Answer:
H0 : μ = 60000
H1 : μ ≠ 60000
Test statistic = 3.464
Step-by-step explanation:
Given :
Sample mean salary, xbar = 80000
Sample standard deviation, s = 10000
Population mean salary , μ = 60000
Sample size, n = 3
Hypothesis :
H0 : μ = 60000
H1 : μ ≠ 60000
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (80000 - 60000) ÷ (10000/√(3))
T = 20000 / 5773.5026
T = 3.464
The Decison region :
If Tstatistic >Tcritical
Tcritical at 10%, df = 2 ; two - tailed = 2.9199
Tstatistic > Tcritical ; He
A farmer has 220 bushels of apples to sell at roadside stand. She sells an average of 14 3/5 each day. Represent the total change in the number of bushels has for sale after 6 days.The total change in the number of bushels has for sale is ???, please answer as a fraction
Answer:
Step-by-step explanation:
He has sold (16+1/4) bushels/day x 5 days = (16 x 5) + (1/4 x 5) = 80 + 5/4 = 81 + 1/4 = 81.25
The change in the number of bushels is 140 - 81.25 = 58.75 or 58 and 3/4 bushels
In other words, he has 58.75 (or 18 and 3/4) bushels remaining and has sold 81.25 (or 81 and 1/4) bushels
What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work.
y = -2x - 7
y = 2x + 17
y = 1/2x + 8
y = -1/2x + 2
Answer:
y = m x + b equation for a straight line
m m' = -1 for perpendicular lines
Thus m' = -1/2 is required
Check:
-1/2 * -6 + 2 = = 3 + 2 = 5 = y for the last equation give
Explain the step by step process of finding a function for a hyperbola given the center (1,4), vertices (-7,4) and (9,4), and a point on the hyperbola at (-11, -6). Make sure to include the location of the foci.
NO LINKS!!
Answer:
(x -1)²/64 -(y -4)²/80 = 1foci (-11, 4) and (13, 4)Step-by-step explanation:
The standard form of a hyperbola whose transverse axis is horizontal is ...
(x -h)²/a² -(y -k)²/b² = 1 . . . . center (h, k); transverse axis 2a; conjugate axis 2b
The distance between the two vertices is given as (9 -(-7)) = 16 = 2a, so the value of a is 8 and we have the partial equation ...
(x -1)²/8² -(y -4)²/b² = 1
Filling in the given point value gives us an equation for b².
(-11 -1)²/8² -(-6 -4)²/b² = 1
9/4 -100/b² = 1
5/4 = 100/b²
b² = 80
So, the equation is ...
(x -1)²/64 +(y -4)²/80 = 1
__
The distance between the foci is 2c, where c² = a² +b².
c² = 64 +80 = 144 = 12²
c = 12, so the foci are at ...
(x, y) = (1 ±12, 4) . . . . . . . 12 units either side of the center
The foci are (-11, 4) and (13, 4).
_____
Additional comment
The steps are ...
use the given information to fill in as much of the equation as you can.use any given points or additional information to find the unknown values in the equationdetermine any additional information asked for (foci, asymptotes, ...)The relevant relations are ...
2a = length of transverse axis (distance between vertices)
2b = length of conjugate axis (distance between co-vertices)
±b/a = slope of asymptotes, which are lines through the center
2c = distance between foci, where c² = a² +b²
The equation is (x -h)²/a² -(y -k)²/b² = 1 for a hyperbola that opens horizontally with center (h, k). Swapping variables x and y will give a hyperbola that opens vertically. If the figure opens vertically, the asymptotes will have slope ±a/b.
The distances from a point to the foci have a constant difference of 2a.
Charles wants to buy an anime book that is on sale for $14.99. Her sister kyra wants to buy a novel book for $17.99. Both of them has to pay a 7% tax. Kyra has a coupon for 15% discount. Whats the difference between the amount that each siblings has to pay?
Answer:
The difference between their total amounts is .34 cents
also it didnt look like i was supposed to count a discount for charles so i didnt :)
Step-by-step explanation:
Charles14.99 times .07 = 1.04
14.99 + 1.04 = 16.03
Kyra17.99 times .15 = 2.69
17.99 -2.69 = 15.30
15.30 times .7 = 1.07
15.30 + 1.07 = 16.37
16.37 - 16.03 = .34
can't believe that you got me in a suit and tie I had to take a pull so I wouldn't cry
You got a line out the church door sayin' goodbye
Yeah, I believe 'em when they say you're in a better place
NAME THE SONG AND THE SINGER 50 POINTS!!!!!
Answer:
give heaven some hell by Hardy
Step-by-step explanation:
y=1/4x−2y=−2x+3 help solve problem.
Answer:
(x, y) = (2 2/9, -1 4/9)
Step-by-step explanation:
Equate the values of y and solve for x.
1/4x -2 = -2x +3
(2 1/4)x = 5 . . . . . . . . add 2+2x to both sides
x = 20/9 = 2 2/9 . . . multiply by 4/9
y = -2(2 2/9) +3 = -4 4/9 +3 . . . . substitute for x in the second equation
y = -1 4/9
The solution is x = 2 2/9, y = -1 4/9.
