Answer:
The test statistics is [tex]z = -1[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The null hypothesis is [tex]H_o : \mu = \$30000[/tex]
The alternative hypothesis is [tex]H_a : \mu < \$ 30000[/tex]
The sample mean is [tex]\= x = \$29,750[/tex]
The standard deviation is [tex]\sigma = \$2,500[/tex]
The level of significance is [tex]\alpha =0.05[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{29750 - 30000 }{ \frac{ 2500}{ \sqrt{100} } }[/tex]
=> [tex]z = -1[/tex]
From the desired test, we have that:
a)
The null hypothesis is: [tex]H_0: \mu \geq 30000[/tex]The alternative hypothesis is: [tex]H_1: \mu < 30000[/tex]b) The t-statistic is t = -1.
Item a:
At the null hypothesis, we test if the average starting salary for clerical employees in the state is not less than $30,000, that is:
[tex]H_0: \mu \geq 30000[/tex]
At the alternative hypothesis, it is tested if the salary is less than $30,000, that is:
[tex]H_1: \mu < 30000[/tex]
Item b:
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 29750, \mu = 30000, s = 2500, n = 100[/tex]
Hence, the t-statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{29750 - 30000}{\frac{2500}{\sqrt{100}}}[/tex]
[tex]t = -1[/tex]
The t-statistic is t = -1.
A similar problem is given at https://brainly.com/question/13873630
Suppose a publishing company estimates that its monthly cost is C(x) = 600{x^2} + 300xC(x)=600x 2 +300x and its monthly revenue is R(x) = - 0.4{x^3} + 700{x^2} - 600x + 500R(x)=−0.4x 3 +700x 2 −600x+500, where x is in thousands of books sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?
Answer:
the answer is A,
P(x) = -0.4x³+100x²-900x+500
Step-by-step explanation:
monthly cost:
[tex]c(x) = 600x {}^{2} + 300x[/tex]
monthly revenue:
[tex]r(x) = - 0.4 {}^{3} + 700x {}^{2} - 600x + 500[/tex]
profit function:
[tex]p(x) = r(x) - c(x)[/tex]
[tex]p(x) = ( - 0.4x {}^{3} + 700 {x}^{2} - 600x + 500) - (600x {}^{2} + 300x)[/tex]
i) remove the first bracket
[tex]p(x) = - 0.4x {}^{3} + 700x {}^{2} - 600x + 500 - (600 {x}^{2} + 300x)[/tex]
ii) there is a negative sign, '-' in front of the second bracket. so, change the sign of each term of the expression inside the bracket
[tex]p(x) = - 0.4x {}^{3} + 700 {x}^{2} - 600x + 500 - 600x {}^{2} - 300x[/tex]
iii) collect like terms
[tex]p(x) = - 0.4x {}^{3} + 700 {x}^{2} - 600 {x}^{2} - 600x - 300x + 500[/tex]
iv) simply the like terms
[tex]p(x) = - 0. 4{x}^{3} + 100 {x}^{2} - 900x + 500 [/tex]
What is the slope and y intercept of this diagram
The Answer is 1/5 and 5
What is the effect on the graph of f(x) = x2 when it is transformed to h(x) = 2 x2 + 15?
Answer:
B
Step-by-step explanation:
The effect on the graph of f(x)=x² when it is transformed to h(x)=2x²+15 is the graph of f(x) is vertically streched by 2 and moved up by 15 unit.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)
Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given two functions, f(x) and h(x). Also, the function f(x) = x² is transformed to form h(x) = 2x² + 15. Therefore, we can write the transformation as,
f(x) vertically streched by a factor of2 first, Therefore,
g(x) = 2f(x)
= 2x²
Now, the function g(x) is moved up by 15 units, therefore,
h(x) = g(x) + 15
= 2x² + 15
Hence, the effect on the graph of f(x)=x² when it is transformed to h(x)=2x²+15 is the graph of f(x) is vertically streched by 2 and moved up by 15 unit.
