A can do a piece of work in 10 days and B can do it 15 days. If both of them are working together, half of the work can be finished in?
Here we find,LCM of 10 and 15 is 30.
A can do ( 1 /10 th ) of the work in one day Or, ( 3/30th ).B can do ( 1/15th ) of the work in one day ( or 2/30th ).Working together, A and B can do
= (3/30) + (2/30) = 5/30= 1/6 th of the work in one day.So, they would require 30/5 or 6 days to complete the task.
At the end of a year, the gross debt of a country stood at about $15 trillion. Express this amount in dollars per person, assuming that the population of the country is about 309 million.
The gross debt is about $nothing per person.
Answer:
The country's debt is $ 48,543.68 per person.
Step-by-step explanation:
Given that at the end of a year, the gross debt of a country stood at about $ 15 trillion, to determine this amount in dollars per person, assuming that the population of the country is about 309 million, the following calculation must be done:
15 trillion = 15,000,000,000,000
15,000,000,000,000 / 309,000,000 = X
15,000,000 / 309 = X
48,543.68 = X
Therefore, the country's debt is $ 48,543.68 per person.
simple interest on certain principle is 1/5 of the amount in 5 yrs find rate.
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Answer:
4%
Step-by-step explanation:
The simple interest formula can be used.
I = Prt
where r is the annual rate and t is the number of years.
1/5 = 1·r·5
(1/5)/5 = r = 1/25 · 100% = 4%
The rate is 4%.
(7-6) + (-1 + 47) -(4-77)
Find a33 of the arithmetic sequence given a1=17 and d=6.
Answer:
209
Step-by-step explanation:
Given the following:
[tex]a_{1} = 17\\d=6[/tex]
The nth term of an arithmetic sequence is expressed as:
[tex]a +(n-1)d[/tex]
a is the first term = 17
d is the common difference =6
Get the 33rd term:
[tex]n=33\\a_{33}=17+(33-1)*6\\a_{33} =17+32(6)\\a_{33}=17+192\\a_{33}=209[/tex]
Hence the 33rd term is 209
How do you figure out -8=8-7n+3n
Answer:
n=4
Step-by-step explanation:
-8-8=-7+3n
-16=-4n
n=4
What is the following product? ^3Vx^2•^4VX^3
Answer:
= 3v^2 x^27
Step-by-step explanation:
Apply exponent rule: aa = a^2
VV = V^2
=3V^2x^24x^3
Simplify x^24 x^3 : x^27
= 3v^2 x^27
2) Consider the quadratic sequence 72, 100, 120, 132
2.1.1) Determine Tn the nth term of the quadratic.
Answer:
Tn = -4n²+40n+36
Step-by-step explanation:
A general quadratic sequence, Tn = an²+bn+c, where n is the term of the sequence.
So, when n = 1, Tn = 72, which means T1 = a+b+c=72.
when n = 2, Tn = 100, which means T2= 4a+2b+c = 100
when n = 3, Tn = 132, which means T3 = 9a+3b+c = 132.
Now, use a calcaulatot to solve the 3 variable simultaneous equation. According to my calculator, a = -4, b = 40, c = 36.
Hence, you a, b, and c in the Tn equation given above.
Therefore, Tn = -4n²+40n+36
Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the region bounded by the curve y = 2x - x^2 and the line y = x about the y-axis.
Answer:
The answer is "[tex]\frac{5\pi}{6}[/tex]"
Step-by-step explanation:
Please find the graph file.
[tex]h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\[/tex]
what is area of square
Step-by-step explanation:
side² is the formula to find area of square.
mark as brainliest
For the function f(x) = 2x +3, evaluate f(3).
Answer:
9
Step-by-step explanation:
f(3) = 2(3) + 3
= 9
Answer:
[tex]{ \tt{f(x) = 2x + 3}}[/tex]
f(3) means x = 3, substitute for x as 3 :
[tex]{ \tt{f(3) = 2(3) + 3}} \\ = 6 + 3 \\ = 9[/tex]
Can someone help me out please
The median is the middle value of a set.
There are 9 numbers. 9/2 = 4.5
Round up to 5, the median is the 5th number in the set.
Median = 6
URGENT!!!!!!! HELP PLEASE!!!!!!
Answer:
[tex]x^\frac{2}{3}[/tex]
Step-by-step explanation:
Using the power of power rule (multiply the exponents)
[tex]x^\frac{4}{3}[/tex] × [tex]^\frac{1}{3}[/tex] [tex]x^\frac{2}{3}[/tex] × [tex]^\frac{1}{3}[/tex]
[tex]x^\frac{4}{9}[/tex] [tex]x^\frac{2}{9}[/tex]
When exponents are multiplied, add the answers:
x ^ ( 4/9 + 2/9 )
x ^ ( 6/9 )
x ^ ( 2/3 )
In the figure, L1 || L2. 2x=174º. Find Za+Zb.
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Answer:
12°
Step-by-step explanation:
We assume you mean ...
∠x = 174°
Angle a is supplementary to angle x, so is ...
∠a = 180° -174° = 6°
Angle b is a vertical angle with respect to angle 'a', so is the same measure.
∠a +∠b = 6° +6° = 12°
the domain of f/g consists of numbers x for which g(x)........0 that are in the domain of both.....and......
Answer:
the domain of f/g consists of numbers x for which g(x) IS NOT EQUAL 0 that are in the domain of both f(x) and g(x)
Step-by-step explanation:
The denominator of a rational function can't be zero (see the first row in the attached table)
The required fill in the blanks is ≠ , f(x) and g(x).
It is required to fill in the blanks.
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given:
The domain of f/g consists of numbers x for which g(x) IS NOT EQUAL 0 that are in the domain of both f(x) and g(x).
The domain of (f/g) (x) consists of all x-values that are in the domain of both f and g, where g(x) ≠ 0. Both f and g have domain all real numbers.
Therefore, the required fill in the blanks is ≠ , f(x) and g(x).
Learn more about function here:
brainly.com/question/24240489
#SPJ2
Harrison Water Sports has three retail outlets: Seattle, Portland, and Phoenix. The Seattle store does 50 percent of the total sales in a year, while the Portland store does 35 percent of the total sales. Further analysis indicates that of the sales in Seattle, 20 percent are in boat accessories. The percentage of boat accessories at the Portland store is 30 and the percentage at the Phoenix store is 25. Overall, the probability that a sale by Harrison Water Sports will be for a boat accessory is
Answer:
The correct answer is "0.43".
Step-by-step explanation:
According to the question,
The probability of boat accessories sale,
= 0.3
The probability of sale in Portland store,
= 0.35
now,
The probability that the decision was signed somewhere at Portland shop will be:
= [tex]\frac{P(boat \ acessories \ sale\times P(sale \ in \ Portland \ store)}{P(boat \ accessories \ sale)}[/tex]
By substituting the values, we get
= [tex]\frac{ 0.3\times 0.35}{( 0.2\times 0.5 + 0.3\times 0.35 + 0.25\times 0.15)}[/tex]
= [tex]\frac{0.105}{0.1+0.105+0.0375}[/tex]
= [tex]0.43[/tex]
Which expression is a perfect cube? -8x^21y^8 -64x^64y^64 -125x^9y^20 -216x^9y^18 I need the answer quick please.
Answer:
Step-by-step explanation:
The expression is too close together. Can you space them out?
Answer:
d) -216x^9y^18
Step-by-step explanation:
How do I solve this ?
Answer:
a = 4/ 1 − | x | h = 0
Step-by-step explanation:
Your friend is studying for an exam. Based on your knowledge of your friend, you believe that if they study for the exam, there is an 80% probability they will be able to pass it. On the other hand, if they do not study, there is only a 30% probability they will be able to pass. Your friend is not a particularly industrious student, and you initially believe there is only a 60% probability your friend will study for the exam. A few days later your friend happily proclaims that they passed the exam. Thus, find the probability that they did in fact study for the test with this knowledge in hand.
Answer:
0.8 = 80% probability that they did in fact study for the test.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Passed the exam.
Event B: Studied.
Probability of passing the test:
80% of 60%(Studied).
30% of 100 - 60 = 40%(did not study). So
[tex]P(A) = 0.8*0.6 + 0.3*0.4 = 0.6[/tex]
Probability of passing the test studying:
80% of 60%, so:
[tex]P(A \cap B) = 0.8*0.6 = 0.48[/tex]
Find the probability that they did in fact study for the test with this knowledge in hand.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.48}{0.6} = 0.8[/tex]
0.8 = 80% probability that they did in fact study for the test.
I need help pleaseee
Answer:
C
Step-by-step explanation:
3.5x4.1x0.5 = 7.175 7.175x7.2=51.66
Answer:
51.66 In³
Step-by-step explanation:
This is a right angle triangular prism ....Hence ...
V=BA×H
BA= ½×4.1 in×3.5 In
BA= 7.175 In²
H= 7.2 In
V=7.175in² × 7.2In
V= 51.66 In³
HELPPP PLEASE. So I have figured out the first one however I cannot seem to figure out the rest as my answers are wrong. How do solve this problem? Please help!
Answer:
it seems as it is adding .15 every time so the next 3 would be .05 .20 and .65
According to the rational root theorem, which is a factor of the polynomial f(x)=3x^3-5x^2-12x+20?
