From knowledge of numerals the answer to the given Question is: a = 3 b = 6 c = 5
What are Numerals?
Numerals are symbols or numerals used to represent numbers. They are used in math and other fields to represent quantities and measurements. Numerals can be written in different forms, such as Arabic numerals (1, 2, 3, etc.) or Roman numerals (I, II, III, etc.). Numerals are also used to label items, such as dates (e.g. May 4th, 2020), addresses (e.g. 1234 Main Street), and telephone numbers (e.g. 555-123-4567). Numerals are an important part of our everyday lives, used to count, measure, and express amounts.
Numerals are just a combination of digits that we know
for example if 0,1,2,3,4,5,6.....9
are the fundamental digits then numbers from these like
12,34,668,389,23,39 etc are called numerals
We can also conclude that all numbers have originated from numerals itself and numerals are basic unit of formation of numbers
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Suppose X and Y are independent random variables such that X has uniform (0,1) distribution and Y has exponential distribution with mean 1. Calculate: (a) E[X +Y (b) EXY] (c) EI(X -Y) (d) Elx2e2y
If x and y are independent variables such that x has uniform distribution (0,1) and y has exponential distribution means 1 then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3 and E x2 e24 is -1/3
[tex]2^{2}[/tex][tex]e^{ty}[/tex]x ≈ u (0,1) > Independent
y ≈ exp (1) > Independent
E (x) = 0+1/2 = 1/2
v (x) = [tex][1- 0 ] ^{2}[/tex] / 12 = 1/12
E [tex]x^{2}[/tex] = v (x) + [tex][ E x]^{2}[/tex]
= 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3
E (y) = 1 v(y)=1 E [tex]y^{2}[/tex]= 1+1= 2
E[tex]e^{ty}[/tex] = [tex]\int\limits^_0[/tex][tex]e^{ty}[/tex][tex]e^{-y} dy[/tex]
E[tex]e^{ty}[/tex] = [tex]\int\limits^_0[/tex][tex]e^{-y} (1-t)[/tex] dy
a : E (x+y) = E (x) + E(y)
E (x+y) = 1/2+1 = 3/2
b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2
c: E [tex][x-y]^2[/tex] = E ([tex]x^{2}[/tex]-2xy+ [tex]y^{2}[/tex]
= E [tex]x^{2}[/tex] - 2 Exy + E [tex]y^{2}[/tex]
= 1/3 - 2 x 1/2 + 2
= 1/3 + 1 = 4/3
d. E [tex]x^{2}[/tex] [tex]e^{24}[/tex]
E ([tex]x^{2}[/tex] ) E [tex]e^{24}[/tex] = 1/3 x -1 = - 1/3
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Calculate how far each of the following travels. A helicopter flies at a speed of 72miles per hour for 10 minutes
Answer:
12 miles
Step-by-step explanation:
72 x [tex]\frac{10}{60}[/tex] = 12
A partial payment is made on the date indicated. Use the United States rule to determine the balance due on the note at the date of maturity. (The Effective Date is the date the note was written.) Assume the year is not a leap year.Principal Rate Effective Date Partial Payment Maturity Date Amount Date $2000 4% April 1 $1000 May 1 June 1 The balance due on the note at the date of maturity is $nothing.(Round to the nearest cent as needed.)
The balance due on the note at the date of maturity is $1010.13.
What is meant by partial payment?The offering of a payment by cheque for less than the whole amount sought by the creditor is known as partial payment. It is standard practice to grant debt forgiveness in exchange for the tender of a "payment-in-full" check.
Given permission to apply the US rule
In the United States, a year is deemed to have 360 days for the purposes of calculating interest.
Given that the principal is $ 2000,
Interest rate = 4% = 0.04
The effective date is April 1.
The whole amount is $1,000.
May 1 = partial payment
Duration = 30 days (May 1 - April 1)
Therefore, interest = PTR = 2000 * 0.04 * 30/360 = $6.67
So value = $ 2000 + $6.67 = $6.67
Partial payment received = $1,000
As a result, value = $ 1006.67 = $2006.67 - $ 1000
Time T= 31
Interest = PTR * 31/360 * 0.04 = 3.46
So the total value is $1006.67 + $3.47 = $1010.13.
The note's outstanding balance at maturity is $1010.13.
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at the beginning of the day, the stock market goes up 30 1/2 points. At the end of the day, the stock market goes down 120 1/4 points. What is the total change in the stock market from the beginning of the day to the end of the day?
The total change in the stock market from the beginning of the day to the end of the day is 89.75
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
At the beginning of the day, the stock market goes up 30 1/2 points.
At the end of the day, the stock market goes down 120 1/4 points.
The total change in the stock market from the beginning of the day to the end of the day.
