Answer:
A mutually exclusive event is when there are two events that can occur, such as flipping a coin, either it will be a head or a tail. Hence, both the events here are mutually exclusive.
An independent event is termed as an event that occurs without being affected by other events. The happening of one event has nothing to do with the happening of the other and there is no cause-effect between the two.
Find f(3) given f(x) = -3x3 + 2x2 + 24
Answer:
-39
Step-by-step explanation:
What is
88x3-7+198-34x15+76-126=
-105
Multiply first, then subtract, then add.
Answer: the answer would be -105.
Please answer this and show the work/explain for me
2/7m - 1/7 = 3/14
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use α = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?
Answer:
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
The possible proportion of patrons that do borrow books from the Owensboro Library is 0.82.
Step-by-step explanation:
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. Test if the proportion is higher in Owensboro, KY.
At the null hypothesis, we test if the proportion is of at most 0.67, that is:
[tex]H_0: p \leq 0.67[/tex]
At the alternative hypothesis, we test if the proportion is of more than 0.67, that is:
[tex]H_1: p > 0.67[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.67 is tested at the null hypothesis:
This means that [tex]\mu = 0.67, \sigma = \sqrt{0.67*0.33}[/tex]
The class randomly selected 100 patrons and found that 82 borrowed books.
This means that [tex]n = 100, X = \frac{82}{100} = 0.82[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.82 - 0.67}{\frac{\sqrt{0.67*0.33}}{\sqrt{100}}}[/tex]
[tex]z = 3.19[/tex]
P-value of the test and decision:
The p-value of the test is the probability of a finding a sample proportion of 0.82 or above, which is 1 subtracted by the p-value of z = 3.19.
Looking at the z-table, z = 3.19 has a p-value of 0.9993.
1 - 0.9993 = 0.0007
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
What is the possible proportion of patrons that do borrow books from the Owensboro Library?
The sample proportion of 0.82.
Plzzz I’m giving a away 25 points
Answer:
sin ß = opposite / hypotenuse
sin45° = x / 4√2
Cross multiply
x = sin 45° × 4√2
x = √2/2 × 4√2
x = 4 × √2 ×√2 / 2
x = 4 × 2 / 2
x = 8 / 2
x = 4
The number of people attending graduate school at a university may be
modeled by the quadratic regression equation y = 8x2 - 40x+6, where x
represents the year. Based on the regression equation, which year is the best
prediction for when 1206 people will attend graduate school?
A. Year 15
B. Year 18
C. Year 24
D. Year 20
Answer:
15 years
Step-by-step explanation:
Given the quadratic regression model:
y = 8x² - 40x+6 ; where
y = Number of people attending graduate school ;
x = number of years
The value of x when y = 1206
The equation becomes :
1206 = 8x² - 40x+6
1206 - 6 = 8x² - 40x
1200 = 8x² - 40x
Divide through by 8
150 = x² - 5x
x² - 5x - 150 = 0
x² - 15x + 10x - 150 = 0
x(x - 15) + 10(x - 15)
x - 15 = 0 or x + 10 = 0
x = 15 or x = - 10
Number of years can't be negative,
Hence, x = 15 years
how do you change 79/8 to a decimal
Answer:
Divide 79 by 8
Step-by-step explanation:
79/8
= 9.875
time in months it would take for a $1500 dollar investment in a TFSA to grow to $1545 if the simple interest at a rate paid was 2% per annum.
It would take 17 months and 14 days for the investment to grow to $1545.
To determine the time in months it would take for a $ 1500 dollar investment in a TFSA to grow to $ 1545 if the simple interest at a rate paid was 2% per annum, the following calculation must be performed:
First, you must obtain 2% of 1545 to determine the interest generated per year.
1545 x 2/100 = X 30.9 = XThen, a cross multiplication must be carried out considering the number of months it took to generate said interest, and compare it with the interest that arises from the subtraction of 1545 - 1500, that is, 45.
