Answer:
3×5×53
Step-by-step explanation:
You can use divisibility rules to find the small prime factors.
The number ends in 5, so is divisible by 5.
795/5 = 159
The sum of digits is 1+5+9 = 15; 1+5 = 6, a number divisible by 3, so 3 is a factor.
159/3 = 53 . . . . . a prime number,* so we're done.
795 = 3×5×53
_____
* If this were not prime, it would be divisible by a prime less than its square root. √53 ≈ 7.3. We know it is not divisible by 2, 3, or 5. We also know the closest multiples of 7 are 49 and 56, so it is not divisible by 7. Hence 53 is prime.
I really need this answr tonight please HELP!!! Use limits to find the area between the graph of the function and the x axis given by the definite integral. ∫_1^5▒(x^2-x+1)dx
Answer:
[tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \frac{100}{3}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \int\limits^5_1 {x^2} \, dx - \int\limits^5_1 {x} \, dx + \int\limits^5_1 {} \, dx[/tex][Integrals] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \bigg( \frac{x^3}{3} - \frac{x^2}{2} + x \bigg) \bigg| \limits^5_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \frac{100}{3}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer: 5\int_0^5 3^(3)\sqrt(x^(2)) dx
Step-by-step explanation:
HURRY Find the domain and range ( 2,3), ( -2, 4), ( 4, 8) , ( -2, 5)
Answer:
See below :)
Step-by-step explanation:
Given ordered pairs :
( 2 , 3 ) , ( - 2 , 4 ) , ( 4 , 8 ) , ( - 2 , 5 )
Domain is the set of all x -coordinates in the set of ordered pairs.
( 2 , 3 ) , ( -2 , 4 ) , ( 4 , 8 ) , ( -2 , 5 )
List them :
Domain = { - 2 , 2 , 4 )
Range is the set of all y - coordinates in the set of ordered pairs.
( 2 , 3 ) , ( - 2 , 4 ) , ( 4 , 8 ) , ( - 2 , 5 )
List them :
Range = { 3 , 4 , 5 , 8 }
Hope I helped !
Best regards!!
Please help me, I don't understand how to do this! :(
Answer:
1/273
Step-by-step explanation:
5/15 * 4/14 * 3/13 * 2/12
= 1/3 * 2/7 * 3/13 * 1/6
= 1/273
2.
Suppose the population of kangaroos in a different province of Australia is modeled by
the following, with t = 0 representing the year 2020:
P() = 76(0.92)
a.) Using a calculator, find P(10) and interpret it in the context of the problem. Be
specific.
b.) What is happening to the population of kangaroos in this problem? What specific value
in the equation causes this? By what percentage is the kangaroo population decreasing
each year?
c.) As the value of t increases to very large numbers, do you think this model will be
realistic? Explain. Using a calculator, find P(100) to help support your answer.
Answer:
a) 30 kangaroos in 2030
b) decreasing 8% per year
c) large t results in fractional kangaroos: P(100) ≈ 1/55 kangaroo
Step-by-step explanation:
We assume your equation is supposed to be ...
P(t) = 76(0.92^t)
__
a) P(10) = 76(0.92^10) = 76(0.4344) = 30.01 ≈ 30
In the year 2030, the population of kangaroos in the province is modeled to be 30.
__
b) The population is decreasing. The base 0.92 of the exponent t is the cause. The population is changing by 0.92 -1 = -0.08 = -8% each year.
The population is decreasing by 8% each year.
__
c) The model loses its value once the population drops below 1/2 kangaroo. For large values of t, it predicts only fractional kangaroos, hence is not realistic.
P(100) = 75(0.92^100) = 76(0.0002392)
P(100) ≈ 0.0182, about 1/55th of a kangaroo
Cicero and Themistocles run for the same political office.
Cicero received w votes in the election, and Themistocles
received v votes.
Which of the following expressions always represents
how many more votes the winner received than the
loser?
