Answer:
What is the expected value when rolling a fair 12-sided die?
132=6.5
Recall the definition of the expected value:
E[X]=∑ni=1xp(x)
Here, we have 12 possible values the die can take on, and the probability of each one is the same: 1/12. So we can just pull the term p(x), the probability of each outcome, out of the summation:
E[X]=112∑12i=1x
A useful trick here is that the sum of the numbers 1..N=N(N+1)2. So:
E[X]=11212(13)2
E[X]=12(13)12(2)
E[X]=132
Step-by-step explanation:
hope it helps you :)
Two sides of a triangle are 12cm and 8cm. Complete the inequality to show the possible lengths for the third side.
The inequalities that represents the third side of the triangle is c ≥ 4 or c ≤ 20
How to find the third side of a triangle?The triangle inequality theorem states that that the sum of any two sides of a triangle is greater than or equal to the third side.
Therefore, the two sides of the triangle are 12 cm and 8 cm.
A triangle with sides a, b and c follows the principle below;
a + b ≥ c.
Therefore,
let
c = third sides
12 + 8 ≥ c
20 ≥ c
c + 8 ≥ 12
c ≥ 4
c + 12 ≥ 8
Therefore, the third third should be greater than or equals to 4 or less than or equals to 20
c ≥ 4 or c ≤ 20
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Ronaldo specializes in creating sewing patterns for dresses, and wants to set up his own website to sell electronic copies. He pays $120 for a domain name and web hosting services for the first year. Ronaldo makes $14.25 for each electronic pattern that he sells. How many patterns must he sell to cover the cost of the website for the first year? Round your answer to a whole number.
Answer:
8
Step-by-step explanation:
120/14.25=8.4 rounded off to a whole number is 8
Solve the differential equation. (x^2 + 11)y' = xy
Separate the variables.
[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]
Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].
[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]
[tex]\ln|y| = \frac12 \ln|u| + C[/tex]
[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]
[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]
[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]
Using separation of variables, the solution to the differential equation is:
y = ksqrt(x² + 11)
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
(x² + 11)y' = xy
Applying separation of variables, we have that:
y'/y = x/(x² + 11)
[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]
[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]
[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]
[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]
Hence the solution is:
y = ksqrt(x² + 11)
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100 000 , 10 000 , 1000 , 100 , A , B
The two missing numbers in the pattern are:
A=___?
B=___?
The two missing numbers in the pattern are 10 and 1
How to determine the missing numbers?The sequence is given as:
100 000 , 10 000 , 1000 , 100 , A , B
From the above sequence, the next term is the quotient of the current term and 10.
So, we have:
A = 100/10 = 10
B = A/10 = 10/10 = 1
Hence, the two missing numbers in the pattern are 10 and 1
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WHEN LOIS MARTIN WAS BORN, HER FATHER DEPOSITED $2000 IN A SAVINGS
ACCOUNT IN HER NAME AT A SAVINGS AND LOAN ASSOCIATION (S&L). AT THE TIME,
THE S&L PAID 6% INTEREST COMPOUNDED SEMI-ANNUALLY. AFTER 10 YEARS, THE
S&L CHANGED TO A RATE OF 6% COMPOUNDED QUARTERLY. WHAT WAS THE
VALUE OF THE ACCOUNT AFTER 18 YEARS WHEN THE MONEY WAS WITHDRAWN TO
HELP PAY FOR HER COLLEGE EXPENSES
The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.
How are the future values determined?The future values of the savings account are calculated in two installments.
The first installment is for 10 years when the account earns 6% compounded semiannually.
Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.
Future values can be determined using the future value formula or an online finance calculator, as follows:
Data and Calculations:Investment of $2,000 for 10 years:N (# of periods) = 20 (10 years x 2)
I/Y (Interest per year) = 6%
PV (Present Value) = $2,000
PMT (Periodic Payment) = $0
Results:
FV = $3,612.22
Total Interest $1,612.22
Investment of $3,612.22 for 8 years:N (# of periods) = 32 (8 years x 4)
I/Y (Interest per year) = 6%
PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)
PMT (Periodic Payment) = $0
Results:
FV = $5,816.85
Total Interest $2,204.63
Thus, the value of the account after 18 years was $5,816.85.
