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Answer:
(f-g)(x) = 4x^3 +7x^2 -6x +1
Step-by-step explanation:
(f -g)(x) = f(x) -g(x)
= (4x^3 +7x^2 -2x -1) -(4x -2)
= 4x^3 +7x^2 +(-2-4)x +(-1+2)
(f -g)(x) = 4x^3 +7x^2 -6x +1
No more than one state of nature can occur at a given time for a chance event. This indicates that the states of nature are defined such that they are
a. conservative events.
b. mutually exclusive.
c. independent outcomes.
d. collectively exhaustive.
Answer:
b. mutually exclusive.
Step-by-step explanation:
The given description is an illustration of mutually exclusive events.
Take for instance, when you roll a die;
It is impossible to have an outcome of 2 and 6 at the same time; these means that 2 and 6 are mutually exclusive.
In a nutshell, when two or more sates of events/states of nature can not happen at the same time; such events/states of nature are mutually exclusive.
which linear inequality represents the graph below?
A. y < -1/4x-4
B. y < 4x-4
C. y < -1/4x+4
D. y < -4x+4
what is the solution to the system of equations below 2x - y = 10 and y=1/2 x+5
Answer:
(10, 10 )
Step-by-step explanation:
Given the 2 equations
2x - y = 10 → (1)
y = [tex]\frac{1}{2}[/tex] x + 5 → (2)
Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)
2x - ([tex]\frac{1}{2}[/tex] x + 5) = 10 ← distribute parenthesis on left side by - 1
2x - [tex]\frac{1}{2}[/tex] x - 5 = 10
[tex]\frac{3}{2}[/tex] x - 5 = 10 ( add 5 to both sides )
[tex]\frac{3}{2}[/tex] x = 15 ( multiply both sides by 2 to clear the fraction )
3x = 30 ( divide both sides by 3 )
x = 10
Substitute x = 10 into (2) and evaluate for y
y = [tex]\frac{1}{2}[/tex] (10) + 5 = 5 + 5 = 10
solution is (10, 10 )
Hello, please help me!!
Answer:
0.14
Step-by-step explanation:
P(A|B) asks for the probability of A, given that B has happened. This is equal to the probability of A and B over the probability of B (see picture)
Here, the question is asking if someone is taking the bus given that they are a senior.
The probability of someone being a senior and taking the bus is 5/100, or 0.05 . The probability of someone being a senior is 35/100, or 0.35
Our answer is then 0.05/0.35 = 1/7 = 0.14
Help!! Picture included
Answer:
The answer is the last option- the fourth root of 16x^4.
Step-by-step explanation:
(16x^4)^(1/4) = 2*abs(x).
Whenever you are dealing with a square root of a variable, if you have an even root and get out an odd power, you're going to need to always include an absolute value.
the sum of the first ten terms of an arithmetic progression consisting of positive integers is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960
Answer:
The correct answer is = 15.
Step-by-step explanation:
Formula:
The sum of the first n terms of an arithmetic progression with first term a and constant difference d is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d[/tex]
using this formula in this problem
Solution:
The sum of the first ten terms is
[tex]S_{10}=\dfrac{10}{2}[2a+(10-1)d[/tex]
[tex]S_{10}=5(2a+9d)[/tex]
The sum of the 20th, 21st, and 22nd terms is three times the 21st term:
[tex]3a_{21}=3(a+(21-1)d)[/tex]
[tex]3a_{21}=3(a+20d)[/tex]
[tex]3a_{21}=3a+60d[/tex]
The problem then tells us
[tex]S_{10}=3a_{21}[/tex]
[tex]10a+45d=3a+60d[/tex]
[tex]7a=15d[/tex]
there are only positive integers and the first term a is less than 20 as given. Since 7 and 15 have no common factor, the only explanation of the requirements is a = 15 and d = 7. So the progression is
then, 15, 22, 29, 36, ...
The problem says to find the number of terms n for which the sum is 960:
putting value in the formula
[tex]30n+7n^{2}-7n=1920\\7n^{2}+23n-1920=0[/tex]
solving quadratic will give n = 15
thus, the correct answer is 15.
In parallelogram ABCD, line AC is congruent to line BD. Is ABCD a rectangle?
A. Yes
B. No
C. Cannot be determined
9514 1404 393
Answer:
A. yes
Step-by-step explanation:
The diagonals of a rectangle are congruent and bisect each other.
The diagonals of a parallelogram bisect each other. If they are also congruent, then the parallelogram is a rectangle.
