9514 1404 393
Answer:
55 units
Step-by-step explanation:
If two angles have the same measure, the triangle is isosceles. That means two sides have the same measure. Since the two given sides are different measures, the remaining side must be one of those. The perimeter will be greatest if the congruent sides are the longest. The greatest perimeter is ...
15 + 20 + 20 = 55 . . . units
Claims from Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. Claims from Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. All claim amounts are independent of the other claims. Fifty claims occur in each group. Find the probability the total of the 100 claims exceeds 1,530,000.
Answer:
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
n instances of a normal variable:
For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
Sum of normal variables:
When two normal variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.
Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. 50 claims of group A.
This means that:
[tex]\mu_A = 10000*50 = 500000[/tex]
[tex]s_A = 1000\sqrt{50} = 7071[/tex]
Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. 50 claims of group B.
This means that:
[tex]\mu_B = 20000*50 = 1000000[/tex]
[tex]s_B = 2000\sqrt{50} = 14142[/tex]
Distribution of the total of the 100 claims:
[tex]\mu = \mu_A + \mu_B = 500000 + 1000000 = 1500000[/tex]
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{7071^2+14142^2} = 15811[/tex]
Find the probability the total of the 100 claims exceeds 1,530,000.
This is 1 subtracted by the p-value of Z when X = 1530000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1530000 - 1500000}{15811}[/tex]
[tex]Z = 1.9[/tex]
[tex]Z = 1.9[/tex] has a p-value of 0.9713
1 - 0.9713 = 0.0287
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
What is the range of possible sizes for side x? Please help!
Answer:
x is smaller than 5.6 and greater than 0
Which of the following pairs of functions are inverses of each other?
O A. f(x) = 2x–9 and g(x) = *7 9
B. f(x)=$+4 and g(x) = 3x-4
C. f(x)=5+*fx and g(x) = 5 - 43
O D. f(x) = 3-6 and g(x) = x26
Answer:
I think its B
Step-by-step explanation:
The pairs of functions which are inverses of each other is A. f(x) = 2x - 9 and g(x) = (x + 9)/2.
What is Inverse Function?Inverse functions are functions which can be reversed in to another function.
Then the function is said to be the inverse of the second function.
If two functions f(x) and g(x) are inverses of each other, then f(g(x) = x and g(f(x)) = x.
A. f(x) = 2x - 9 and g(x) = (x + 9)/2
f(g(x)) = f((x + 9)/2) = 2 [(x + 9)/2] - 9 = x + 9 - 9 = x
g(f(x)) = g(2x - 9) = (2x - 9 + 9) / 2 = 2x / 2 = x
So, the functions are inverses of each other.
B. f(x) = (x/3) + 4 and g(x) = 3x - 4
f(g(x)) = f(3x - 4) = [(3x - 4)/3] + 4 ≠ x
So not inverses of each other.
C. f(x) = 5 + ∛x and g(x) = 5 - x³
f(g(x)) = f(5 - x³) = 5 + ∛(5 - x³) ≠ x
So not inverses of each other.
D. f(x) = (2/x) - 6 and g(x) = (x + 6)/2
f(g(x)) = f((x + 6)/2) = [2 / ((x + 6)/2)] - 6 ≠ x
So not inverses of each other.
Hence the correct option is A.
Learn more about Inverse functions here :
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A. If x:y= 3:5, find = 4x + 5 : 6y -3
Answer:
17 : 27
Step-by-step explanation:
x=3
y=5
4(3)+5 : 6(5)-3
= 12+5 : 30-3
= 17 : 27
I need help with this
In the equation z/6 =
36, what is the next step in the equation solving sequence?
Isolate the variable
using inverse operations.
Combine like terms.
Identify and move the coefficient and variable.
Move all numbers without a variable.
Hi there!
»»————- ★ ————-««
I believe your answer is:
"Isolate the variable using inverse operations."
»»————- ★ ————-««
Here’s why:
To solve for a variable, we would have to isolate it on one side.
To isolate it, we would use inverse operations on both sides on the equation until the variable is isolated.
There are no like terms in the given equation.
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'z'...}}\\\\\frac{z}{6} = 36\\-------------\\\rightarrow (\frac{z}{6})6 = (36)6\\\\\rightarrow \boxed{z = 216}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
First option: Isolate the variable using inverse operations
Step-by-step explanation:
z/6 = 36
Since we already have the equation set up and cannot simplify any further, we must try to isolate the variable, z, by using inverse operations.
The inverse operation of division is multiplication, so to isolate z, we multiply 6 on each side:
z/6 · 6 = 36 · 6
z = 216
sin x - cos x - 1/√2 = 0
Find the value of x
Answer:
Step-by-step explanation:
5) If the local professional basketball team, the Sneakers, wins today's game, they have a 2/3 chance of winning their next game. If they lose this game, they have a 1/2 chance of winning their next game.
