Answer:
0.62% probability that randomly chosen salary exceeds $40,000
Step-by-step explanation:
Problems of normally distributed distributions are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 30000, \sigma = 4000[/tex]
What is the probability that randomly chosen salary exceeds $40,000
This is 1 subtracted by the pvalue of Z when X = 40000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40000 - 30000}{4000}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.62% probability that randomly chosen salary exceeds $40,000
A Florida neighborhood is comprised of a total of 250 houses of which 12% are in foreclosure. A random sample of 91 homes from this neighborhood was selected. The standard error of the proportion is ________.
Answer:
the standard error of the proportion is 0.0272
Step-by-step explanation:
We have that if the sample size is greater than 5% of the entire population, a finite population correction factor (fpc) is multiplied with the standard error :
fpc = [tex]\sqrt{\frac{N -n}{N -1} }[/tex]
We know that N = 250 n = 91, replacing:
fpc = [tex]\sqrt{\frac{250 - 91}{250 -1} }[/tex]
fpc = 0.799
Now, the formula would then be:
SE = [tex]\sqrt{\frac{p * (1 -p)}{n} }[/tex]*fpc
Now replacing, knowing that p = 0.12
SE= [tex]\sqrt{\frac{0.12 * (1 - 0.12)}{91} }[/tex]*0.799
SE = 0.0272
So the standard error of the proportion is 0.0272
Find the perimeter of the figure when l = 15 m, w = 9 m, x = 3 m, and y = 6 m
Answer:
54
Step-by-step explanation:15+15+9+9+3+3=54
The general form of a circle is given as x^2+y^2+4x-10y-7=0.
What are the coordinates of the center of the circle?
What is the length of the radius of the circle?
Answer:
center: (-2, 5)radius: 6Step-by-step explanation:
We can complete the squares of the x- and y-terms by adding the square of half the linear term coefficient.
(x^2 +4x) +(y^2 -10y) = 7
(x^2 +4x +4) +(y^2 -10x +25) = 7 + 4 + 25
(x +2)^2 +(y -5)^2 = 6^2
Compare to ...
(x -h)^2 +(y -k)^2 = r^2 . . . . . standard form equation of a circle
We see that the center is ...
(h, k) = (-2, 5)
and the radius is ...
r = 6
What’s the correct answer for this question?
Answer:
[tex] \frac{11}{24} [/tex]
Answer:
D. 11/24
Step-by-step explanation:
Total students' reading preferences = 240
Using electronic device = 110
Probability of having electronic device = 110/240
= 11/24
In the diagram provided line L is parallel to line M. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose More than one correct answer
Answer:
1 and 4 are alternate interior angles.
m5 + m1 = 180
m5 = m3 + m2
Question:
The complete version of your question as found in other site is stated below:
In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer.
1 and 4 are alternate interior angles.
m4 + m5 + m6 = 180.
m5 + m1 = 180.
m5 = m3 + m2
Step-by-step explanation:
Given: line l is parallel to line m
We need prove that the interior angles of a triangle have a sum of 180°. In order to do that, the angles in the triangle = 180°
∠1 + ∠2 + ∠3 = 180°
Alternate angles:
∠1 = ∠4
∠6 = ∠2
∠5 = ∠3 + ∠6
Checking the options and inserting the values above in them:
a) 1 and 4 are alternate interior angles
∠1 = ∠4
This gives one of the side of the interior angles. The alternate angles enables us to find the sum of the interior angles. It is correct
b) m4 + m5 + m6 = 180
∠4 + ∠5 + ∠6 = 180°
∠1 + (∠3 + ∠6) + ∠2 = 180°
The above option wont give ∠1 + ∠2 + ∠3 = 180°. Hence it is wrong.
c) m5 + m1 = 180
(∠3 + ∠6) + ∠1 = 180°
∠5 = (∠3 + ∠6) = ∠3 + ∠2
∠3 + ∠2 + ∠1 = 180°
This option is correct
d) m5 = m3 + m2
∠5 = ∠3 + ∠2
From the diagram, ∠5 + ∠1 = 180° (angles on a straight line)
∠5 = ∠3 + ∠2
This option can be used to get sum of interior angles.
a number,x, rounded to 1 significant figure is 40 write down the error interval for x
Answer:
Error interval is [tex]35\leq x< 45[/tex]
Step-by-step explanation:
Given: A number x becomes 40 if it is rounded to 1 significant figure
To find: error interval for x
Solution:
In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.
