No photo attached, but no need.
We're given that f(0) = 1 and f(2) = 5, and that
[tex]\displaystyle \int_0^2 f(x) \, dx = 7[/tex]
Integrate x f'(x) by parts, with
[tex]u = x \implies du = dx[/tex]
[tex]dv = f'(x) \, dx \implies v = f(x)[/tex]
Then
[tex]\displaystyle \int_0^2 x f'(x) \, dx = uv\bigg|_{x=0}^{x=2} - \int_0^2 v \, du \\\\ = x f(x) \bigg|_{x=0}^{x=2} - \int_0^2 f(x) \, dx[/tex]
Now just plug in everything you know:
[tex]\displaystyle \int_0^2 x f'(x) \, dx = 2f(2) - 0f(0) - \int_0^2 f(x) \, dx = 10 - 0 - 7 = \boxed{3}[/tex]
Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and six have a master’s degree. If the department chairperson selects three applicants at random for an interview, find the probability that all three have a PhD
Using the hypergeometic distribution, it is found that there is a 0.0175 = 1.75% probability that all three have a PhD.
The applicants are chosen without replacement, hence the hypergeometric distribution is used to solve this question.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, the values of the parameters are as follows: N = 20, k = 6, n = 3.
The probability that all three have a PhD is P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,20,3,6) = \frac{C_{6,3}C_{14,0}}{C_{20,3}} = 0.0175[/tex]
0.0175 = 1.75% probability that all three have a PhD.
More can be learned about the hypergeometic distribution at https://brainly.com/question/24826394
which of the values shown are potential roots of f(x)=3x^3-13x^2-3x+45? Select all that apply
Answer: 3 and 5 (b and g)
Step-by-step explanation:
I got it correct on Edge
Please help me with this
As the first step, you have to distribute
2x - 12 + 4x + 16 = 40 Now combine the like items
6x + 4 = 40
6x = 36
x = 6
HELP PLEASE!
can anyone help me with this math question? im quite confused on where to begin..
please explain & show the steps!
===================================================
Explanation:
In the first parenthesis grouping, we have these three terms
[tex]9x^2y[/tex]
[tex]6xy^2[/tex]
[tex]-3xy[/tex]
and we're dividing each of them over the denominator -3xy.
Think of it like the distributive property. In fact, division is a disguised version of multiplication, which is why the distributive property is not a coincidence. Example: 10/2 = 10*(1/2) = 10*0.5 = 5
If we divide each term over -3xy, then we get these three separate results:
[tex](9x^2y) \div (-3xy) = -3x[/tex]
[tex](6xy^2) \div (-3xy) = -2y[/tex]
[tex](-3xy) \div (-3xy) = 1[/tex]
The last equation is probably self explanatory: any number divided by itself is 1, as long as the number isn't zero. Eg: 4/4 = 1.
The first two equations might not be obvious. For the first equation, we divide the coefficients 9 and -3 to get -3 as the final coefficient on the right hand side. Then the variable terms cancel when pairing them up. Check out the diagram below to see what I mean by this canceling. It's optional, but it might help to think of [tex]x^2[/tex] as [tex]x*x[/tex]
A similar situation happens in the second equation as well.
After doing those three division operations, we then add up the results to arrive at -3x+(-2y)+1 which is the same as -3x-2y+1
(20 points!) (photo attached for context)
Line segment ST is congruent to which line segment?
20x20x2 please I really need to answer this question
Answer:
800
Step-by-step explanation:
20*20=400
400*2=800
will give brainiest IF CORRECT
32 is what percent of 50?
64%
70%
1.5%
156%
Answer:
64% hope this helps
Step-by-step explanation:
I'm just smart
Answer:
The answer is 64%
Step-by-step explanation:
5= 10% multiply 5 by 6 and you get 30. the 2 equals 4 percent so the percent is 64%. I hope this helps.
What time will it take to obtain double of the interest on Rs. 2000 for 3 years at the rate of 15% per annum?
Answer:
6 years
Step-by-step explanation:
Given values :
Principal amount = Rs. 2000Time period = 3 yearsRate = 15% per annumTo Find :
Time taken to obtain twice the interestSolving :
First, find the interest.I = PrtI = 2000 x 0.15 x 3I = 6000 x 0.15I = Rs. 900 So twice the interest = Rs. 1800Now using the [I = Prt] formula,t = I/Prt = 1800/(2000 x 0.15)t = 1800 / 300t = 6 yearsa binder normally costs $8.99. use this information to answer the questions below
Answer:
You are asking a question that cannot be solved by anyone outside of your school.
Step-by-step explanation:
What information is below?
A study was conducted of 351 species of mammals worldwide. The
scientists conducting the study found that 140 species could be
found in Asia and 94 species could be found in Africa, and of those,
22 could be found in both continents.
