Answer:
We know that every number can be written as a product of prime numbers.
The method to find the factorized form of a number depends on the number, we just try to find the different factors by dividing by them, for example for the number 1000 we have:
1000 is an even number, then we can divide it by 2 (2 is a prime number)
1000 = 2*500 (so we already found a prime factor)
500 is also an even number, so we can divide it by 2
1000 = 2*500 = 2*2*250 (we found another prime factor)
dividing by 2 again we get:
1000 = 2*2*250 = 2*2*2*125
1000 = (2*2*2)*125
now we just need to factorize 125
we know that 125 is a multiple of 5, such that:
125 = 5*25 = 5*5*5
(5 is a prime number, so it is completely factorized).
Then the factorization of 1000 is:
1000 = (2*2*2)*(5*5*5) = 2^3*5^3
Now with another example, 1422
1422 is an even number, so we again start using the factor 2:
1422 = 2 = 711
then:
1422 = 2*711
we already found a factor.
711 is a multiple of 3 (the sum of its digits is a multiple of 3), then:
711/3 = 237
We can write our number as:
1422 = 2*3*237
237 is also a multiple of 3
237/3 = 79
then:
1422 = 2*3*3*79
and 79 is a prime number, so we already have 1422 completely factorized.
Insert a digit in place of each “…” to make numbers that are divisible by 6 if it
is possible:
4…6
?
Answer: Either 2, 5, or 8
This means the number 426 is divisible by 6. So are 456 and 486
===============================================================
Explanation:
A number is divisible by 6 if both of the following are true
The number is divisible by 2The number is divisible by 3This is simply because 6 = 2*3. So if 6 is a factor of a number, then 2 and 3 must be factors.
To have 2 be a factor, the units digit must be in the set {0,2,4,6,8} which is the case here (the units digit is 6 in this case). Therefore we know the number is a multiple of 2 regardless of what the other digits are. To have 3 be a factor, the digits must add up to a multiple of 3. Through trial and error, we see that 0 doesn't work because 4+0+6 = 10 which is not a multiple of 3. Same goes for 4+1+6 = 11, but 4+2+6 = 12 is a multiple of 3.Therefore, 426 is a multiple of 6
Increment that middle digit 2 by 3 and we jump from 426 to 456. Those three digits add to a multiple of 3 as well (4+5+6 = 15). Following that line of logic, we go from 456 to 486 as the last possible three digit number that has these conditions of having 4 first and 6 last, and the number is a multiple of 6.
-------------------------------
In short,
The numbers 426 and 456 and 486 are all multiples of 6 since they are multiples of 2 and 3 at the same time.
So we could replace that middle digit with either 2, 5 or 8.
Sam thinks of a 4 digit number. The digit in the one’s place is 3 less than the digit in the ten’s place and digit in thousand’s place is 5 less than the digit in hundred’s place. The value of the hundred’s place is 800. The digit in ten’s place is the greatest even number. What is the number Sam is thinking of?
9514 1404 393
Answer:
3885
Step-by-step explanation:
The hundreds digit is 8, and the thousands digit is 5 less, so is 3.
The tens digit is 8 (the largest even digit), and the ones digit is 3 less, so is 5.
The number is ...
3885
what is the factors of p(x)=x^2+7√2x+4
PLEAE HELP!
Answer:
aasha here it is.
Step-by-step explanation:
3x−1)(2x+3)
6x2+7x−3
=6x2+9x−2x−3
=3x(2x+3)−1(2x+3)
=(2x+3)(3x−1)
and hiii
Simplify this algebraic expression y-3 over 3+12
Answer:
(Y-3)/(3+12)
(Y-3)/(15)
Y-1/5
so the answer is
(Y-1)
Answer:
[tex]y - 3 \: over \: 3 + 12 \\ y - 3.3 + 12 \\ y - 3.3 + 12 = y + 8.7 \\ y - 33 + 12 \\ y + 8.7[/tex]
Which expression is equivalent to v2/3v2? 1/4 6v2 v2 v2/2
Answer:
Step-by-step explanation:
[tex]2^{1/2} - 2^{-1/3} = 2^{1/2 + 1/3} = 2^{3/6} = 2^{1/2} = \sqrt{2}[/tex]
Answer:
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
2 ^ 1/2 ÷ 2 ^ 1/3
We know that a^b ÷ a^ c = a^(b-c)
2 ^ (1/2 -1/3)
2^ (3/6 - 2/6)
2 ^ 1/6
[tex]\sqrt[6]{2}[/tex]
What is the prime factorization of 30?
O A. 2.2.3.5
O B. 5.6
O C. 3.10
O D. 2.3.5
D. 2.3.5 is the correct answer
Need helpppppppppppppppppp
Answer:
-18
Step-by-step explanation:
B=-6 C=2 P.E.M.D.A.S.
b - 6(c)
-6 - 6(2)
-6 - 12 . The negatives cancel out, adding each other
-6 + -12
= -18 :)
Answer:
b - 6c
= -6 - 6x2
= -6 x( 1+2)
= -6x3
= -18
Can someone help me please..