As a number x becomes 40 if it is rounded to 1 significant figure, error interval is [tex]35\leq x< 45[/tex].
A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.
plifying a Radical
Find the values for a, b, and c that complete the simplificatio
12.95
Y Z
12
y8 .y . z. z = x y z Syz
a =
I
b =
Answer: answer is D
Step-by-step explanation:
Answer: The correct answer is 6,4,2
Step-by-step explanation: Doing a 100 point giveaway stay tuned!
Four expressions are shown below which expression are equivalent A:10 (10 +5y) B:5(20x + 25y) C:5 (2x + y) D: 0.25(400x + 500y)
Answer:
Step-by-step explanation:
remove parentheses by multiplying factors.
use exponent rules to remove parentheses in terms with exponents.
combine like terms by adding coefficients.
combine the constants.
At 5 \text{ p.m.}5 p.m.5, start a text, space, p, point, m, point, end text, the temperature is halfway between the temperature at 2 \text{ p.m.}2 p.m.2, start a text, space, p, point, m, point, end text and the temperature at 8 \text{ p.m.}8 p.m.8, start a text, space, p, point, m, point, end text
What coordinates represent the temperature at 5 \text{ p.m.}5 p.m.5, start a text, space, p, point, m, point, end text?
Answer:
(5,2)
Step-by-step explanation:
From the graph attached below:
The coordinate for the temperature (in degree Celsius) at 2 p.m. is (2,7) The coordinate for the temperature (in degree Celsius) at 8 p.m. is (8,-3)Since the temperature at 5 p.m. is halfway between the temperature at 2 p.m. and 8 p.m. , the coordinate of the temperature at 5 p.m. is the midpoint of (2,7) and (8,-3).
For two coordinate points [tex]A(x_1,y_1)$ and B(x_2,y_2)[/tex]
[tex]\text{Midpoint of AB }=\dfrac{1}{2} \left( x_1+x_2,y_1+y_2 \right)[/tex]
Therefore, the coordinates for 5p.m.
[tex]=\dfrac{1}{2} \left( 2+8,7+(-3) \right) \\=\dfrac{1}{2} \left( 10,4 \right)\\\\=(5,2)[/tex]
For each problem clearly describe the conditional distribution of each coordinate given the others. Then describe the procedure for running Gibbs sampling to sample from the joint distribution. Assume that Gibbs sampling works for continuous densities as well as discrete distributions. Guess the conditional from the structure of the joint distribution. Avoid doing integration as much as possible. Use your knowledge of the all the named one dimensional distributions/ densities.
a. Sample from the mixed joint pmf/pdf:
f(p, n) = p(1 - p)^-1, 0
Answer:
Step-by-step explanation:
Mary is building a sandcastle with rectangular prism molds. One mold is 4 inches long, 6 inches wide, and 2 inches tall. The other mold is 3 inches long, 5 inches wide, and 1 inch tall. If she creates a castle by stacking these molds on top of each other, what volume of sand will be contained in her castle?
Answer:
63 cubic inches
Step-by-step explanation:
You have to first find the volume of each mold:
6 × 4 × 2= 48 cubic inches
3 × 5 × 1= 15 cubic inches
Add these two volumes together to find the overall volume of the whole sand castle.
48+15= 63 cubic inches
Answer:
The whole castle can hold 63 in² of sand.
Step-by-step explanation:
First, find the volume of the first mold.
V = whl Substitute
V = (6)(2)(4) Multiply
V = 48 in²
Now, find the volume of the second mold.
V = whl Substitute
V = (5)(1)(3) Multiply
V = 15 in²
Add together both volumes to find the volume of the whole castle.
48 + 15 = 63 in²
The radius of a circle is 1 meter. What is the area of a sector bounded by a 135º arc?
Answer:
d=2
Step-by-step explanation:
Shape: Circle
Solved for diameter
Radius: 1
Formula: d=2r
Formula: Radius
Answer: 2
Hope this helps.
