Using the normal distribution, it is found that 60.06% of the salespersons earn between $32,000 and $42,000.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 40000, \sigma = 5000[/tex]
The proportion of salespersons that earn between $32,000 and $42,000 is the p-value of Z when X = 42000 subtracted by the p-value of Z when X = 32000, hence:
X = 42000:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{42000 - 40000}{5000}[/tex]
Z = 0.4
Z = 0.4 has a p-value of 0.6554.
X = 32000:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32000 - 40000}{5000}[/tex]
Z = -1.6
Z = -1.6 has a p-value of 0.0548.
0.6554 - 0.0548 = 0.6006 = 60.06%.
60.06% of the salespersons earn between $32,000 and $42,000.
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Answer: 60.06% of the salespersons earn between $32,000 and $42,000.
15 1/2 times 2 1/8 ??
Answer:
[tex]32 \times \frac{15}{16} [/tex]
Step-by-step explanation:
15 1/2 times 2 1/8 ??
[tex](15 \times \frac{1}{2} ) \times( 2 \times \frac{1}{8} )[/tex]
15 ×2 =30 +1 =31/2
2×8=16+1=17/8
[tex] \frac{31}{2} \times \frac{17}{8} [/tex]
[tex] \frac{527}{2 \times 8} [/tex]
527/16
[tex]32 \frac{15}{16} [/tex]
year 9 students from a school were asked to choose one language to study the table shows information about their choices LANGUAGE French students=17 German students=35 Italian students=38 Students in math class 9s1 were told to draw a pie chart to illustrate the language work out all of the angles of each sector of the pie chart
Answer:
French 17
German 35
Italian 38
total 90
French = 17/90 ×360 =68°
German = 35/90 ×360= 140°
Italian 38/90 ×360= 152°
write down the first five terms of the following sequences. a) start at 26 and subract 3. b)start at -3 and add 10.
Answer:
26, 23, 20, 17, 14, 11
-3, 7, 17,27,37,47
Step-by-step explanation:
sequence add and subject
If superheroes were to fly 300 miles with one will get there first.
Superhero A: 4 miles in 4 minutes
Superhero B: 7 miles in 2 minutes
Superhero C: 2 miles in 2 minutes
Answer:
Superhero B
Step-by-step explanation:
7 miles in 2 minutes is much farther than 1 mile A minute
Find the slope and the y-intercept of the linear function shown below
Answer:
You give no Problem or answers to choose from
Step-by-step explanation:
Sorry
[tex]\sf How \; do \; you\; solve\; this?[/tex]
[tex]\bf 9\left(2x+1\right)=\:9x-18[/tex]
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Here we go :} [/tex]
[tex]\qquad \sf \dashrightarrow \:9(2x + 1) = 9x - 18[/tex]
[tex]\qquad \sf \dashrightarrow \:18x + 9 = 9x - 18[/tex]
[tex]\qquad \sf \dashrightarrow \:18x - 9x = - 18 - 9[/tex]
[tex]\qquad \sf \dashrightarrow \:9x = - 27[/tex]
[tex]\qquad \sf \dashrightarrow \:x = - 27 \div 9[/tex]
[tex]\qquad \sf \dashrightarrow \:x = - 3[/tex]
[tex] \textsf{Hence, value of x is -3} [/tex]
The golf club can send a team of four students
to the next golf tournament. If there are 18
Students in the club, How many different teams
Of 6 can be selected?
Answer:
18,564
Step-by-step explanation:
The formula is n! / (r!(n-r)!
n is the total number of people and r is the number of people to be picked
n = 18, r = 6
18! / (6!(18-6)!)
18! / (6!*12!)
Total combinations = 18,564
Answer:
3
Step-by-step explanation:
18 ÷ 6 = 3
check and make sure the answer is right so you do the opposite
3 × 6 = 18
find the measure of each arc.
a. JL
b. KM
c. JLM
d. JM
The measure of each arc.
a. JL = 132
b. KM =147
c. JLM = 200
d. JM =120
What is angle?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint.
The measure of JL
=m JK+ m KL
= 53+79
= 132
The measure of KM
=m KL+ m LM
= 79+68
=147
The measure of JLM
= 53+68+79
= 200
The measure of JM
=360-200
=120
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I need help finding the unknown measures and equations pls.
Answer:
Step-by-step explanation:
10x + 8x = 180 (angles on straight line)
x = 10
AFH = 10x = 100
AFE = 8x = 80
(Look at photo)
54. Given that P is a positive number, N is a negative
number, and | P | > | N |, which of the following
expressions has the greatest value?