30.9 = 1245 = X45 x 12 / 30.9 = X540 / 30.9 = X17.47 = X 1 = 300.47 = X14 = XTherefore, it would take 17 months and 14 days for a $ 1500 dollar investment in a TFSA to grow to $ 1545.
Learn more about interest in https://brainly.com/question/19903178.
A company pays $20 per hour for up to 8 hours of work, and $30 per hour for overtime hours (hours beyond 8 hours). For up to 8 hours worked, the equation for total pay (y) for hours worked (x) is y = 20x. For over 8 hours worked, what is the equation for total pay (y) as a function of total hours worked (x)?
Answer: y = 30x
Step-by-step explanation:
Because we are talking about over 8 hours. The question states that you get 30$ per hour for overtime hours. That means if you work over 8 hours your dollars per hour increases to 30. So because the amount of dollars increases to 30 you can infer that all you have to do is make the same equation as the 20 dollar's per hour equation. Except you put 30 making it y = 30x.
Suppose y varies inversely with x, and y = 32 when x = 4. What is the value of y when x = 8?
a. 1/8
b. 64
c. 16
d. 8
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Answer:
16
Step-by-step explanation:
Inverse variation is of the form
xy = k where k is a constant
x=4 and y = 32
4*32 = k
128 = k
xy = 128
Let x = 8
8y = 128
Divide each side by 8
8y/8 = 128/8
y =16
The retail of a price of an LCD TV was $7000 what was the original price before the GST of 10% was added?
Answer:
$636.36
Step-by-step explanation:
7000 = 110% of total cost
Try to get it to 100 percent
700/11 = 63.(63)
63.(63)*10= 636.36
lyng
whose zeros and
Zeros: - 4, 4, 8; degree: 3
Need this in polynomial form
What is the height of a room which is 8m long, 6m wide and contains 144 meters cube of air?
Cho A=( căn x -4x /1-4x -1) : (1+2x/1-4x -2căn x/ 2căn x -1 -1)
Answer:
0.85714285714286 x 100 = 85.7143%.
Step-by-step explanation:
Solve for x
6x + 11= - (6x + 5)
Answer:
x = -4/3
Step-by-step explanation:
6x + 11 = -6x - 5
12x = -16
x = -4/3
Answer:
x = -4/3
Step-by-step explanation:
6x + 11= - (6x + 5)
Distribute the minus sign
6x+11 = -6x-5
Add 6x to each side
6x+11 +6x = -6x-5+6x
12x+11 = -5
Subtract 11 from each side
12x+11-11 = -5-11
12x = -16
Divide by 12
12x/12 = -16/12
x = -4/3
Use AABC to find the value of sin B.
Answer:
35/37
Step-by-step explanation:
sin(B)=(AC)/(AB) = 35/37
For the right angle, find the missing quantity indicated below the figure.
Answer:
The Answer is 28.........
In each figure below, find m<1 and m<2 if a is parallel to b. You don't have to show work.
please help i need this by tonight will give brainliest
Answer:
m <5 = 71 degrees.
m <8 = 109 degrees.
Each side of a regular polygon is 3.2 cm in length. The perimeter of the polygon is 19.2 cm. How many sides does the polygon have? What is the name of the polygon?
Answer:
The polygon consists of 6 sides and the given polygon is a regular hexagon.
Step-by-step explanation:
The definition of perimeter is the total measure of the side lengths of a polygon. If the polygon said is regular, it means the polygon has equal sides and equal angles.
So the perimeter of a regular polygon is given by the formula:
P = (length of one side) x (number of sides)
In this case, the perimeter of the polygon is 19.2 cm and one side is equal to 3.2 cm.
DIVIDE (use the formula but in division to maintain a proportonal relationship):
19.2 ÷ 3.2 = 6
You could alsk check if its correct using the formula:
19.2 = 3.2 x 6 (TRUE)
A 6 sided regular polygon is known as a HEXAGON.
Hope this helps!