A) Make a Markov Chain for this problem; give the matrix of transition probabilities and draw the transition diagram.
B) If there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next game?
C) If they won today, what are the chances of winning the game after the next?
Answer:
If they win today's game, the probability to win the next game = 2/3
Therefore the probability that they lose the next game when they win today's game = 1-(2/3) =1/3.
If they lose today's game, the probability to win the next game = 1/2
so, the probability to lose is 1/2.
a) [tex]\begin{bmatrix} \frac{2}{3}&\frac{1}{2} & \\\\ \frac{1}{3}&\frac{1}{2} & \end{bmatrix}[/tex]
b) [tex]p=\begin{bmatrix} \frac{1}{2}\\\\ \frac{1}{2} \end{bmatrix}[/tex]
[tex]p^{'} =\begin{bmatrix} \frac{7}{12}\\\\ \frac{5}{12} \end{bmatrix}[/tex]
c) Let them win today's game
[tex]p=\begin{bmatrix} 1\\ 0 \end{bmatrix}\\\\\\p^{'} =\begin{bmatrix} \frac{2}{3}\\\\\frac{1}{3} \end{bmatrix}[/tex]
[tex]p^{''}= \left[\begin{array}{c}\frac{11}{18} \\\\\frac{7}{18} \end{array}\right][/tex]
The chances that they win their next game are 58.33%, while if they won today, the chances of winning the game after the next are 38.88%.
ProbabilitiesGiven that if the local professional basketball team, the Sneakers, wins today's game, they have a 2/3 chance of winning their next game, while if they lose this game, they have a 1/2 chance of winning their next game, to determine, if there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next game, and determine, if they won today, what are the chances of winning the game after the next, you must perform the following calculations:
(2/3 + 1/2) / 2 = X1,666 / 2 = X0.58333 = X((2/3 + 1/2 / 2) x 2/3 = X0.58333 x 0.666 = X0.3888 = XTherefore, the chances that they win their next game are 58.33%, while if they won today, the chances of winning the game after the next are 38.88%.
Learn more about probabilities in https://brainly.com/question/10182808
Diagnostic statistics will lead the researcher to choose an appropriate model; there may be ____________________ optimal model.a. no single.
b. at least one.
c. only one.
d. only two.
if the volume of a cube is 2197cm3, find the height of the cube
b) What is the 4 times of the sum of 3and9?
Answer:
108
Step-by-step explanation:
sum is a fancy word for add so 3+9=27 and 27*4=108
is “x = -3” a function
Answer:
No
Step-by-step explanation:
x = -3 is a vertical line at x= -3
Tow points on the line are
(-3,1) and (-3,2)
This means one x value goes to 2 different y values so it is not a function
Answer: No
Step-by-step explanation: The line x = -3 is a vertical or straight up and down line that is parallel to the y-axis. On the vertical line x = -3, when x = -3, y can be 0, 1, 2, -5, or any other number, there are in infinite number of possibilities.
The technical definition of a function is written as "a relation in which each element in the domain is paired with one and only one element in the range."
(4 pts) If a rock is thrown vertically upward from the surface of Mars with an initial velocity of 15m/sec
then the height of the rock after t seconds is h=15t-1.86t^2 (h in meters and t in seconds). The
rock will reach its maximum height when the velocity=0 m/sec. How long does it take for the rock to
reach its maximum height, and what is the maximum height?
Answer:
Step-by-step explanation:
I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.
The position equation is
[tex]s(t)=-1.86t^2+15t[/tex] That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.
The first derivative of position is velocity:
v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):
0 = -3.72t + 15 and solve for t:\
-15 = -3.72t so
t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:
s(4.03) = -1.86(4.03)² + 15(4.03) so
s(4.03) = 30.2 meters.
Calculus is amazing. Much easier than most methods to solve problems like this.
Please help …………………….
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Answer:
(-3, 3)
Step-by-step explanation:
The blanks are trying to lead you through the process of finding the point of interest.
__
The horizontal distance from T to S is 9 . (or -9, if you prefer)
The ratio you're trying to divide the line into is the ratio that goes in this blank:
Multiply the horizontal distance by 2/3 . (9×2/3 = 6)
Move 6 units left from point T.
The vertical distance from T to S is 6 .
Multiply the vertical distance by 2/3 . (6×2/3 = 4)
Move 4 units up from point T.
__
Point T is (3, -1) so 6 left and 4 up is (3, -1) +(-6, 4) = (3-6, -1+4) = (-3, 3). The point that is 2/3 of the way from T to S is (-3, 3).
consider the function f(x) = -2x^2 - 7. which of the following functions shifts the graph of f(x) up three units and vertically shrinks it by a factor of 1/2?
a. g(x) = -x^2 - 10
b. g(x) = -x^2 - 4
c. g(x) = x^2 - 4
d. g(x) = -1/2x^2 - 4
Answer: The answer is B.
