]\text{fun}(\text{fun}^{-1}(x)) = x\\\text{fun}^{-1}(\text{fun}(x)) = x[/tex]
The usual trig identities apply:
sin²(x) +cos²(x) = 1
sec²(x) -tan²(x) = 1
sin(x) = 1/csc(x)
__
So, the expression simplifies to ...
[tex](S)\cdot(H)\cdot(E)\cdot(e)\cdot(\theta)\cdot(\epsilon+1+1)\cdot(\xi)\cdot(s)\cdot(h)[/tex]
Home sizes in Anytown, USA have a mean of 2400 square feet and a standard deviation of 450 square feet. What is the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet
Answer:
0.00084
Step-by-step explanation:
We are given that
Mean,[tex]\mu=2400[/tex] square feet
Standard deviation, [tex]\sigma=450[/tex]square feet
n=50
We have to find the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet.
[tex]P(x<2200)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}<P(\frac{2200-2400}{\frac{450}{\sqrt{50}}})[/tex]
[tex]P(x<2200)=P(Z<\frac{-200}{\frac{450}{\sqrt{50}}})[/tex]
Using the formula
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]P(x<2200)=P(Z<-3.14)[/tex]
[tex]P(X<2200)=0.00084[/tex]
Hence, the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet=0.00084
Responde las preguntas 10 y 11 con base al siguiente gráfico. A 10. ¿Cuáles son los nombres de los ángulos de color azul y rojo respectivamente? A. Obtuso y llano. B. Llano y obtuso. C. Obtuso y agudo. D. Agudo y llano. 11. ¿Cuáles son los colores de un ángulo agudo y uno recto respectivamente? A. Naranja y verde. B. Morado y rojo. C. Morado y naranja. D. Verde y naranja. firmaciones ac
Answer:
10) Los ángulos en azul y rojo son llano y obtuso, respectivamente. (Respuesta: B)
11) Los ángulos agudo y recto están diferenciados por los colores morado y naranja, respectivamente. (Respuesta: C)
Step-by-step explanation:
Basándonos estrictamente en lo descrito en la figura, tenemos la siguiente clasificación por colores:
Agudo - Morado.
Plano o Recto - Naranja.
Obtuso - Rojo.
Llano - Azul.
Completo - Negro.
A continuación, se consigna las respuestas en forma de oración:
10) Los ángulos en azul y rojo son llano y obtuso, respectivamente. (Respuesta: B)
11) Los ángulos agudo y recto están diferenciados por los colores morado y naranja, respectivamente. (Respuesta: C)
The value of a car will “depreciate” over time. For example, a car that was worth $24 000 when it was new, is being sold for $13 500 three years later. Determine the annual depreciation rate on this car. Express your final answer as a percent, rounded to one decimal place.
Answer:
The car will depreciate at a rate of 21.14% per year.
Step-by-step explanation:
Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:
13,500 x (1 + X) ^ 1x3 = 24,000
13,500 x (1 + 0.2114) ^ 3 = 24,000
X = 21.14%
Therefore, the car will depreciate at a rate of 21.14% per year.
The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?
A) ( 2, infinit)
B) (0,2)
C) (-infinit,0) U (2,infinit)
D) (- infinit,0] U [2,infinit)
9514 1404 393
Answer:
A) (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it
Step-by-step explanation:
We want ...
C(x)/x < 100
(20x +160)/x < 100
20 +160/x < 100 . . . . . separate the terms on the left
160/x < 80 . . . . . . . subtract 20
160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0
x > 2 . . . . . . simplify
In interval notation this is (2, ∞). matches choice A
__
Technically (mathematically), we also have ...
160/80 > x . . . . and x < 0
which simplifies to x < 0, or the interval (-∞, 0).
If we include this solution, then choice C is the correct one.
_____
Comment on the solution
Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.
p and q are two numbers.whrite down an expression of. a.) the sum of p and q. b) the product of p and q
6. A boy pushes his little brother in a box with a force of 500 N for 324 m How much work is this if the force of
friction acting on the sliding box is (a) 100 N (6) 250. N?
Answer:
(a) 129600 J
(b) 81000 J
Step-by-step explanation:
The work done is given by the product of force and the displacement in the direction of force.
Force, F = 500 N
distance, d = 324 m
(a) friction force, f = 100 N
The work done is
W = (F - f) x d
W = (500 - 100) x 324
W = 129600 J
(b) Friction, f = 250 N
The work done is
W = (F - f) d
W = (500 - 250) x 324
W = 81000 J
Simplify the expression3x 3√648x4y8
Answer:
= 1296x √ xy
Step-by-step explanation:
Apply exponent rule: a^b . a^c = a^b + c 3 . 3 = 3^ 1 + 1
= x . 3^1+1 √648x . 4y . 8
Add the numbers: 1 + 1 = 2
= x . 3^2 √648x . 4y . 8
= 3^2 . 144x √ xy
Refine
= 1296x √ xy
What is the derivative of x^2?
Answer:
[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
At the gas station, each liter of gas costs $3 but there's a promotion that for every beverage you purchase you save $0.20 on gas.
