Answer:
The p-value of the test is 0.0119 < 0.06, which means that the data provides statistically significant evidence at the 0.06 level that the average teaching stay in the metro Atlanta area is greater than the state average.
Step-by-step explanation:
The average teaching salary in Georgia is $48,553 per year. The school districts in the metro Atlanta area boast that they pay more.
At the null hypothesis, we test if they pay the average, that is:
[tex]H_0: \mu = 48553[/tex]
At the alternate hypothesis, we test if they pay more, that is:
[tex]H_1: \mu > 48553[/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.
48553 is tested at the null hypothesis:
This means that [tex]\mu = 48553[/tex]
Sample of 228 teachers from the metro Atlanta area and record their salaries. The sample mean is $49,021, with a standard deviation of $3,127.
This means that [tex]n = 228, X = 49021, \sigma = 3127[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{49021 - 48553}{\frac{3127}{\sqrt{228}}}[/tex]
[tex]z = 2.26[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 49021, which is 1 subtracted by the p-value of z = 2.26.
Looking at the z-table, z = 2.26 has a p-value of 0.9881
1 - 0.9881 = 0.0119
The p-value of the test is 0.0119 < 0.06, which means that the data provides statistically significant evidence at the 0.06 level that the average teaching stay in the metro Atlanta area is greater than the state average.
Answer:
it's D
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
The three statements that are always true regarding this diagram are:
m∠3 + m∠4 + m∠5 = 180°
m∠2 + m∠3 + m∠5 = 180°
m∠2 + m∠3 = m∠6
Here's why:
The sum of the measures of the interior angles of a triangle is always 180°. Therefore, m∠2 + m∠3 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠4 = m∠2 + m∠5, and m∠3 + m∠4 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠6 = m∠2 + m∠3.
The other two statements are not always true. For example, if m∠5 = 100° and m∠3 = 80°, then m∠5 + m∠3 = 180°, but m∠4 ≠ 0°. Similarly, if m∠5 = 100° and m∠6 = 80°, then m∠5 + m∠6 ≠ 180°.
Step-by-step explanation:
Two piggy banks have a sum of $36.50. The first piggy bank has $13.75. How much does the second piggy bank have in it?
Answer:
22.75
Step-by-step explanation:
ur welcome hOWdAy
how long would it take me to binge a show with 27 episodes if every episode is 23 minutes long?
Answer:
10 hrs 35 min
Step-by-step explanation:
ohh yeahh which show tell me in comment lol
btw it would take u total
621 minutes to complete the show
which meaning 10 hrs and 35 min
and if you touch the grass then it would take few hours more
A spinner at the fair has 5 sections. The sections are numbered 10, 20, 30, 40, and 50. During the first hour, players spun the spinner 200 times. The results are shown in the table below. Results for the First Hour Spinner Number Number of Times Spun 50 10 40 20 30 40 20 50 10 80 During the last hour of the fair, the arrow on the spinner was spun 50 times. Based on information from the table, what number is the most reasonable prediction of the number of times the arrow stopped on 30?
Answer:
im guessing 30 or 40
Step-by-step explanation:
75 yd
40 yd
What is the length of the hypotenuse.
Help
Exam Questions
James finds a hotel to book for 6 nights in Cape Town.
The hotel has an offer for the time they will be staying,
Special Offer
4 nights for the price of 3
Double room
2170 South African Rand per night
James books one double room for 6 nights.
At the time of booking he pays a deposit of 15% of the total cost
He will pay the rest of the total cost when they arrive at the hotel.
(a) How much will James have to pay when they arrive at the hotel?
Answer:chciken
Step-by-step explanation:
n% of 28 is 14 `percentage`
Answer:
The Percentage is 50% because 14 is the half of 28.