Need help fast worth 20 points
Select the correct answer.
Which set of absolute values is compared correctly
OA. 1-10] < |-5| < |17| < 151
OB. 1-5| > |-10| > |-12| > |17||
OC. |10| > |-15] > [-5| > 12||
OD. |-101 < [12] < |-15| < |17||
Answer:
i think its b.
Step-by-step explanation:
correct me if im wrong. and it was worth 10 points instead of 20.
HELP! Due in 5 minutes
ANSWER:
the first one: 30x+48
The second one: x y^2(10 y + 15)
The third one: 30 x y - 5 x^2
Hope this helped!
sorry if im wrong. :)
GOOD LUCK!! <3
Please help me in this 4th grader question, its a homework and i was sick over the weekend
Answer:
what is your question ask then I shall answer you
anyone willing to help??
Pls look at the picture for question.
Answer:
Only option A is correct
Step-by-step explanation:
Positive numbers are always greater than negative numbers no matter the quantities. Also, the greater the negative number is, the less it becomes.
Hope this helps :D
An angle measures 136°. What is the measure of its supplement?
Answer:
44⁰.
Step-by-step explanation:
Its supplement = 180 - 136
= 44 degrees.
Help help help help math
Answer:
158
Step-by-step explanation:
We know the supplement of angle 6 is 22, due to the fact that they are corresponding angles. Simply subtract 22 from 180 to get the answer. 180-22=158
Answer:
158 degrees
Step-by-step explanation:
Angle 6 has a same side interior relationship with the 22 degrees, so the sum of these angles are equal to 180 degrees.
To find the missing angle, subtract 180 by 22 degrees.
180-22= 158
Find the perimeter of the rectangle
Answer:
70Step-by-step explanation:
Find the perimeter of the rectangle
add the lengths of the rectangle's four sides
24 + 11 + 24 + 11 = 70
Stuck on this, need help on this.
Answer:
Domain: (-∞ , ∞)
Range: y <= 8 [8 , -∞)
Step-by-step explanation:
x = 2
f(x) = 8
x<=2
f(x) <=8
The label on a 4-quart container of orange juice states that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.
(a) Develop the appropriate null and alternative hypotheses.
a) H0: μ = 1
b) Ha: μ ≠ 1
a) H0: μ > 1
b) Ha: μ ≤ 1
a)H0: μ ≥ 1
b) Ha: μ < 1
a) H0: μ < 1
b) Ha: μ ≥ 1
a) H0: μ ≤ 1
b) Ha: μ > 1
(b)What is the type I error in this situation? What are the consequences of making this error?
a) It is claiming μ < 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.
b) It is claiming μ > 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.
c) It is claiming μ ≥ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.
d) It is claiming μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.
(c) What is the type II error in this situation? What are the consequences of making this error?
a) It is concluding μ > 1 when it is not. This error would conclude that the product is not meeting its label specification when it really is meeting its specification.
b) It is concluding μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.
c) It is concluding μ ≥ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.
d) It is concluding μ < 1 when it is not. This error would conclude that the product is not meeting its label specification when it really is meeting its specification.
The x-value of the vertex of f(x) = x2 - 10x + 3 is
Answer:
x- coordinate = 5
Step-by-step explanation:
Given a parabola in standard form , f(x) = ax² + bx + c ( a ≠ 0 ) , then
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - 10x + 3 ← is in standard form
with a = 1 , b = - 10 , then x- coordinate of vertex is
x = - [tex]\frac{-10}{2}[/tex] = 5
In a chess club there are 10 males and 15 females. What percentage of the club is females?
Answer:
Step-by-step explanation:
Joe lost his part-time job, which reduced the net family income by 20%. His wife Janice decided to work overtime to compensate for the lost income. Other things being equal, by what percentage must her net salary increase in order to arrive at the same net family income as they had before Joe lost his job?
The percentage by which Janice's net salary must be increased in order to arrive at the same net family income as they had before Joe lost his job is 25%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let the salary of Joe be represented by x, while the salary of Janice is represented by y.
Since the sum of the salary of Joe and Janice is the net income of the family. Therefore, the net salary when Joe had a job will be,
x + y₁ = 100%
Now, it is known that Joe lost his job, which reduced the net family income by 20%. Therefore, the net salary now will be only 80% which will be equal to the salary of Janice. Thus, we can write,
y₁ = 80%
Further, Janice decided to work overtime to compensate for the lost income. Therefore, we can write,
y₂ = 100%
Furthermore, the percentage change in salary of Janice can be written as,
Percentage Change = [(100% - 80%)/80% ] × 100%
= 20/80 × 100%
= 25%
Hence, the percentage by which Janice's net salary must be increased in order to arrive at the same net family income as they had before Joe lost his job is 25%.
Learn more about Percentages:
https://brainly.com/question/6972121
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What is the possible degree of a polynomial if it has a root of -3 with multiplicity of 2 and, a root of 4 with a multiplicity of 1?
