Answer:
Step-by-step explanation:
Average height = 176.55 cm
Height of tallest man = 249 cm
Standard deviation = 7.23
z score of tallest man
= (249 - 176.55) / 7.23
= 10.02
Average height = 176.55 cm
Height of shortest man = 120.2 cm
Standard deviation = 7.23
z score of smallest man
= ( 176.55 - 120.2 ) / 7.23
= 7.79
Since Z - score of tallest man is more , his height was more extreme .
3) The radius of circle is 11 miles. What is the area of a sector bounded by a
300° arc?
Answer:
[tex] Area = 316.6 mi^2 [/tex]
Step-by-step explanation:
Given:
Angle of arc = 300°
Radius of circle = 11 miles
Take π as 3.14
Required:
Area of the major sector
Solution:
Area of sector is given as: angle of arc/360*πr²
Thus,
[tex] Area = \frac{300}{360}*3.14*11^2 [/tex]
[tex] Area = 316.616667 [/tex]
[tex] Area = 316.6 mi^2 [/tex] (rounded to the nearest tenth)
Graph the equation below by plotting the y-intercept and a second point on the line. When you click Done, your line will appear
Answer:
Step-by-step explanation:
Equation of the line has been given as,
[tex]y=\frac{3}{2}x-5[/tex]
By comparing this equation with the y-intercept form of the equation,
y = mx + b
Slope of the line 'm' = [tex]\frac{3}{2}[/tex]
and y-intercept 'b' = -5
Table for the points to be plotted on a graph will be,
x y
-4 -11
-2 -6
0 -5
2 -4
4 -3
By plotting y-intercept (0, -5) and any one of the points given in the table we can get the required line.
Answer: actually the answer to this question is (0, -5) and ( 2, -2)
Step-by-step explanation: I just took the test on Plato and got it right :)
Two passenger trains traveling in opposite directions meet and pass each other. Each train is 1 12 mi long and is traveling 50 mph. How many seconds after the front cars of the trains meet will their rear cars pass each other?
Answer:
Time taken = 6 sec (Approx)
Step-by-step explanation:
Given:
Total distance = 1/12 mi = 0.083333
Speed of train = 50 mph = 50 / 3600 = 0.01388889 mps
Find:
Time taken
Computation:
Time taken = Total distance / Speed
Time taken = Total distance / Speed of train
Time taken = 0.0833333 / 0.01388889
Time taken = 6 sec (Approx)
Out of 600 people sampled, 66 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.
Required:
Use a 90% confidence level, and give your answers as decimals, to three places.
Answer:
11% of the Total the entire voting population
Step-by-step explanation:
Let's bear in mind that the total number of sample candidates is equal to 600.
But out of 600 only 66 preffered candidate A.
The proportion of sampled people to that prefer candidate A to the total number of people is 66/600
= 11/100
In percentage
=11/100 *100/1 =1100/100
=11% of the entire voting population
Wholemark is an internet order business that sells one popular New Year greeting card once a year. The cost of the paper on the which the card is printed is $0.05 per card, and the cost of printing is $0.15 per card. The company receives $2.15 per card sold. Since the cards have the current year printed on them, unsold cards have no salvage value. Their customers are from the four areas: Los Angeles, Santa Monica, Hollywood, and Pasadena. Based on past data, the number of customers from the each of the four regions is normally distributed with mean 2,000 and standard deviation of 500. (Assume these four are independent.)
What is the optimal production quality for the card? (Use Excel's NORMSINV{} function to find the Z-score. Round intermediate calculations to four decimal places. Submit your answer to the nearest whole number.)
Answer:
The optimal production quantity is 9,322 cards.
