1 you are offered a gamble on the toss of a coin. if the coin shows tails, you lose $100. if the coin shows heads, you win $150. Yes one can accept it.
As per the given data:
If you toss the coin.
Coin shows tails [tex]$\rightarrow$[/tex] lose $ 100
Coin shows heads [tex]$\rightarrow$[/tex] win $ 150
We would consider expected gain for us in each scenario.
Since, the probability of head is,
[tex]P(H) = \frac{1}{2}[/tex]
The probability of Tail is,
[tex]P(T)=\frac{1}{2}[/tex]
Therefore, expected gain [tex]$=150 \times \frac{1}{2}+(-100) \times \frac{1}{2}$$$[/tex]
= 75 - 50
= $ 25
Since, gain is positive number of 25 .
We can say on an average we can gain some Profit.
Hence one would accept the offer.
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20) If the area of a rectangular playground is
p^2 -6p - 7 square feet, what is the perimeter of the
playground?
Answer:
Explanation:
Write an equation to solve the problem.
Area of rectangle = L(w)
Assuming that the width measures x meters, the length measures x + 5 meters.
500 = x(x + 5)
500 =
x
2
+ 5x
0 =
x
2
+ 5x - 500
As you may already know, a trinomial of the form
a
x
2
+ bx + c, a = 1, you must find 2 numbers that multiply to c and that add to b. Two numbers that multiply to -500 and add to +5 are +25 and -20
0 = (x + 25)(x - 20)
x = -25 and 20
Since a negative length is impossible, the width mesures 20 meters and the length measures 25 meters.
Practice exercises:
A rectangle has a perimeter of 90 meters. Find the maximum area.
The area of a right triangle is 120
m
2
. The base measures half the sum of the height and one. Find the perimeter.
Find the area and perimeter of a right triangle the has a height that is 2 more than the double of the width and that has a hypotenuse that measures
√
68
meters.
Good luck!
Step-by-step explanation:
Karolyn puts 4,500 into a life insurance policy that pays 7.5% annual interest. If no additional investment is made into the policy how much accumulated interest should Karolyn expect at the end of 10 years?
Answer: $4,774.64
Step-by-step explanation:
The amount after 10 years assuming 7.5% compound interest is:
= Amount * ( 1 + rate) ^ no. of years
= 4,500 * ( 1 + 7.5%)¹⁰
= $9,274.64
The accumulated interest is:
= Amount after 10 years - Present amount
= 9,274.64 - 4,500
= $4,774.64
please help!!No links
What are the zeros of f(x) = x2 + 3x - 10?
A. X= -5 and x = 2
B. x= -5 and x = -2
C. X= 5 and x = -2
D. x = 5 and x = 2
Answer:
(x+5) (x-2)
SO -5 and 2 option A
Step-by-step explanation:
factor it. and set equal to zero.
How can I Solve this problem Solve. for g.
18 = 3g
g
Answer:
[tex]g = 6[/tex]
Step-by-step explanation:
1) Diving both sides by 3.
[tex] \frac{18}{3} = g[/tex]
2) Simplify 18/3 to 6.
[tex]6 = g[/tex]
3) Switch sides.
[tex]g = 6[/tex]
Therefor, the answer is g = 6.
A quality control expert at a drink bottling factory took a random sample of 9 bottles from a
production run of over 1,000 bottles and measured the amount of liquid in each bottle in the
sample. The sample data were roughly symmetric with a mean of 505 mL and a standard
deviation of 6 mL.
Based on this sample, which of the following is a 95% confidence interval for the mean
amount of liquid per bottle (in mL) in this production run?
Answer: It's in the screenshot
Step-by-step explanation:
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the mean amount of liquid per bottle (in mL) in this production run is (500.39, 509.61).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[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.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 9 - 1 = 8 df, is t = 2.306.
The other parameters are given as follows:
[tex]\overline{x} = 505, s = 6, n = 9[/tex]
Hence:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 505 - 2.306\frac{6}{\sqrt{9}} = 500.39[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 505 + 2.306\frac{6}{\sqrt{9}} = 509.61[/tex]
The 95% confidence interval for the mean amount of liquid per bottle (in mL) in this production run is (500.39, 509.61).
More can be learned about the t-distribution at https://brainly.com/question/16162795
Find the missing length. The triangles in each pair are similar.
Answer:
........................................