Answer:
3rd degree
Step-by-step explanation:
factors are
a(x + 3)(x + 3)(x - 4)
polynomial is
a(x² + 6x + 9)(x - 4)
a(x³ + 2x² - 15x - 36)
where (a) could be any real number
What is the equation of the line: * parallel to the line y = -¼x + 5 and * passing through the point (2, -1)
y = -¼x - 1/2
y = ¼x + 2
y = -¼x + 4
y = ¼x - 1
Answer:
last one
Step-by-step explanation:
In an economics class, 4 students earned an A, 6 earned a B, 5 earned a C, 5 earned a D, and 3 earned an F. If a single student is picked at random, what is the probability that they earned an B or C?
Provide your answer as a simplified fraction.
Answer:
11/23
Step-by-step explanation:
B = 6
C = 5
6+5=11
11/23
If the letters in the word NEIGHBOR are
randomly rearranged, what is the probability
that the arrangement ends with the letter B?
For A = {B, C, D} and B = {A, E, I, O, U}, which set is empty?
Answer:
B is empty
Step-by-step explanation:
Natalie walked
3
5
mile in
1
2
hour. How fast did she walk, in miles per hour?
A.
5
6
miles per hour
Answer:
7 miles / hour
Step-by-step explanation:
I'm taking this to mean she walked 3.5 miles. She did this 1/2 hour.
Givens
d (distance ) = 3.5 miles
t (time) = 1/2 hour
r (rate) = ?
Formula
r = d/t
Solution
The easiest way to do this is to change the fractions to decimals.
t = 1/2 = 0.5 hours
r = 3.5 / 0.5
r = 7 miles per hour.
At TGI Fridankay's you order a drink for $2.99, an appetizer for $9.99, the cajun chicken pasta for $11.50, and a dessert for $7.99. You had amazing service and know that you are going to tip your waiter 20%! The waiter also gave you a 10% coupon to use. There is also a 7% sales tax on the bill. What is your total bill after the tip, discount, and tax?
The total bill after the tip, discount, and tax is $37.76.
The total cost of the order is reduced by the coupon and increased by the tax paid and tip.
Total cost of the items bought = cost of the drink + appetizer + Cajun + dessert
$2.99 + $9.99 + $11.50 + $7.99 = $32.47
Value of the tip = 20% x $32.47 = $6.49
Cost of the items after the coupon: (100% - 10%) x $32.47
90% x $32.47
0.9 x $32.47 = $29.22
Cost of the items after the tax: (1.07) x $29.22 = $31.27
Total cost of the items = $31.27 +$6.49 = $37.76
To learn more about taxes, please check: https://brainly.com/question/25311567
Rewrite in simplest terms: (4x + 4) - (-4x - 9)
Answer:
Submit Answer
Answer:
8x+13
Step-by-step explanation:
do you need this part?
The teen club had a cupcake sale.
They sold 2/3 of their cupcakes in the morning. They sold 1/6 of their cupcakes in the afternoon. They sold 200 cupcakes altogether.
How many cupcakes were left to sell?
40. Let C be the total number of cupcakes. Then 2/3 x C + 1/6 x C = 200.
Combining , 5/6 x C = 200. So C = 240.
240–200= 40
Every Thursday, Matt and Dave's Video Venture has “roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an
amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a
second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a
second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.
If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total
amount paid for these second movies will exceed $15.00?
I saw other questions for this but why is the standard deviation 0.15*sqrt of 30 and not 0.15*30 because I thought this is a linear transformation
Using the normal distribution, it is found that there is a 0.1357 = 13.57% probability that the total amount paid for these second movies will exceed $15.00.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard error is [tex]s = \sigma\sqrt{n}[/tex]In this problem:
Mean of $0.47, standard deviation $0.15, hence [tex]\mu = 0.47, \sigma = 0.15[/tex]30 instances, hence [tex]n\mu = 30(0.47) = 14.1, s = 0.15\sqrt{30} = 0.8216[/tex]The probability is 1 subtracted by the p-value of Z when X = 15, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Considering the n instances:
[tex]Z = \frac{X - n\mu}{s}[/tex]
[tex]Z = \frac{15 - 14.1}{0.8216}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643.
1 - 0.8643 = 0.1357.
0.1357 = 13.57% probability that the total amount paid for these second movies will exceed $15.00.
A similar problem is given at https://brainly.com/question/25769446
Please help me prove that RST is congruent to RUT!
Answer:
See image
Step-by-step explanation:
On line 3, the reason is filled in that "All right angles are congruent" so kind of working backwards, the statement must say that two right angles are congruent. Use the angles in the previous two statements. Line 4 has the statement completely filled in, the reason is bc it is given in the list of given statements beside the diagram. Line 5 says that RT is congruent to itself. That is reflexive property, like a reflection in a mirror. Same ~= same.
You can see from the markings on the image that you have Angle-Side-Angle, which is one of several ways that we can show that triangles are congruent. ASA is what is shown in statements 1-5. See image.