Learn more about Transforming functions:
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Please give me the correct answer
Answer:
5×1,000,000,000
Step-by-step explanation:
since 5×1=5
5×1,000,000,000 would be 5,000,000,000
this is what I think and I'm sorry if I'm wrong
Find the angle of N
Will give branialist
Answer:
n=66
Step-by-step explanation:
6+12x+120+80+19x-1=360
205+31x=360
31x=155
x=5
Which graph represents the function h(x) = |x| + 0.5?
Answer:
B
Step-by-step explanation:
You have measured the systolic blood pressure of a random sample of 25 employees of a company located near you. A 95% confidence interval for the menu systolic blood pressure for the employees of this company is (122, 138). Which of the following statements gives a valid interpretation of the confidence level?a. 95% of the sample of employees have a systolic blood pressure between 122 and 138.b. 95% of tire population of employees have a systolic blood pressure between 122 and 138c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population means systolic blood pressure.d. The probability that the population mean blood pressure is between 122 and 138 is .95
Lee is making scarfs for a shelter. He purchased 11 skeins of yarns. Each skein has 660 feet of yarn. He needs 200 yards of yarn to make one scarf.
Answer:
Give me sum
Step-by-step explanation:
Answer:
Most scarves will use one to two skeins of yarn. According to the chart above, you will probably need about 300–650 yards, depending on the weight of yarn, the colors, the stitches, style, and length amongst other factors.
Step-by-step explanation:
If p varies jointly as q and the cube of r, when
p=270 when q=6 and r=3, find the constant of
variation. Write your answer as a fraction.
y=kxz
The value of constant of variation is, 5.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
⇒ p varies jointly as q and the cube of r.
Since, p varies jointly as q and the cube of r.
Hence, We can formulate;
⇒ p = k × q × r²
Where, k is constant of variation.
Here, p = 270 when q = 6 and r = 3.
Substitute all the values, we get;
⇒ p = k × q × r²
⇒ 270 = k × 6 × 3²
⇒ 270 = 54k
⇒ k = 270 / 54
⇒ k = 5
Learn more about the proportion visit:
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Steel is an alloy of iron and carbon (98% iron, 2% carbon). Stainless steel is steel and chromium, (90% steel, 10% carbon). What amount of iron, carbon, and chromium are needed for 500 kg of stainless steel?
500 kg x 90% = 500x 0.9 = 450 kg of Steel is needed.
450 kg x 98% = 450 x 0.98 = 441 kg of iron needed.
450 x 0.02 = 9 kg of carbon is needed for the steel.
50 kg of chromium is needed.
Chromium is 10% carbon, 50x 0.1 = 5 kg of carbon is needed for the chromium.
Total iron = 441 kg
Total carbon = 9 + 5 = 14 kg
Total chromium = 50 kg
|7-8| • 4 + 3 (-1) ???????
Answer:
1
Step-by-step explanation:
|7-8| • 4 + 3 (-1) =
= |-1| • 4 + (-3)
= 1 • 4 - 3
= 4 - 3
= 1
Find the value of x.
Group of answer choices
25
40
65
115
Answer:
40
Step-by-step explanation
x=40 because if you time these in like this:
3(40)-10= 110
40+15=55
If you user 65 it'll be wrong because:
3(65)-10=185
And the whole thing is only 180 :]
Can someone help me please
Answer:
7920
Step-by-step explanation:
all you have to do is just multiply the the feet in a mile by how any miles there are so basically
=> 1.5 * 5280 = 7920
Answer:
7,920 ft
Step-by-step explanation:
1.5 miles
1 mile = 5,280 feet
1.5 × 5,280 = 7,920 ft
or
5,280 ÷ 2 = 2,640
2,640 + 5,280 = 7,920 ft
Bob needs to read 3 novels each month. Let N be the number of novels Bob needs to read in M months, Write an equation relating N to M. Then use this equation to find the number of novels Bob needs to read in 17 months.