Answer: Choice G [tex]\left| \frac{p-n}{n} \right|[/tex]
============================================================
Explanation:
Pick a positive number for p, and a negative value for n. Make sure that p is further away from 0 than n is (so that [tex]|p| > |n|[/tex] is a true statement).
I'll go for these values
p = 5n = -2Replace every copy of p with 5, and replace every copy of n with -2. Then evaluate or simplify. Use your calculator if needed.
Let's start with choice F.
[tex]F = \left| \frac{p-n}{p} \right|\\\\F = \left| \frac{5-(-2)}{5} \right|\\\\F = \left| \frac{5+2}{5} \right|\\\\F = \left| \frac{7}{5} \right|\\\\F = \left| 1.4 \right|\\\\F = 1.4\\\\[/tex]
Now onto choice G
[tex]G = \left| \frac{p-n}{n} \right|\\\\G = \left| \frac{5-(-2)}{-2} \right|\\\\G = \left| \frac{5+2}{-2} \right|\\\\G = \left| \frac{7}{-2} \right|\\\\G = \left| -3.5 \right|\\\\G = 3.5\\\\[/tex]
Next up is evaluating the expression for choice H.
[tex]H = \left| \frac{p+n}{p-n} \right|\\\\H = \left| \frac{5+(-2)}{5-(-2)} \right|\\\\H = \left| \frac{5-2}{5+2} \right|\\\\H = \left| \frac{3}{7} \right|\\\\H \approx \left| 0.4286\right|\\\\H \approx 0.4286\\\\[/tex]
Then let's compute expression J.
[tex]J = \left| \frac{p+n}{p} \right|\\\\J = \left| \frac{5+(-2)}{5} \right|\\\\J = \left| \frac{5-2}{5} \right|\\\\J = \left| \frac{3}{5} \right|\\\\J = \left| 0.6 \right|\\\\J = 0.6\\\\[/tex]
Lastly, compute expression K.
[tex]K = \left| \frac{p+n}{n} \right|\\\\K = \left| \frac{5+(-2)}{-2} \right|\\\\K = \left| \frac{5-2}{-2} \right|\\\\K = \left| \frac{3}{-2} \right|\\\\K = \left| -1.5 \right|\\\\K = 1.5\\\\[/tex]
-----------------------------------
To summarize, when plugging p = 5 and n = -2 into each expression, we got these results:
F = 1.4G = 3.5H = 0.4286 (approximate)J = 0.6K = 1.5Expression G leads to the largest output.
Therefore, [tex]\left| \frac{p-n}{n} \right|[/tex] has the largest value when p > 0 and n < 0.
The expression |(p-n)/n| has the greatest value. Therefore, option G is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, p is a positive number, n is a negative number, and |p| > |n|.
Let us consider p=5 and n=-2
Now,
F) |(p-n)/p|
= |(5-(-2))/5|
= |7/5|
= 1.4
G) |(p-n)/n|
= |(5-(-2))/(-2)|
= |7/(-2)|
= 3.5
H) |(p+n)/(p-n)|
= |(5-2)/(5-(-2))|
= |3/7|
= 0.43
J) |(p+n)/p|
= |(5-2)/5|
= |3/5|
= 0.6
K) |(p+n)/n|
= |(5-2)/2|
= |3/2|
= 1.5
The expression |(p-n)/n| has the greatest value. Therefore, option G is the correct answer.
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Which statement below is always true?
A. Two parallel lines intersect at a right angle.
B. Two parallel lines lie in the same plane.
C. Two lines that are skew to each other intersect at one point.
D. A transversal never intersects another line.
Answer:
The answer is B. Two parallel lines lie in the same plane.
Step-by-step explanation:
Parallel lines never cut (intersect) or meet each other, and they lie on the same plane.The answer is Choice B
Step-by-step explanation:
Parallel lines never intersect
Lines that are skew don't have to intersect
Transversal lines intersect other lines
A pet store has three fish tanks, each holding a different volume of water and a different number of fish.
Tank A holds 40 L and 5 fish. Tank B holds 100 L and 12 fish. Tank C holds 180 L and 23 fish.
Order the tanks by volume per fish from least to greatest.