= 120(1/4) - 30(1/2)
= 481/4 - 61/2
= 120.25 - 30.5
= 89.75
Thus,
The total change in the stock market from the beginning of the day to the end of the day is 89.75
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!!50 Points!! Pls help ASAP!!!
Simplify
[tex](3\sqrt{-5} + 2)(4\sqrt{-12} - 1)[/tex]
The simplification of the expression (3√-5 + 2)(4√-5 -1) gives 5√-5 - 62
How to simplify numbers and expressions?Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.
Given: the expression (3√-5 + 2)(4√-5 -1)
(3√-5 + 2)(4√-5 -1)
Clear the parenthesis:
(3√-5 + 2)(4√-5 -1) = 3√-5(4√-5) + 3√-5 (-1) + 2(4√-5) + 2(-1)
= -60 - 3√-5 + 8√-5 -2
= 5√-5 - 62
Therefore, the expression (3√-5 + 2)(4√-5 -1) simplifies to 5√-5 - 62
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A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point.
The area of the triangle as the function of x is [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)
The point on the line = (2, 1)
The give three points are (0, y), (2, 1) and (x, 0)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
Consider the point (0, y) and (2, 1)
Slope = (1-y) / (2-0)
= (1-y) /2
Consider the point (2, 1) and (x, 0)
Slope = (0-1) / (x-2)
= -1/x-2
Both slopes are equal
(1-y) /2 = -1/x-2
(1-y) = -2 / (x-2)
y = 1 + (2/(x-2))
y = x / (x-2)
The area of the triangle = (1/2)bh
Where b is the base
h is the height
The area of the triangle = (1/2) × x × (x / (x-2))
= [tex]x^2[/tex] / 2x - 4
The domain is x∈(2, ∞)
Hence, the area of the triangle is [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)
The complete question is
A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (2,1). Write the area of the triangle as a function of x, and determine the domain of the function.
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what is answers in 2 this items help me please
1) missing number is 7 (answer #2)
Each circles' numbers add up to 20. (the first one is 1 + 9 + 10, the second is 5 + 4 + 11.)
20 minus 10 minus 3 is 7, so that's the missing number.
2) missing number is 3 (answer #4)
This one's similar to the previous question. Each square's numbers have a sum of 10, this time. (First square is 2 + 7 + 1 + 0, second is 4 + 3 + 1 + 2.)
10 minus 6 minus 1 minus 0 is the same as 10 minus 7. This equals 3- so there's the number that's missing!
Hopefully this helps!
Write an equation of the line that passes through (18, 2) and is parallel to the line 3y−x=−12.
Answer: No solution
Step-by-step explanation:
3y - x = (3 * 2 - 18) = 6 - 18 = -12
3y - x = -12
x - 3y = 12
since parallel lines, by definition, have NO point of intersection, there is no solution.
I am thinking of a number. When I divide my number by $7$ and subtract $\dfrac{3}{5},$ I get back my original number. What is my number?
PLEASE HELP ASAP!!
Geometry Help!!
5) <OSL
Vertical pair angles are equal angles formed by intersecting lines
6) <MSN (or <LOS)
Supplementary angles are angles that add up to 180 degrees
determine the zeros of f(x)=28x^2−7
The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The function is given below.
f(x) = 28x² - 7
For the zeroes of the function, put f(x) = 0, then we have
f(x) = 0
28x² - 7 = 0
x² = 1/4
x = ± 1/2
The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.
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Tom and rosie are designing a game. In each turn, a player rolls five 666-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=51+1+1+1+1=51, plus, 1, plus, 1, plus, 1, plus, 1, equals, 5 points, and the highest is 6+6+6+6+6=306+6+6+6+6=306, plus, 6, plus, 6, plus, 6, plus, 6, equals, 30 points.
Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.
Based on the expected value, Rosie's statement is correct.
The expected value, denoted as E(X), represents the average or mean value of a random variable, in this case, the sum of points in a given turn when rolling the five dice.
Tom's statement, "A player will most likely get 17.5 points in any given roll," is not accurate. The expected value of 17.5 points does not necessarily mean that a player is most likely to get exactly 17.5 points in any single roll. Instead, it indicates that over many rolls, the average value of points earned in a turn is 17.5 points.
On the other hand, Rosie's statement, "Over 100 turns, we can expect a total of about 175 points," is correct. Since the expected value is 17.5 points per turn, over 100 turns, we can expect the total sum of points to be approximately 100 turns × 17.5 points/turn = 1750 points.
In summary, the expected value of 17.5 points represents the average outcome over multiple rolls, and based on this value, Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.
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The complete question:
Tom and Rosie are designing a game. In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=5 points, and the highest is 6+6+6+6+6=30 points.
