Answer:
The GMAT score corresponding to the 16th percentile is 473.
Step-by-step explanation:
Empirical Rule.
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
68% of the measures within 1 standard deviation of the mean.
This means that they are between the 50 - (68/2) = 50 - 34 = 16th percentile(one standard deviation below the mean) and the 50 + (68/2) = 50 + 34 = 84th percentile(one standard deviation above the mean).
In this question:
Mean of 549, standard deviation of 76.
16th percentile:
One standard deviation below the mean, so 549 - 76 = 473.
The GMAT score corresponding to the 16th percentile is 473.
The cost of producing x units of a product is $1.25 per unit plus $1,000 in flat production costs. If you spend $3,000 on production costs, how many units were produced?
3,000=1.25x+1,000
Answer:
1600
Step-by-step explanation:
1.25x + 1000 = 3000
Subtract 1000 from both sides
1.25x = 2000
Divide both sides by 1.25
x = 1600
Determine the missing angle in the picture below.
Answer:
x =41.18114952
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
We know the hypotenuse and adjacent sides
cos theta = adjacent / hypotenuse
cos x = 14.3/19
taking the inverse cos of each side
cos^-1 (cos x) = cos ^-1 ( 14.3/19)
x =41.18114952
Answer:
Step-by-step explanation:
take x degree as reference angle
using cos rule
cos x=adjacent/hypotenuse
cos x=14.3/19
cos x=0.75
x=cos 41
x= 41 degree
Find the value of x.
What is the median of these numbers 2.4,2.8,2.3,2.9,2.9
Answer:
2.8
Step-by-step explanation:
x2.3, x2.4, 2.8, x2.9, x2.9
plsss help!! is this a right triangle if no or yes please explain why??
Answer:
yes, it is a right triangle
Step-by-step explanation:
the other two angles are 35 and 55 degrees
Answer:
is NOT a right triangle
Step-by-step explanation:
is a right triangle if it checks the Pythagorean Th.
12² = 10² + 7²
144 = 100+49
144 = 149 False
Last week at the business where you work , you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items
Answer:
240
Step-by-step explanation:
They spent $120 buying 120 items, so they have -$120. By selling the items at 3x the price, they gained the 120 back and made a profit of 240 (120 x 2).
Suppose you are investigating the relationship between two variables, traffic flow and expected lead content, where traffic flow is a predictor of lead content. You find the 95% CI for expected lead content when traffic flow is 15, based on a sample of n= 10 observations, is (461.7, 598.1).
Required:
What parameter is this interval estimating?
Answer:
The answers is " Option B".
Step-by-step explanation:
[tex]CI=\hat{Y}\pm t_{Critical}\times S_{e}[/tex]
Where,
[tex]\hat{Y}=[/tex] predicted value of lead content when traffic flow is 15.
[tex]\to df=n-1=8-1=7[/tex]
[tex]95\% \ CI\ is\ (463.5, 596.3) \\\\\hat{Y}=\frac{(463.5+596.3)}{2}\\\\[/tex]
[tex]=\frac{1059.8}{2}\\\\=529.9[/tex]
Calculating thet-critical value[tex]t_{ \{\frac{\alpha}{2},\ df \}}=-2.365[/tex]
The lower predicted value [tex]=529.9-2.365(Se)[/tex]
[tex]463.5=529.9-2.365(Se)\\\\529.9-463.5=2.365(Se)\\\\66.4=2.365(Se)\\\\Se=\frac{66.4}{2.365} \\\\Se=28.076[/tex]
When [tex]99\%[/tex] of CI use as the expected lead content: [tex]\to 529.9\pm t_{0.005,7}\times 28.076 \\\\=(529.9 \pm 3.499 \times 28.076)\\\\=(529.9 \pm 98.238)\\\\=(529.9-98.238, 529.9+98.238)\\\\=(431.662, 628.138)\\\\=(431.6, 628.1)[/tex]
jack bought a mother bike the original price was 1300 but he got a discount of 20% what was the discounted price of the bike
I need help with this three problems (with procedure)
Answer:
13. [tex]x^{3} y^3[/tex] cubic units
14. 43 million; 79 million; 3.6 × [tex]10^7[/tex]
15. 2.68 × [tex]10^5[/tex]
Step-by-step explanation:
30p+2
can you please answer
Answer:
2(15p+1)
Step-by-step explanation:
hope this helps
Which is the volume of a sphere with diameter
50 cm?
Answer:
V =65416.666666 cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The diameter is 50 so the radius is 1/2 of the diameter
r = 1/2 (50) = 25
V = 4/3 ( pi) (25)^3
V = 4/3 (pi) 15625
V =20833.3333 pi
Using 3.14 for pi
V =65416.666666 cm^3
Answer:
V =65416.666666 cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The diameter is 50 so the radius is 1/2 of the diameter
r = 1/2 (50) = 25
V = 4/3 ( pi) (25)^3
V = 4/3 (pi) 15625
V =20833.3333 pi
Using 3.14 for pi
V =65416.666666 cm^3
What is the outlier for the data set?