Step-by-step explanation:
The information provided is:
Cost of the paper = $0.05 per card
Cost of printing = $0.15 per card
Selling price = $2.15 per card
Number of region (n) = 4
Mean demand = 2000
Standard deviation = 500
Compute the total cost per card as follows:
Total cost per card = Cost of the paper + Cost of printing
= $0.05 + $0.15
= $0.20
Compute the total demand as follows:
Total demand = Mean × n
= 2000 × 4
= 8000
Compute the standard deviation of total demand as follows:
[tex]SD_{\text{total demand}}=\sqrt{500^{2}\times 4}=1000[/tex]
Compute the profit earned per card as follows:
Profit = Selling Price - Total Cost Price
= $2.15 - $0.20
= $1.95
The loss incurred per card is:
Loss = Total Cost Price = $0.20
Compute the optimal probability as follows:
[tex]\text{Optimal probability}=\frac{\text{Profit}}{\text{Profit+Loss}}[/tex]
[tex]=\frac{1.95}{1.95+0.20}\\\\=\frac{1.95}{2.15}\\\\=0.9069767\\\\\approx 0.907[/tex]
Use Excel's NORMSINV{0.907} function to find the Z-score.
z = 1.322
Compute the optimal production quantity for the card as follows:
[tex]\text{Optimal Production Quantity}=\text{Total Demand}+(z\times SD_{\text{total demand}}) \\[/tex]
[tex]=8000+(1.322\times 1000)\\=8000+1322\\=9322[/tex]
Thus, the optimal production quantity is 9,322 cards.
When testing the claim that p 1p1equals=p 2p2, a test statistic of zequals=2.04 is obtained. Find the p-value obtained from this test statistic.
Answer:
0.0414 with an upper tailed test
Step-by-step explanation:
Claim: P1P1 = P2P2
The above is a null hypothesis
The alternative hypothesis for a two-tailed test would be:
P1P1 \=/ P2P2
Where "\=/" represents "not equal to".
Using a z-table or z-calculator, we derive the p-value (probability value) for the z-score 2.04
With an upper tailed test, the
2 × [probability that z>2.04] = 2[0.0207] = 0.0414
This is the p-value for the test statistic.
Focus is on the alternative hypothesis.
Use the given categorical data to construct the relative frequency distribution. Natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of Monday through Sunday) with the frequencies 53, 63, 68, 58, 61, 43, 54. Does it appear that such births occur on the days of the week with equal frequency?
Answer: Yes
Step-by-step explanation:
See explanations in the attached document
A compressive uniform stress distributed on a rectangular areas of sides. located on the two opposite vertical/radial faces of step. If Force = 1.87kN and stress = 0.987MPa calculate the h * t in m^2
Answer:
Area = 0.019 m²
Step-by-step explanation:
stess = applied Force over Area
since stress = 0.987 MPa
and the force = 1.87 Kn
then Area = h * t
Q = F / (h * t)
0.987 mPa = 1.87 kN / (h* t)
since h * t = Area then 1.87 / 0.987
Area = 1.89 x 0.01 =
Area = 0.019 m²
Let T:V→W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W.
Answer:
The range of T is a subspace of W.
Step-by-step explanation:
we have T:V→W
This is a linear transformation from V to W
we are required to prove that the range of T is a subspace of W
0 is a vector in range , u and v are two vectors in range T
T = T(V) = {T(v)║v∈V}
{w∈W≡v∈V such that T(w) = V}
T(0) = T(0ⁿ)
0 is Zero in V
0ⁿ is zero vector in W
T(V) is not an empty subset of W
w₁, w₂ ∈ T(v)
(v₁, v₂ ∈V)
from here we have that
T(v₁) = w₁
T(v₂) = w₂
t(v₁) + t(v₂) = w₁+w₂
v₁,v₂∈V
v₁+v₂∈V
with a scalar ∝
T(∝v) = ∝T(v)
such that
T(∝v) ∈T(v)
so we have that T(v) is a subspace of W. The range of T is a subspace of W.
A pianist plans to play 5=pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second etc. to create a good flow. How many different recital programs are possible?
Answer:
2432902008176640000 programs are possible using 20 distinct (different) songs.
Step-by-step explanation:
There are 20 choices for the first song, 19 choices for the second, ...1 song for the last for a total of
N = 20*19*18*...*3*2*1 = 20!= 2432902008176640000 programs
The number 20! is the number of permutations for 20 distinct objects put in order.
20! is pronounced as 20 factorial.
Example: factorial of 5 is 5*4*3*2*1 = 120
Answer:
20*19*18*17*16=1 860 480 different programs
Step-by-step explanation:
So there are 20 pieces total and each of them can be first.