They let X represent the sum in a given turn, and they find the expected value of X is E(X) = 17.5 points.
Tom says, "A player will most likely get 17.5 points in any given roll."
Rosie says, "Over 100 turns, we can expect a total of about 175 points."
Whose statement is correct based on the expected value?
On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The data shown below ($) contains the rate per 5 CCF of residential water for 42 randomly selected U.S. cities.10.38 9.08 11.7 6.4 12.32 14.43 15.4610.02 14.4 16.08 17.5 19.08 17.88 12.7516.7 17.25 15.54 14.7 18.81 17.89 14.818.32 15.95 26.75 22.22 22.66 20.88 23.3518.95 23.6 19.16 23.65 27.7 26.95 27.0426.89 24.58 37.76 26.41 38.91 29.36 41.55(a)Formulate hypotheses that can be used to determine whether the population mean rate per 5 CCF of residential water charged by U.S. public utilities differs from the $21.62 rate charged by Tulsa. (Enter != for ≠ as needed.)H0:Ha:(b)What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.)What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.)(c)At α = 0.05, can your null hypothesis be rejected? What is your conclusion?Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.(d)Repeat the preceding hypothesis test using the critical value approach.State the null and alternative hypotheses. (Enter != for ≠ as needed.)H0:Ha:Find the value of the test statistic. (Round your answer to three decimal places.)State the critical values for the rejection rule. Useα = 0.05.(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)test statistic≤test statistic≥State your conclusion.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.
The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .
The charge at which anything happens is referred to as the velocity at which it happens.
The required details for mean rate :
(a) H0: µ = 21.62
Ha: µ ≠ 21.62
(b) t = -1.231
p-value = 0.2253
(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.
(d) H0: µ = 21.62
Ha: µ ≠ 21.62
t = -1.231
check statistic ≥ 2.020
Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.
The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.
The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.
The crucial values for t at this level of significance are t=2.019.
Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.
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A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches. How tall would a Rocky Mountain Juniper tree be if at the same time of day it casts a shadow of 20.3 feet? Round your answer to the nearest hundredth of a foot and enter only the NUMERIAL VALUE of your answer.
The length of Rocky Mountain Juniper tree will be 1.269 feet.
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches.
Now,
Let the height of Rocky Mountain Juniper tree = x feet
And, A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches.
So, The height of a Rocky Mountain Juniper tree be if at the same time of day it casts a shadow of 20.3 feet will be find as;
⇒ 5.1 / 81.6 = x / 20.3
Solve for x as;
⇒ 5.1 × 20.3 / 81.6 = x
⇒ 103.53 / 81.6 = x
⇒ x = 1.269 feet
Thus, The length of Rocky Mountain Juniper tree will be 1.269 feet.
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Marta and her family landed in Hong Kong at 1405 hrs then caught another flight, which got them to Dubai at 2250 hrs. If it takes 8 hours and 5 minutes to travel from Hong Kong to Dubai, how long did they have to wait for their second flight?
The had to wait for the second flight for 40 mins.
How long was the wait?We know that sometimes when a person is travelling there may be need to have a flight that connects a person from one place to another and at times you would have to wait for a connecting flight and this wait would add to the total time that is required for the journey.
Now we are told in the question that it takes 8 hours and 5 minutes to travel from Hong Kong to Dubai and that they left Dubai at 2250 hrs but landed in Hong King at 1405 hrs. The time in between must be; 2250 hrs - 1405 hrs = 8: 45 hrs thus the time of waiting is 40 minutes.
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help meeeeeeeeeeeeeeeeeee pleaseee!!!!
Answer:
A
Step-by-step explanation:
Eliminate B and C because they don't pass through (0,1).
Eliminate D because it doesn't decrease quickly enough.
TRUE OR FALSEfor 95% of the samples from the population, the confidence interval we compute will contain the true mean.
The statement if true, for 95% of the samples from the population, the confidence interval we compute will contain the true mean.
In the given question we have to check whether the given statement is TRUE or FALSE.
The given statement is:
For 95% of the samples from the population, the confidence interval we compute will contain the true mean.
Because the underlying approach succeeds on 95% of random samples, we have a 95% confidence that this confidence interval contains the population mean.
Approximately 95% of the estimated intervals will contain the actual value of the population mean if samples are taken frequently and 95% confidence intervals are generated.
So the given statement is true.
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In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means thatthe estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constantthe estimated mean of Y is 2 when X1 equals zero.the relationship between X1 and Y is significant.
The solution is y will increase by 2 units with every unit increase in x1
What do you mean by multiple regression?A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.
What is the difference between multiple and single regression?X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.
In the above question:-
Interpretation of b1=2
it means that y will increase every 2 units for every unit increase in x1
holding x2 constant.
Hence option B is the correct answer.
