Answer:
The probability that the laughter after one of the comedians jokes lasts for more than 7 seconds is approximately 0.474
Step-by-step explanation:
The nature of the distribution of the given data = Evenly distributed data
The range of the laughter times = Between 4 seconds and 9.7 seconds
The probability density function, f(x), is given as follows;
[tex]f(x) = \dfrac{1}{b - a}[/tex]
The mean of the uniform distribution, μ, is given as follows;
[tex]\mu = \dfrac{a + b}{2}[/tex]
The standard deviation, σ, is given as follows;
[tex]\sigma = \sqrt{\dfrac{\left (b - a\right)^2}{12} }[/tex]
Where;
a = 4, and b = 9.7, we have;
μ = (4 + 9.7)/2 = 6.85
σ = √((9.7 - 4)²/12) ≈ 1.64545
The probability density function, f(x) = 1/(b - a) for a ≤ x ≤ b
∴ f(x) = 1/(9.7 - 4)
For P(x > 7), we have;
P(x > 7) = 1 - P(x < 7) = 1 - (7 - 4) × 1/(9.7 - 4) ≈ 0.474
The probability that the laughter after one of the comedians jokes lasts for more than 7 seconds P(x >7) ≈ 0.474.
Amy has a box that is 6 1/2 feet long, 3.25 feet wide, and 2 feet high. What is the volume of the box? V=lwh
Answer:
42.25 feet ³
Step-by-step explanation:
Volume of the box = length × width × height
Length = 6 1/2 feet = 6.5 feet
Width = 3.25 feet
Height = 2 feet
Volume of the box = length × width × height
= 6.5 feet × 3.25 feet × 2 feet
= 42.25 feet ³
Volume of the box = 42.25 cubic foot
10. Find the total surface area of the triangular prism
shown below.
Answer:
I think its 132.
The total surface area of the triangular prism is 200 cm².
Triangular prism surface areaSurface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
How to find the surface area of the triangular prism?First, find the height of the prism.
Let h is the height of the prism
Use the pythagoras theorem
then
5² = (6/2)² + h²
5² = 3² + h²
25 = 9 + h²
h² = 25 - 9
h² = 16
h =4
Now apply the surface area formula
total surface area = ( 5 + 5 + 6) 11 + 6×4
= 16 × 11 + 24
= 176 +24
= 200 cm²
Hence the surface area is 200 cm²
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Inverse function of y=x^2+3
Answer:
y = ±[tex]\sqrt{x-3}[/tex]
Step-by-step explanation:
step 1: substitute 'x' for 'y'
x = y² + 3
y² = x - 3
last step: solve for 'y'
y = ±[tex]\sqrt{x-3}[/tex]
Sam has the lead role in the school play. He still has to memorize 1/2 of his lines. Suppose Sam memorizes 1/3 of his lines today. What fractions of his lines will he have left to memorize?
Answer: 1/6
Step-by-step explanation:
Since Sam has to memorize 1/2 of his lines and he memorizes 1/3 of his lines today, the fractions of his lines that he has left to memorize will be gotten by subtracting 1/3 from 1/2. This will be:
= 1/2 - 1/3
= 3/6 - 2/6
= 1/6
Therefore, he has 1/6 of his lines left to memorize.
Answer:
1/6
Step-by-step explanation:
The fractions of his lines will he have left to memorize is calculated as:
Number of lines he has to memorize - Number of line he memorized today
Number of lines he has to memorize = 1/2
Number of line he memorized today = 1/3
Hence,
= 1/2 - 1/3
Lowest Common Denominator = 6
= 3 - 2/6
= 1/6
If c = 4 what is the value of the following expression:
50 - 40 + C*
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
50 - 40 + c
50 - 40 + 4
10 + 4
14
Which expression is equivalents to 6 (3r + 4)
Answer:
21
Step-by-step explanation:
x + 2y = 5
3x + 5y = 14
Solve the system of equations.
(3, 1)
(2,3/2)
(7,-1)
Answer:
[tex]x+2y = 5\\x = 5 -2y\\\\Substitute \ x \ in \ second \ equation \\\\3(5-2y) +5y = 14\\15 -6y +5y = 14\\-y = 14 -15\\-y = -1\\y = 1\\Substitute \ y = 1 \ in \ x = 5 -2y:\\ x = 5 -(2\cdot 1) = 5-2=3\\[/tex]
Option (3, 1)
Answer:
The solution is (3, 1)
Step-by-step explanation:
Use the method "elimination by addition and subtraction." Multiply all terms of the first equation by -3, obtaining
-3x - 6y = -15
and combine this result with the second equation:
-3x - 6y = -15
3x + 5y = 14
-----------------------
-y = -1, or y = 1.
Substituting this result, y = 1, into the first equation yields
x + 2(1) = 5, or x + 2 = 5, or x = 3.
The solution is (3, 1)
Reflect triangle A in the line y = 1.
5
A
4 3
2
1
-5 -4 -3 -2 -1 0
x
1 2 3 4 5
-2
4
5
Can I please get help with this question on future value of annuities? I also am really confused on how to do the table of values.
Answer:
D
Step-by-step explanation:
I've attached one of those tables below
I'm going to solve this using the FV annuity formula
[tex]R(\frac{(1+i)^n-1}{i})[/tex]
where i is the effective rate of interest
r is the payment
n is the number of periods
to find the effective rate of interest we need to divide .08/2 (because the interest is compounding once every six months)
and the number of periods is 4*2 (because there are two periods a year(
[tex]1500(\frac{(1+.04)^8-1}{.04})=13821.33[/tex] which is equal to D
To use the table go to the effective rate of interest (4%) and then number of periods (8)
The number is 9.2142
mulitply that by the payment (1500) and get 13821.3 (D)
*the reason that the answers are slightly different is because the annuity table rounded whereas in the formula it was more exact*
9514 1404 393
Answer:
D. $13,821.30
Step-by-step explanation:
The table is given in terms of interest rate per period and number of periods. The table assumes that money is invested at the same interval that interest compounding occurs.
Since you're investing $1500 every 6 months for 4 years, the 8% annual interest rate becomes 8%·(6/12) = 4% interest each 6-month period. In 4 years, there are 8 periods of 6 months. So, you look for the multiplier shown in the table that is at the intersection of 4% interest and 8 periods.
That multiplier is 9.2142, so the future value is ...
FV = amount invested per period × multiplier from table
= $1500 × 9.2142 = $13,821.30
__
The above is how you use the table.
You can also choose the correct answer based only on your number sense, without bothering with the table.
You are paying into the annuity 8 payments of $1500 each. That is a total input of 8 × $1500 = $12,000. You will be earning interest on that money, so the future value of the annuity is more than $12,000. Only one answer choice fits that description:
D. $13,821.30
28 minutes to 1 hour simplest form
Answer:
7min:15min
Step-by-step explanation:
28min:1 hour
28min:60 minutes
14min:30min
7min:15min
what if you have a grade of 80% and you fail a homework of 50 points
Answer:
I don't know but you might end up with a C
Step-by-step explanation:
OR A D
Volume of cone round to the nearest 10th
Answer: 63
Maybe?
If it’s wrong sorry :)
Please help on this!!!! Thanks!!
Answer:
TU = 2 (HD)
Hence, TU = 80
Step-by-step explanation:
line formed by joining 2 mid points of a traingle = 0.5 times of length of 3rd side.
Answer:
I think it is 92. UV and TV are the two sides of the triangle, and yoy are left with the longest side (hypotenuse). Therefore you can use the pythagorean theorem to find your answer a²+b²=c²
So 40+52=92
PLS ANSWER!! +GIVING BRAINLIEST FOR 1ST CORRECT ANSWER
Answer:
18
Step-by-step explanation:
mark me as
brainliest
18
Answer:
144 ounces
Step-by-step explanation:
Help!!!
Consider the following equation.
2^(x)+3=3^(-x)
If the equation is solved using successive approximation, match the value of x to the following iterations.
9514 1404 393
Answer:
no iterations shown; the root is approximately -1.12911
Step-by-step explanation:
If your method of successive approximation is the Bisection Method, and if your initial interval is [-2, -1], then successive values of x used for reducing the interval are ...
-1.5, -1.25, -1.125, -1.1875, -1.15625
__
If your method of successive approximation is Newton's method, and if your initial guess is -1.5, then successive values of x will be ...
-1.1905079, -1.1309053, -1.1291151, -1.1291135
Another iteration confirms this last value is accurate to 8 significant figures.
Answer:
-5/4
-9/8
-19/16
Step-by-step explanation:
This is the answer given
A percent is a rate of a value compared to what number?
Answer:
x
Step-by-step explanation:
33%
The diagram shows a square ABDE and an isosceles triangle BCD.
Angle C = 40°
Work out the size of angle EBC.
А
B
40°
E
Answer:
ans = <ebc= 115°
hope this will help
.
.
The area of the rectangle is 40% larger than the area of the triangle.What is the length ,L, of the rectangle?
Answer:
10 units
Step-by-step explanation:
Area of the triangle (A') = 1/2bh
A' = 1/2bh............ Equation 1
Where b = base of the triangle, h = height of the triangle
From the diagram,
Given: b = 12.5 unit, h = 4 unit
Substitute into equation 1
A' = 1/2(12.5)(4)
A' = 25 squared unit.
Also,
Area of the rectangle (A) = Lenght(L)×width(w)
A = Lw............ Equation 2
From the question,
If the area of the rectangle is 40% larger than the area of the triangle
Therefore,
A = 1.4A'
A = 1.4(25)
A = 35 squared unit.
Also given: w = 3[tex]\frac{1}{2}[/tex] = 7/2
Substitute into equation 2
35 = L×7/2
7L = 35×2
7L = 70
L = 70/7
L = 10 units
What’s the answer to all 4
Answer:
wdym
Step-by-step explanation:
i dont get it
Step-by-step explanation:
1 reflection 2.rotation 3 reflection 4 rotation
Which inequality is true when the value of u is 10?
u – 3<-6 , u-3>-6 , -u-3>6 , -u-3>-6
Answer:
The answer is: u-3>-6
This is because 10-3=7 and 7>-6
help me with this math question please I'm giving away brainliests
Answer:
[tex]50\:\text{kg water}[/tex]
Step-by-step explanation:
This question implies the constant rate or proportion of water to mass. Therefore, we can set up the following equation:
[tex]\frac{60}{90}=\frac{x}{75},\\\\x=\frac{75\cdot 60}{90}=\boxed{50\:\text{kg water}}[/tex]
Answer:
50 kg
Step-by-step explanation:
90 kg = 60kg
/90 /90
1 kg = 0.667kg
1 kg = 0.667kg
* 75kg * 75kg
75kg = 50 kg
An item costs `x` dollars and then a 20% discount is applied. ----------------------------------- b) Sam says that 20/100x` will not work. Do
Answer:
Step-by-step explanation:
Cost of item = x
Percentage discount = 20%
Discount on item :
20% * x
20/100 * x
0.2x
Cost of item after discount :
Initial cost - discount
x - 0.2x
0.8x
In the figure at right, BC = 10. Find AC.
45°
А
B
Answer:
The answer is AC=45
Step-by-step explanation:
it's an Isosceles triangle
In UVW, the measure of W=90°, WU = 32 feet, and UV = 51 feet. Find the
measure of V to the nearest tenth of a degree.
Answer:
38.9
Step-by-step explanation:
Sin x = opposite/hypotnuse
Sin-1 = 32/51
=38.86
=38.9
If APML - ATRO, find QR.
P
35
T
.
14
14
و - r
R
The value of QR in the triangle is 16 units
What is congruent triangle?Recall that Congruence of triangles represents the similarity of triangles. Two triangles are congruent if their corresponding sides and angles are congruent
The question states that ΔPML≅ΔTRQ
This implies that ML/QR = PM/TR
⇒(7x-9)/2x+2 = 35/14
Cross and multiplying we have
14(7x-9) = 35(2x+2)
=98x-126 = 70x +70
98x-70x = 70+126
⇒28x = 196
Making x the subject of the formula
x= 196/28 = 7
Recall that the side QR = 2x+2
Then by substitution,
2(7) +2
14+2 =16
This therefore keeps the side QR as 16 units.
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Can someone help a bab with geometry?
Solve for y= 1/2x -1
help with this math question
Write the equation of a line that is parallel to x
= 8 and that passes through the point (-3,-2).
Answer:
x=-3
Step-by-step explanation:
Hi there!
1) Determine the slope
Parallel lines always have the same slope. However, the given line x=8 is a vertical line organized in the form x=d, where d is the x-intercept. Therefore, the slope is undefined, and our line will also have an undefined slope.
Now, because this line will also be a vertical line, it will also be organized like:
x=d
2) Determine the x-intercept (d)
Note that all the points a vertical line passes through will have the same x-coordinate. We're given that this line passes through the point (-3,-2), so therefore, the x-intercept will be (-3,0).
Plug this into x=d:
x=-3
I hope this helps!
Leia is setting up 417 417417 toy cars. Each car needs 3 33 batteries to drive. How many batteries does Leia need for her cars? batteries
Answer: 1251
Step-by-step explanation:
Given
Leia is setting up 417 toy cars
Each car needs 3 batteries to drive
So, 417 cars need
[tex]\Rightarrow 417\times 3\\\Rightarrow 1251\ \text{batteries}[/tex]
Thus, 1251 batteries is needed.