Lauren can spend no more then 10$ at a video game arcade. Each game in the arcade costs 0.25$
HELPPPPPPPPPPPPPPPPPPPPPPP
30
I DONT KNOW BUT THAT'S MY ANSWER HOPE IT HELP
Step-by-step explanation:
Is it +30 or - 30
If it was -ve under root it will be complex or imaginary number but it is a easy question
Part A
Open the angle translation application. The right angle is a translation 7 units right of the left angle. Drag the left angle and try to move it onto the right angle. Are the angles the same? What does this mean about how angles change when you translate them?
Part B
Open the angle rotation application. The right angle is a 90° clockwise rotation of the left angle. Click the 90° clockwise button. Are the angles the same? What does this mean about how angles change when you rotate them?
Part C
Open the angle reflection application. The top angle is a reflection across the x-axis of the bottom angle. Click the reflection over x-axis button. Are the angles the same? What does this mean about how angles change when you reflect them?
Part D
Open the parallel lines translation application. The right set of parallel lines is a translation right 10 units of the left set of parallel lines. Drag the left set of parallel lines and try to move them onto the right set. Are the two sets of parallel lines the same? What does this mean about how parallel lines change when you translate them?
Part E
Open the parallel lines rotation application. The right set of parallel lines is a 90° rotation counterclockwise of the left set of parallel lines. Click the 90° counterclockwise button. Are the two sets of parallel lines the same? What does this mean about how parallel lines change when you rotate them?
The following question is about the Translation of Angles and Parallel lines. See a detailed answer below.
What is Angle Translation?In geometry, when you translate an object, it means that you have turned that object in a different direction. Hence a translated angle is an angle that has been turned in a different direction.
From the first option in part A, it is clear from the image that the angle didn't change. It moves 7 units from the positive to the negative part of the x-axis. From Part B, the angles also do not change. Note that when an angle is rotated or translated, it does not modify the angles.From Part C, what we have is the reflection of the angles. This means that both angles are equal because they are a reflection of each other.From Part D, the two sets of parallel lines will remain parallel to each other also long as they are both translated as the same time.From part E, although in each set of parallel lines, the two sets of lines remain equidistant to each other, the parallel line that is at an angle to the Y-axis will not intersect that which is at an angle to the x-axis if they are extended infinitely.Learn more about Angle Translation at:
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Need emergency help and want correct answers with explanation
Answer:
250 degrees
Step-by-step explanation:
The arc intercepted by the angle formed by a secant and a tangent is twice the measure of the angle. See the attached image. The intercepted arc measures 110 degrees.
x is the measure of the rest of the circle, so it is 360 - 110 = 250 degrees.
calculate the surface area
help plsss
12 Aftab wants a patio in his garden. He is going to use concrete slabs to make the patio. Each concrete slab is a square with sides of length 0.5 m. A sketch of the planned patio is shown below. 3 m Patio 3 m 2
(a) What is the area of Aftab's patio? Give units with your answer.
Aftab pays £3.10 per concrete slab. (b) How much will it cost Aftab to buy enough concrete slabs to make the patio?
Answer:
5-3=2m
3x2=6m^2
Step-by-step explanation:
I can’t explain
LETTER B I DON’T KNOW THE ANSWER
NEED HELP!!!!!!! ASAP!!!!!!
Answer:
5
Step-by-step explanation:
base length = 2a/h -b
A coin is tossed, and a die is rolled. Find the probability of getting heads and then rolling a 6.
Answer:
1/2 and 1/6
Step-by-step explanation:
value of y please help me
SOMEONE PLEASE HELP!! i need it due right now!
a) 4a= 32 : (a) = ____
b) 4 = 32b : (b) = ____
c) 10c = 26 : (c) = ____
d) 26 = 100d : (d) = ____
(a)4a÷4=32÷4
a=8
(b)4/32=32b/32
1/8=b
therefore b=1/8
(c)10c/10=26/10
c=13/5
(d)26/100=100d/100
13/50=d
therefore d =13/50
4. Torrie has $430 and Sonia has $760. John has the same number of dollars more than Torrie as he has less than Sonia. How much money does John have?