B A C
Answer:
Step-by-step explanation:
Remark
The general formula is
Volume per fish = volume of water / number of fish
Givens
40 L and 5 fish
100 L and 12 fish
180 L and 23 fish
Solution
Tank A = 40 L / 5 fish = 8 L / fish
Tank B = 100 L /12 fish = 8.3 L / fish
Tank C = 180 L / 23 fish = 7.83L / fish
Answer
From Least to greatest = C A B
how do i do this question?
Answer:
Step-by-step explanation:
since 2 sides are equal i.e. 6=6, It is an isosceles triangle
56+x+x=180
2x=180-56
x=62°
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Have a good day!
A triangle has sides with lengths of 9 centimeters, 12 centimeters, and 15 centimeters. Is it a right triangle?
Answer:
yes, it is a right triangle.
Step-by-step explanation:
trust
If the interest on Rs. 100 be Rs. 6.25p. what is the interest on Rs. 320?
6.25 / 100 = 0.0625 ( interest rate)
320 x 0.0625 = 20
answer: 20
1.Mary has ( 20xy - 10x²) sweets. She wants to divide the sweets equally among her (5x) friends.
if X=6 and Y=4, how many sweets:
how many friends does Mary have?
Answer:
Mary has 120 sweets and 30 friend.Step-by-step explanation:
if x = 6 and y = 4
then
20xy - 10x² = 20×(6)×(4)-10×(6^2) = 120
Therefore,
Mary has 120 sweets
……………………………………
if x = 6 and y = 4
then
5x = 5 × (6) = 30
…………………………
120 ÷ 30 = 4
Then 4 sweets per friend.
PLEASE HELP !!!!!!!!!
Answer:
17,17,17,0.6 805-774-0842 38.05-1.06.52-2.06 1.46-2.56l8.5-4.5c1.34 98.0.4758.101Step-by-step explanation:
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Write a function rule for “The output is three less than the input x.”
Answer:
y=x-3
Step-by-step explanation:
The weekly salary of a security guard, $S, is based on the formula, S=B+8H where B is the basic wage in dollars, and H is the number of hours he is on duty per week.
(a) Given that the security guard received $710 for a total of 45 hours of work in a particular week, find the basic wage.
(b)
(i) Calculate the salary he received after working for 42 hours in one week.
(ii) At the end of another week, the security guard earned $662. Find the number of hours worked that week.
[tex]\\[/tex]
ty! ~
Answer:
A. 350
B. (i) $686 (ii) 39 Hours
Step-by-step explanation:
Based on what's given..
A)
[tex]\sf S=B+8H[/tex]
[tex]\sf 710=B+8\times45[/tex]
[tex]\sf 710=B+360[/tex]
[tex]\sf B=710-360[/tex]
[tex]\boxed{\sf B= 350}[/tex]
B)
(i)
[tex]\sf S=350+8\times42[/tex]
[tex]\sf S=350+336[/tex]
[tex]\boxed{\sf S=686}[/tex]
(ii)
[tex]\sf 662=350+8H[/tex]
[tex]\sf 8H=662-350[/tex]
[tex]\sf H=312 \div 8[/tex]
[tex]\boxed{\sf H=39}[/tex]
HELP. HOW DO I SOLVE THIS?
The margin error is 2.82%.
What is Margin of Error?A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample
The margin of error for a sample proportion is given by
[tex]z_{\alpha /2}\sqrt{ \frac{p(1-p)}{n} }[/tex]
where p is the sample proportion and n is the sample size.
Consider the confidence level of 95%, then [tex]z_{\alpha /2}[/tex] = 1.96
p = 53% = 0.53 and n =1200
Thus, Margin of error=
[tex]z_{\alpha /2}\sqrt{ \frac{p(1-p)}{n} }[/tex]
=1.96[tex]\sqrt{ \frac{0.53(1-0.53)}{1200} }[/tex]
=1.96*0.0144
=0.0282
= 2.82%
Hence, margin error is 2.82%.
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[(-3)+9] × [(-10)-(-9)]
please solve this
The radius of a circle is 8 meters. What is the circle's area? Use 3.14 for .
Step-by-step explanation:
A = πr^2
When r=8m and π = 3.14,
A = 3.14*8*8=200.96sq.m
Answer:
[tex]\huge\boxed{\bf\:200.96\:m^{2}}[/tex]
Step-by-step explanation:
If,
Radius (r) = 8 mπ = 3.14Area (A) of the circle = ?