19, 19, 27, 21, 77, 18, 23, 29
Answer: 77
Step-by-step explanation:
Plz help me!!(ᗒᗣᗕ)՞
Plz!
Answer:
A) 64 cm²
Step-by-step explanation:
Trapezoid area formula:
[tex]A=\frac{a+b}{2} h[/tex]
Given:
a = 6
b = 10
h = 8
Work:
[tex]A=\frac{a+b}{2} h\\\\A=\frac{6+10}{2} *8\\\\A=\frac{16}{2} *8\\\\A=8*8\\A=64[/tex]
Can someone help me pls pls help with this question
Answer:
D.
Step-by-step explanation:
The mean is 11,000
4d = -16
what’s the value of d
[tex]4d = - 16 \\ \\ d = \cancel \frac{ - 16}{4} \\ \\ d = - 4[/tex]
Hope This Helps YouAnswer:
The value of d is -4. When you multiply 4 by -4 you get -16. If you want me to elaborate, let me know.
Step-by-step explanation:
Cathy lives in a state where speeders are fined $15 for each mile per hour over the speed limit. Cathy was given a ticket for $105 for speeding on a road where the speed limit is 60 miles per hour. How fast was Cathy driving?
Given :
Cathy lives in a state where speeders are fined $15 for each mile per hour over the speed limit.
Cathy was given a ticket for $105 for speeding on a road where the speed limit is 60 miles per hour.
To Find :
How fast was Cathy driving.
Solution :
Let, speed of Cathy is v miles per hour.
Number of miles per hour over the speed limit, n = v - 60 miles per hour.
It is given that speeders are fined $15 for each mile per hour over the speed limit.
So, total amount of fine for Cathy is :
105 = 15×( v - 60 )
v-60 = 7
v = 67 miles per hour
Therefore, Cathy was driving with speed of 67 miles per hour.
What is the diameter of a circle with a circumference of 11.27pi ft? Use pencil and paper.
The diameter is ... ft
Answer:
[tex]circumference = \pi \: d \\ 11.27\pi = \pi \: d \\ d = 11.27 \: ft[/tex]
A 15-foot ladder leans against the side of a house with its base 4 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth.
Answer: The ladder reaches 14.46 feet up of the building.
Step-by-step explanation:
According to Pythagorean theorem,
In a right triangle,
(Hypotenuse)²= (Base)²+(perpendicular)^2
Using given information, we have
[tex](15)^2=(4)^2+(height)^2\\\\225=16+(height)^2\\\\(height)^2=209\\\\ (height)^2=\sqrt{209}\approx14.46\ feet[/tex]
Hence, the ladder reaches 14.46 feet up of the building.
Help will be appreciated
Answer:
48
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
48
the picture 20 words or longer for the answer so this is extra text
The value of the 2 in 43,290 is
times the value
of the 2 in 32,865.
9514 1404 393
Answer:
1/10
Step-by-step explanation:
The value of any digit is found by setting all other digits to zero.
The value of the 2 in 43,290 is 200.
The value of the 2 in 32,865 is 2,000.
200 is 200/2000 = 1/10 times 2000
The value of 2 in 43,290 is 1/10 times the value of 2 in 32865.
Find the solution of the differential equation f' (t) = t^4+91-3/t
having the boundary condition f(1) =1/4
Answer:
[tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Antiderivatives - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f'(t) = t^4 + 91 - \frac{3}{t}[/tex]
[tex]\displaystyle f(1) = \frac{1}{4}[/tex]
Step 2: Integration
Integrate the derivative to find function.
[Derivative] Integrate: [tex]\displaystyle \int {f'(t)} \, dt = \int {t^4 + 91 - \frac{3}{t}} \, dt[/tex]Simplify: [tex]\displaystyle f(t) = \int {t^4 + 91 - \frac{3}{t}} \, dt[/tex]Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle f(t) = \int {t^4} \, dt + \int {91} \, dt - \int {\frac{3}{t}} \, dt[/tex][1st Integral] Integrate [Integral Rule - Reverse Power Rule]: [tex]\displaystyle f(t) = \frac{t^5}{5} + \int {91} \, dt - \int {\frac{3}{t}} \, dt[/tex][2nd Integral] Integrate [Integral Rule - Reverse Power Rule]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - \int {\frac{3}{t}} \, dt[/tex][3rd Integral] Rewrite [Integral Property - Multiplied Constant]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3\int {\frac{1}{t}} \, dt[/tex][3rd Integral] Integrate: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex]Our general solution is [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex].
Step 3: Find Particular Solution
Find Integration Constant C for function using given condition.