To solve this problem, we can set up the following equation:
Torrie + John = Sonia - John
This equation represents the fact that John has the same number of dollars more than Torrie as he has less than Sonia. We can then substitute the given values for Torrie, Sonia, and John to solve for John:
430 + John = 760 - John
Combining like terms, we get:
2 * John = 330
Dividing both sides of the equation by 2, we get:
John = 165
Thus, John has $165.
THIS ONE TOO PLEASE
A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
The line going through the origin equation is also y=2x.
A line that crosses the origin is symbolized by the equation y=mx.
Also, y=2x satisfies the point (0,0)
A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.
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Explain in words how you know this inequality statement is true. Think about where they would be on a number line. 8 1/4 > - 8 1/4
Step-by-step explanation:
8 1/4 > - 8 1/4
when you plot these two numbers on number line
8 1/4 will lie on the right of the zero and - 8 1/4 will be on the left of the zero. The numbers on right of the zero are +ve and numbers on the left of zero are -ve. +ve numbers are always greater than -ve numbers. So 8 1/4 > - 8 1/4
find x
y=\frac{1}{4} x+3
Work Shown:
[tex]\text{y} = \frac{1}{4}\text{x}+3\\\\\text{y}-3 = \frac{1}{4}\text{x}\\\\\frac{1}{4}\text{x}=\text{y}-3\\\\\text{x}=4(\text{y}-3)\\\\\text{x}=4\text{y}-12\\\\[/tex]
S Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money? First, determine what information you need to answer this question, then click here to display that info (along with other info). • How much water does Janine drink in a day? She normally drinks 6 bottles a day, each 16.9 ounces. How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $3.99. • How much does a reusable water bottle cost? About $10. • How long does a reusable water bottle last? Basically forever (or until you lose it). . • How much does a water filter cost? How much water will they filter? o A faucet-mounted filter costs about $28 and includes one filter cartridge. Refill filters cost about $33 for a 3-pack. The box says each filter will filter up to 100 gallons (378 liters) o A water filter pitcher costs about $22 and includes one filter cartridge. Refill filters cost about $20 for a 4-pack. The box says each filter lasts for 40 gallons or 4 months • An under-sink filter costs $130 and includes one filter cartridge. Refill filters cost about $60 each. The filter lasts for 500 gallons. Which option is cheapest over one year (365 days)? faucet-mount filter The cheapest option saves her $ Give your answer to the nearest cent. Pro-rate the costs of additional filters (so if you only use part of a filter, only count the corresponding fraction of the filter cost) and pro-rate the cost of the bottled water (so if you only use part of a case, only count the cost for the portion of the case used). over a year.
Janine currently spends about $150.11 on bottled water every year.The total sum of the cost for the pitcher filter is $42. The sink filter costs $130
The first step in finding how much money Janine will save is to calculate how much water Janine drinks and how much bottled water costs her in one year.
To find how much money Janine currently spends on water, calculate the number of cases of water she buys each year (365 days / (24 bottles in a case/ 3 bottle per day) and multiply this number by the price per case ($3.29) to find that Janine currently spends about $150.11 on bottled water every year.To calculate the amount of water Janine drinks each year we multiply the amount she drinks in one day (3 bottles x 16.9oz per bottle) by 365 and then since there are 128 ounces in a gallon, we divide this number by 128 to find that she drinks 144.6 gallons of water each yearThe next step in this problem is to calculate the cost of each water filter in the first year. To find this, add the cost of the reusable water bottle, the cost of the filter, and the cost of any additional filters needed.