A = πr² [tex]\dashrightarrow[/tex] Formula
A = 3.14 × (8)²
A = 3.14 × 64
A = 200.96 m²
[tex]\rule{150pt}{2pt}[/tex]
F
F
A
B
units
G is the centroid of triangle ABC.
What is the value of x?
What is the length of segment DG?
What is the length of segment AG?
What is the length of segment AD?
x + 2
units
units
X-15
G
G
D
E
C
с
Answer:
x = 37DG = 22AG = 44AD = 66Step-by-step explanation:
We presume your "centroid ratio theorem" tells you that AG = 2·DG, so ...
(x+7) = 2(x -15)
x + 7 = 2x - 30 . . . . eliminate parentheses
37 = x . . . . . . . . . . .add 30-x
Then AG = 37+7 = 44
and DG = 37-15 = 22.
Thus, AD = AG +GD = 44 +22 = 66
if f(x)=x^2+2x-10 what is f(-2)
Answer:
-2
Step-by-step explanation:
f(2)= 2^2 + 2(2) - 10
= 4+4-10
=8-10
= -2
Find the area of the regular polygon
Answer:
162m²
Step-by-step explanation:
distance from corner to center = 1/2 of the diagonal
all sides are equal, and this has 4 sides, so it is a square
9m = 1/2 of diagonal
multiply both sides by 2 to isolate the diagonal
18m = diagonal
area of square = length²
length * √2 = diagonal
given the diagonal, we can find the length and then the area
length * √2 = diagonal
divide both sides by √2 to find the length
18m/√2 = length ≈12.7
square the length to find the area
area = 162 m²
z^2 + 11z+ 28 find the factor of polynomial
Answer:
(z+7)*(z+4)
Step-by-step explanation:
The first term is, z2 its coefficient is 1 .
The middle term is, +11z its coefficient is 11 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 1 • 28 = 28
Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is 11 .
-28 + -1 = -29
-14 + -2 = -16
-7 + -4 = -11
-4 + -7 = -11
-2 + -14 = -16
-1 + -28 = -29
1 + 28 = 29
2 + 14 = 16
4 + 7 = 11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 7
z2 + 4z + 7z + 28
Step-4 : Add up the first 2 terms, pulling out like factors :
z • (z+4)
Add up the last 2 terms, pulling out common factors :
7 • (z+4)
Step-5 : Add up the four terms of step 4 :
(z+7) • (z+4)
Which is the desired factorization
HELP ME OMG PLEASEEEEEEEEEEEEE
[tex]v = \frac{lwh}{3} [/tex]
[tex]v = \frac{12 \times 10 \times 3}{3} [/tex]
[tex]v = 120 \: {ft}^{3} [/tex]
Volume of the rectangular prism:[tex]v = lwh[/tex]
[tex]v = 12 \times 10 \times 7[/tex]
[tex]v = 840 \: {ft}^{3} [/tex]
Total volume:[tex]v = 120 + 840[/tex]
[tex]v = 960 \: {ft}^{3} [/tex]
pyramid:
lwh/2
=12×10×3/3
=120 ft^3
prism:
whl
=12×10×7
=840 ft^3
all together:
=960 ft^3
NEED HELP PLEASE
I can’t figure this question out. Hopefully you could help!
Answer:
see image
Step-by-step explanation:
If 21 people study French and everyone studies some language, then the other 4 people must be Spanish only students. 25 - 21 =4
Since 13 people study Spanish,
13-4=9
9 people must study both Fr and Sp.
If 9 people study BOTH, then
21-9=12,
12 people must be the Fr only people.
The arch-looking, upsidedownU is intersect.
Fr intersect Sp are the StudyBOTH people.
P(Both) = Both/Total
= 9/25
If you need %, divide 9÷25 and times by 100. That's 36%
F' means Not French people, which is Spanish only people (thankfully there are no No-Language-studiers bc they would count too)
P(F')
= P (not Fr)
= P (Sp Only)
= 4/25 = 16%
Find the value of of the thing-
[tex]5(x+4)=40[/tex]
[tex]~~~~~~5(x+4) = 40\\\\\implies x +4 = \dfrac{40} 5\\\\\implies x +4 = 8\\\\\implies x= 8-4\\\\\implies x = 4[/tex]
Find the value of X.
Answer:
x=2
Step-by-step explanation:
[tex]2^{3x+1}+52=180^o[/tex]
[tex]2^{3x+1}+52-52=180-52[/tex]
[tex]2^{3x+1}=128[/tex]
[tex]3x+1=7[/tex]
[tex]x=2[/tex]