Bisi leaves 5km from school. She walks 1km at 4km/h and travels the rest of the way by bus at 16km/h . what is the average speed for the whole distance
Answer:
1/2 hour
Step-by-step explanation:
I am assuming you meant "lives 5km"
The first km would take 1/4 an hour because she is going 4km/h for one hour. One hour she would go 4km but we only need 1 mile so it would be cut to a fraction.
The same fraction goes for the bus. 4 is 1/4 of 16 so you would have to add them together and have 1/2 and hour to get home.
A local hamburger shop sold a combined total of 621 hamburgers and cheeseburgers on Friday there were 71 more cheeseburgers old and hamburgers how many hamburgers were sold on Friday
Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation 7x2+24xy−34x+24y−185=07x2+24xy−34x+24y−185=0
Rotating the graph of [tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] with [tex]B\ne0[/tex] counterclockwise by [tex]\theta[/tex] eliminates the [tex]xy[/tex] term, where [tex]\cot2\theta=\frac{A-C}{B}.[/tex] Plugging in, we have [tex]\cot2\theta=\frac{7}{24},[/tex] since [tex]C=0.[/tex] Solving, we have [tex]\theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.[/tex]
Please answer this correctly
Answer:
13 2/3 cm
Step-by-step explanation:
To find the perimeter, add up all the sides
2 1/2 + 3 1/3+ 4 1/2 + 3 1/3
Add up the whole numbers
2+3+4+3 = 12
Add up the fractions
1/2+1/3+1/2+1/3
2/2 + 2/3
1 +2/3
Put them together
12+1+2/3
13 2/3
Answer: 13 2/3 cm
Step-by-step explanation:
1. Turn mixed fractions into improper fractions:
2 1/2 = 5/2
3 1/3 = 10/3
3 1/3 = 10/3
4 1/2 = 9/2
2. Formula for perimeter: left side + right side + upper base + lower base
3. Put your numbers in replace: 10/3 + 10/3 + 5/2 + 9/2
4. Solve: 41/3
5. Simplify into mixed fraction: 41/3 = 13 2/3
6. Don't forget to add the unit!
A teacher needs to cut pieces of yarn, each 3/4 yards in length. How many
pieces can he cut from a string of yarn that is 6 yards long?
Answer:
8 pieces
Step-by-step explanation:
Take 6 yds and divide by the length of each piece
6 ÷ 3/4
Copy dot flip
6 * 4/3
24/3
8
We can get 8 peices
A firm can produce only 2500 units per month. The monthly total cost is given by C(x) = 400 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 350x − 1 100 x2 dollars, how many items, x, should the firm produce for maximum profit?
Answer:
2500
Step-by-step explanation:
Monthly total cost, C(x) = 400 + 200x dollars
Monthly total revenue, R(x) = [tex]350x -\dfrac{1}{100}x^2[/tex] dollars
Profit = Revenue - Cost
[tex]=R(x)-C(x)\\=(350x -\dfrac{1}{100}x^2)-(400 + 200x)\\=350x -\dfrac{1}{100}x^2-400 - 200x\\P(x)=150x-\dfrac{1}{100}x^2-400[/tex]
To determine how many items, x, the firm should produce for maximum profit, we maximize P(x) by taking its derivative and solving for its critical points.
[tex]P(x)=150x-\dfrac{1}{100}x^2-400\\P'(x)=150-\dfrac{x}{50}\\\\$Set $ P'(x)=0\\150-\dfrac{x}{50}=0\\150=\dfrac{x}{50}\\$Cross multiply\\x=150*50\\x=7500[/tex]
Next, we check if the point x=7500 is a maxima or a minima.
To do this, we find the second derivative of P(x).
[tex]P''(x)=-\dfrac{1}{50} $ which is negative[/tex]
Hence, the point x=7500 is a point of maxima. However, since the firm can only produce 2500 units per month.
Therefore, the company needs to produce 2500 units to maximize profit.
daryl hit a home run 8 out of 32 times.if he is at bat 224 times how many home runs will he hit
Answer:
56 out of 224 times
Step-by-step explanation:
8 out of 32 = 1 out of 4
56 out of 224 = 1/4
Answer:56
Step-by-step explanation:
A hotel wants to know if there's a relationship between gender and the way customers make room reservations. A manager takes a random sample of 160 reservations. She records whether they were made by a man or a woman, and also records how the reservation was made. She gets the following data: Phone 28 Men Women Fax 9 12 Email 37 29 45 Perform a chi-square significance test of association with a = .05. Be sure to include your null and alternative hypotheses, a justification for the use of this test, your test statistic calculations, your P-value, and your conclusion.