Answer:
(x-2), (x+2), (3x-5)
Step-by-step explanation:
Factors of 3: ±1, ±3
Factors of 20: ±1, ±2, ±4, ±5, ±10, ±20
Possible factors of the polynomial: ±1, ±2, ±3, ±4, ±5, ±10, ±20, .... (there's a lot more but you probably do not need to list them all)
Pick a number to divide the polynomial by (I picked 2)
(3x³-5x²-12x+20)÷(x-2) = 3x²+x-10
So (x-2) is a factor of f(x) = 3x³-5x²-12x+20
Factor 3x²+x-10 = (3x-5)(x-2) these are the other factors of f(x) = 3x³-5x²-12x+20
Help me please look at image I’ll give brainliest to first correct answers
Answer:
1
4
3
6
2
5
Step-by-step explanation:
Too lazy to explain 6 factorings on mobile. Trust me if it pleases you.
da
A
Solve the equation 2x^2+3=0
Answer:
x = ±i(√6 / 2)
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Solving quadraticsAlgebra II
Imaginary root i
√-1 = iStep-by-step explanation:
Step 1: Define
Identify
2x² + 3 = 0
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 3 on both sides: 2x² = -3[Division Property of Equality] Divide 2 on both sides: x² = -3/2[Equality Property] Square root both sides: x = ±√(-3/2)Simplify: x = ±i(√6 / 2)Which of the following statements is likely to be true?
a) The median personal income of California taxpayers would probably be near the mean.
b) For personal incomes in California, outliers in either tail would be equally likely.
c) The interquartile range offers a measure of income inequality among California residents.
d) For income, the sum of squared deviations about the mean is negative about half the time.
Answer:
c. The interquartile range offers a measure of income inequality among California residents.
Step-by-step explanation:
The range is the midspread which measures statistical dispersion. This is also known as H-spread which is equal to the difference between 75th percentile and 25th percentile. In the given scenario the interquartile range offers measure of income inequality among California residents.
What is the maximum amount of a loan you can get if you pay $700 each month at a yearly rate of 0.89% for 10 years?
Answer:
$785.17
Step-by-step explanation:
Given data
PV is the loan amount
PMT is the monthly payment
i is the interest rate per month in decimal form (interest rate percentage divided by 12)
n is the number of months (term of the loan in months)
PMT =$700
n = 10 years
i = 0.89%
The formula for the loan amount is
ASAP!!!!!!!!!!!!!!!!!!!
Answer:
V = 2143.57 cm^3
Step-by-step explanation:
We want to find the volume of the sphere
V = 4/3 pi r^3 where r is the radius and pi = 3.14
V = 4/3 ( 3.14) ( 8)^3
V = 2143.57333 cm^3
Rounding to the nearest hundredth
V = 2143.57 cm^3
Answer: 2,143.57
Step-by-step explanation: because the formula to do it is the use the radius and search up the sphere formula and do it
A researcher is studying the effect of 10 different variables on a critical measure of business performance. In selecting the best set of independent variables to predict the dependent variable, the stepwise regression technique is used. How are variables selected for inclusion in the model?
A. Smallest regression coefficient.
B. Largest p-value.
C. Smallest p-value.
D. Highest increase in the multiple R2.
Answer:
D. Highest increase in the multiple R2.
Step-by-step explanation:
Included variables in a multiple regression model are those variables which have the most effect on the model ; variables which have no effect on the performance of the model ar discarded. Model performance are based on the variables affect the multiple R² value of the model. The R² value is the coefficient of determination which gives the proportion of change in predicted value based on the regression line. Higher R² value means the variable has greater effect in the model performance. Therefore, variables which have the highest increase on the multiple R² value , are included.
Follow the process of completing the square to solve x = 4x +3.
x -
Which of the following equations is used in this process?
(2x - 42.19
(2x4,2= 12
(2x 42-28
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Answer:
the correct choice is marked
Step-by-step explanation:
The process for completing the square would generally put x-terms on one side of the equal sign and the constant term on the other side:
x^2 +4x = 3
Then the square of half the x-coefficient would be added to both sides. Here, that is (4/2)^2 = 4.
x^2 +4x +4 = 7
In order to make this match one of the answer choices, we must multiply both sides by 4.
4x^2 +16x +16 = 28
Now, we can factor the left side to see a match to the last answer choice.
(2x +4)^2 = 28
_____
Additional comment
As you can see, we had to deviate from the "complete the square" process to arrive at an equation that matches an answer choice. It cannot be said that the chosen equation "is used in the process." It might be useful to discuss this question with your teacher.
(6 + 8) (3 - 2) = help plz
Answer:
Step-by-step explanation:
(6+8i)(3-2i)
use FOIL
18 - 12i + 24i - (16[tex]i^{2}[/tex])
18 + 12i - (-16)
18 + 12i + 16
34 + 12i
Hi can someone reply me I am not sure how to factorise (2x+3)(4x-1)-(3+2x)(x-5)
I hope this is a real answer