Select the statement that describes this expression: 10 + fraction 1 over 4x (5 + 3) − 3. (2 points)
10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3
fraction 1 over 4 of 10 times the sum of 5 and 3, minus 3
3 more than 3 plus 5 multiplied by fraction 1 over 4, then add 10
10 times fraction 1 over 4 plus 3 and 5, minus 3
Answer:
10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3
plz mark as brainliest
hope it helps
Answer:10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 2
Step-by-step explanation:
need help
problem/question in image below
Answer:
Option A would be the correct answer
I don't have an explanation to type but you can trust me :)
Please mark as brainliest for further answers :)A triangle has one side that is 5 inches long and another that is 7 inches long. How many different lengths, in inches,are possible for the last side of the triangle?
Answer:
2 < c < 12
Step-by-step explanation:
Let the last side of the triangle = c
The sum of any two sides must be greater than the third side. Let's say we have triangle ABC, where a = 5 inches and b = 7 inches
a + b > c (1)
a + c > b (2)
b + c > a (3)
From (1);
a + b > c
7 + 5 > c
c < 12
From (2):
a + c > b
7 + c > 5
7 - 5 < c
c > 2
From (3):
b + c > a
5 + c > 7
c > 7 - 5
c > 2
So the possible lengths of c are: 2 < c < 12
Please helppp
The function ƒ(x) = 2x − 1 indicates:
a downward shift of 1 unit.
a shift of 1 unit to the left.
an upward shift of 1 unit.
None of these choices are correct.
Answer:
It is a downward shift of one unit
Find the total length of rope that is brought on the trip.
A. 25 3 4 yards
B. 29 3 4 yards
C. 33 3 4 yards
D. 37 3 4 yards
i have the quiz before and the answer is D: 37 3/4 yards
:)
Find the value of a. Round your answer to the nearest tenth.
Answer:
Polly do you know the formula for law of Cosines?
find it if you don't
Step-by-step explanation:
a = sqrt( b^2 +c^2 - 2bcCos(A) )
a = sqrt( 100 + 62.41 -34.197)
a = sqrt(128.213)
a = 11.323
a = 11.3 ( to the nearest tenth )
What is the distance between points A (3,-5) and B(-8,2) on the coordinate plane?
Answer:
[tex]\sqrt{-51}[/tex]
or aprox 7.14
hopefully this helps
Alternate interior angles are always congruent. TRUE OR FALSE
Answer:
false
Step-by-step explanation:
Answer:
False.
Step-by-step explanation:
Alternate interior angles are congruent only when the two lines intercepted are parallel.
I can choose and create diagrams to help me compare two situations.
SOMEONE PLEASE HELP MY TEACHER WANTS TO PUT ME IN SUMMER SCHOOL SO I NEED TO GET MY HW DONE ASAP SO PLEASE REPLY WITH AN ANSWER PLSS!!!
Answer:
blurred poate
Step-by-step explanation:
blurred po ate
prove this qsn plzz and fast
Step-by-step explanation:
Let use the first of the medians. Medians AX.
Median AX is the midpoint of BC so our median is
[tex] \frac{1}{2} (b + c) - a[/tex]
Let use the second median.
Median BY is the midpoint of AC so our median is
[tex] \frac{1}{2} (a + c) - b[/tex]
Let use the final median.
Median CZ is the midpoint of AB so our median is
[tex] \frac{1}{2} (a + b) - c[/tex]
Now add all them up
[tex] \frac{1}{2} (b + c ) - a + \frac{1}{2} (a + c) - b + \frac{1}{2} (a + b) - c[/tex]
[tex] \frac{1}{2} b + \frac{1}{2} c - a + \frac{1}{2} a + \frac{1}{2} c - b + \frac{1}{2}a + \frac{1}{2} b - c[/tex]
Add like terms.
[tex] \frac{1}{2} b + \frac{1}{2} b - b = 0[/tex]
[tex] \frac{1}{2} a + \frac{1}{2} a - a = 0[/tex]
[tex] \frac{1}{2} c + \frac{1}{2} c - c = 0[/tex]
[tex]0 + 0 + 0 = 0[/tex]
So
AX+BY+CZ=0
find the x-intercepts of y= x^2+4x+8 using the quadratic formula.
Answer: To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
2
+
2
√
3
,
0
)
,
(
2
−
2
√
3
,
0
)
y-intercept(s):
(
0
,
8
)
Step-by-step explanation: To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
2
+
2
√
3
,
0
)
,
(
2
−
2
√
3
,
0
)
y-intercept(s):
(
0
,
8
)
Which expression is equivalent to (3x2+3x−3)−(6x2−4x−2)?