Answer:
Step-by-step explanation:
Here,
H_o: The way of reservation is independent of gender.
H_a: The way of reservation is not independent of gender.
We use a chi square test because we can calculate the expected frequencies for this chart.
Doing an Expected Value Chart,
33.7625 9.7125 30.525
39.2375 11.2875 35.475
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 4.482385929
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 3
b = 2
df = 2
Thus, the critical value is
significance level = 0.05
chi^2(critical) = 5.991464547
Also, the p value is
P = 0.106331579
Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]
Find the length of the portion of the line y = 4 that lies inside a circle of radius 7
centered at the origin
Answer: 2sqrt(33)
Step-by-step explanation:
We want to find the length of the line y = 4 in the circle x^2+y^2=49.
Substitute y = 4 to get x^2 = 33, so x = sqrt(33) or -sqrt(33).
That means the total length is sqrt(33) * 2 = 2sqrt(33).
Hope that helped,
-sirswagger21
The approximate length of the portion of the line is 11.49.
Circle centered at (h,k) with radius r is [tex](x-h)^{2} + (y-k)^{2}=r^{2}[/tex]
A circle of a radius 7 centered at the origin:
[tex]x^{2} +y^{2}=49[/tex] ......... (i)
[tex]y=4[/tex] ..........(ii)
We have a circle and a line. We need to find the points of
intersection and find the distance between those two points.
Replace y with 4 in the 1st equation and solve for x.
[tex]x^{2} +4^{2} =49\\x^{2} =49-16\\x^{2} =33\\[/tex]
[tex]x=[/tex] ±[tex]\sqrt{33}[/tex]
We have the 2 values of x where the line intersects the circle.
Plug those into one of the original equations to find the associated
y values.
[tex]\sqrt{33} ^{2} +y^{2} =49\\y^{2}=49-33\\y=4[/tex]
Two points on the circle are [tex](\sqrt{33} , 4)[/tex] and [tex](-\sqrt{33} , 4)[/tex]
Using the distance formula:-
[tex]=\sqrt{(4-4)^{2}+(-\sqrt{33}-\sqrt{33)} ^{2} } \\=\sqrt{(2\sqrt{33}) ^{2} } \\=2\sqrt{33}\\[/tex]
≈ 11.49
Therefore, the length of the portion of the line is approximately 11.49.
For more information:
https://brainly.com/question/24214108
A piece of wire is 290 cm long.
Dawid cuts three 25 cm lengths off the wire.
He then cuts the rest of the wire into as many 30 cm lengths as possible.
Work out how many 30 cm lengths of wire Dawid cuts.
Answer:
8
Step-by-step explanation:
(290-25)/30
265/30
8 and 5/6
so how many full 30 cm lengths?
8
Answer:
7
Step-by-step explanation:
3 × 25 = 75cm
He cuts 75cm of 290cm so the remaining length is 290 - 75 = 215 cm
→ He then cuts the rest of the wire into as many 30 cm lengths as possible.
215 ÷ 30 = 7.17
(3x+12)+x=180 Find the value of x.
Answer:
x =42
Step-by-step explanation:
(3x+12)+x=180
Combine like terms
4x +12 = 180
Subtract 12 from each side
4x +12-12=180-12
4x = 168
Divide by 4
4x/4 =168/4
x =42
Answer:
x=42
Step-by-step explanation:
180-12=168
168 divided by 4 = 42
x=42
Staples sells boxes of pens ($10) and rubber bands ($5). Leona ordered a total of 24 cartons for $200. How many boxes of each did Leona order? Hint: Let P = Pens.
Answer:
number of box of pen = 16
number of box of ribbon bands = 8
Step-by-step explanation:
Let
number of boxes of pen = p
number of boxes of rubber bands = r
He ordered 24 boxes of both items. Therefore,
p + r = 24...............(i)
The total cost of what he ordered is $200 . Therefore,
10p + 5r = 200.......(ii)
combine the equations
p + r = 24...............(i)
10p + 5r = 200.......(ii)
from equation (i)
p = 24 - r
insert the value of p in equation (ii)
10(24 - r) + 5r = 200
240 - 10r + 5r = 200
240 - 200 = 5r
40 = 5r
divide both sides by 5
r = 40/5
r = 8
insert the value of r in equation(i)
p + 8 = 24
p = 24 - 8
p = 16
number of box of pen = 16
number of box of ribbon bands = 8
What is the vertex of the graph of f(x) = |x-13[ + 11?