The faucet filter costs $28 dollars and includes a filter, plus each additional filter costs $11. Since the filter will last for 100 gallons, we can subtract that amount from the total water she drinks in a year to find the cost of filtering the remainder of the water in the year (144.6 gallons- 100gallons /$11). The total sum of the cost of the faucet filter and reusable water bottle in the first year is $42.91.The pitcher filter costs $22 and each additional filter costs $5. Since the included filter lasts 4 months, Janine will need two additional replacement filters for the other 8 months of the first year. The total sum of the cost for the pitcher filter is $42.The sink filter costs $130 and since the included filter will work for 500 gallons of water, Janine will not need to purchase additional filters in the first year. The total cost of the sink filter is $140.From these calculations, you can see that the pitcher filter is the cheapest option and will save Janine $108.11 in her first year of using this filter.Lastly the question asks you to pro-rate the cost of each filter
Since the faucet filters cost $11 each and filter 100 gallons of water, this filter costs 11 cents per gallon and $15.91 per year. She will have to begin replacing these filters approximately 8 months after the initial purchase of the filter.Filtering 40 gallons and costing $5 each the pitcher filter costs 12.5 cents per gallon and $18.08 per year. She will have to replace these filters every 4 months.The sink filter filters 500 gallons of water and costs $60, so it costs 12 cents per gallon and $17.35 per year. She will not have to replace this filter for about 3 and half years after the initial purchase.Learn more about cost at:
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FIRST PERSON TO GET CORRECT GETS BRAINLIEST!!!!!!!!1
A circle is graphed on a coordinate grid and then reflected across the y-axis. If the center of the original circle was located at (x, y), which ordered pair represents the center of the new circle after the transformation?
1. x,y
2. x, -y
3. -x,y
4. -x,-y
Answer:
Option C. (-x,y)
Step-by-step explanation:
we know that
A point reflected across the y-axis has the following rule
(a,b)------> (-a,b)
so
If the center of the original circle was located at (x, y)
then
the center of the new circle after the transformation will be (-x,y)
Answer: 3. -x, y
Step-by-step explanation: we know that
A point reflected across the y-axis has this rule
(a,b)------> (-a,b) so if the center of the original circle was located at (x, y) then the center of the new circle after the transformation will be (-x,y)
29. What is length of x?
Please explain this one too me since I did not understand it thanks
The length x is found to be 10 yards and is calculated using Polygon Triangulation.
What is Polygon Triangulation?
The polygonal triangulation is a method in which the area of polygon is divided into triangles to simplify calculation.
From the attached figure, we can find a using Pythagorus Theorem
a = [tex]\sqrt{6^{2} - 4.8^{2} }[/tex] = 3.6
cos θ = [tex]\frac{4.8}{6}[/tex] = 0.8
In ΔXYZ
cos θ = [tex]\frac{8 + 4.8 }{x+ 6} \\\\[/tex]
0.8 = [tex]\frac{12.8}{x + 6}[/tex]
Solving for x,
x = 10 yards
Therefore the length of x found using polygonal triangulation method is 10 yards.
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what is 3 1/2 x 2 1/3
Answer:
8 1/6
Step-by-step explanation:
The product of fractions 3 1/2 × 2 1/3 = 49/6 or can also express it as a mixed fraction: 8 1/6.
To multiply mixed fractions like 3 1/2 and 2 1/3, follow these steps:
Step 1: Convert the mixed fractions into improper fractions.
3 1/2 = (3 × 2 + 1) / 2 = 7/2
2 1/3 = (2 × 3 + 1) / 3 = 7/3
Step 2: Multiply the numerators and denominators of the fractions.
(7/2) × (7/3) = (7 × 7) / (2 × 3) = 49/6
Step 3: Simplify the resulting fraction, if possible.
49/6 cannot be simplified further.
Therefore, 3 1/2 × 2 1/3 = 49/6 or can also express it as a mixed fraction: 8 1/6.
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Which of these ratios are equivalent? Choose all that apply.
