Answer:
102,232 = 2·2·2·13·983
Step-by-step explanation:
102,232 ends in 32, so is divisible by 4
102,232/4 = 25558 ends in 2, so is divisible by 2
25558/2 = 12779
is not even, so is not divisible by 2
has a sum of digits mod 9 of 8, so is not divisible by 3 or 9
does not end in 0 or 5, so is not divisible by 5
gives the result 1277-2·9 = 1259; 125-2·9 = 107; 10-2·7 = -4, which is not zero, so 12779 is not divisible by 7
gives the result (1+7+9)-(2+7) = 8, which is not divisible by 11, so 12779 is not divisible by 11
gives the result 1277 +4·9 = 1313, which is divisible by 13, so 12779 is divisible by 13
12779/13 = 983 needs to be tested for divisibility by primes between 17 and 31, namely 17, 19, 23, 29, 31. It is not divisible by any of these, so this is the last prime factor of 102,232:
102,323 = 2·2·2·13·983
_____
Divisibility rules:
Note that for any transformation rule, the rule can be repeated on the reduced result. The digits of a sum of digits can be summed, for example.
2: ends in even digit
3: sum of digits is divisible by 3
5: ends in 0 or 5
7: subtracting 2 times the last digit from the rest is divisible by 7
11: difference of sums of alternate digits is divisible by 11
13: there are several rules. A couple of useful ones are
the sum of 4 times the last digit and the remaining number will be divisible by 13 (used above)the difference of the sums of alternate groups of 3 digits will be divisible by 13 (232-102 = 130, for the number above; is divisible)17: subtracting 5 times the last digit from the rest is divisible by 17
19: the sum of 4 times the last 2 digits and the remaining number will be divisible by 19
23: the sum of 3 times the last 2 digits and the remaining number will be divisible by 23
29: the sum of 9 times the last 2 digits and the remaining number will be divisible by 29
31: subtracting 3 times the last digit from the rest is divisible by 31
What is 10,000 steps in feet
Answer: 10,000 steps is 5 miles aka 2,000 feet
Step-by-step explanation:
Children in 50 Households
Number of Children Number of
Households
0
5
1
11
2
13
3
10
4
9
5
2
Using a proportion, what can you infer about the number of households in her town that have more than thre
About 242 households have more than three children.
About 269 households have more than three children.
About 296 households have more than three children.
About 565 households have more than three children.
Answer:I think it’s 269 because when you do 1,350 divided by 50 it’s 27 then you add 9+2 to get 11/50 then you do 27x11 which gives you 270 and the closest answer to that is 269
Step-by-step explanation:
Answer:
About 296 households have more than three children.
Step-by-step explanation:
I got it right on edge
Subtract fifteen and eighty-eight ten-thousandths from thirty-six. Express your answer in numerical and word form.
Answer:
20 and nine thousand nine hundred and twelve ten thousandth
Step-by-step explanation:
fifteen and eighty-eight ten thousandth =15 88/10000
Thirty six=36
36 - 15 88/10000
36 - 150088/10000
(36x10000 - 150088)/10000
(360000 - 150088)/10000
209912/10000=20 9912/10000
20 and nine thousand,nine hundred and twelve ten thousandth
The value of the expression [36 - (15 + 88 / 10,000)] is 20.9912.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Subtract fifteen and eighty-eight ten-thousandths from thirty-six. Then the expression is given as,
⇒ 36 - (15 + 88 / 10,000)
The value of the expression is calculated as,
⇒ 36 - (15 + 88 / 10,000)
⇒ 36 - (150,088/10,000)
⇒ (360,000 - 150,088) / 10,000
⇒ 209,912 / 10,000
⇒ 20.9912
More about the Algebra link is given below.
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PI is the _ of a circle's _ to its _
Answer:
ratiocircumferencediameterStep-by-step explanation:
Pi is the ratio of a circle's circumference to its diameter.
_____
We suspect you have answer choices for filling in these blanks. Besides the words shown above, there are other ways they can be filled:
Pi is the ratio of a circle's area to its radius squared.
Pi is the measure of a circle's central angle to its diameter endpoints.
is -18/3 a integer yes or no?
Answer:yes
Step-by-step explanation:
An integer is a number that can be written without fractional exponent
-18/3=-6 so it is an integer
A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate. Please show written work for question a to c below. a) Find critical value(s). b) "Find the Margin of Error" c) Find confidence interval for the problem.
Answer:
a) z = 2.327
b) The margin of error is of 0.065.
c) The 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate is (0.3083, 0.4383).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 300, \pi = \frac{112}{300} = 0.3733[/tex]
a) 98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]z = 2.327[/tex] is the critical value.
b)
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
So, applying to this question:
[tex]M = 2.327\sqrt{\frac{0.3733(1-0.3733)}{300}} = 0.065[/tex]
The margin of error is of 0.065.
c) Find confidence interval for the problem.