Choose 1 answer:
W-V
|w - u
None of the above
Answer:
|w - v| or |v - w|
Step-by-step explanation:
The answer is the absolute value of the difference of the two numbers written in either order.
|w - v| or |v - w|
Answer:
B |w-v|
Step-by-step explanation:
khan academy
Find the vector projection of B onto A if A = 5i + 11j – 2k,B = 4i + 7k
Answer:
[tex]\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\[/tex]
Step-by-step explanation:
Given A = 5i + 11j – 2k and B = 4i + 7k, the vector projection of B unto a is expressed as [tex]proj_ab = \dfrac{b.a}{||a||^2} * a[/tex]
b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)
note that i.i = j.j = k.k =1
b.a = 5(4)+11(0)-2(7)
b.a = 20-14
b.a = 6
||a|| = √5²+11²+(-2)²
||a|| = √25+121+4
||a|| = √130
square both sides
||a||² = (√130)
||a||² = 130
[tex]proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\[/tex]
Hence the projection of b unto a is expressed as [tex]\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\[/tex]
Solve x ^2 + 9x + 8 = 0 by completing the square. What are the solutions?
Answer:
-1 and -8
Step-by-step explanation:
x^2+2*9/2*x+(9/2)^2-(9/2)^2+8=0
(x+9/2)^2+32/4-81/4=0
(x+9/2)^2-49/4=0
(x+9/2)^2=(7/2)^2
so
x+9/2=7/2
x=7/2-9/2
x=-2/2
x=-1
or
x+9/2=-7/2
x=-7/2-9/2=-16/2
x=-8
the sum of 81 and a number is greater than 4 times the same number
Answer: The number has to be less than 27.
Step-by-step explanation:
81 + n > 4n
-n -n
81 > 3n
n<27
Declan says that for any number n the product 4 x n is greater than 4 which vaule of n shows why Declan incorrect
Answer:
see below (I hope this helps!)
Step-by-step explanation:
When n < 1, Declan's statement is incorrect because 4 * 0 = 0 which is not greater than 4 and this continues for all n values that are less than 1.
The temperature in San Diego, California is 5 degrees warmer than twice the temperature in Boise, Idaho. The temperature in San Diego is 61 degrees. Write an equation to determine the temperature in Boise.
Answer:
2x + 5 = 61
Step-by-step explanation:
Let x be equal to the temperature in Boise.
Since the temperature in San Diego is 5 degrees warmer than twice the temperature in Boise, we must double the temperature in Boise and then add 5 degrees. To do this we put a 2 in front of the x and then add 5 to that.
2x + 5
Since we know the temperature in San Diego is 61 we can make the equation equal to 61.
2x + 5 = 61
PLEASE HELP! I Will Give You 20 POINTS!! Solve with absolute value. -|12-3.5x|=-5
Answer:
2 and 4 6/7
Step-by-step explanation:
- |12 - 3.5x| = -5 ⇒ cancelling negative signs|12 - 3.5x| = 512 - 3.5x = ± 5 ⇒ getting rid of absolute1. First equation
12 -3.5x = 53.5x = 12 -53.5x = 7x = 7/3.5x= 22. Second equation
12 - 3.5x = -53.5x = 12 +53.5x = 17x= 17/3.5x= 34/7 x= 4 6/7What value goes in box A?
What value goes in box B?
What value goes in box C?
What value goes in box D?
URGENT HURRYY PLEASE
Step-by-step explanation:
Hello!
For this you multiply the numbers that intersect at that box
Box A 2x and 4 intersect
2x * 4 = 8x
Box B 3 and 4 intersect
3 * 4 = 12
Box C 2x and x intersect
2x * x = [tex]2x^{2}[/tex]
Box D 3 and x intersect
3 * x = 3x
To solve this we put all these together
[tex]2x^{2} +3x+8x+12[/tex]
Combine like terms
[tex]2x^{2} +11x+12[/tex]
Hope this helps!
A pancake recipe calls for 1 cup of flour. Derek has already used 1/4 cup of flour. How many more cups of flour does Derek need to add?
Answer:
Derek needs to add 3/4 cups of flour.
Step-by-step explanation:
If Derek has already used 1/4 cup of flour, he needs 3 more cups of flour to get to 1 full cup of flour.
Answer:
Step-by-step explanation:A batch of cookies requires 2 1/4 cup of flour and 1 egg. You have in your kitchen 8 cups of flour and a half dozen eggs. a) How many batches of cookies
Select the choice that translates the following verbal phrase correctly to algebra: (2 points) the product of 12 and y increased by 11 12y + 11 12(y + 11) 12(11y) 12+ 11y
The correct answer is A. 12y + 11
Explanation:
In mathematics, the word "product" is mainly used to refer to multiplication. For example, the product of 5 and 2 is 10 as 5 x 2 = 10. This means, the section "the product of 12 and y" means 12 needs to be multiplied by y, which can be expressed as 12y. Additionally, the word "increased" refers to addition, which means 11 needs to be added to 12y. This means the final expression is 12y + 11, and therefore the correct answer is the first one or option A.