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Compute the probability of event E if the odds in favor of E are 28 to 29.
Answer:
28/57
Step-by-step explanation:
odds in favor of event occurring = (probability event occurs)/(probability event does not occur)
Let p = probability event occurs.
Then the probability the event does not occur is 1 - p.
Let the odds = a/b.
a/b = p/(1 - p)
a(1 - p) = bp
a - ap = bp
bp + ap = a
p(a + b) = a
p = a/(a + b)
p = 28/(28 + 29)
p = 28/57
As per the given scenario, the probability of event E is 28/57 or approximately 0.4912.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
If the odds in favor of an event E are "a to b," then the probability of E is given by:
P(E) = a / (a + b)
In this case, the odds in favor of E are 28 to 29, which means that there are 28 favorable outcomes for E and 29 unfavorable outcomes against E.
So, using the formula above, we can compute the probability of E as:
P(E) = 28 / (28 + 29)
P(E) = 28 / 57
Therefore, the probability of event E is 28/57 or approximately 0.4912.
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A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze and the second brand is 55% pure antifreeze. In order to obtain 160 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
64 gallons 30%96 gallons 55%Step-by-step explanation:
The amount of each brand can be found by writing and solving an equation that makes use of the given relations.
SetupLet x represent the quantity of 55% pure antifreeze needed in the mixture. Then the quantity of the 30% brand is (160-x). The amount of pure antifreeze in the mixture is ...
0.55x +0.30(160 -x) = 0.45(160)
SolutionSubtracting 0.30(160), we have ...
x(0.55 -0.30) = 160(0.45 -0.30)
x = 24/0.25 = 96 . . . . . simplify, divide by the coefficient of x
96 gallons of the 55% brand, and 64 gallons of the 30% brand must be used.
__
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Question 5
Find the interest rate for a principal of $6570 and charged $30105 in interest for 12 years.
The Formula is
I
PT
x 100
Take the interest divide by the principal
then divide by the years
then times by 100
Round your answer to 1 decimal place.
Answer:
R=i
Step-by-step explanation:
R=i×100÷p×t
r=30105×100÷6570×12
r=3010500÷78840
r=38.18
List the angles in order from the largest to the smallest for ΔABC. AB⎯⎯⎯⎯⎯⎯⎯=14, AC⎯⎯⎯⎯⎯⎯⎯⎯=15, BC⎯⎯⎯⎯⎯⎯⎯⎯=16
Answer:
BC 1
AC 2
AABC 3
Step-by-step explanation:
BC=16
AC = 15
AABC= 15
Answer: C, B, A
Step-by-step explanation: It just is
Please I need the answer this is due in on monday!!
The number sets that each number belong too are given as follows:
1. Rational.
2. Irrational.
3. Rational.
4. Whole.
5. Whole.
6. Integer.
What is the classification of the number -4.2?It is a terminating decimal, hence it is a rational number.
What is the classification of the number 3 times square root of 5?The square root of 5 is not exact, hence it is a non-terminating decimal, meaning that is an irrational number.
What is the classification of the number 5/3?It is a fraction, hence it is a rational number.
What is the classification of the number 9?It is a positive non-decimal number, hence it is a whole number.
What is the classification of the square root of 16?The square root of 16 is of 4, which is a positive non-decimal number, hence it is a whole number.
What is the classification of the square root of -8/2?The result of the division is of -4, which is a negative non-decimal number, hence it is an integer number.
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Question 8 of 10
Factor the polynomial: -5x³ - 10x² - 15x
OA. 5x(x²+2x-3)
OB. -5x(-x2 - 2x - 3)
C. -5x(x2 + 2x - 15)
OD. -5x(x2+2x+3)
Hi,
Could anyone help with this please?
Many thanks,
Length: 2.6 meters
Width: 1.8 meters
Area: 4.68 meters
Since the scale is 1/40, we can multiply the centimeter measurements by 40 thus making it our scale factor.