A
−3x2+7x−1
B
−3x2−x−5
C
−3x2+7x−5
D
−3x2−x−1
Answer:
A. -3x^2+7x-1
Step-by-step explanation:
(3x^2+3x-3)-(6x^2-4x-2)
3x^2+3x-3-6x^2+4x+2
-3x^2+7x-1
How may candies did Thad get all together? Pls help quickly
Answer:
all together there is 141 candies in all
What are the roots of this equation x^2-2x+3=0
Step-by-step explanation:
hope it's help.
see answer attached
Bounty paper towels cost $8.49 for 8 rolls. Brawny paper towels cost $13.99 for 12 rolls. Which is the better buy?
Answer:
Bounty Paper Towels is the better deal
Step-by-step explanation:
8.49 divided by 8 = 1.06125 ($1.01)
13.99 divided by 12 = ~1.16583 ($1.16)
The Brawny is more expensive per roll, so Bounty would be a better deal
what's the answer to this problem?
[tex]5x + 35 = 45[/tex]
Answer:
5x+35=45
5x=45-35
5x=10
x=2
what is the discriminant of the polynomial below 2x^2+5x-8
A. 89
B. -39
C. 31
D. -59
Answer:
Hi! The answer to your question is A. 89
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
8.8C
What value of x makes this equation true?
12x - 15 = 6 - 3x
The dollar store buys a hat for $0.80. Then they mark up the price by 20%.
How much will they sell the hat for?
Answer:
$0.96
Step-by-step explanation:
20% of 0.80 is 0.16
0.80 + 0.16 = 0.96
Answer:
$0.96
Step-by-step explanation:
Multiply 0.80 times 0.2
0.80 x 0.2=0.16
Then add up 0.16 and 0.80 to get your answer
0.80 + 0.16=0.96
Hope it helps
Question 4 (1 point)
The image shows quadrilateral ABCD.
Find the area of ABCD. Explain or show your reasoning.
Answer:
25
Step-by-step explanation:
Using the Pythagorean Theorem, we can find the side length of each side.
a^2 + b^2 = c^2
=> 3^2 + 4^2 = x^2
=> 9 + 16 = x^2
=> x = 5
By applying the same formula for each side, we will get that each side is 5 units.
So, the area = 5*5 = 25
The quadrilateral is a square and the area of square is 25 square units.
What is a quadrilateral?
A quadrilateral is 2-dimensional geometric closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.
For the given situation,
The quadrilateral ABCD has points A(0,4), B(3,0), C(7,3), D(4,7).
The distance these points can be found by
[tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
AB = [tex]d=\sqrt{(3-0)^{2}+(0-4)^{2} }[/tex]
⇒ [tex]AB = \sqrt{3^{2}+4^{2} }[/tex]
⇒ [tex]AB=\sqrt{9+16}[/tex]
⇒ [tex]AB=\sqrt{25}[/tex]
⇒ [tex]AB=5[/tex]
BC = [tex]d=\sqrt{(7-3)^{2}+(3-0)^{2} }[/tex]
⇒ [tex]BC=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]BC=5[/tex]
CD = [tex]d=\sqrt{(4-7)^{2}+(7-3)^{2} }[/tex]
⇒ [tex]CD=\sqrt{(-3)^{2} +4^{2} }[/tex]
⇒ [tex]CD=5[/tex]
DA = [tex]d=\sqrt{(4-0)^{2}+(7-4)^{2} }[/tex]
⇒ [tex]DA=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]DA=5[/tex]
Since AB = BC = CD = DA, the quadrilateral is a square.
The formula of area of quadrilateral is
[tex]A=(side)^{2}[/tex]
⇒ [tex]A=5^{2}[/tex]
⇒ [tex]A=25[/tex]
Hence we can conclude that the quadrilateral is a square and the area of square is 25 square units.
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Which of the following functions translates the graph of the parent
function f(t) = x² horizontally left 6 units?
Answer:
shawty us bad with the scratchers in
PLEASE HELP I WILL MARK YOU BAINLIEST AND SHOW YOUR WORK PLEASE
A school is raising money to build a new auditorium! It costs $6,500 to hire a worker to put in new floors in the auditorium. The other information about the cost of the project is below:
The teachers have already raised $500.
There are twelve teachers trying to help the school raise money and each teacher raises the same amount of money.
The teachers organize a car wash and earn $10 for each car they wash.
How many cars must each teacher wash to raise enough money to complete the new auditorium?
Answer:
54
Step-by-step explanation:
6500/12=541....
540/10
54
What is the slope, m, of the line through (-9, -17) and (-9, 12)?
Express the slope as a fraction in lowest terms.
If the slope is undefined, enter undefined into the text box.
m =
Answer:
m = undefined
Step-by-step explanation:
(-9, -17) and (-9, 12)
Slope:
m=(y2-y1)/(x2-x1)
m=(12+17)/(-9+9)
m=29/0
Since 0 is the denominator, the slope is undefined