[tex]\pi - M = 0.3733 - 0.065 = 0.3083[/tex]
[tex]\pi + M = 0.3733 + 0.065 = 0.4383[/tex]
The 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate is (0.3083, 0.4383).
A box contains 180 wooden cubes. You open the top of the box and count 9 cubes across the front and 4 cubes along a side. How many layers of wooden cubes are in the box?
Answer:
14 or 13 layers
Step-by-step explanation:
Answer:
A box contains 180 wooden cubes. You open the top of the box and count 9 cubes across the front and 4 cubes along a side. How many layers of wooden cubes are in the box?
5 layers
What if f(x)=(1/7)(7x), what is f(3)
Answer:
3
Step-by-step explanation:
f(x) = (1/7)(7x) can be simplified to ...
f(x) = x
Then for x=3, ...
f(3) = 3
arc length of a half of a circle with radius of 9
Answer:28.26
Step-by-step explanation:
Φ=180 since it's in a straight line
Radius=r=9
π=3.14
Length of arc=Φ/360 x 2 x π x r
Length of arc=180/360 x 2 x 3.14 x 9
Length of arc=0.5 x 2 x 3.14 x 9
Length of arc=28.26
I keep gettin it wrong please help!!!
Answer:
-5≤ x ≤5 or [-5,5]
Step-by-step explanation:
domain is related to independent variable x
black dots means that number is included in the domain
in this case function is from -5,5 included or -5≤ x ≤5 or [-5,5]
Simplify the following expression.
(57x + 79) - (-30x + 6)
Answer:
87x + 73
Step-by-step explanation:
Combine like terms. Combining the x terms yields 87x; combining the constants yields 73. Thus, the desired expression is 87x + 73.
Answer:87x+73
Step-by-step explanation:
Distribute the Negative Sign:
=57x+79+−1(−30x+6)
=57x+79+−1(−30x)+(−1)(6)
=57x+79+30x+−6
Combine Like Terms:
=57x+79+30x+−6
=(57x+30x)+(79+−6)
=87x+73
Lena is 10 years old. She asks her dad how old he is. He tells her that the lcm of their ages is 14 times the hcf of their ages. She knows that her dad is at least 30 years old but younger than 45. Work out how old her dad is.
Answer:
35
Step-by-step explanation:
Let x represent the HCF of the ages. Then we can have ax = 10 represent Lena's age, and bx can represent her dad's age.
The LCM will be abx = 14x, so we have ab = 14.
Factors of 14 are 1·14 and 2·7. Since the ratio of ages is between 30/10 = 3 and 45/10 = 4.5, we must have b/a in that range. This will be the case for ...
a=2, b=7
For a=2 and ax=10, we have x=5.
The dad's age is bx = 7·5 = 35.
Using the numbers 4.3, -1.07, and -2.971, write an expression containing both addition and subtraction that simplified to a positive number.
Answer:
4.3 + (-1.07)+(-2.971)
Step-by-step explanation:
4.3 + (-1.07)+(-2.971)
4.3 -1.07-2.971
4.3 - 4.041= 0.259
What is the slope (m) and y- and y-intercept (b) of the equation y = -4x + 6
Explanation: Linear equations can be written in the form y = mx + b where the multiplier, m, or the coefficient of the x term represents the slope of the line and the b is your constant term which represents the y-intercept of the line
This linear equation has a slope equal to -4 since it's
the coefficient of the number in front of your variable.
This equation has a y-intercept that is equal to 6 since it's
in the place of the b in the equation y = mx + b.
Solve for a,b,and/or c
Help solve ASAP!
Answer:
a=90-67=23°
.................
After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles for 10 of his clients and checked online price quotes for their policies. Then, based on paired data on the 10 clients (the price he offered them and the corresponding online quote) and using Excel’s t-test for paired data, he obtained t-statistic = 0.709 p-value = 0.248 Note that the above is based on the difference between his price and online quotes.
What are the null and alternative hypotheses, respectively?
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_d[/tex] = 0
Alternate Hypothesis, [tex]\mu_d\neq[/tex] 0
Step-by-step explanation:
We are given that a local insurance agent randomly selected profiles for 10 of his clients and checked online price quotes for their policies.
Then, based on paired data on the 10 clients (the price he offered them and the corresponding online quote), he obtained t-statistic = 0.709 p-value = 0.248.