Substitute in condition [Function]: [tex]\displaystyle f(1) = \frac{1^5}{5} + 91(1) - 3ln|1| + C[/tex]Substitute in function value: [tex]\displaystyle \frac{1}{4} = \frac{1^5}{5} + 91(1) - 3ln|1| + C[/tex]Evaluate exponents: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3ln|1| + C[/tex]Evaluate natural log: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3(0) + C[/tex]Multiply: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91 - 0 + C[/tex]Add: [tex]\displaystyle \frac{1}{4} = \frac{456}{5} - 0 + C[/tex]Simplify: [tex]\displaystyle \frac{1}{4} = \frac{456}{5} + C[/tex][Subtraction Property of Equality] Isolate C: [tex]\displaystyle -\frac{1819}{20} = C[/tex]Rewrite: [tex]\displaystyle C = -\frac{1819}{20}[/tex]Substitute in C [Function]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]∴ Our particular solution to the differential equation is [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex].
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
Calculate the variance and the standard deviation for the following sample data. Scores: 7, 9, 0, 1, 7, 4, 4, 7, 6
Answer:
Variance = 9
Standard deviation = 3
Step-by-step explanation:
Step 1
Find the Mean
Means = Sum of values/Number of values
= 0 + 1 + 4 + 4 + 6 + 7 + 7 + 7 + 9/9
= 45/9
= 5
Step 2
The formula for Sample variance
= (x - Mean)²/n - 1
Where
n = number of values = 9
Hence:
Sample variance =
( (0 - 5)² + (1 - 5)²+ (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (7 - 5)² + (7 - 5)² + (9 - 5)²)/9 - 1
= (-5² + -4²+ -1² + -1² + 1² + 2² + 2² + 2² + 4²) /8
= (25 + 16 + 1 + 1 + 1 + 4 + 4 + 4 + 16)/8
= 72/8
= 9
Sample Standard deviation = √Sample variance
= √9
= 3
Jeanette's Pie Shop recently sold 14 pies, of which 4 were blackberry pies. What is the experimental probability that the next pie sold will be a blackberry pie?
Write your answer as a fraction or whole number.
P(blackberry pie)=
Answer:
2/7
Step-by-step explanation:
All I did was just simplify the fraction 4/14
4/14=2/7
Question 4(Multiple Choice Worth 1 points) (06.07 LC) Which expression is equal to 3x? Ox+ 3 Ox+ x + x O x + x2 0 2x + 1 ting
Answer:
the answer is :.......
x+x+x
Answer:
x+x+x
Step-by-step explanation:
Pedro solves the quadratic equation x^2+6x –14 using the quadratic formula. In which step did Pedro make an error?
9514 1404 393
Answer:
correct choice is marked
Step-by-step explanation:
The error is in step 2. The square root cannot be distributed to a sum.
Student spend 5 minutes of every 60 minutes at school moving from class to class. Which fraction is equivalent to the number of minutes student spend moving from class to class?
A. 10/120
B.no answer provided
C. 2/10
D. 10/60
E. 1/15
c and d for 20 pts
aaaaaaaaaaaaaaaaa
Answer:
C. a = 7
D. c = -3
Step-by-step explanation:
C. 7(2a + 3) + 21 = 100+ 40
14a + 21 + 21 = 140
14a = 140 - 21 - 21
14a = 98
a = 7
D. 6+ 14 - 12c = 56
20 - 12c = 56
-12c = 56 - 20
-12c = 36
c = - 3
Answer:
Step-by-step explanation:
c.7(2a+3)+21=100+40
14a+21+21=140
14a+42=140
14a=140-42
a=98/14
a=7
d.6+14-12c=56
20-12c=56
-12c=56-20
c=36/-12
c=-3
How many solutions will the following equation have? 2x - 7 = -3x + 5
a. One Solution
b. Infinite Solutions
c. No Solutions
Answer:
one solution lets see[tex]2x - 7 = 3x + 5 \\ - x = 12 \\ x = - 12[/tex]
If you just want to check then substitute the value
[tex]2x - 7 = 3x + 5 \\ 2 \times ( - 12) - 7 = 3 \times ( - 12) + 5 \\ - 24 - 7 = - 36 + 5 \\ - 31 = - 31[/tex]
Hope it helps
Which is the inverse of the following statement?
If the measure of an angle is 90°, then it is a right angle.
Jim sells hot dogs for $2.95 each and steak sandwiches for $9.95 each out of his food cart. During a busy outdoor festival, he sold a total of 985 items for $7343.75. How many steak sandwiches did he sell?
Answer:
634 steak sandwiches.
Step-by-step explanation:
Let's say X is the number of hot dogs and Y is the number of steak sandwiches.
2.95x + 9,95y = 7343.75
x + y = 985
y = 985 - x
2.95x + 9.95(985-x) = 7343.75
2.95x + 9800.75 - 9.95x = 7343.75
7x = 2457
x = 351
y = 985 - 351
y = 634