Answer:
Yes.
Step-by-step explanation:
Press option yes
4. The average salary for public school teachers for a specific year was reported to be $39,385. A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975. Is there sufficient evidence at the a _ 0.05 level to conclude that the mean salary differs from $39,385
Answer:
The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385
Step-by-step explanation:
The average salary for public school teachers for a specific year was reported to be $39,385. Test if the mean salary differs from $39,385
At the null hypothesis, we test if the mean is of $39,385, that is:
[tex]H_0: \mu = 39385[/tex]
At the alternative hypothesis, we test if the mean differs from this, that is:
[tex]H_1: \mu \neq 39385[/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.
39385 is tested at the null hypothesis:
This means that [tex]\mu = 39385[/tex]
A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975.
This means that [tex]n = 50, X = 41680, \sigma = 5975[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{41680 - 39385}{\frac{5975}{\sqrt{50}}}[/tex]
[tex]z = 2.72[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample mean differs from 39385 by at least 2295, which is P(|Z| > 2.72), which is 2 multiplied by the p-value of Z = -2.72.
Looking at the z-table, Z = -2.72 has a p-value of 0.0033
2*0.0033 = 0.0066
The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385
PLEASE HELP SOON Find the value of x. Round to the nearest tenth. 27° х 34° 11 X = ? [?] 9 Law of Sines: sin A sin C sin B b a Enter
The picture of the problem has been attached below :
Answer:
13.5
Step-by-step explanation:
Applying the sine rule to solve for x
SinA /a = SinB / b = SinC/ c
Sin 34 / x = Sin 27/11
Cross multiply :
11 * sin34 = x * sin 27
6.1511219 = 0.4539904x
Divide both sides by 0.4539904
6.1511219/0.4539904 = x
13.549 = x
x = 13.5
Please help solve and explain this
can you put the whole question here
3z+8=12+3x-z
I need help someone help me
Answer:
z=3x/4+1 x=4z/3-4/3
Step-by-step explanation:
9.
For a normal distribution with mean 20 and standard deviation 5, approximately what percent of
the observations will be between 5 and 35?
A. 50%
B. 68%
C. 95%
D. 99.7%
Answer: D. 99.7%
Step-by-step explanation:
Scores that lies within the first deviation(1σ) =
(20 - 5) to (20 + 5) → 15 to 25
Scores that lies within the second deviation(2σ) =
(20 - 5 - 5) to (20 + 5 + 5) → 10 to 30
Scores that lies within the third deviation(3σ) =
(20 - 5 - 5 - 5) to (20 + 5 + 5 + 5) → 5 to 35
As shown by the distribution graph below, 99.73% of the scores lies within the third deviation(3σ).
In point estimation a. data from the sample is used to estimate the population parameter. b. the mean of the population equals the mean of the sample.
Answer:
a. data from the sample is used to estimate the population parameter.
Step-by-step explanation:
Given
Point estimation
Required
The true statement
Point estimation literally means taking data from the sample to estimate the corresponding population parameter
For instance:
Sample mean estimates population mean
Sample standard deviation estimates population standard deviation
Sample variance estimates population variance
Hence;
(a) is correct
what's the answer to this
Answer:
the volume = 1152cm^2
Step-by-step explanation:
> The volume of cylinder =4 spheres
> Volume of sphere = v= 4/3πr³
> radius =6cm
volume of 4 spheres =
[tex]v \: = 4 \times \frac{4}{3} \times \pi \times {6}^{3} \\ \\ v = 1152cm {2} [/tex]
Answer:
the unused volume is 18095,57cm cubed
For which of these research situations would linear regression be the best statistical test to perform?
A) independent variable = city of residence
dependent variable = miles driven per week
B) independent variable = gender
dependent variable = salary
C) independent variable = age
dependent variable = reaction time in milliseconds
D) independent variable = college major
dependent variable = political affiliation
Answer:
C) independent variable = age
dependent variable = reaction time in milliseconds
Step-by-step explanation:
The linear regression statistical test is best used for research experiment where there is a single dependent and one independent variable whjre both variables are numeric. In the given options above, the city of residence, gender, college major and political affiliation are all possible categorical variables and age, salary, miles driven and reaction time are all numerical variables. Hence, the best situation in which to use linear regression is a test where both the independent and dependent variables are either age, salary, reaction time or miles driven.