A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 11.3. In his class, an "A" is any exam score of 90 or higher. This quarter she has 22 students in her class. What is the probability that 6 students or more will score an "A" on the final exam?
prob =
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
---------------
For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.
Additionally, to find the proportion of students who scored an A, the normal distribution is used.
----------------
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success.
----------------
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , 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.
----------------
Proportion of students that scored an A:
Scores have a mean of 79 and a standard deviation of 11.3, which means that [tex]\mu = 79, \sigma = 11.3[/tex]
Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 79}{11.3}[/tex]
[tex]Z = 0.97[/tex]
[tex]Z = 0.97[/tex] has a p-value of 0.8340.
1 - 0.8340 = 0.166
The proportion of students that scored an A is 0.166.
----------------
Probability that 6 students or more will score an "A" on the final exam:
Binomial distribution.
22 students, which means that [tex]n = 22[/tex]
The proportion of students that scored an A is 0.166, which means that [tex]p = 0.166[/tex]
The probability is:
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184[/tex]
[tex]P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807[/tex]
[tex]P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687[/tex]
[tex]P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239[/tex]
[tex]P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117[/tex]
[tex]P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517[/tex]
Then
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551[/tex]
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449[/tex]
Thus
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
For a problem that used the normal distribution, you can check https://brainly.com/question/15181104, and for a problem that used the binomial distribution, you can check https://brainly.com/question/15557838
sketch the graph of y=x(x-6)^
Answer:
i have attached pic of the graph
i hope this helps you
Given the following coordinates complete the glide reflection transformation.
9514 1404 393
Answer:
A"(-1, -2)B"(4, 0)C"(6, -3)Step-by-step explanation:
The reflection over the x-axis is ...
(x, y) ⇒ (x, -y)
The shift left 3 units is ...
(x, y) ⇒ (x -3, y)
So, the two transformations together will be ...
(x, y) ⇒ (x -3, -y)
A(4, 2) ⇒ A"(1, -2)
B(7,0) ⇒ B"(4, 0)
C(9, 3) ⇒ C"(6, -3)
give that 1/x+2/y=1/2, express y in terms of x and 2
9514 1404 393
Answer:
y = 4x/(x -2)
Step-by-step explanation:
Subtract 1/x
2/y = 1/2 -1/x
Combine terms
2/y = (x-2)/(2x)
Cross multiply
4x = y(x -2)
Divide by the coefficient of y
y = 4x/(x -2) . . . . simplest
y = 2^2/(x -2) . . . . in terms of x and 2
You are considering the services of three different employment agencies, all of which can get you a job that starts at $2,000 a month. Agency A charges 50 percent of the first month's gross salary. Agency B charges 10 percent of your monthly salary for the first six months. Agency C charges a $100 up-front fee and a flat fee of $500 when you are placed. Compare the three choices. Which of these offers the least expensive overall fee?
Answer:
Agency C offers the least expensive overall fee
Step-by-step explanation:
Alone from gross salary, you would make 24000 a year.
Agency A
24000 - ( 2000 x 0.5)
= 23,000
$1000 fee
Agency B
24000 - ( 2000 x 0.1 ) x 6
= 24000 - 200 x 6
= 24000 - 1200
= 22,800
$1200 fee
Agency C
24000 - (500 + 100)
= 24000 - 600
= 23,400
$600 fee
A 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm. What is the mass density, of the polymer in kg/m3?
The mass density in kg/m3 will be - 15 x [tex]10^{-2}[/tex] Kg/m3.
We have a 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm.
We have to determine its mass density in kg/m3.
What is Mass density ?The amount of mass per unit volume present in the body is called its mass density.