Length
2.6 x 40 = 260
260 cm = 2.6 m
Width
4.5 x 40 = 180
180 cm= 1.8 m
Area
1.8 x 2.6 = 4.68 m
Length: 2.6 meters
Width: 1.8 meters
Area: 4.68 meters
how is the e - lambda figured out as 0.00248?
Answer:
Step-by-step explanation:
e^-6 = 1/e^6 = about 0.00248
Someone please help me with this question thank youuu
Answer: 148 degrees
Step-by-step explanation:
The total measure of all exterior angles of a convex pentagon is 360 degrees.
If four of them equal 53 degrees then all those together is 212 degrees
53 times 4 = 212
Then you would just subtract 212 from 360 to see the measure of the last exterior angle. Which is 148 degrees!
Hope this helps :)
Find the number if 11% of it is 55
Answer:
Step-by-step explanation:
.11x = 55
11x = 5500
x = 500
Show all work to write the expression in simplified rational exponent form:
[tex]\sqrt[4]{17x^{2}}[/tex]
(Fourth root of 17 x squared)
Answer:
[tex](17x)^{\frac{2}{4}}[/tex]
Step-by-step explanation:
There's not much work to show for this problem, but I'll explain it for you
Use the exponent rule for roots to combine the 4 and the 2 like a fraction
2 on the top and 4 on the bottom
[tex](17x)^{\frac{2}{4} }[/tex]
That's it! Pretty easy
Good Luck!
pls mark brainliest
Please Help!!!
Type the correct answer in the box. Use numerals instead of words.
The surface area of a cone is square units. The height of the cone is times greater than the radius.
What is the length of the radius of the cone to the nearest foot?
The radius is about
feet.
Answer:
Step-by-step explanation:
9.05737
The length of the radius of the cone to the nearest foot is 5 feet.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, The surface area of a cone is 216π sq units and the height of the cone is (5/3) times of the radius.
∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.
∴ πrl = 216π.
√{(34/9)r³ = 216.
1.9r³ = 216.
r³ = 113.7.
r = 4.8 feet Or 5 feet.
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Five interlocked, colored rings make up the Olympic symbol. The rings are
blue, black, red, yellow, and green and represent Africa, the Americas, Asia,
Australia, and Europe. The symbol looks like this:
1. In how many ways could the five colors of the Olympic symbol have been
arranged among the rings?
Answer:
120
Step-by-step explanation:
5 rings 5 colors
for the first ring there are 5 colors to choose from
4 colors for the second
3 for the third
2 for the fourth
1 for the last one
so 5! = 120
Find the point at which the line with parametric equations x = 2 3t, y =-4t, z =5 t intersects the plane 4x 5y -2z=18
It looks like you have
[tex]\begin{cases}x=2+3t\\y=-4t\\z=5+t\end{cases}[/tex]
Substituting these in to the plane equation, we have
[tex]4x+5y-2z = 4(2+3t) + 5(-4t) - 2(5+t) = -2-10t = 18 \\\\ \implies-10t = 20 \implies t = -2[/tex]
When [tex]t=-2[/tex], we get the point
[tex]\begin{cases}x=2+3(-2)\\y=-4(-2)\\z=5+(-2)\end{cases} \implies (x,y,z) = \boxed{(-4,8,3)}[/tex]
What is the value of 2 + (- 2/3)^2 ÷ 1/3 ?
16
3
-2
0
Answer:
3
Step-by-step explanation:
2+ (-2/3)^2 ÷ 1/3
make -2/3 postive because its being raised by an even exponent
you never divide by fractors so make 1/3 into 3 and make it multiplication
2+ (2/3)^2 × 3
raise the fraction to the power of 2
2+ (4/9)× 3
cancel out the GCF
2+ 4/3
add
10/3
simplify
3.3 ≅ 3
Tyson uploaded 500 videos to the Internet. Sarita uploaded fewer videos than Tyson. Write an inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded.