What is the Value of the expression 1/4(c cubed + d squared) when c = -4 and d = 10
Answer: 9
Step-by-step explanation:
[tex]\frac{1}{4} (c^{3}+d^{2})[/tex]
c = -4d = 10Substitute in the values into the expression:
[tex]\frac{1}{4} ((-4)^{3}+10^{2})\\\\=\frac{1}{4}(-64+100)\\\\=\frac{1}{4}(36)\\\\=\frac{36}{4} =9[/tex]
Multiply 3x (2x - 1)
Answer:
6x^2 - 3x
[tex]6x^2-3x[/tex]
Step-by-step explanation:
3x (2x-1)
multiply 3x by 2x -> 6x^2
multiply 3x by -1 -> -3x
Answer:
The answer is [tex]6x^{2} -3x[/tex].
Step-by-step explanation:
To solve for the answer, start by using the distributive property. The distributive property is a property of multiplication used in addition and subtraction and states that two or more terms in addition or subtraction with a number are equal to the addition or subtraction of the product of each of the terms with that number.
The distributive property for this problem will look like [tex](3x*2x)+(3x*-1)[/tex], and when the problem is simplified, it will look like [tex]6x^{2} -3x[/tex]. The final answer is [tex]6x^{2} -3x[/tex].
the poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities.A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron.Formulate the linear programming model for this situation.
Answer:
- Min Z = $400C + $200A
Step-by-step explanation:
The linear programming model deals with the minimization or maximization of a linear function of several variables and inequalities. This method assists the industries in minimizing costs and maximizing production.
In the given situation,
The Linear programming model would be:
Min Z = $400C + $200 A
which is based on:
150 mg of vitamin K in corn C + 250 mg of vitamin K in AlfaAlfa ≥ 500
75 mg of iron in Corn + 50 mg of iron in AlfaAlfa ≥ 400
∵ C, A ≥ 0
Thus, the equation would be,
Min Z = $400C + $200 A
Private nonprofit four-year colleges charge, on average, $26,208 per year in tuition and fees. The standard deviation is $7,040. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(
26208
Correct,
7040
Correct)
b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 22,924 per year.
c. Find the 60th percentile for this distribution. $
(Round to the nearest dollar.)
Answer:
#########
Step-by-step explanation:
i’ll give brainliest to the right answer
Answer:
First one , 0.0000805
Step-by-step explanation:
With negative exponents the decimal is moved to the left the amount of the exponent. The spaces are filled with zeros.
With positive exponents the opposite occurs. The decimal moves to the right.
Solve using the elimination method. 2x + 7y = 36
6x - 7y = - 60
Answer:
[tex]x=-3[/tex]
[tex]y=6[/tex]
Step-by-step explanation:
Elimination method:
[tex]2x+7y=36[/tex]
[tex]6x-7y=-60[/tex]
Add these equation to eliminate y:
[tex]8x=-24[/tex]
Then solve [tex]8x=-24[/tex] for x:
[tex]8x=-24[/tex]
[tex]\frac{8x}{8} =\frac{-24}{8}[/tex]
[tex]x=-3[/tex]
Add the value of x to solve y:
[tex]2x+7y=36[/tex]
Substitute [tex]-3[/tex] for x in [tex]2x+7y=36[/tex]
[tex](2)(-3)+7y=36[/tex]
[tex]7y-6=36[/tex]
[tex]7y=36+6[/tex]
[tex]7y=42[/tex]
[tex]y=42/7\\[/tex]
[tex]y=6[/tex]
{ [tex]x=-3[/tex] and [tex]y=6[/tex] }
hope this helps....
Which of these tables represents a function
Answer:
W and X
Y and Z arent functions because some of their domains (x value) have different inputs. Each domain can only have one input.
Which equation represents the line that passes through points (1, –5) and (3, –17)?
Answer:
y = -6x + 1
Step-by-step explanation:
y = mx + b
b = slope = (-5 - (-17))/(1 - 3) = 12/(-2) = -6
y = -6x + b
-5 = -6(1) + b
b = 1
y = -6x + 1
Answer:
[tex]y=-6x+1[/tex]
Step-by-step explanation:
The linear equation with slope m and intercept c is given as follows:
[tex]y=mx+c[/tex]
The formula for slope of line with points [tex](x_{1} ,y_{2} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] can be expressed as,
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
The line passes the points that are [tex](1,-5)[/tex] and [tex](3,-17)[/tex]
The slope of the line can be obtained as follows:
[tex]m=\frac{-17-(-5)}{(3)-1}[/tex]
[tex]m=\frac{-12}{2}[/tex]
[tex]m=-6[/tex]
The slope of the line is [tex]-6[/tex]
The line passes through the point [tex](3,-17)[/tex]
Substitute 3 for x, - 6 for m and -17 for y in equation [tex]y=mx+c[/tex] to obtain the value of c.
[tex]-17=-6(3)+c[/tex]
[tex]-17=-18+c[/tex]
[tex]-17+18=c[/tex]
[tex]1=c[/tex]
The equation is [tex]y=-6x+1[/tex]
Hence, the equation of the line that passes through the points [tex](1,-5)[/tex] and [tex](3,-17)[/tex] is [tex]y=-6x+1[/tex]
Which System of inequalities has this graph as its solution?
A. y<2x-3
y<1/3x+4
B. y>2x-3
y>1/3x+4
C. y>2x-3
y<1/3x+4
D. y<2x-3
y>1/3x+4
Answer: B
Step-by-step explanation:
The line [tex]y=2x+3[/tex] is dotted and shaded above.
Eliminate A and D.Similarly, the line [tex]y=\frac{1}{3}x+4[/tex] is also shaded above.
Eliminate C.This leaves B as the correct answer.
Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n
inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer,
while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches
greater than the box he originally planned to build?
O 3n2 + 2n
312 + 3n+3
O 6n2 + 3n
O 6n2 + 3n+3
Given:
Edge of a cubic box = n inches.
He decided to make the box 1 inch taller and 2 inches longer, while keeping its depth at n inches.
To find:
How many cubic inches greater than the box he originally planned to build?
Solution:
Edge of a cubic box is n inches, so the volume of the original cube is:
[tex]V_1=(edge)^3[/tex]
[tex]V_1=n^3[/tex]
According to the given information,
New width of the box = n+1
New length of the box = n+2
New height of the box = n
So, the volume of the new box is:
[tex]V_2=Length\times width\times h[/tex]
[tex]V_2=(n+2)(n+1)n[/tex]
[tex]V_2=(n^2+2n+n+2)n[/tex]
[tex]V_2=(n^2+3n+2)n[/tex]
[tex]V_2=n^3+3n^2+2n[/tex]
Now, the difference between new volume and original volume is:
[tex]V_2-V_1=n^3+3n^2+2n-n^3[/tex]
[tex]V_2-V_1=3n^2+2n[/tex]
So, the volume of new box is 3n^2+2n cubic inches more than the original box.
Therefore, the correct option is A.
A farmer sells four of his farm products Maize, Potatoes, carrots and tomatoes in each of 2 towns into classes of 3 customers. Consumers, Retailers, and wholesellers .
Town1 Maize, Potatoes Carrots tomatoes
consum. 4. 6. 7. 4.
Retailer. 3. 2. 1. 6.
wholesa. 4. 3. 5. 3.
Town2. Maize. Potatoes.Carrots.tomatoes
consum. 4. 5. 3. 6.
Retailer. 7. 8. 4. 4.
wholesa. 2. 4. 6. 1.
In order to sell his produce in these towns , the farmer pays commission to salesman, town managers and division managers as shown.
salesman.townmanagers.divisionmanage
6%. 5%. 2%
4%. 3%. 3%
Selling price per bag is:
Maize Sh 200
Potatoes sh 1000
Carrots sh 700
Find total sales in units by potatoes.
Answer:
Step-by-step explanation:
Simplify the radical expression below square root of 5/64
A square root 5/8
B 5/64
C square root 5/64
D 5/8
Answer:
a
Step-by-step explanation:
square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8
How many orders are possible to view 6 videos from a stack of 8 videos?
Answer:
28
Step-by-step explanation:
We know that ,
n C r = n! / ( n - r)! r! 8! / ( 8 - 6)! 6!8! / 2! × 6! 7 × 8 / 2 × 1 28A city has a population of 350,000 peopleSuppose that each year the population grows by 7.75%What will the population be after 6 years Use the calculator provided and round your answer to the nearest whole number
Answer:
335%
Step-by-step explanation:
15. The area of a triangle is 72 in the base is 12 in. Find the height.
Answer:
[tex]hright =12[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the area of a triangle is [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.
But we already know the area and the base. So to find the height, let's substitute 72 for [tex]A[/tex] and 12 for [tex]b[/tex], and solve.
[tex]72=\frac{1}{2}(12)(h)[/tex]
[tex]72=6h[/tex]
Here, divide both sides by 6
[tex]12=h[/tex]
--------------------
Hope this is helpful.
Answer:
height = 12
Step-by-step explanation:
.............