1) 16:4
2) 2:1
3) 32:2
4) 480:120
5) 4:16
6) 4:1
The ratios which are equivalent are as follows:
1) 16:4
4) 480:120
6) 4:1
Step-by-step solution:
1) 16:4
[tex]=\frac{16}{4}[/tex]
[tex]=\frac{4}{1}[/tex]
4:1
2) 2:1
[tex]=\frac{2}{1}[/tex]
2:1
3) 32:2
[tex]=\frac{32}{2}[/tex]
[tex]=\frac{16}{1}[/tex]
=16:1
4) 480:120
[tex]=\frac{480}{120}[/tex]
[tex]=\frac{4}{1}[/tex]
=4:1
5) 4:16
[tex]=\frac{4}{16}[/tex]
[tex]=\frac{1}{4}[/tex]
=1:4
6) 4:1
[tex]=\frac{4}{1}[/tex]
=4:1
Therefore, the correct solution to this question is:
1) 16:4
4) 480:120
6) 4:1
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Answer:
16:4 and 480:120 and 4:1 are equivalent.
Step-by-step explanation:
4x+5y=-7
-5x-3y=-1
I need help with this question since im not smart
Answer:
To solve this system of equations, you can use the method of elimination. To do this, you can add the two equations together:
4x + 5y - 5x - 3y = -7 - 1
-x + 2y = -8
Then, you can divide both sides of the equation by -1 to solve for y:
x - 2y = 8
y = (x - 8) / 2
Now that you have solved for y, you can substitute this expression back into either of the original equations to solve for x. For example, you can substitute y = (x - 8) / 2 into the first equation to get:
4x + 5((x - 8) / 2) = -7
4x + 5x - 40 = -7
9x = 33
x = 3.67
Now that you have solved for both x and y, you can find the solution to the system of equations:
x = 3.67
y = (3.67 - 8) / 2 = -2.17
So, the solution to the system of equations is x = 3.67 and y = -2.17.
An English teacher reviewed 2 3 of an essay in 1 4 of an hour. At this rate, how many essays can she review in 1 hour? Simplify your answer and write it as a proper fraction, mixed number, or whole number. essays
The essays that she can review in 1 hour would be; 2 2/3.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.
Thus, Fraction of the essay reviewed = 2/3
Amount of time used = 1/4
Therefore, the fraction of essay for an hour can be calculated as;
= Fraction of the essay reviewed / Amount of time used
= 2/3 ÷ 1/4
= 2/3 × 4
= 8/3
= 2 2/3
Hence, She will review 2 2/3 essay.
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which regression equation best fits these data?
x:-6,-4,-3,-1,1,2,3,4
y:12,15,17,17,15,11,9,6
on graph:(-6,12)(-4,15)(-3,17)(-1,17)(1,15)(2,11)(3,9)(4,6)
a. y=11.73*0.94^x
b. y=0.32x^2+1.26x+15.81
c. y=-0.67x+12.41
d. y=-0.32x^2-1.26x+15.81
Answer:
y = - 0.32x² - 1.26x + 15.81
Step-by-step explanation:
From the graph, it can be deduced that the graph isn't linear nor exponential. The graph shown is a quadratic graph. Hence the regression equation which best fits the model is represented in the form :
y = Ax² + Bx + C
Using technology, the regression model obtained by fitting the data is :
y = - 0.32x² - 1.26x + 15.8
Fitted model is attached below
The graph of which function has an amplitude of 3 and a right phase shift of ?
y = 3+ sin 2(x - 5)
y = 3sin 2(2
y = 3+ sin 2 (2+)
y = 3sin 2(x + 5)
Answer:
Option 4
Step-by-step explanation:
Equation representing the sine function is,
y = Asin[B(x- C)] + D
Here, A = Amplitude
B = [tex]\frac{2\pi }{\text{Period}}[/tex]
C = Phase shift
D = Vertical shift
If the amplitude of the the given function = 3 and right phase shift = [tex]\frac{\pi }{4}[/tex]
Therefore, equation of the sine function will be,
[tex]y=3\text{sin}B(x-\frac{\pi }{4})+D[/tex]
By comparing this equation with the given options,
Equation representing right phase shift = [tex]\frac{\pi }{4}[/tex] and amplitude = 3,
[tex]y=3\text{sin}2(x-\frac{\pi}{4})[/tex]
This equation represents right phase shift = [tex]\frac{\pi }{4}[/tex] and amplitude = 3.
Therefore, Option 4 is the correct option.