оооо
о(-11, 13)
о(-13, 11)
О(11, 13)
О (13, 11)
Answer:
(13, 11)
Step-by-step explanation:
The vertex of g(x) = |x| is (0, 0).
When the function is transformed to ...
f(x) = g(x -h) +k
the vertex is moved to (h, k).
Here, we have (h, k) = (13, 11), translating the function to ...
f(x) = |x -13| +11
and moving the vertex to (13, 11).
Answer:
D. (13, 11)
Step-by-step explanation:
EDGE 2020 :)
Please help ;-; what is the answer?
Answer:
5.7
Step-by-step explanation:
The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...
AD/BD = BD/CD
Cross multiplying gives ...
AD·CD = BD²
(x+3)(2x+3) = 5²
2x² +9x = 16 . . . . . perform the multiplication, subtract 9
2(x² +4.5x) = 16
2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square
2(x +2.25)² = 26.125 . . . . . write as a square
x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root
x = -2.25 +√13.0625 . . . . subtract 2.25 to find x
We want the value of CD, so ...
CD = 2x +3 = 2(-2.25 +√13.0625) +3
CD = -1.5 +2√13.0625 ≈ 5.7284
The length of CD is about 5.7 units.
Lucy obtains a 1-year payday loan for $5000.00 at 12% interest compounded monthly. To get the loan, she
also pays an origination fee of $125.00. What is the total cost of the loan to Lucy? Enter your answer as a
dollar amount, such as: 1400.68.
Answer:
$5759.12
Step-by-step explanation:
$5759.12
At the end of the year, the compound interest on her loan is: $5000(1+0.1212)12=$5000(1.01)12≈$5634.12. To pay off the loan at the end of the year, she pays 5634.12+125=$5759.12.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. [tex]F(x) = (\frac{3}{4}x )^2-1[/tex]
Step-by-step explanation:
The correct answer is "A," because the function F(x), shifted downwards 1 unit. This means that the function has to have a -1 being subtracted. Note that when the number in front of x is less than one, the function widens. In this case, [tex]\frac{3}{4}[/tex] is less than one, making it grow bigger as shown on the graph above.
Suppose that you are testing the hypotheses Upper H 0: pequals0.16 vs. Upper H Subscript Upper A: pnot equals0.16. A sample of size 350 results in a sample proportion of 0.21. a) Construct a 90% confidence interval for p. b) Based on the confidence interval, can you reject Upper H 0 at alphaequals0.10? Explain. c) What is the difference between the standard error and standard deviation of the sample proportion? d) Which is used in computing the confidence interval?
Answer:
Given:
Sample size, n = 350
Sample proportion, P' = 0.21
H0 : p = 0.16
Ha : p ≠ 0.16
a) A 90% confidence interval for P.
Significance level = 1 - confidence interval = 1 - 0.90 = 0.10
For Z critical, we have:
Z critical = [tex] Z_0_._1_/_2 = Z_0_._0_5 = 1.645 [/tex] (using z table)
Standard error, S.E = [tex] \sqrt{\frac{P'(1 - P')}{n}} = \sqrt{\frac{0.21(1 - 0.21)}{350}} = 0.02177 [/tex]
Margin of error, E = 1.645 * 0.02177 =0.03581
The 90% confidence interval =
0.21 ± 0.03581
The lower limit: 0.21 - 0.03581 = 0.17419
The upper limit: 0.21+0.03581 =0.24581
b) Based on the confidence interval at significance level = 0.10,
We reject null hypothesis, H0, since 0.16 is not cointained in the confidence interval. We conclude that p ≠ 0.16.
c) Standard error is based on sample proportion p^ while standard deviation is based on hypothesized proportion Po.
d) Standard error is used to compute the confidence interval.
What is imaginary 34
Answer:
raising a number to the 34th power
Step-by-step explanation: