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Explanation:
2/3 is the probability of passing a test, so 1/3 is the probability of failing
Note how 2/3 and 1/3 add to 3/3 = 1 to represent 100%
The probability of failing 3 tests in a row is (1/3)^3 = (1/3)*(1/3)*(1/3) = 1/27 assuming each test event is independent from one another.
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Side note: the probability of passing at least one test is 1-1/27 = 26/27 and the probability of passing all three tests in a row is (2/3)^3 = 8/27
Joe’s dad works 45 hours per week. He receives a weekly salary of $850, plus a 3.5% commission on sales over $6,500. Given the functions f(x) = 0.035x and g(x) = x - 6,500 and the fact that Joe’s dad sold enough this week to earn commission, which composition function represents Joe’s dad’s commissions ? (Ques 26)
Answer:
f(x) * g(x)
Step-by-step explanation:
Hours worked per week = 45 hours
Weekly salary = $850 plus ;
3.5% commission on sales above $6,500
Given the functions :
f(x) = 0.035x and
g(x) = x - 6,500
and the fact that Joe’s dad sold enough this week to earn commission, which composition function represents Joe’s dad’s commissions ?
Commission = 3.5 / 100 = 0.035
Let his sales for the week = x ; since his sales exceeds 6,500
Hence, sales on which commission is payable is x - 6,500
Hence, commission for the week :
0.035 × (x - 6,500)
f(x) = 0.035 ; g(x) = (x - 6,500)
Composition function:
f(x) * g(x)
Any places a dot on a coordinate plane (-3,6) she wants to place another dot across the y axis and it must be 8 points away . Where will any place the other dot
Answer:
(5,6)
Step-by-step explanation:
move the dot 8 spaces to the right because that is the across the y axis.
Let f(x)
-4x - 6 and g(x) = 3x + 5. Find (fºg)(-3).
Answer:
Step-by-step explanation:
f(g(-3)
g(-3) = 3(-3) = -9 - 5 = -14
f(-14)= -4(-14) - 6 = 56 - 6 = 50
Gordon types 3,666 words in 47 minutes. Find the unit rate.
Answer:
78 Words per minute
Step-by-step explanation:
A unit rate is simply comparable to an average. Given this, we can say the following:
Unit_Rate = 3666 Words / 47 minutes
Unit_Rate = 78 Words per minute
Cheers.
Field data have indicated that Unit A has a failure rate of 0.0004 failure per hour. Calculate the reliability of the unit for a 150-hour mission.
Answer:
Reliability= 149.94
Step-by-step explanation:
Field data have indicated that Unit A has a failure rate of 0.0004 failure per hour.
Reliability per hour=1- failure rate
Reliability per hour= 1-0.0004
Reliability per hour= 0.9996
Reliability= rate if reliability * number of hours
Rate of reliability= 0.9996 per hour
Number of hours= 150 hours
Reliability= 0.9996*150
Reliability= 149.94
y=x^2-6x-16 in vertex form
Answer:
[tex]y=(x-3)^{2} -25[/tex]
Step-by-step explanation:
The standard form of a quadratic equation is [tex]y=ax^{2} +bx+c[/tex]
The vertex form of a quadratic equation is [tex]y=a(x-h)^{2} +k[/tex]
The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.
To find the h-value of the vertex, you use the following equation:
[tex]h=\frac{-b}{2a}[/tex]
In this case, our quadratic equation is [tex]y=x^{2} -6x-16[/tex]. Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.
[tex]h=\frac{-b}{2a}[/tex] ⇒ [tex]h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3[/tex]
Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is [tex]y=x^{2} -6x-16[/tex]
[tex]y=x^{2} -6x-16[/tex] ⇒ [tex]y=(3)^{2} -6(3)-16[/tex] ⇒ [tex]y=9-18-16[/tex] ⇒ [tex]y=-25[/tex]
This y-value that we just found is our k-value.
Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: [tex]y=a(x-h)^{2} +k[/tex]
a: 1
h: 3
k: -25
[tex]y=(x-3)^{2} -25[/tex]
Hope this helps!
The radius of a circle measures 8 yd. What is the circumference of the circle? Use 3.14 for pi, and do NOT round your answer. Be sure to include the correct unit in your answer.
Answer:
The answer is
50.24 ydStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius
From the question
r = 8 yd
π = 3.14
Substitute the values into the above formula and solve
Circumference = 2(8)(3.14)
We have the final answer as
50.24 ydHope this helps you
A rectangle's perimeter is 92 ft. Its length is 5 ft shorter than two times of its width. Use an equation
to find the rectangle's length and width.
What is the volume of a sphere that has
a radius of 11.5 units?
Answer:
6370.63 is the volume
Step-by-step explanation:
V=4
3πr3=4
3·π·11.53≈6370.6263
use the figure to determine the intersection of planes EAB and EFG
FG
EA
EF
no intersection
Answer:
Option (3). EF
Step-by-step explanation:
From the figure attached,
Plane defined by EAB can be represented by the face EABF of the square prism also.
Similarly, plane EFG can be represented by the face EFGH of the prism.
Now these sides EABF and EFGH are joining each other at the edge EF of the cuboid.
Therefore, intersection of the given planes is EF.
Option (3) will be the answer.
(b - 11) / -29 = -18
Answer:
b=22
Step-by-step explanation:
1 Remove parentheses.
b-11-29=-18b−11−29=−18
2 Simplify b-11-29b−11−29 to b-40b−40.
b-40=-18b−40=−18
3 Add 4040 to both sides.
b=-18+40b=−18+40
4 Simplify -18+40−18+40 to 2222.
b=22b=22
3.7m∧5÷3.7m∧2 How do I complete this expression?
The average ocean depth is 3.7 × 103 m, and the area of the oceans is 3.6 × 1014 m2. What is the total volume of the ocean in liters? (One cubic meter contains 1000 liters. Round your answer to one decimal place.)
Need help with this question. Will crown brainliest
a/x + b/x =c, c ne0
i’ll give more points
Answer:
x = (a +b)/c
Step-by-step explanation:
Perhaps you want to solve for x.
Multiply by x:
a + b = cx
x = (a +b)/c . . . . . divide by c
Solve for v. -8 +5v=-33
Answer:
v = -5
Step-by-step explanation:
Step 1: Write out equation
-8 + 5v = -33
Step 2: Add 8 on both sides
-8 + 8 + 5v = -33 + 8
5v = -25
Step 3: Divide both sides by 5
5v/5 = -25/5
v = -5
Answer:
Solve
-8 +5v=-33
So 5v=-33+8
(-8 became 8 because we brought it back to the other side to have the v 《5v》 alone and the numbers alone )
5v= -25
So v=-25/5
We simplify -25/5
v=-5
Need help on this question anyone please!
Answer:
f(3)=2
Step-by-step explanation:
To find f(3), we simply need to find the ordered pair at x=3.
From the graph, we can see that the ordered pair at x=3 is (3,2).
Thus, f(3)=2.
And we're done!
Introduction to interval notation
Finding Domain and range
If costheta=4/5 then what is sec^2theta
Answer:
[tex]\sec^2(\theta)=\frac{25}{16}[/tex]
Step-by-step explanation:
Recall what the relationship between cosine and secant:
[tex]\sec(\theta)=\frac{1}{\cos(\theta)}[/tex]
In other words, secant is the reciprocal of cosine.
So, if we know cosine, we only need to find its reciprocal to find secant.
We are given that cosine is:
[tex]\cos(\theta)=\frac{4}{5}[/tex]
Then secant must be:
[tex]\sec(\theta)=\frac{5}{4}[/tex]
So:
[tex]\sec^2(\theta)=(\frac{5}{4})^2[/tex]
Square:
[tex]\sec^2(\theta)=\frac{25}{16}[/tex]
And we're done!
I am thinking of a number... 1. The number is greater than 6 x 4.2. The number is even. 3. The number is a multiple of 3. 4. The
difference of the digits is four. 5. What is my number?
Ready? Enter your answer here.
Answer:
48
Step-by-step explanation:
48 is greater then 6×4.2
It's even
It's a multiple of 3
the difference is 4
Write 20% as a decimal.
Answer:
0.2
Steps:
To convert to a decimal, divide the percent number by 100.
So, 20 divided by 100 = 0.2
Summarize the data by filling in the frequency (to the nearest whole number), the relative frequency (3 decimals), and the percent frequency (1 decimal) values below. Class Frequency Relative Frequency Percent Frequency 12-14 ( ) ( ) ( ) 15-7 ( ) ( ) ( ) 18-20 ( ) ( ) ( ) 21-23 ( ) ( ) ( ) 24-26 ( ) ( ) ( ) Total ( ) ( ) ( )
Answer:
The answer is below
Step-by-step explanation:
The relative frequency is the proportion of a class or interval within a category. It is represented by the formula:
Relative frequency = frequency / total frequency
The percent frequency is the relative frequency expressed in percentage, it is given by the formula:
Percent frequency = Relative frequency × 100%
Using the formulas above, the table is filled:
The total frequency = 39
Class Frequency Relative frequency Percent frequency
12 - 14 2 2/39 = 0.0513 0.0513 × 100% = 5.13%
15 - 17 8 8/39 = 0.2051 0.2051 × 100% = 20.51%
18 - 20 11 11/39 = 0.2821 0.2821 × 100% = 28.21%
21 - 23 9 9/39 = 0.2308 0.2308 × 100% =23.08%
24 - 26 9 9/39 = 0.2308 0.2308 × 100% =23.08%
Class Frequency Relative frequency Percent frequency
12 - 14 2 0.0513 5.13%
15 - 17 8 0.2051 20.51%
18 - 20 11 0.2821 28.21%
21 - 23 9 0.2308 23.08%
24 - 26 9 0.2308 23.08%
3/4+5/36+7/144+.......+17/5184+19/8100
(a)0.95 (b)1 (c) 0.99 (d)0.98
Answer:
B) 1
Step-by-step explanation:
All I did was simplify the equation
1509/1600
(Decimal: 0.943125)
HOPE THIS HELPS!!!! :)
<333333333333
8x-9x = 150/10 helpp
Answer:
x =-15
Step-by-step explanation:
[tex]8x-9x = \frac{150}{10} \\\\\mathrm{Add\:similar\:elements:}\:8x-9x=-x\\-x=\frac{150}{10}\\\\\mathrm{Divide\:the\:numbers:}\:\frac{150}{10}=15\\-x=15\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{15}{-1}\\\\Simplify\\x=-15[/tex]
Please answer I need this asap
Answer:
84
Step-by-step explanation:
The equation that models this situation is 1110 = 15x + 150 where x = cameras sold (note that this doesn't include the first 20 cameras, we'll add those on at the end). Let's solve for x!
1110 = 15x + 150
960 = 15x
x = 64 so the answer is 64 + 20 = 84 cameras.
at an average speed of 3 feet per second. Fuad records the distances and times in a table like the one shown below at this rate, how long will it take the car to travel 21 feet?
Answer:
7 Sec
Step-by-step explanation:
Answer:
7.0 sec
Step-by-step explanation:
100 POINTS!! A company has 400 employees. There are 300 female employees. There are 80 employees who are under the age of 25. The probability of randomly selecting an employee who is female or is under the age of 25 is 85%. What is the probability of randomly selecting an employee who is female and under the age of 25?
95%
10%
20%
75%
15%
Answer:
probability of randomly selecting an employee who is female and under the age of 25= 0.15
In percentage= 15%
Step-by-step explanation:
There are 300 female employees. There are 80 employees who are under the age of 25
Probabilty of choosing a female employees= 300/400
Probabilty of choosing a female employees= 0.75
Probabilty of choosing an employees under the age of 25
= 80/400
Probabilty of choosing an employees under the age of 25
= 0.2
probability of randomly selecting an employee who is female and under the age of 25= 0.2*0.75
probability of randomly selecting an employee who is female and under the age of 25= 0.15
In percentage= 0.15*100
In percentage= 15%
Find the approximate side length of a square game board with an area of 125in2.
Answer: 11.18
Step-by-step explanation: To find one side of a square, you need to square root it’s area. The square root of 125 is 11.18.
Find the following integral.
Integrate x + 5/x^2 +10x +26 dx
Answer:
[tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsDefinite/Indefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx[/tex]
Step 2: Integrate Pt. 1
Set variables for u-substitution.
Set u: [tex]\displaystyle u = x^2 + 10x + 26[/tex][u] Differentiate [Addition/Subtraction, Basic Power Rule]: [tex]\displaystyle du = 2x + 10 \ dx[/tex]Step 3: Integrate Pt. 2
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{2(x + 5)}{x^2 + 10x + 26}} \, dx[/tex][Integrand] Expand: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{2x + 10}{x^2 + 10x + 26}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{1}{u}} \, du[/tex][Integral] Logarithmic Integration: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}ln|u| + C[/tex]Back-Substitute: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}ln|x^2 + 10x + 26| + C[/tex]Simplify: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Ashley Traveled 10 miles north, then 8 miles east, then 9 miles south on her boat
Jackson mows 1/3 of his neighbors lawn in 1/6 of an hour. At this rate, how many lawns of the same size could he mow in one hour?