Answer:
Equation: n=3m; Bob needs to read 51 novels over 17 months.
Step-by-step explanation:
Since the number of novels Bob needs to read (n) depends on the amount of months (m) we can say that n is the dependent variable and m is the independent. Since x is always independent and y is always independent we can say that m is going to stand for x and n is going to stand for y. Each month Bob reads 3 novels so we can write the equations as n=3m. To find out how many books he needs to read in 17 months plug it into the equation. n=3(17) -------------------> n=51
someone help me out please
Answer:
The answer would be B :)
Step-by-step explanation:
Jenny bought a pair of shoes for $49.76 with a 30% off coupon. How much will she pay in total after 7% sales tax?
Answer: the final price is $37.26
Step-by-step explanation:
Always when we have an increase in a percentage X%, with an initial amount A, the new amount will be:
A + A*(X%/100%)
And for a decrease, the equation is_
A - A*(X%/100%)
Then if the initial price is $49.76, and there is a decrease of the 30%, the new price will be
$49.75 - (30%/100%)*$49.75 = $34.83
Now we have an increase of the 7% because of the IVA, then the final price is:
$34.83 + (7%/100%)*$34.83 = $37.26
Randy saving for console cost $290 he got a $50 gift card from grandma $15 each week, how many weeks until he get money?
Answer:
it will take him 16 weeks
Step-by-step explanation:
290 subtract 50 equals 240
240 divided by 15 equals 16
NEED HELP ASAP!!!! WILL MARK BRAINLIEST!!!!!
Which statement best compares the rate of change of the two functions?
O The rate of change of both functions is 2
O The rate of change of both functions is 3.
O The rate of change of function A is greater. than the rate of change of function B.
O The rate of change of function B is greater than the rate of change of function A.
Answer: The rate of change is 2
Step-by-step explanation:
Divide the Y by X for each of them and they all are 2
CAN SOMEONE HELP ME WITH THIS??? I WILL MARK BRAINLIEST!!!
Answer:
no
Step-by-step explanation:
it has no number behind it so it is just 12 which is a integer
Answer:
Amelia is correct.
According to Google, an integer is a whole number, not a fraction. Therefore, she is correct.
Acardboard popcom container is shaped like a cone that is 11 inches high and has a radius of 2.5 inches What is the volume of the container? Use 3 14 for pi Round your answer to the nearest hundredth
Answer:
71.99 in³
Step-by-step explanation:
The formula to apply is that of volume of a cone where;
V=π*r²*h/3 --------where V is the volume of the container, r is the radius of the container and h is the height of the container
Given that : π=3.14 , r is 2.5 inches , h= 11 inches then apply values to the container as;
V= 3.14 * 2.5²* 11/3
V= 3.14 * 6.25 * 3.67
V= 71.9948
V= 71.99 in³
Answer:
Volume of Cone= 71.9583
Step-by-step explanation:
Volume of Cone= (1/3)πr²h
Volume of Cone= (1/3)×3.14×(2.5)²×11
Volume of Cone= 71.9583
please solve needed asap
Answer:
x = 56°
Step-by-step explanation:
Base angles of an isosceles triangle are equal.
This:
The angle of the triangle to our right, which is the third unequal angle = 180 - 2(31)
= 180 - 62
= 118°
The base angle of the triangle to our left = 180 - 118 (angles on a straight line)
= 62°
x = 180 - 2(62)
x = 180 - 124
x = 56°
i will give brainliest to whoever answers thiss!!
Answer:
y=3
Step-by-step explanation:
-5y=-11-4
-5y=-15
y=-15/-5
y=3
Hope this helps u...
Answer:
y=3
Step-by-step explanation:
Please help 8th grade math!
need answer thanks!!!!!!!
Step-by-step explanation:
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What is long division answer to 6 divided by 92
The data below gives the mean price (in cents) of a liter of regular gasoline at self-service filling stations at a sample of six urban centers in Canada in May 2011.