Step-by-step explanation:
James Madison High School
Write y=2/3x+7 in standard form using intergers
Answer:
a.
Step-by-step explanation:
y = 2/3 x + 7
3 * y = 3 * (2/3 x + 7)
3y = 2x + 21
2x - 3y = -21
-2x + 3y = 21
Answer: a.
Muhammad lives twice as far from the school as Hita. Together, the live a total of 12 km
from the school. How far away drom the school does each of them live?
Answer:
Muhammad lives 8 km away from the school.
Hita lives 4 km away from the school.
Step-by-step explanation:
First of all, find a number that, when you double that number and add both numbers, you will get 12. That number is 4. So double 4 and get 8. Then add both to get 12.
The product of 86 and the depth of the river
Answer:
Step-by-step explanation:
Are you trying to find a variable expression? the product of 86 means multiplication so 86*n or 86n. Other than that I dont understand the question.
If u= 70% and o=5%, what % of scores fall within 3 standard deviations from the mean?
Answer:
"85%" is the right answer.
Step-by-step explanation:
Given:
[tex]\mu = 70[/tex] (%)
[tex]\sigma = 5[/tex] (%)
As we know,
The 99.7% observation fall within the 3rd standard deviation, then
⇒ [tex](\mu \pm \sigma ) = (70-(3\times 5)) \ to \ (70+(3\times 5))[/tex]
[tex]=(70-15) \ to \ (70+15)[/tex]
[tex]=55 \ to \ 85[/tex] (%)
Thus the above is the correct solution.
Serkan teacher regularly buys 75 TL of gasoline in his car every week.
At the end of the 13th week, how much is the total gasoline expenditure made by the serkan teacher?
A)390 B)420 C)900 D)975
Answer:
d
Step-by-step explanation:
75 per week,
after 13 weeks, 75*13 = 975
Given that fx=2x2-4x+1, then f(-1)is.
Answer:
[tex]f(-1)=7[/tex]
Step-by-step explanation:
I am going to assume your question meant the equation
[tex]f(x)=2x^{2} -4x+1[/tex]
So [tex]f(-1)[/tex] can be found by substituting all the x terms in the equation with -1
[tex]f(-1)=2(-1)^{2} -4(-1)+1[/tex]
And simplifying for our answer
[tex]f(-1)=2(1)+4+1[/tex]
[tex]f(-1) = 2+4+1[/tex]
[tex]f(-1)=7[/tex]
The table shows the marginal relative frequencies of surveyed drivers’ plans for their next vehicle.
A 2-way table. A 5-column with 4 rows titled Plan for Next Vehicle. Column 1 has entries Current vehicle, bought new, bought used, leased total. Column 2 is labeled Buy new with entries 0.156, 0.076, 0.02, 0.252. Column 3 is labeled Buy used with entries 0.024, 0.584, 0.008, 0.616. Column 4 is labeled Lease with entries 0.024, 0.036, 0.072, 0.132. Column 5 is labeled Total with entries 0.204, 0.696, 0.1, 1.000.
Which statements appropriately interpret data from the table? Check all that apply.
The majority of drivers, about 62 percent, plan to buy a used vehicle next.
About 25 drivers plan to buy a new vehicle next.
Ten percent of drivers lease their current vehicle.
Only 1.3 percent of drivers plan to lease next.
The least percentage of people will lease their next car.
:Answer:
1.) The majority of drivers, about 62 percent, plan to buy a used vehicle next.
3.) Ten percent of drivers lease their current vehicle.
5.) The least percentage of people will lease their next car.
Correct on EDGE2021
Answer:
A)The majority of drivers, about 62 percent, plan to buy a used vehicle next.
C)Ten percent of drivers lease their current vehicle.
E)The least percentage of people will lease their next car.
Step-by-step explanation:
edge 2023
What is the solution of the inequality shown below?
-3+a<-7
Answer:
[tex]{ \tt{ - 3 + a < - 7}} \\ { \tt{a < - 4}}[/tex]
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000
Answer:
The correct answer is "76.98%".
Step-by-step explanation:
According to the question,
⇒ [tex]P(34000<x<46000) = P[\frac{34000-40000}{5000} <\frac{x- \mu}{\sigma} <\frac{46000-40000}{5000} ][/tex]
[tex]=P(-1.2<z<1.2)[/tex]
[tex]=P(z<1.2)-P(z<-1.2)[/tex]
[tex]=0.8849-0.1151[/tex]
[tex]=0.7698[/tex]
or,
[tex]=76.98[/tex]%
A student writes
1 1/2 pages of a report in 1/2
an hour. What is her unit rate in pages per hour?