Each of residual 19 can be the second
Each of residual of 18 can be the third
Each of residual 17 can be the fourth
Each of residual 16 can be the fifth
Total amont of possible different programs ( the order of the pieces matters)
is : 20*19*18*17*16=1 860 480 different programs
Select the correct answer. Consider matrices A, B, and C:
Answer:
i think it is c. i may be incorrect, i am sorry!
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I did the math
Solve the following system of equations. Express your answer as an ordered pair in the format (a,b). 3x+4y=17 -4x-7y=-18
Answer:
Step-by-step explanation:
3x+4y = 17 _______ equation 1
-4x -7y= -18 _______ equation 2
muliply by 4 in equation 1
12x + 16y = 68 ______ equation 3
multiply by 3 in equation 2
-12x - 21y = -54 ________ equation 4
add equation 3 & 4
- 5y = 14
y = - 14/5
substitute y in equation 1
3x + 4 (-14/5) =17
3x = 17+ (56/5)
3x =( 85 + 56) / 5
3x = 141/5
x = 47/5
hence (a,b) = (47/5, -14/5)
A national survey of 1000 adult citizens of a nation found that 25% dreaded Valentine's Day. The margin of error for the survey was 3.6 percentage points with 90% confidence. Explain what this means.
Answer:
There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.
Step-by-step explanation:
The summary of the statistics from the information given is ;
At 90% confidence interval, 25% dreaded Valentine's Day and the margin of error for the survey was 3.6 percentage points
SO;
[tex]C.I = \hat p \pm M.O.E[/tex]
[tex]C.I = 0.25 \pm 0.036[/tex]
C.I = (0.25-0.036 , 0.25+0.036)
C.I = (0.214, 0.286)
The 90% confidence interval for the proportion of the adult citizens of the nation that dreaded Valentine’s day is 0.214 and 0.286.
There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.
the result of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20 degrees and 52 degrees. find the magnitude of the large force
Answer:
Larger force= 66.28 pounds
Step-by-step explanation:
The angle of the resultant force 80 pounds = 180-(52+20)
The angle of the resultant force 80 pounds = 180-72
The angle of the resultant force 80 pounds = 108°
The larger force is the force with 52°
Let the larger force be x
Magnitude of the larger force
x/sin52 = 80/sin108
X= sin52 *(80/sin 108)
X= 0.7880*(80/0.9511)
X = 0.7780*(84.1131)
X = 66.28 pounds
Richard is buying a subscription for video game rentals. The plan he has chosen has an
initial fee of $20 plus $2 per video game rented. This plan can be represented by the
function f(x) = 2x + 20. How much money will Richard pay this month if he rents 5 video
games?
Answer:
Richard will pay $30.
Step-by-step explanation:
Because "x" is equivalent to the amount of video games he rents, you would replace "x" with 5. Do the math, and you would get 10+20=30! Hope this helps!
Copy the problem, mark the givens in the diagram, and write a Statement/Reason proof. Given: MN ≅ MA ME ≅ MR Prove: ∠E ≅ ∠R
Answer:
Step-by-step explanation:
Given: MN ≅ MA
ME ≅ MR
Prove: ∠E ≅ ∠R
From the given diagram,
YN ≅ YA
EY ≅ RY
<EMA = <RMN (right angle property)
EA = EY + YA (addition property of a line)
NR = YN + RY (addition property of a line)
EA ≅ NR (congruent property)
ΔEMA ≅ ΔRMN (Side-Side-Side, SSS, congruence property)
<MNR ≅ MAE (angle property of congruent triangles)
Therefore,
<E ≅ <R (angle property of congruent triangles)
expand(x+y2)2 plzzzzzzzzzzzzzzzz
Answer:
[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]
Hope it helps!!❤❤Please mark me as the brainliest!!!Thanks!!!!
Consider a sample with a mean of 60 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
a. 50 to 70, at least %
b. 35 to 85, at least %
c. 51 to 69, at least %
d. 47 to 73, at least %
e. 43 to 77, at least %
Answer:
a)75%
b)96%
c)69.4%
d)85.2%
e)91.3%
Step by step explanation:
Given:
Mean=60
Standard deviation= 5
We were told to use chebyshev's theorem.to determine the percentage of the above given data within each of the following ranges
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION.