Urban area Price/liter
St. John, NL 137.1
Halifax 133.6
Montreal 136.2
Regina 132.3
Saskatoon 132.2
Yellowknife 138.9
Required:
a. Find the sample mean (in cents).
b. Find the sample standard deviation (in cents).
c. Find a 90% confidence interval for the mean gasoline price per liter across urban Canada in May 2011. Provide the lower and upper limits for your confidence interval.
d. Find a 95% confidence interval for the mean gasoline price per liter across urban Canada in May 2011. Provide the lower and upper limits for your confidence interval.
Answer:
135.05 ; 2.762 ; (133.201, 136.899) ; (132.840, 137.260)
Step-by-step explanation:
Given the data:
Urban area Price/liter
St. John, NL 137.1
Halifax 133.6
Montreal 136.2
Regina 132.3
Saskatoon 132.2
Yellowknife 138.9
Mean = (137.1 + 133.6 + 136.2 + 132.3 + 132.2 + 138.9) / 6
= 810.3 / 6
= 135.05
Standard deviation (σ) : √Σ(X - mean)²/n-1
(137.1 - 135.05)^2 + (133.6 - 135.05)^2 + (136.2 - 135.05)^2 + (132.3 - 135.05)^2 + (132.2 - 135.05)^2+ (138.9 - 135.05)^2 = 38.135
√(38.135 / (6 - 1))
= √7.627
= 2.7617023
= 2.762
C.)
90% confidence interval of the mean :
Mean ± Zcrit * σ/√n
Zcrit at 90% = 1.64
135.05 ± 1.64 * (2.762/√6)
135.05 ± 1.64 * 1.1275817
Lower Value = (135.05 - (1.64 * 1.1275817)) = 133.201
Upper Value = (135.05 + (1.64 * 1.1275817))) = 136.899
Confidence interval = (133.201, 136.899)
D.)
95% confidence interval of the mean :
Mean ± Zcrit * σ/√n
Zcrit at 95% = 1.96
135.05 ± 1.96 * (2.762/6)
135.05 ± 1.96 * 1.1275817
Lower Value = (135.05 - (1.96 * 1.1275817)) = 132.840
Upper Value = (135.05 + (1.96 * 1.1275817)) = 137.260
Confidence interval = (132.840, 137.260)
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Answer:
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Step-by-step explanation:
shvwhehdjdjdnbddvbxnxjjxjdjdnbdnekskdjdjnebeeekekkenenennenemskkddkejennene hope this helps :3
100
3
80
6
60
9
40
20
0
100
web and Windows
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02 AM
NETT Dann
Answer:
Uhhhh what?
Step-by-step explanation:
I am confused...
In a random sample of 300 people in a town, 193 were female. What is the sample portion of female
Answer: 0.643
Step-by-step explanation:
There are 300 people and 193 were female.
The sample portion that is female is therefore;
= 193/300
= 0.643
Match these?
LA
If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the triangles are congruent.
ASA
If the hypotenuse and a leg of one right triangle are equal to the hypotenuse and leg of another right triangle, then the triangles are congruent.
HL
If three sides of one triangle are equal to three sides of anther triangle, then the triangles are congruent.
SAS
If a leg and an acute angle of one right triangle are equal to the corresponding parts of another right triangle, then the triangles are congruent.
SSS
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
Answer:
see below
Step-by-step explanation:
If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the triangles are congruent.
This is angle side angle ASA
If the hypotenuse and a leg of one right triangle are equal to the hypotenuse and leg of another right triangle, then the triangles are congruent.
This is hypotenuse leg HL
If three sides of one triangle are equal to three sides of anther triangle, then the triangles are congruent.
This is side side side SSS
If a leg and an acute angle of one right triangle are equal to the corresponding parts of another right triangle, then the triangles are congruent.
This is leg angle LA
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
This is side angle side SAS