Answer:
3 pages per hour
Step-by-step explanation:
Take the number of pages and divide by the time
1 1/2 ÷ 1/2
Write the mixed number as an improper fraction
3/2÷1/2
Copy dot flip
3/2 * 2/1
3
9514 1404 393
Answer:
3 pages per hour
Step-by-step explanation:
To find the number of pages per hour, divide pages by hours.
(1.5 pages)/(0.5 hours) = 3 pages/hour
Coordinate plane with quadrilaterals EFGH and E prime F prime G prime H prime at E 0 comma 1, F 1 comma 1, G 2 comma 0, H 0 comma 0, E prime negative 1 comma 2, F prime 1 comma 2, G prime 3 comma 0, and H prime negative 1 comma 0. F and H are connected by a segment, and F prime and H prime are also connected by a segment. Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H'. Which characteristic of dilations compares segment F'H' to segment FH
Answer:
[tex]|F'H'| = 2 * |FH|[/tex]
Step-by-step explanation:
Given
[tex]E = (0,1)[/tex] [tex]E' = (-1,2)[/tex]
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]G = (2,0)[/tex] [tex]G' =(3,0)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
[tex](x,y) = (1,0)[/tex] -- center
[tex]k = 2[/tex] --- scale factor
See comment for proper format of question
Required
Compare FH to F'H'
From the question, we understand that the scale of dilation from EFGH to E'F'G'H is 2;
Irrespective of the center of dilation, the distance between corresponding segment will maintain the scale of dilation.
i.e.
[tex]|F'H'| = k * |FH|[/tex]
[tex]|F'H'| = 2 * |FH|[/tex]
To prove this;
Calculate distance of segments FH and F'H' using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Given that:
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
We have:
[tex]FH = \sqrt{(1- 0)^2 + (1- 0)^2}[/tex]
[tex]FH = \sqrt{(1)^2 + (1)^2}[/tex]
[tex]FH = \sqrt{1 + 1}[/tex]
[tex]FH = \sqrt{2}[/tex]
Similarly;
[tex]F'H' = \sqrt{(1 --1)^2 + (2 -0)^2}[/tex]
[tex]F'H' = \sqrt{(2)^2 + (2)^2}[/tex]
Distribute
[tex]F'H' = \sqrt{(2)^2(1 +1)}[/tex]
[tex]F'H' = \sqrt{(2)^2*2}[/tex]
Split
[tex]F'H' = \sqrt{(2)^2} *\sqrt{2}[/tex]
[tex]F'H' = 2 *\sqrt{2}[/tex]
[tex]F'H' = 2\sqrt{2}[/tex]
Recall that:
[tex]|F'H'| = 2 * |FH|[/tex]
So, we have:
[tex]2\sqrt 2 = 2 * \sqrt 2[/tex]
[tex]2\sqrt 2 = 2\sqrt 2[/tex] --- true
Hence, the dilation relationship between FH and F'H' is::
[tex]|F'H'| = 2 * |FH|[/tex]
Answer:NOTT !! A segment in the image has the same length as its corresponding segment in the pre-image.
Step-by-step explanation:
Find the area of the sector formed by central angle
θ
in a circle of radius
r
if
θ
=
2
;
r
=
6
m
Answer: 0.2pi
Step-by-step explanation:
1. Find the area of the entire circle
2. Set up a proportion that compares the relationship of the Area of sector and the Area of circle to the Arc measure and the circle measure
3. Solve!
5x+2y-z=-5
-x+3y+4z=12
x-y-3z=-8
Answer:
4
Step-by-step explanation:
233
lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies. She then had 3/7 of the container of sugar left. How much sugar was in the container at first
Answer:
At the beginning, there were 2,678.26 grams of sugar in the container.
Step-by-step explanation:
Since Lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies, and she then had 3/7 of the container of sugar left, to determine how much sugar was in the container at first, the following calculation must be performed:
880 + 1 / 10X = 3 / 7X
880 + 0.1X = 0.4285X
880 = 0.4285X - 0.1X
880 = 0.3285X
880 / 0.3285 = X
2,678.26 = X
Therefore, at the beginning there were 2,678.26 grams of sugar in the container.
Write the quadratic function in the form g(x) = a (x-h)^2 +k.
Then, give the vertex of its graph.
g(x) = 2x^2 + 8x + 10
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Answer:
g(x) = 2(x +2)² +2
vertex: (-2, 2)
Step-by-step explanation:
It is often easier to write the vertex form if the leading coefficient is factored from the variable terms:
g(x) = 2(x² +4x) +10
Then the square of half the x-coefficient is added inside parentheses, and an equivalent amount is subtracted outside.
g(x) = 2(x² +4x +4) +10 -2(4)
g(x) = 2(x +2)² +2
Comparing to the vertex form, we see the parameters are ...
a = 2, h = -2, k = 2
The vertex is (h, k) = (-2, 2).