What is the slope of the line passing through the points (6,7) and (1,5)
Answer:
2/5
Step-by-step explanation:
(7-5)/(6-1)
What is the inverse of the logarithmic function
f(x) = log2x?
f –1(x) = x2
f –1(x) = 2x
f –1(x) = logx2
f –1(x) = StartFraction 1 Over log Subscript 2 Baseline x EndFraction
Answer:
B. edge 2021
B. is correct for the next one too.
Step-by-step explanation:
B. is the correct answer for the first one
B. is also the correct answer for the second one
Which is the value of this expression when p = 3 and q = negative 9? ((p Superscript negative 5 Baseline) (p Superscript negative 4 Baseline) (q cubed)) Superscript 0 Negative one-third Negative StartFraction 1 Over 27 EndFraction StartFraction 1 Over 27 EndFraction One-third Edge 2020
Answer:
I am pretty sure that the answer is D. The value should be 1.
Step-by-step explanation:
Answer:
Answer is D
Step-by-step explanation:
On Edge 2020
There were 3 adults and 9 children on the bus. What was the ratio of adults to children? Enter your answer in reduced form. (add explanation please!) (70 points!!!!!)
Answer:
1/3
Step-by-step explanation:
Ratios are basically comparisons of multiple numbers that shows their quantity relationship with each other. If we want to find the ratio of x to y, then the ratio is written as x : y or x/y.
Here, we want the ratio of adults to children. There are 3 adults and 9 children, so we have:
adults / children = 3 / 9 = 1/3
The answer is thus 1/3.
~ an aesthetics lover
Answer:
1:3
Step-by-step explanation:
The ratios of two terms is written as x:y.
3 ⇒ adults
9 ⇒ children
The ratio of adults to children:
3:9
Simplify the ratio.
1:3
6x²-7x=20 solve the following quadratic equation
Answer:
x = -4/3 and x = 5/2.
Step-by-step explanation:
6x² - 7x = 20
6x² - 7x - 20 = 0
To solve this, we can use the quadratic formula to solve this.
[please ignore the A-hat; that is a bug]
[tex]\frac{-b±\sqrt{b^2 - 4ac} }{2a}[/tex]
In this case, a = 6, b = -7, and c = -20.
[tex]\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}[/tex]
= [tex]\frac{7±\sqrt{49 + 80 * 6} }{12}[/tex]
= [tex]\frac{7±\sqrt{49 + 480} }{12}[/tex]
= [tex]\frac{7±\sqrt{529} }{12}[/tex]
= [tex]\frac{7±23 }{12}[/tex]
[tex]\frac{7 - 23 }{12}[/tex] = [tex]\frac{-16 }{12}[/tex] = -8 / 6 = -4 / 3
[tex]\frac{7 + 23 }{12}[/tex] = [tex]\frac{30}{12}[/tex] = 15 / 6 = 5 / 2
So, x = -4/3 and x = 5/2.
Hope this helps!
Answer:
[tex]x1 = - \frac{4}{3} [/tex][tex]x2 = \frac{5}{2} [/tex]Step-by-step explanation:
[tex]6 {x}^{2} - 7x = 20[/tex]
Move constant to the left and change its sign
[tex] {6x}^{2} - 7x - 20 = 0[/tex]
Write -7x as a difference
[tex]6 {x}^{2} + 8x - 15x - 20 = 0[/tex]
Factor out 2x from the expression
[tex]2x(3x + 4) - 15x - 20 = 0[/tex]
Factor out -5 from the expression
[tex]2x(3x + 4) - 5(3x + 4) = 0[/tex]
Factor out 3x + 4 from the expression
[tex](3x + 4)(2x - 5) = 0[/tex]
When the product of factors equals 0 , at least one factor is 0
[tex]3x + 4 = 0[/tex]
[tex]2x - 5 = 0[/tex]
Solve the equation for X1
[tex]3x + 4 = 0[/tex]
Move constant to right side and change its sign
[tex] 3x = 0 - 4[/tex]
Calculate the difference
[tex]3x = - 4[/tex]
Divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{ - 4}{3} [/tex]
Calculate
[tex]x = - \frac{4}{3} [/tex]
Again,
Solve for x2
[tex]2x - 5 = 0[/tex]
Move constant to right side and change its sign
[tex]2x = 0 + 5[/tex]
Calculate the sum
[tex]2x = 5[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{5}{2} [/tex]
Calculate
[tex]x = \frac{5}{2} [/tex]
[tex]x1 = - \frac{4}{3} [/tex]
[tex]x2 = \frac{5}{2} [/tex]
Hope this helps...