Answer:
Quadratic formula
Step-by-step explanation:
The function is quadratic because it is a parabola. Exponential functions shoot either upwards or downwards rapidly, and it is clearly not linear due to it's curve. It also isn't piecewise because the function never stops or starts irregularly.
Evaluate these questions 27(1/3)2
Answer:
18
Step-by-step explanation:
1/3 of 27 is 9. 9 times 2 is 18.
Find the measure of each angle whose degree measure is represented in terms of x in the given
triangle.
Please help :)
Answer:
Step-by-step explanation:
Answer:
That's barely readable! Anyway the solution is:
7x + 7x +2 +5x +7 = 180 degrees
19x + 9 = 180 degrees
19x = 171 degrees
x = 9
So the angles are:
7x = 63 degrees
7x + 2 = 65
5x + 7 = 52
Double check:
Since ALL 3 triangle sides add up to 180:
63 + 65 + 52 = 180 degrees
Step-by-step explanation:
Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5% significance level.
Test H0 : p=0.2 vs Ha : p≠0.2 using the sample results p^=0.27 with n=1003
Round your answer for the test statistic to two decimal places, and your answer for the p-value to three decimal places.
Answer:
The value of teh test statistic is [tex]z = 5.54[/tex]
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that the proportion differs from 0.2.
Step-by-step explanation:
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.
0.2 is tested at the null hypothesis:
This means that [tex]\mu = 0.2, \sigma = \sqrt{0.2*0.8} = 0.4[/tex]
Using the sample results p^=0.27 with n=1003
This means that [tex]X = 0.27, n = 1003[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.27 - 0.2}{\frac{0.4}{\sqrt{1003}}}[/tex]
[tex]z = 5.54[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample proportion differs from 0.2 by at least 0.07, which is P(|z| > 5.54), that is, 2 multiplied by the p-value of z = -5.54.
Looking at the z-table, z = -5.54 has a p-value of 0.
2*0 = 0.
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that the proportion differs from 0.2.
Work out m and c for the line:
y – 37 = 5
Answer:
first thing is y - 35 = 5
then y = 35 + 5 because when = come here - will be + and
then we should do+ y=40 answer
Celia was a contestant on Jeopardy. At the
beginning of the round her score was -40.
Celia's score at the end of the round was -
35. How many points did Celia score (or
lose) during the round?
Answer:
75
Step-by-step explanation:
She is in the negatives right now so add 40 to get Celicia points equal to 0. Then add an extra 35 points (which is what she ended with). Overall, she gained 75 points to end with 35.
7. Draw an equilateral triangle of side 6.5 cm and after locating its circumcentre. Draw its circumcircle. send it with image
Answer:
Step-by-step explanation:
A circumcircle can be referred to as a circumscribed circle to a triangle. The steps to follow is stated below:
i. Since the triangle is equilateral, draw the triangle with sides 6.5 cm
ii. Bisect any of its two sides. The two bisecting lines would intersect at center, O, of the triangle.
iii. With the center and either radius OA, OB or OC, draw a circumscribed circle to the triangle.
The construction is attached to this answer for clarifications.
Find the distance between the two points in simplest radical form. (-6,1) and (−8,−4)
Answer: 5
Step-by-step explanation: I think it is 5
What is the absolute value of -20?
there was a number line so
——————————————
-20 -10 0 10 20
and the options were
A.) -20
B.) 0
C.) 20
D.) 40
Answer:
C) 20
Step-by-step explanation:
The absolute value of a number represents the positive distance between the number and zero. Absolute value is therefore always positive.
The distance between -20 and 0 is 20 and therefore the answer is C) 20.
Answer:
20
Step-by-step explanation:
Absolute value = | -20 |
= 20
Option C is correct .
Simplify 6/x^2−2x/x^2+3.
Answer:
3x2−2x+6/x2
Step-by-step explanation:
have a great day <33333
For this problem I believe the answer is option A, B and C. But just wanted to confirm. Is that correct or is my answer wrong?
Answer:
Just A and C
Step-by-step explanation:
B doesn't count because you would not be looking at the 9. Only the 4.
You only look at one number to the right.
Answer:
A and C are correct, but not B
Step-by-step explanation:
When you round, you only look at the number behind the place you are rounding.
6.04 doesn't round to 6.1, so that is not correct
a rectangle box has length 12 inches, width 15 inches, and a height of 17 inches. Find the angle between the diagonal of the box and the diagonal of its base. The angle should be measured in radiands
Answer:
0.7246 radians
Step-by-step explanation:
According to the Question,
Given that, a rectangle box has length 12 inches, width 15 inches, and a height of 17 inches
The length of the base diagonal (d) can be found using the Pythagorean theorem on length and width:d = √{ (12)² +(15)² } = √(144+225) = √369inches
The tangent of the angle is the ratio of the height of the box to this lengthTan∅ = 17/√369
Taking the [tex]Tan^{-1}[/tex] , we have
∅ = [tex]Tan^{-1}[/tex](17/√369) ≈ 0.7246 radians
calculate the value of X in the diagram
Answer:
[tex]EA = \frac{21 \times 15}{7} = 45 \\ { \tt{ \frac{21}{7} = \frac{x}{45} }} \\ x = 135[/tex]
Write an algebraic expression for the situation. 28 divided by a number n An algebraic expression for the situation is
Answer:
[tex]\frac{28}{n}[/tex]
Step-by-step explanation:
Z varies directly as Square x and inversely as y. If z = 187 when x = 64 and y = 6, find z if and 9. (Round off your answer to the nearest hundredth.)
