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Answer:
680624 = 2^4 · 7 · 59 · 103165649 = 11^2 · 37^2Step-by-step explanation:
Using the division method, you find prime divisors that give integer quotients until the final quotient is a prime. For small divisors, it is beneficial to make use of divisibility rules. For larger ones, you just have to try the list of primes to see what you get.
680624The last two digits are divisible by 4, so the number can be divided by 2 twice (at least). We can keep dividing by 2 as long as the 1s digit is even.
680624/2 = 340312
340312/2 = 170156
170156/2 = 85,078
85078/2 = 42539
The next prime is 3. The divisibility rule for 3 is the sum of digits must be divisible by 3. 4+2+5+3+9 = 23, not divisible by 3.
The next prime is 5. For divisibility by 5, the number must end in 0 or 5. This is not divisible by 5.
The next prime is 7. For divisibility by 7, there are several possible rules you can use. One I find relatively easy to remember is to subtract double the 1s digit from the rest of the number and see if that is divisible by 7. Here, that gives ...
4253 -2(9) = 4235; 423 -2(5) = 413; 41 -2(3) = 35 . . . divisible by 7
Continuing, we have ...
42539/7 = 6077
There are additional divisibility rules for 11 and 13 that can be applied. For divisibility by 11, we can add pairs of digits: 77 +60 = 137, not divisible by 11.
For divisibility by 13, we can add 4 times the last digit to the rest:
4253 +4(9) = 4289; 428 +4(9) = 464; 46 +4(4) = 62 . . . not divisible by 13
__
After this point, it is a matter of trying the primes one by one to see what the number may be divisible by. This "trial and error" will show you ...
6077/59 = 103 . . . 103 is prime, so we're done
The final factorization is ...
680624 = 2^4 · 7 · 59 · 103
__
165649As luck would have it, this is a perfect square, so we can immediately reduce the problem to something a little easier.
√165649 = 407
We can see "immediately" that this is not divisible by 2, 3, 5, or 7. However, 04+07 = 11, so this is divisible by 11.
407/11 = 37 . . . 37 is prime, so we're done
The final factorization is ...
165649 = 11^2 · 37^2
_____
As you can probably tell, it is convenient to have a list of prime numbers available. Here is a list of the first few primes.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103
_____
Additional comment
If you start with the smallest primes, (2, 3, 5}, once you find a prime divisor, you only need to try primes greater than or equal to that one on the quotient. In any event, you only need to try primes up to the square root of the value you're trying to factor. If none of those work, then the number itself is a prime.
In the first problem, once we got to 6077, we would only need to try primes up to √6077 ≈ 77. That is, if 6077 turned out to be not divisible by any prime equal to 73 or less, then 6077 would be the last prime factor. (As we found, 6077 is composite, not prime, so using that number is just to illustrate the point regarding the largest value needed to be tested.)
5 2/10 x -10 1/3
WILL GIVE BRAINLIEST!!!
Answer:
[tex]106 \frac{3}{5}[/tex]
Explanation:
Convert any mixed numbers to fractions.
Reduce fractions where possible.
Then your initial equation becomes:
[tex]\frac{26}{5} \times \frac{-31}{3}[/tex]
Next, apply the fractions formula for multiplication. Formula below:
[tex]\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d}[/tex]
[tex]= \frac{26 \times -41}{5 \times 2}= \frac{-1066}{10}[/tex]
Simplifying -1066/10, (you can do this by using division) the answer is:
[tex]106 \frac{3}{5}[/tex]
Answer:
-3 1/3
Step-by-step explanation:
5 2/10 x -10 1/3
10/10 x -10/3
1 x-10/3
-10/3
-3 1/3
your question is unclear. I think I understand it correctly
what is the least common factor for 9 8 7
Answer:504
This is the answer
504
¿How you solve?
A pool is 8 m long, 6 m wide and 1.5 m deep. It is painted at $6 per square meter.
a) How much will it cost to paint it?
b) How many litres of water will be needed to fill it?
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Answer:
a) $540 cost to paint
b) 72000 liters to fill
Step-by-step explanation:
Relevant formulas are ...
P = 2(L +W) . . . . perimeter of a rectangle of length L and width W
A = LW . . . . . . area of a rectangle of length L and width W
V = LWH . . . volume of a cuboid of length L, width W, and height H
__
a) The total painted area is the area of the pool walls plus the area of the pool bottom. The wall area is the product of pool perimeter and wall height. The bottom area is the product of pool length and width.
A = PH + LW = 2(L +W)H +LW
A = 2(8 m +6 m)(1.5 m) + (8 m)(6 m) = 42 m² +48 m² = 90 m²
At $6 per square meter, the cost of painting the pool is ...
($6 /m²)(90 m²) = $540 . . . . cost to paint the pool
__
b) The volume in liters is best figured using the dimensions in decimeters.
V = (80 dm)(60 dm)(15 dm) = 72000 dm³ = 72000 L
72000 liters will be needed to fill the pool.
add 10 and g, then subtract f from the result
Answer:
(10+g) -f
Step-by-step explanation:
Add 10 and g
10 +g
Subtract f from the result
(10+g) -f
For a given function ƒ(x) = x2 – x + 1, the operation –ƒ(x) = –(x2 – x + 1) will result in a
A) reflection across the x-axis.
B) horizontal shrink.
C) reflection across the y-axis.
D) vertical shrink.
Given:
The function is:
[tex]f(x)=x^2-x+1[/tex]
To find:
The result of the operation [tex]-f(x)=-(x^2-x+1)[/tex].
Solution:
If [tex]g(x)=-f(x)[/tex], then the graph of f(x) is reflected across the x-axis to get the graph of g(x).
We have,
[tex]f(x)=x^2-x+1[/tex]
The given operation is:
[tex]-f(x)=-(x^2-x+1)[/tex]
So, it will result in a reflection across the x-axis.
Therefore, the correct option is A.
Answer:
A) reflection across the x-axis.
Step-by-step explanation: I took the test
Twice a certain number is subtracted from 9 times the number. The result is 21. Find the number.
Answer:
3
Step-by-step explanation:
Let x represent the number.
Create an equation to represent the situation, and solve for x:
9x - 2x = 21
7x = 21
x = 3
So, the number is 3.
Find x. Round your answer to the nearest tenth of a degree.
Answer: x=52.6°
Step-by-step explanation:
To find the value of x, we have to use our SOHCAHTOA. We can eliminate sine and cosine because both uses hypotenuse, which is not labelled. Therefore, we use tangent.
[tex]tan(x)=\frac{17}{13}[/tex]
To find x, we want to use inverse tangent.
[tex]x=tan^{-1}(\frac{17}{13} )[/tex] [plug into calculator]
[tex]x=52.6[/tex]
Now, we know that x=52.6°.
The diagram shows APQR. Which term describes point S?
Answer:
c) centroid
Step-by-step explanation:
14. The data below show the average ages and number of volunteer hours for five randomly chosen persons. Given the equation of the regression line is y' = 9.309x - 167.012, predict the number of hours a person will volunteer if her age is 27.5 years. Age, x Volunteer Hours, y 24.9 66.5 25.6 70.0 26.1 74.8 27.3 89.6 27.0 82.6
The Predicted time a person will serve is "88.9855 months". A complete solution is provided below.
Given equation is,
→ [tex]\hat{y}=9.309x - 167.012[/tex]
Her age,
→ x = 27.5 years
By substituting the value of "x" in the given equation, we get the predicted time,
hence,
→ [tex]\hat{y}=9.309\times 27.5 - 167.012[/tex]
[tex]= 255.9975- 167.012[/tex]
[tex]=88.9855 \ months[/tex]
Thus the above is the right answer
Learn more:
https://brainly.com/question/1783478
the cost of using 19 hcf of water is $36.48 and the cost of using 32 hcf is 56.63 what is the cost of using 28 hcf of water?
Answer:
$54.32
Step-by-step explanation:
19=$36.48/19 =1.94
1=$1.94 * 28= 54.32
28=54.32
Need tha answer explained
Answer:
Bri what do you mean explanation your answer is correct
Please mark me brainliest thanks
Answer:
It is 77.2, so your anwer is correct.
Step-by-step explanation:
Finding decimal divided by decimal too hard? Don't worry, I've got your back! To do division, you can do it the hard way by just dividing it, but there's something more simple.