Here , we will use the concept of Paired data test statistics because the prices that the local insurance agent offered and the corresponding online quotes are from the same single data. These information has not been taken from the two independent samples.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_d[/tex] = 0
Alternate Hypothesis, [tex]\mu_d\neq[/tex] 0
Here, null hypothesis states that there is no difference between the price he offered them and the corresponding online quote.
On the other hand, alternate hypothesis states that there is difference between the price he offered them and the corresponding online quote.
Hence, this would be the correct null and alternative hypothesis.
What percentage of students who take honors English are taking a non-honors math class?
Answer:
B
Step-by-step explanation:
Took quiz GL
Answer:
the answer is not B
Step-by-step explanation:
the answer is A I actually took the quiz
can someone help me and provide steps, please?
Answer:
Step-by-step explanation:
Okay so basically what you need to do is find out how much you can take from 360, in this you you would add the two numbers (70+105) and subtract from 360.
Will mark brianliest if correct,
If Oliver paid $22,how many times did he ride the Ferris wheel?
Math
If u need more information please tell me. Look at the picture
Answer:
11 times
Step-by-step explanation:
So if you look at the point where the line is on two real numbers at the top of the grid, it shows that it cost $10 for every 5 rides. So if you find the unit rate, divide 10 by 5 to see how much each ride cost, you get that each ride cost $2. Then just divide $22 by $2 and you get 11. Hope this helps, comment if you need more help
There are 12 inches in 1 foot. Write 75 inches in feet and inches
Answer:6.25
Step-by-step explanation:
Simplify 3 + 5(x - 4)
Answer:
5x - 17
Step-by-step explanation:
3 + 5x - 20
= 5x - 17
given h(x)=4x-4, solve for x when h(x)=0
Answer:
x=1
Step-by-step explanation:
4x-4=0
4x=4
Therefore, x=1
Describe using the word x. It simply means to translate the amount you've discovered into the variable x.
Given
h(x)=4x-4
once h(x) = 0
0 = 4x-4
4x = 4
x =4/4
x = 1
The phrase "f (x)" denotes a formula with x serving as its input variable.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.Four main categories can be used to classify different sorts of functions. The following relationships are based on the element: One to One Function, Many to One Function, Onto Function, One to One and Onto Function, Into Function.To learn more about h in terms of X refer to:
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Rewrite as a simplified fraction.
0.1 with the 1 repeating
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
[tex]\frac{1}{9} =0.111111111111111111[/tex]
can someone assist me on this
Answer:
The perimeter of the triangle would be 21.2. The area would be 18 ft^2
Step-by-step explanation:
Hope this helps :)
Attached is the work I did to get the answers
Sara created the poster shown below what would be the dimensions of the poster at 1/4 times it’s current size?
The width is 32 cm and the length is 28 cm
Answer:
Width: 8cm Length: 7cm
Step-by-step explanation:
Answer:
Length = 7cm, width = 8cm
Step-by-step explanation:
Divide 32 and 28 by 4
I really just need a simple STEP-BY-STEP explanation on how you do percentages.
Need help with this..
Answer:
Step-by-step explanation:
m4 + m3 = 180 (Supplementary angle on 1 line)
m6 +m3 = 180 (Supplementary angle)
-> m6=m4
-> x+80 = 4x-10
-> 90 = 3x
-> x = 30
-> m6=m4 = 80+30 = 110
...
m1+m4 = 180 (Supplementary angle on 1 line)
-> m1 = 180 -110 = 70
Given: m∠APC = 27°, m DC = 27° Find: m AB
Answer:
The unknown angle = 126°
Step-by-step explanation:
From angles in a triangle.
The total sum of angles in a triangle = 180°
Let the unknown angle be x
27 + 27 + x = 180
X = 180-27-27
X= 180-54
X = 126°
Answer: 81°
Step-by-step explanation:
m<p is a secant exterior angle which equals arcAB-arcDC divided by 2.
plug the numbers in and arcAB-27 / 2 =54 Arc AB is 27+54=81 degrees
Assume the average weight of an American adult male is 180 pounds with a standard deviation of 34 pounds. The distribution of weights follows a normal distribution. What is the probability that a man weighs somewhere between 120 and 155 pounds?
Answer:
Step-by-step explanation:
Find a-score of both
z-score = (x-mean)/SD
for 120
z =( 120- 180)/34 = -1.765
For 155
z = (155-180)/34 = -0.735
The probability to look for using z-score table is;
P(-1.765<z<-0.735) = 0.19239
Solve for a given 2e^a =4b
Answer:
a = ln (2b)
Step-by-step explanation:
2e^a =4b
Divide each side by 2
2/2 e^a =4/2b
e^a = 2b
Take the natural log of each side
ln(e^a) = ln(2b)
a = ln (2b)