Answer:
Z = 50
Step-by-step explanation:
Given the following data;
Z = 187
x = 64
y = 6
Translating the word problem into an algebraic expression, we have;
Z = k√x/y
First of all, we would find the constant of proportionality, k;
187 = k√64/6
187 * 6 = k√64
1122 = 8k
k = 1122/8
k = 140.25
To find z, when x and y = 9
Z = 140.25√9/9
Z = (140.25 * 3)/9
Z = 420.75/9
Z = 46.75 ≈ 50
Note: The values in the latter part of the question isn't explicitly stated, so I assumed a value of 9 for both x and y.
Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 2.5 month. 34 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.
Answer:
Step-by-step explanation:
a.) it's just mean, variance
so here it's just 12,6.25
b.) For the x bar thing just divide the variance by the number of people (mean stay the same)
the variance is then (2.5²/34)= .1838
which makes it (12,.1838)
c.) here we don't use x bar (and so it's normal (12,2.5²))
p(11.6) = (11.6-12)/(2.5)= -.16 = .4364
p(12.4)= (12.4-12)/2.5 = .16= .5636
.5636-.4364= .1272
d.) here we use x bar because it's asking for an average so it's normal (12, .1838)
same deal
p(11.6)=(11.6-12)/√.1838= -.93295= .1762
p(12.4)= (12.4-12)/√.1838= .93295= .8238
.8238-.1762= .6476
d.) no because they're probably IID
f.) It's average so here we use x bar
q1 is just the 25th percentile
the 25th percentile is -.6745
-.6745=(x-12)/(√.1838)= 11.711
q3 is the 75th percentile
.6745=(x-12)/√.1838
x=12.289
The interquartile range is just the difference between the two
12.289-11.711= .5784
Verify that the equation is an identity.
Step-by-step explanation:
We need to prove that ,
cot x / csc x - csc x / cot x = - tan x sec x .
LHS :-
> cot x / csc x - csc x / cot x
> cos x / sin x ÷ csc x - sin x × csc x / cos x
> cosx - 1/ cos x
> cos² x - 1 / cos x
> - sin²x / cosx
> -sin x / cos x × sin x
> -tan x sin x
= RHS
Hence Proved !
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 144 millimeters, and a variance of 49 . If a random sample of 46 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 2 millimeters? Round your answer to four decimal places.
Answer:
0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean diameter of 144 millimeters, and a variance of 49.
This means that [tex]\mu = 144, \sigma = \sqrt{49} = 7[/tex]
Sample of 46:
This means that [tex]n = 46, s = \frac{7}{\sqrt{46}}[/tex]
Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?
Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.
Probability the sample mean is below 142:
p-value of Z when X = 142, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{142 - 144}{\frac{7}{\sqrt{46}}}[/tex]
[tex]Z = -1.94[/tex]
[tex]Z = -1.94[/tex] has a p-value of 0.0262
2*0.0262 = 0.0524
0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.
I need help with this problem.
Answer:
-4
Step-by-step explanation:
2t=-1-7
t=-8/2
t=-4
i am not sure also
is y=3x^2-x-1 a function
Answer: Yes it is a function.
This is because any x input leads to exactly one y output.
The graph passes the vertical line test. It is impossible to draw a single vertical line through more than one point on the parabolic curve.
The product of 2 integers is 72. One number is two less than five times the other. Which equation can be used?
Answer:
should be (5y-2)y = 72
Step-by-step explanation:
since the product of the two is 72, it's true that xy = 72. and it is also true that x is equal to five times y minus 2, so you can rewrite x as 5y-2. plug that in for x in the first equation, and you're set. hope this helps :)
22/24 Marks
51%
The diagram shows a star made by surrounding a
regular octagon with triangles.
Explain why angle a must be 135º.
+
I
Answer:
Step-by-step explanation:
shape Sides Sum of interior angles Each Angle
Triangle 3 180° 60°
Quadrilateral 4 360° 90°
Pentagon 5 540° 108°
Hexagon 6 720° 120°
Heptagon 7 900° 128.57...°
Octagon 8 1080° 135°
Nonagon 9 1260° 140°
Solve each inequality. Graph the solution on a number line.
Answer:
n>2 2/3
Draw a filled dot at a little more than 2 1/2 and continue the line to the right.
Step-by-step explanation:
Subtract 1/3 from both sides to get
2 2/3
Flip the inequality
n> 2 2/3
I hope this helps!