Move the dividend's decimal point to the right until it's not a decimal. Do the same with the divisor, but it depends on how many decimal places on the dividend was moved by. So in this case, you move it by 2 decimal places for BOTH! Then you just simply divide it. It gives you the same answer.
BTW if I didn't make my explanation clear, please comment.
(2i+1)/(1+i) is equal to
Answer:
Step-by-step explanation:
(1 + 2i) / (1 + i) Rationalize the denominator.
(1 + 2i)(1+i) / (1 + i)(1-i) Remove the brarckets
(1 + i + 2i - 2) / (1 - i + i - i^2) Combine
-1 + 3i / (2) i^2 = - 1 in the denominator
Suppose an average student can answer 6 homework questions in 30 minutes. If X follows an exponential distribution and measures the length of time between starting two homework questions. What is the value of μ?
Answer:
10
Step-by-step explanation:
Make a ratio like
6 : 30
2 : x
Then cross multiple
6x = 60
Make x subject formula
x = 10
I hope it helped
A card is drawn from a well shuffled deck of 52 cards what is the probability of drawing an ace or a six
Answer:
8/52
Step-by-step explanation:
The first thing to do is write it out;
How many aces are in a deck and how many sixes?
There are 4 of each so, 4+4 = 8 therefore our beginning ratio will be;
8/52 cards are going to be an ace or a six.
I need help with these questions
9514 1404 393
Answer:
17. 25 mile per gallon
18. Eduardo did should have divided by -4.
Step-by-step explanation:
17. The least mileage will be had when the most gas is used to go a given distance. For the given distance, the most gas that could have been used (without adding any) is 18 gallons. Then the least mileage is ...
(450 mi)/(18 gal) = 25 mi/gal
__
18. The appropriate method for solving this inequality is ...
-4x/(-4) < 120/(-4) . . . . divide both sides by -4 (and reverse the > symbol)
x < -30
The step Eduardo took of adding 4 will give ...
-4x +4 > 124 . . . . . puts him one step farther away from a solution
Eduardo chose an operation to perform that did not get him closer to a solution.
3/4 of the households in a rural area have pets. how many households have pets in this area if there are 1500 total households
Answer:
1,125 households would have pets in the area.
Step-by-step explanation:
We have 1,500 total households. We also know that 3/4 (or 0.75) of these households have pets. We would multiply 1,500 by 0.75 (which is equal to 3/4), resulting in 1,125. Therefore, 1,125 households would have pets in the area.
Answer:
1125 households
Step-by-step explanation:
3/4 of total households in area = # of households that have pets in the area
3/4 of 1500 = # of households that have pets in the area
3/4 · 1500 = # of households that have pets in the area
75/100 · 1500 = # of households that have pets in the area
0.75 · 1500 = 1125
1125 households
Solve the inequality is it a,b,c,d?
Answer:
B
Step-by-step explanation:
-2/3x<31/3
x>-31/2
x>-15 1/2
Answer:
x > - 15 1/2
Step-by-step explanation:
-2/3 x -10 < 1/3
Multiply each side by 3
3(-2/3 x -10 < 1/3)
-2x -30 < 1
Add 30 to each side
-2x-30+30 <1+30
-2x < 31
Divide by -2 remembering to flip the inequality
-2x/-2 > 31/-2
x > -31/2
x > - 15 1/2
What is 9,000,000 + 8,000 + 90,000,000 + 100 + 2 + 90,000 + 90 in standard form?
Answer:
9×10^7 + 9×10^6 + 9×10^4 + 8×10^3 + 1 ×10^2 + 9×10 + 2
please mark this answer as brainlist
Need the value of P please
Answer:
B. 35°
Step-by-step explanation:
First, find the two interior angles that are adjacent to angles 90° and 125° respectively.
Thus:
Interior angle 1: 180° - 90° = 90° (linear pair)
Interior angle 2: 180° - 125° = 55° (linear pair)
P + 90° + 55° = 180° (sum of interior angles in a triangle)
P + 145° = 180°
Subtract 145° from each side
P = 180° - 145°
P = 35°
A truck can be rented from Company A for $120 a day plus $0.80 per mile. Company B charges $50 a day plus $0.90 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
700 miles driven in a day
Step-by-step explanation:
Create an equation to represent the situation, where x is the number of miles.