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(2x² + 3x − 9)
Factor
The sum of three numbers is 23.
Three times the smallest is 4 less than the largest, while the sum of the largest
and smallest is 16. Use a linear system in three variables to find the three numbers.
The three numbers are __ , __
and __
Answer:
The three numbers are 3, 7 and 13
Step-by-step explanation:
Considering the 3 numbers: x, y and z
x + z = 16
z=16-x
3x=z-4
3x=16-x-4
4x=12
x=3
3+z=16
z=16-3
z=13
3+13+y=23
y=23-13-3
y=7
Hope this helps :)
In the diagram, A and B are points
on the circle AC and BC are
tangents to the circle and meet
at C. Work out the angle ACB.
The angle ACB would be 80 degrees.
What is tangent to a circle?
The tangent always makes a single-point contact with the circle. It never intersects the circle twice. Tangents from an external point to a circle have the same length.
In the given figure,
angle AOB = 40.
So angle OBA = 40.
Then the angle AOB = 180 - 40 -40
AOB = 100.
By the theorem of circles,
AOB + ACB = 180
100 + ACB = 180
ACB = 80.
Hence, the angle ACB would be 80 degrees.
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Is Figure B a scale copy of Figure A
Answer:
YES!!Step-by-step explanation:
First of all let's look at the side lengths of both figures.
Let's see how the corresponding sides relate:-
[tex]\sf 6*\cfrac{1}{3} =3[/tex]
[tex]\sf 3*\cfrac{1}{3} =1[/tex]
We can see that all sides scale by the same factor of 1/3.
Therefore, YES A is a scaled copy of Figure B.
______________________
Hope this helps!
Have a great day!
Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.
S:{−2, −3}
S:{−3, −4}
S:{−4, −5}
S:{−2, −5}
Answer:
[tex]S=\{-2,-3\}[/tex]
Step-by-step explanation:
Required integers are: -2 and -3
Drew's grandmother is 72 years old. Drew's mother is y years younger than Drew's grandmother, and she is 45 years old. Write an equation using subtraction that represents this situation.
What is 17 x 5.8 SHOW YOUR WORK please send a photo of work by pressing
Answer:
98.6
Step-by-step explanation:
in photo!!
A random sample of 64 sat scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. the 95onfidence interval for the population mean sat score is: ________
a. 1.96. b. 1.998.
c. 1.645. d. 1.28.
The 95% confidence interval for the population mean SAT score is given as follows:
(1340, 1460).
How to calculate the confidence interval?The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.
The bounds are obtained according to the equation defined as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 1400, n = 64, s = 240[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.
Then the lower bound of the interval is of:
1400 - 1.998 x 240/sqrt(64) = 1340.
The upper bound of the interval is of:
1400 + 1.998 x 240/sqrt(64) = 1460.
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help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Answer:
6115
Explanation:
[tex]70000(1-0.15)^{15} \approx 6115[/tex]
Calculate the average rate of change from x = −2 to x = 1 of the function below. f(x) = x2 + 5x − 12 First, find the change in y by evaluating the function at −2 and 1:
The average rate of change over the interval x = -2 and x = 1 is 4
How to determine the average rate of changeThe equation is given as
f(x) = x² + 5x - 12
The interval is given as:
x = -2 to x = 1
Start by calculating the functions f(-2) and f(1)
So, we have
f(-2) = (-2)² + 5(-2) - 12 = -18
f(1) = (1)² + 5(1) - 12 = -6
So, the average rate over these intervals is calculated as:
Average rate = [f(1) - f(-2)]/[1 - -2]
This gives
Average rate = [-6 - -18]/[1 - -2]
Evaluate
Average rate = 4
Hence, the average rate of change is 4
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help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!
Answer:
the remaining mass is 7.3 g
Step-by-step explanation:
a=30g
t=200 years
h=98 years
f(98)=a([tex](\frac{1}{2})^ \frac{t}{h}[/tex]
f(98)=30([tex](\frac{1}{2})^ \frac{200}{98}[/tex]
f(98)=7.3
there are 4 different mathematics courses, 5 different science courses, and 2 different history courses. must take one of each how many different ways can this be done
A student can take one of each subject in 40 different ways as calculated using the properties of permutation and combination..
So there are four separate math classes, five different science courses, and two different history courses.
There are now 4 ways to complete a math course.
There are 5 different ways to take science courses.
There are two ways to take a history course.
Total ways are now calculated as the product of the potential ways for each course, which equals 4 × 5 x 2 or 40 ways.
As a result, there are 40 possible combinations for three subjects.
In mathematics, a permutation of a set is, if the set also has an ordered structure, the rearranging of its members into a sequence or linear order. The technique of altering an ordered set's linear order is known as permutation.
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