According to question, we have -
Length of polymer cable = 100.0 m
diameter of polymer cable = 0.4 cm = 0.004 m
Therefore, its radius = 0.002 m
The mass density of the wire will be -
[tex]\rho =\frac{m}{\pi r^{2} l}[/tex]
[tex]\rho[/tex] = [tex]\frac{1885}{3.14 \times0.002 \times 0.002 \times 100 }[/tex]
[tex]\rho = \frac{1885}{0.001256}[/tex] = 1500796.1 g/m3
1 Kg = 1000g
1g = 1/1000kg
1500796.1g = 1500.7 Kg = 15 x [tex]10^{-2}[/tex] Kg
Therefore, mass density = 15 x [tex]10^{-2}[/tex] Kg/m3
Hence, the mass density in kg/m3 will be - 15 x [tex]10^{-2}[/tex] Kg/m3.
To solve more questions on mass density, visit the link below -
https://brainly.com/question/4893600
#SPJ2
5 people cleared a plot of land in 15 days. How many people would I need to hire to clear three times that plot in 5 days?
PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)
–6
3
–59
26
Answer:
1st option
Step-by-step explanation:
Evaluate f(- 5) then substitute the value obtained into g(x)
f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then
g(3) = - 4(3) + 6 = - 12 + 6 = - 6
ive gotten it wrong like 4 times n i cannot figure it out pls help
Answer:
x = 74.74 m
Step-by-step explanation:
you need simple trigonometry to solve it
cosine of an angle is the ratio of the adjacent side to the hypotenuse
cos(42.2) is about 0.74
so X / Hypotenuse = 0.74
we know hypotenuse is 101 m
X / 101 = 0.74
x = 74.74 m
hope this helped!
Four friends go to the movies. How many different ways can they sit in a row?
Answer:
120 ways
..................
Answer:
24
Step-by-step explanation:
4 friends
1st seat: 4 different people could sit here
Now there are 3 friends left
2nd seat: 3 different people could sit here
Now there are 2 friends left
3rd seat: 2 different people could sit here
Now there are 1 friends left
4th seat: 1 different people could sit here
4*3*2*1
24 ways
If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1/R = 1/R1 + 1/R2 . If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast is R changing when R1 = 60 Ω and R2 = 80 Ω? (Round your answer to three decimal places.)
The rate of change of R with time in the given equation is 0.004 ohm/s
Given parameters:
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{dR_1}{dt} = 0.3 \ ohm/s\\\\\frac{dR_2}{dt} = 0.2 \ ohm/s\\\\R_1 = 60 \ ohms\\\\R_2 = 80 \ ohms[/tex]
To find:
The rate of change of R with time in the given equation.First determine the value of R from the given equation;
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{1}{R} = \frac{1}{60} + \frac{1}{80} \\\\\frac{1}{R} = \frac{4 + 3}{240} \\\\\frac{1}{R} = \frac{7}{240} \\\\R = \frac{240}{7} = 34.286 \ ohms[/tex]
Finally, to determine the rate of change of R, differentiate the given equation.
[tex]\frac{-1}{R^2} \frac{dR}{dt} = \frac{-1}{R_1^2} \frac{dR_1}{dt} - \frac{1}{R_2^2} \frac{dR_2}{dt} \\\\\frac{1}{R^2} \frac{dR}{dt} = \frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt}\\\\\frac{dR}{dt} = R^2(\frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt})[/tex]
[tex]\frac{dR}{dt} = 34.286(\frac{1}{(60)^2} \times 0.3 \ \ \ + \ \ \ \frac{1}{(80)^2} \times 0.2)\\\\\frac{dR}{dt} = 34.286(8.333 \times 10^{-5} \ \ \ + \ \ \ 3.125 \times 10^{-5})\\\\\frac{dR}{dt} = 34.286(11.458 \times 10^{-5})\\\\\frac{dR}{dt} = 0.00393\\\\\frac{dR}{dt} \approx 0.004 \ ohm/s[/tex]
Thus, from the given equation the rate of change of R with time is 0.004 ohm/s
Learn more here: https://brainly.com/question/14796851
Answer:
the verified answer is wrong.
Step-by-step explanation:
OP forgot to square R (34.286)