Best regards!!
A P E X!!!! URGENT :The annual interest rate of Belinda's savings account is 8.6% and simple interest is calculated quarterly. What is the periodic interest rate of Belinda's account?
Answer:
The answer is 2.15%
Step-by-step explanatio
find the lowest common denominator of 3/x^3y and 7/xy^4
[tex]\dfrac{3}{x^3y} +\dfrac{7}{xy^4}\\\\\\\dfrac{1}{xy}(\dfrac{3}{x^2} +\dfrac{7}{y^3})[/tex]
It's xy.
Find the present value of an investment that is worth $19,513.75 after earning 3% simple interest for 512 years.
Answer:
$16,750.00
Step-by-step explanation:
Simple interest:
I = Prt
Value of an investment of value P over t years at r interest rate:
F = P + Prt
F = P(1 + rt)
19,513.75 = P(1 + 0.03 * 5.5)
1.165P = 19,513.75
P = 16,750
Answer: $16,750.00
The present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as:
Rate of Interest (R) = 3% = 3/100 = 0.03
Time (T) = 512 years
Value of an investment of value P over t years at r interest rate:
A = P + Prt
A = P(1 + rt)
19,513.75 = P(1 + 0.03 × 5.5)
19,513.75 = 1.165P
1.165P = 19,513.75
P = 19,513.75/1.165
P = 16,750
Thus, the present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
Learn more about the simple interest here:
brainly.com/question/22621039
#SPJ2
Which pairs of angles are alternate exterior angles? select yes or no
A - No
B - No
C - Yes
D - Yes
.
C and D are alternate exterior angles
When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. P B or B = 1 Choose the correct answer below. A. It is impossible that the selected adult has type B blood or does not have type B blood. B. It is certain that the selected adult has type B blood. C. It is certain that the selected adult has type B blood or does not have type B blood. D. It is certain that the selected adult does not have type B blood.
Answer: The rule of complements is apprising us that, the person selected will.eithwr have a type B blood or will not have a type B blood
Step-by-step explanations:
Find explanations in the attachment
What point lies on the line described by the equation below? Y+3=2 (x-1
Answer:
[tex]\boxed{(1, -3)}[/tex]
Step-by-step explanation:
[tex]y+3=2 (x-1)[/tex]
Put equation in slope-intercept form.
[tex]y=mx+b[/tex]
[tex]y=2(x-1)-3[/tex]
[tex]y=2x-2-3[/tex]
[tex]y=2x-5[/tex]
Let x = 1
[tex]y=2(1)-5[/tex]
[tex]y=2-5[/tex]
[tex]y=-3[/tex]
The point (1, -3) lies on the line.
One number is 6 more than another. Their product is -9. Need help fast
Answer: the numbers are 3 and -3
Step-by-step explanation:
let the unknown number be x
The first UNKNOWN NUMBER = X
The second unknown number is = 6 + x
Their product = -9
(X)(6 + X) = -9
6x +[tex]x^{2}[/tex]=-9
[tex]x^{2}[/tex] +6x +9=0
we multiply the coefficient of x which is 1 with 9
now, we look for two numbers that when multiplied will give us 9 and when added will give 6 and that is 3 and 3
[tex]x^{2}[/tex] +3x+3x +9 = 0
x(x+3) +3(x+3) = 0
(x +3 ) = 0
or (x +3)=0
x +3 =0
x=0 -3
x =-3
x +3=0
x =0-3
x =-3
since the numbers are the same ,we pick one
therefore,the first number =x =-3
the second number is 6 + x=6 + (-3)
6-3=3