Answer: the answer is 12y + 11
Step-by-step explanation:
i too the test and got a 100
A school P is 16km due west of a school Q. what is the bearing of Q from P
Answer:
16Km due east of school P
Step-by-step explanation:
Given
A school P is 16km due west of a school Q
Thus, we can say that distance PQ = 16 km.
________________________________
now we have to find the bearing of Q from P
As distance is same
distance PQ = distance QP
Thus,
Distance will remain same of 16 km.
For direction,
If Q is west of P, then P will be east of Q[tex]P------------------>Q[/tex]
as shown in figure P is west of Q,
now from point P , Q is west P.
Thus,
Bearing of School Q from P is 16Km due east of school P
Given the equation p = 2n – 3, what is p when=3
Answer:
n = 3
Step-by-step explanation:
Hello!
p = 2n - 3
the question asks for when p is equal to 3 so we put 3 in for p
3 = 2n - 3
Now we can solve this
3 = 2n - 3
Add 3 to both sides
6 = 2n
Divide both sides by 2
3 = n
The answer is n = 3
Hope this Helps!
55 POINTS Camille and Hiroshi are trying to determine the most number of lines that can be drawn using any two of four random points. Is either correct? Explain.
please explain i want to understand it
Hiroshi is correct; after you draw
the line from the first point to the other three, one of
the lines from the second point is already drawn.
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results: ANOVA df SS MS F Significance F Regression 1.00 13555.42 13555.42 156.38 0.00 Residual 8.00 693.48 86.68 Total 9.00 14248.90 What is the value of the standard error of estimate
Answer:
9.31
Step-by-step explanation:
Given the following :
- - - - - - - - - - df - - - - - SS - - - MS - - - F - - - signiF
Regression - 1 - 13555.42 - 13555.41 - 156.38 - 0
Residual - - 8.00 - 693.48 - - 86.68
Total - - - - 9.00 - 14248.90
What is the value of the standard error of estimate?
The standard error estimate :
Mean square error or Residual (MSE)
Standard Error (SE): √MSE
MSE = 86.68
Standard Error = √86.68
Standard error = 9.3102094
= 9.31
For 15 points!!!
If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
Please I'm looking for the explanation. i already know the answer is 2, i just don't know how.
Answer:
(D) 2
Step-by-step explanation:
If two or more vectors are linearly dependent, then one of them can be expressed as a linear combination of the rest. In other words, vectors are dependent linearly on one another if the determinant of the matrix that they form is zero.
Given vectors:
i+j+2k
i+pj+5k
5i+3j+4k
Now, since they are linearly dependent, then the determinant of their matrix should be zero. i.e
Let their matrix be A and is given by;
A = [tex]\left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right][/tex]
Where;
the first column holds the i components of the vectors
the second column holds the j components of the vectors and
the third column holds the k components of the vectors
=> |A| = det(A) = 0
[tex]det(A) = det \left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right] = 0[/tex]
Now, let's calculate the determinant.
[tex]det \left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right] = 1(4p - 15) - 1(4 - 25) + 2(3 - 5p) = 0[/tex]
=> 4p -15 - 4 + 25 + 6 - 10p = 0
=> 4p - 10p + 12 = 0
=> 6p = 12
=> p = 2
Therefore, the value of p for which the vectors are linearly dependent is 2
Please help! I’ll mark you as brainliest if correct
Answer:
3. C
Step-by-step explanation:
16 / 4 = 4 which is a counting number.
- 30 / 5 = -6 which is a integer.
-31/8 = -3.875 which is rational number
30/9 = 10/3 = 3.333333333.... which is an irrational number
So your answer is C
Veronica wants to check her work after evaluating . What steps can she follow to verify her answer?
Divide her answer by –6 and see if the result is –108.
Divide her answer by –108 and see if the result is –6.
Multiply her answer by –6 and see if the result is –108.
Multiply her answer by –108 and see if the result is –6.
Answer:The answer is C
Step-by-step explanation:
I just had the question and i got it right :D
a triangular flag has an area of 0.75 square feet and height of 1.5 foot. what is the base
Answer:
1 foot
Step-by-step explanation:
Using the formula for the area of a triangle, fill in the given information and solve for the unknown.
A = (1/2)bh
0.75 = (1/2)b(1.5)
b = 0.75/0.75 = 1 . . . . divide by the coefficient of b
The base is 1 foot.
2) Write an equation of a line that would be perpendicular to y = -x-8?
Answer:
Step-by-step explanation:balls
Mark thinks the equation y=6x+4 will match the red solid graph. Mia thinks it will match the blue dotted graph. Who’s right? Explain your answer.
Answer:
Technically neither, but Mia is correct.
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Since our slope m is equal to 6, it is a positive number. That means that the slope/line will be positive, so the line should be going up, not down. That means the blue line would be correct. Therefore, Mia is correct.
Technicality:
Since the blue line is dotted, the equation should be a inequality and not a linear equation. No solutions on the line would technically work. If the equation was y < 6x + 4 or something with an inequality sign, then it would be correct.
You travel from City X to City Y. You know that the round-trip distance is 647 miles. City Z, a city you pass on the way, is 27 miles from City X. Find the distance from City Z to City Y. The distance from City Z to City Y is miles.
Answer:
296.5 miles
Step-by-step explanation:
Round trip distance of City X to City Y is 647 miles.
Round trip includes to and fro.
i.e. City X to City Y and then City Y to City X back.
Let the distance between City X and City Y = D
Distance traveled in round trip between City X and City Y = D + D = 2D
Given than 2D = 647
OR
D = [tex]\frac{647}2[/tex] = 323.5 miles
Kindly refer to the attached diagram, for the location of City Z.
Distance between XY = Distance from X to Z + Distance from Z to Y.
Distance XY = XZ +ZY
323.5 = 27 +ZY
ZY =296.5 miles
find the x-intercept for y=x^2+4x+5
Answer: There is no x-intercept for this quadratic equation.
Step-by-step explanation:
An x-intercept is when the y-value of the point if equal to zero. There is no x-intercept for this quadratic equation. This can be supported by the fact that this equation cannot be factored.
Please help me please
Answer:
B
Step-by-step explanation:
So we have a 45-45-90 triangle.
This is a special right triangle. In a 45-45-90 triangle, the side lengths are x, and the hypotenuse will be x√2
Since the hypotenuse is 3, we can set it equal to x√2 to solve for x. Therefore:
[tex]x\sqrt2=3[/tex]
Divide both sides by √2:
[tex]x=\frac{3}{\sqrt2}[/tex]
Rationalize:
[tex]x=\frac{3\sqrt2}{2}[/tex]
Our answer is B.
Please help me
Write an equation for the question
You withdraw $100 from the ATM machine. The new balance is $372. What was the ordinary balance b of your account?
Answer:
B-$100=$372
The is is the smartest way I could look at this
OR
$372 - $100= b
Hope this helps
MARNIE OUT!
Find the equation that best represents the following word problem: In a certain freshman class, the number of girls is 83 less than twice the number of boys (b). The total number of students in that freshman class is 259. How many boys and girls are in that class? A) b + 2b = 259 - 83 B) b + 2b – 83 = 259 C) b + 83 – 2b = 259 D) b + 2b = 259
Answer:
(B) [tex]b + 2b - 83 = 259[/tex]
Step-by-step explanation:
We can first create the equation [tex]b + g = 259[/tex], since we know that there are a total of 259 students in this freshman class.
Now, the amount of girls is 83 less than twice the number of boys, so that is [tex]2b - 83[/tex].
Now, we can substitute this in the previous equation as g.
[tex]b + 2b - 83 = 259[/tex]
Hope this helped!
Answer:
b
Step-by-step explanation:
in a school ,there are 150 students .out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for physics class . The students enrolled for English cannot attend any other class , but the students of mathematics and physics can take two course at times. find the number of students who have taken both physics and mathematics.
Answer:
40
Step-by-step explanation:
First we need to subtract the 50 students enrolled in English class.
150 - 50 = 100
Next, let's add the mathematics students and the physics students.
80 + 60 = 140
Then we subtract the total amount of mathematics and physics students by the total number of students.
140 - 100 = 40
Therefore, there are 40 students who take both mathematics and physics.