What is the probability of randomly selecting a species of mammal
that is neither found in Asia nor Africa? Write your answer as a
fraction.
Answer:
95/351
Step-by-step explanation:
the first thing you must do is to add 140 and 94 and 22 together
you get 256
then you subtract 351 with 256 and get 95
and then you do this
95/351
for what values of A does the acute angle formed by the lines 3x+2y=10 and Ax-2y=3 have measure of 45 degree
Answer:
Step-by-step explanation:
25 % of what number is 5.
SHOW YOUR WORK!!!!
Answer:
The answer is 1.25
Step-by-step explanation:
5% of 25 = ?
5/100 × 25
1/20 × 25 = 25/20 = 5/4 = 1.25
Thus, 5% of 25 is 1.25
For every pizza Caron's family ate, Caron ate 2 of the 8 slices. If Caron's family brought 4 pizzas, write the ratio of the total number of slices Caron ate to the total number of slices the family ate.
Answer:
[tex]\frac{8}{32}[/tex]
Step-by-step explanation:
2×4=8
Caron are a total of 8 slices.
8×4=32
There were 32 slices between all 4 pizzas.
Eight times x is less than or equal to 29
Translate the sentence into an inequality
[tex]8x \leqslant 29[/tex]
Answer:
8x ≤ 29
Step-by-step explanation:
The reason why is because, 8 times 'x' also means 8 multiplied by x.
The words less than or equal to mean ≤, this is because the less than sign (<) denotes that the product of 8 and 'x' is below 29 and the line underneath the less than sign (<) means that it is equal to.
Hey y’all! Can I please have some help??? :)
Answer:
Rhombi and Squares
Step-by-step explanation:
1) KY (pythagorean Thm) 5² + x² = 13² ...= 12
2) PK Diagonals bisected. also = 12
3) Diagonals of rhombi are perpendicular. <YKZ = 90
4) 67. Alternate interior angles are congruent.
5) 3. Diagonals are bisected and congruent for squares.
6) 45° . Angles are bisected by diagonals.
7) 90° . All angles of squares are right angles.
8) 6. Diagonals are bisected. So 3 is doubled to 6.
9) I need graph paper.. hol'up
Please answer ASAP! I am very confused. Please explain steps if possible.
Answer:
943 exponent 14
Step-by-step explanation:
The question deals with indices(exponents). Therefore,all laws of indices related to the question must be applied to clearly solve and understand the question.
so,(943 exponent 78 · 943 exponent 1)/943 exponent 65
· means multiplication so simply,(943 exponent 78 × 943 exponent 1)/943 exponent 65
The laws of indices clearly state that, when two indices of the same base are multiplying, you add their exponents and when dividing,you subtract their exponents.
As all the indices have the same base which is "943", we can quickly add & subtract the exponents.
(Leaving base out of calculation now to make it easier to directly deal with exponents)
(78+1)-65(From the rules)
79-65=14,which means 943 exponent 14
∴The answer is 943 exponent 14
Can the sides of a triangle have lengths 2, 1, and 2?
yes
no
Submit
Answer:
YES
Step-by-step explanation:
Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (Any side of a triangle is always shorter than the sum of the other two sides)
1+2 >2
2+2>1
2 1/2 pounds =. Ounces
I need help
Answer:
32 and a half
Step-by-step explanation:
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
75, 90, 108, ...
Find the 7th term.
The 7th term of the sequence to the nearest thousandth is 223.949
What are geometric sequences?These are sequence that increases in an exponential form.
The formula for calculating the nth term of a geometric sequence is expressed as:
Tn = ar^n-1
Given the following parameters
a = 75
r = 1.2
n = 7
Substitute the given parameter into the formula
T7 = 75(1.2)^6
T7 = 223.949
Hence the 7th term of the sequence to the nearest thousandth is 223.949
Learn more on geometric sequence here: https://brainly.com/question/9300199
If 75% of a number is 255 and 20% of the same number is 68, find 95% of that
number
Answer:
323
Step-by-step explanation:
.75 x = 255
x = 255 / .75 = 340
340 * .95 = 323
Answer:
[tex]95[/tex]% of x ([tex]340[/tex]) = [tex]\boxed{\bf\:323}[/tex]
Step-by-step explanation:
Let the number be taken as 'x'.
Given,
[tex]75[/tex]% of x = [tex]255[/tex] [tex]20[/tex]% of x = [tex]68[/tex][tex]95[/tex]% of x = [tex]\boxed{?}[/tex]Then,
1) [tex]75[/tex]% of x = [tex]255[/tex]
[tex]\frac{75}{100} x = 255\\\frac{3}{4}x=255 \\x=255\times \left(\frac{4}{3}\right) \\x=\frac{255\times 4}{3} \\x=\frac{1020}{3} \\\underline {\bf\:x=340} \: \: \: \: \dashrightarrow eq. 1[/tex]
2) [tex]20[/tex]% of x = [tex]68[/tex]
[tex]\frac{20}{100} x = 68\\\frac{1}{5} x = 68\\x = 68 \times 5\\\underline{\bf\:x = 340 } \: \: \: \:\dashrightarrow eq.2[/tex]
We can see from eq.1 & eq.2 that we get the value of 'x' equal to [tex]\boxed{\bf\:340}[/tex] .
Now,
3) [tex]95[/tex]% of x = [tex]\boxed{?}[/tex]
[tex]\frac{95}{100}\times(340) \\= \frac{19}{20}\times 340 \\= \frac{19\times 340}{20} \\= \frac{6460}{20} \\= \boxed{\bf\:323 }[/tex]
[tex]\rule{150pt}{2pt}[/tex]
help me for five fazcoins and a copy of the morbius movie
Answer:
D
Step-by-step explanation:
down 110 ft over time 10 min
time can't be negative
Find the area of the rectangle.
l=10 in, w=7.5 in
Answer:
It should be 75 inches
Step-by-step explanation:
Help please
What is 600 square feet converted to square yards?
Answer:
66.6667
Step-by-step explanation:
100% correct mark brainliest
Which shows the Identity Property?
A. 2 +7=7 +2
B. 4 + 0 = 4
C. 6+ (4 + 8) = (6 + 8) + 4
Answer:
B shows the Identity Property.
Step-by-step explanation:
x+0=x
How many times larger is 8 x 106 than 2 x 103?
Х
Answer: ~4.12 times larger
Step-by-step explanation:
1. find the values for both equation, (8*106=848) and (2*103=206).
2. divide the larger number by the smaller one. 848/206
which gives us 4.11650485, or 4.12 rounded.
hope this helped! ♡
can someone help me answer this
Answer:
sum the numbers of favorite food together.
pizza- 58.
hamburger- 36.
pasta- 14.
others- 17.
Addition of the favorite food will give us .
58+36+14+17=125.
pizza ..58/125 × 100 =46.4
HELP ASAP I WILL GIVE YOU BRAINLEAST
WHAT IS THE EQUATION OF THE GRAPH?
Problem 1 (on the left)
It appears we have an exponential function curve through the points (0,4) and (1,7)
The general exponential function is of the form
y = a*b^x
The value of 'a' is the y intercept or initial value. So a = 4
Plug in (x,y) = (1,7) to help solve for b
y = a*b^x
y = 4*b^x
7 = 4*b^1
7 = 4b
b = 7/4 = 1.75
Therefore, the function is y = 4*(1.75)^x
Plug in x = 0 and you should get y = 4. Plug in x = 1 and you should get y = 7These two facts help confirm we have the correct exponential equation.
Answer: y = 4*(1.75)^x===========================================================
Problem 2 (on the right)
The steps will follow the same idea as the previous question.
The exponential curve goes through (-1, 120) and (0,40)
We have a = 40 this time due to the y intercept (0,40)
Plug in the coordinates of the other point to find b
y = a*b^x
y = 40*b^x
120 = 40*b^(-1)
120 = 40/b
120b = 40
b = 40/120
b = 1/3
Answer: y = 40*(1/3)^xHelp!!! 8. Determine whether each pair of functions f and g are inverses. Explain your reasoning.
Answer:
(b) is inverse while (a) is not inverse.
Step-by-step explanation:
we can see this since the values of x and y should flip if the function is inverse. we see this in (b) but not in (a).
The equation to model Exponential Growth is: y=a(1+r)t y= total amount a= starting amount r= the growth rate as a decimal t= number of growth periods Question 4 A sample of bacteria cells in a petri dish increases by 50% every hour. A scientist starts with a sample of 30 bacteria cells. Write an equation that can be used to determine the number of cells after x hours.
Answer:
[tex]y=30(1.5)^x[/tex]
where:
y = total amount of bacteria cellsx = number of hoursStep-by-step explanation:
Given exponential growth equation:
[tex]y=a(1+r)^t[/tex]
where:
y = total amounta = starting amount r = the growth rate as a decimal t = number of growth periodsIf a sample of bacteria cells in a petri dish increases by 50% every hour, the growth rate is:
r = 50% = 0.5If the starting amount of bacteria cells is 30 then:
a = 30Therefore, the equation that can be used to determine the number of cells after x hours is:
[tex]y=30(1.5)^x[/tex]
where:
y = total amount of bacteria cellsx = number of hours