0.8x + 120 = 0.9x + 50
Solve for x:
120 = 0.1x + 50
70 = 0.1x
700 = x
So, the rental costs will be the same at 700 miles driven in a day.
question is in picture
Answer: A
Step-by-step explanation:
(tangent is opposite over adjacent)
[tex]tan(40)=\frac{x}{3.8}\\x=3.8*tan(40)[/tex]
The sum of two numbers is 21. Five times the first number added to 2 times the second number is 66. Find the two numbers.
what is the value of g
Answer:
the value of g is gram .
may this answer is helpful for you
Please I need the answer ASAP!!!!
Step-by-step explanation:
D
*not sure about this answer pls tell me i ak right or wrong
An education researcher would like to test whether 2nd graders retain or lose knowledge during the summer when they are presumably not in school. She asks nine 2nd graders to take a comprehension exam at the end of the school year (May), and then asks those same students to come back after the summer (late August) to retake a different but equivalent exam, to see if their level of comprehension has changed. Using the data below, test this hypothesis using an (alpha level of 0.05.)
May August
95 100
72 80
78 95
50 65
89 85
92 98
75 70
90 96
65 87
Required:
What is the appropirate test?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
May August
95 100
72 80
78 95
50 65
89 85
92 98
75 70
90 96
65 87
The appropriate test is a paired t test :
d = difference between May and August
d = (-5, -8, -17, -15, 4, -6, 5, -6, -22)
The hypothesis :
H0 : μd = 0
H1 : μd ≠ 0
The test statistic :
T = dbar / (Sdbar/√n)
Where, dbar and Sdbar are the mean and standard deviation of 'd' respectively.
Using calculator :
dbar = - 7.777 ; Sdbar = 9.052
Test statistic = - 7.777 / (9.052 /√9)
Test statistic = - 2.577
The Pvalue, df = n - 1 = 9 - 1 = 8
Pvalue(-2.577, 8) = 0.0327
At α = 0.05
Pvalue < α ; WE reject the H0 ; and conclude that there has been a change in score
Given f (x) = 3x - 5 find f (x - 2)
Answer:
3x-11
Step-by-step explanation:
f (x) = 3x - 5
f(x-2)
Replace x in the function with x-2
f (x-2) = 3(x-2) - 5
=3x-6 -5
=3x-11
If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
A. 13
B. 52
C. 208
D. 104
Answer:
D. 104
Step-by-step explanation:
[tex]y \: \alpha \: \frac{1}{ {x}^{2} } \\ \\ y = \frac{k}{ {x}^{2} } [/tex]
when y is 26, x is 4:
[tex]26 = \frac{k}{ {(4)}^{2} } \\ k = 416[/tex]
when x is 2:
[tex]y = \frac{416}{ {x}^{2} } \\ \\ y = \frac{416}{ {(2)}^{2} } \\ y = 104[/tex]
Answer:
D; 104
This is the correct answer
Change the following to percentages:
a) 83 out of 100
b) 24 out of 50
c) 9 out of 25
d) 7 out of 20
e) 6 out of 10
f)72 out of 200
g)12 out of 40
h)36 out of 60
Answer:
a.83%
b. 48%
c.36%
d.35%
e.69%
f.36%
g.30%
h.69%
what is 4 and 5???????
Answer:
586 cm^3 and 486 in^2
Step-by-step explanation:
4) The volume of the triangular prims is (1/2)*(a*c*h) = 0.5*(8*9*16)=586 cm^3
5) Wrapping paper needed is equal to the surface area of the cube, 6s^2=486 in^2
In ∆ ABC,AD is the altitude from A to BC .Angle B is 48°,angle C is 52° and BC is 12,8 cm. Determine the length of AD
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Answer:
7,6 cm
Step-by-step explanation:
The law of sines can be used to find the length AB.
AB/sin(C) = BC/sin(A)
A = 180° -48° -52° = 80°
AB = BC·sin(C)/sin(A) = 12,8·sin(52°)/sin(80°)
The sine function can be used to find AD from AB.
AD/AB = sin(48°)
AD = AB·sin(48°) = 12,8·sin(48°)sin(52°)/sin(80°)
AD ≈ 7,61 cm
__
The dimension of interest is ha in the attachment, the height from vertex A.