→WILL MARK BRAINLIEST←
The inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y
Inequalitynumber of videos Sarita uploaded = vnumber of videos Tyson uploaded = 500Total videos updated = yInequality for number of videos Sarita uploaded:
v - 500 < y
Therefore, the inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y
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Answer:
- v < 500
Step-by-step explanation:
Question 1 Which number has the greatest value? O 0.095 O 1.24 1.215 O 0.365 Confident
Answer:
1.24
Step-by-step explanation:
because 1.24>1.215>0.365>0.095
According to a recent poll at a university,70.7 % of high school seniors in a certain region had a driver's license. A sociologist thinks this rate has declined. The sociologist surveys randomly selected high school seniors and finds that have a driver's license. a. Pick the correct null hypothesis. b. Pick the correct alternative hypothesis. c. In this context, what does the symbol p represent?
your mother i swear
Step-by-step explanation:
ask yo mom
Juan and Ari went to the farmers market to buy fruit. Juan’s bag of apples that he bought weighed StartFraction 31 over 7 EndFraction pounds. Ari’s bag of oranges that he bought weighed StartFraction 19 over 3 EndFraction pounds. Using compatible fractions, estimate how much heavier Ari’s bag is compared to Juan’s bag.
Answer:
approximately 2 lb
Step-by-step explanation:
Juan: 31/7
Ari: 19/3
Juan's fraction is close to 32/8 = 4
Ari's fraction is close to 18/3 = 6
6 - 4 = 2
Answer: approximately 2 lb
If 2 angles have the same angle measure they are said to be what
2 angles that have the same angle measure are congruent.
Given that the two angles have the same angle measure.
Congruence is a term reserved for geometry. Two metrics are congruent when you can perfectly map to each other by mirroring, rotating, and translating without distortion.
We know that two shapes or objects are congruent if they have the same shape and the same size. For two angles to be congruent, they must coincide when they are overlapped. This is only possible if the two angles are equal.
Therefore, if two angles have the same measure, then they are said to be congruent.
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Assume the graph is derivative f(x). Answer for f(x)
The intervals which the original function f(x) concave down are (-5, -2) and (3, 5)
How to determine the intervals which the original function f(x) concave down?The information that completes the question are added as an attachment
The question requires that we determine the intervals which the original function f(x) concave down
From the attached graph, we have the following turning points
(-2, -4) and (3, 2)
From the domain of the graph, the curve starts at (-5, 0), turns at (-2, -4), also turns at (3, 2) and then stops at (5, 0)
So, we have:
(-5, 0), (-2, -4), (3, 2) and (5, 0)
Remove the y coordinates
x = -5, -2, 3 and 5
Express as intervals
(-5, -2) and (3, 5)
Hence, the intervals which the original function f(x) concave down are (-5, -2) and (3, 5)
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Graph on the number line all values of x that satisfy 2x+2/x+7 >= 0
Please help, if you help me I will give you a brainlist.
All values of x that satisfy 2x+2/x+7 >= 0 are represented as x >= -1
How to graph the inequality on a number line?The inequality expression is given as:
2x+2/x+7 >= 0
Multiply both sides by x + y
2x+2 >= 0
Subtract 2 from both sides
2x > -2
Divide both sides by 2
x >= -1
Hence, all values of x that satisfy 2x+2/x+7 >= 0 are represented as x >= -1
See attachment for the number line of x >= -1
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There are 96 football players at all levels at Davenport High School. If two-thirds of the players make the honor roll for their grades how many olayers are on the list?
64 players
48 players
72 players
54 players
question:
|x-2|, if x > 5
simplify without the absolute value sign
Answer:
x - 2, if x > 5
Step-by-step explanation:
The vertical lines either side of the expression mean absolute value.
The absolute value of a number is its positive numerical value.
if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive. Therefore, we can disregard the absolute value.
Therefore:
x - 2, if x > 5
To find the range (output values) of the expression, substitute x = 5 into the expression:
⇒ 5 - 2 = 3
Therefore, |x - 2| > 3, if x > 5
Find the cube root of Z =1+i the power of 5
Answer:
Cube Root Calculator
Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.
It will help you alot.
Step-by-step explanation:
