The prime factorization of each of these integers are
a) 88 = 2 x 2 x 11
b) 126 = 2 x 3 x 3 x 7
c) 729 = 3 x 3 x 3 x 3 x 3
d) 1001 = 7 x 11 x 13
e) 1111 = 3 x 3 x 3 x 37
f) 909,090 = 2 x 3 x 3 x 5 x 7 x 11 x 13
What is prime factorization?Generally, Prime factorization is the process of expressing a positive integer as a product of its prime factors.
For example, the prime factorization of 15 is 3 x 5, since 3 and 5 are prime numbers and 15 can be expressed as the product of 3 and 5.
Here is the prime factorization of another positive integer:
36 = 2 x 2 x 3 x 3
In this example, the prime factorization of 36 is 2 x 2 x 3 x 3, since 36 can be expressed as the product of the prime numbers 2 and 3.
Prime factorization is useful for finding the greatest common divisor (GCD) of two or more integers, and for determining whether a number is prime or composite. It can also be used to simplify fractions by cancelling out common factors.
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A topological group G is a group that is also a topological space satisfying the T1 axiom, such that the map of G×G into G sending x×y into x⋅y, and the map of G into G sending x into x−1, are continuous maps.
The topological group G is a group that is also a topological space satisfying the T1 Axiom that is, there is a topology on the elements of G and all sets of a finite number .
Given :
A topological group G is a group that is also a topological space satisfying the T1 axiom, such that the map of G * G into G sending x * y into x⋅y, and the map of G into G sending x into x^−1, are continuous maps.
When we say the map of G * G into G defined as (x, y) 7 → x·y is continuous, we use the product topology on G * G. Since inversion maps G to G, the topology on G is used both in the domain and co - domain.
Every group G is a topological group. We just equip G with the discrete
topology. Continuity of the binary operation follows at (x, y) ∈ G * G by taking the open set O = { x · y } (the “δ set” ) for any given open set in G * G containing (x, y) (the “ε set”).
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Find the degree to the nearest point
The degree to turn before walking 673 paces is 59 degrees
How to determine the degree to walk?From the question, we have the following parameters that can be used in our computation:
Lengths = 989 paces, 673 paces and 861 paces
These paces can be represented as
x = 989
y = 673
z = 861
The measure of the required angle (angle Z) i.e. the degree to walk can be calculated using the following cosine rule
z² = x² + y² - 2xy * cos(Z)
Substitute the known values in the above equation, so, we have the following representation
861² = 989² + 673² - 2 * 989 * 673 * cos(Z)
Evaluate the exponents, the products and the summation
So, we have the following representation
741321 = 1431050 - 1331194 * cos(Z)
Evaluate the like terms
- 1331194 * cos(Z) = -689729
Divide both sides by - 1331194
cos(Z) = 0.51812808651
Take the arc-cos of both sides
Z = 58.7
Approximate
Z= 59 degrees
Hence, the measure of the angle is 59 degrees
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Keisha and David each found the same value for cos0, as shown below, given sin0=-8/17. Keisha's Solution
tan²8+1 = sec²e
sin² e
cos² e
=+1=
17
cos² e
(-) + Co
+1=
1
cos² e
cos² e
+ cos²9=1
64
cos 9-1-
-- 289
15
cose=17
David's Solution
sin²+ cos² = 1
cos²8-1-(-17)
Со
cos = ±
225
289
15
cose=¹17 whose procedure is correct?
The procedure is correct is 1 + tan²(theta) = sec²(theta)
What is Fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
And
cos²(theta) = 1 - sin²(theta)
Are both valid identities
Keisha and the David.
As per the question Kisha and the David found the same value of the cosine theta as given by the Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).
Thus the answer is both procedures are correct.
As they both wanted to find the solutions to the numerical problems they made two different methods.
Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).
Hence both options are the same and true.
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Knowledge Check
Find x
x=
Answer:
x is 44 Hope that helps.
How many three digit odd numbers are there? Assume that the first digit cannot be 0
three digit odd numbers are 450.
What is odd number?
Whole numbers that cannot be split perfectly into pairs are referred to be odd numbers. When two is divided by an odd number, one is left over.
Odd numbers 1, 3, 5, 7, 9, 11, 13, etc. are in order.
In the place of the ones, odd numbers have the digits 1, 3, 5, 7 or 9.
9 digits = (1,2,3,4,5,6,7,8,9) are the digits that may be used to fill in any spot.
There are nine different methods to fill the thousand's position, hence the 100 spot cannot be zero.
There are 10 different methods to fill the number ten.
There are 5 different methods to fill the unit location (1,3,5,7,9)
Three-digit odd totals are (9*10*5), which equals 450.
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The table below gives the 5 number summary
From the 5-number summary table, the answers came out as a) 60 students b) 90 students c) 20 students d) 40 students
What are quartile ranges?
The interquartile range in descriptive statistics reveals the spread of your distribution's middle half.
Any distribution that is sorted from low to high is divided into four equal portions using quartiles. The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.
Median marks is the marks secured by 50% of students.
Hence, if there 120 students and the median marks is 73, the number of students who got more than 73 is 50% of 120, which is 60.
Q1 or the first quartile range is the marks obtained by 25% of students.
Hence, 25% of 120 students scored 55 and 75% of 120 students scored more than 55, which is 90.
For the 80 students in evening classes, 25% of the secured grade less than 45, the first quartile, which is 25% of 80, that is 20.
Similarly 50% of 80 students scored grade more than between 45 and 82, which is 40.
From the 5-number summary table, the answers came out as a) 60 students b) 90 students c) 20 students d) 40 students
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2(x - 6) + 2 = 4x - 4
Answer:
x = - 3
Step-by-step explanation:
2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify
2x - 12 + 2 = 4x - 4
2x - 10 = 4x - 4 ( subtract 4x from both sides )
- 2x - 10 = 4x - 4 ( add 10 to both sides )
- 2x = 6 ( divide both sides by - 2 )
x = - 3
Answer:
SOLUTION
2(X-6)+2=4X-4
open the blanket by multiplication
2x-12+2=4x-4
2x-10=4x-4
collect like term
2x+4x=-4+10
6x=6
divide both side by 6
x=1
Can someone please solve this its on computer and im only good on paper
By graphing, the solution to the system, y = 5x + 2 and y = x - 2 is: A. (-1, -3)
How to Solve a System of Equations by Graphing?The solution to a system of equations is the coordinates of an ordered pair that will make both of the equations to be true. This coordinates is determined by graphing.
To do this, plot both lines on a coordinate plane, then determine the coordinates of the point of intersection of both lines.
Given the system of equations,
y = 5x + 2
y = x - 2
The graph that shows both equations are attached below where the red line is y = 5x + 2, and y = x - 2 is the blue line.
The point of intersection is at (-1, -3). Therefore, the solution is:
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Two independent samples have been selected, 6262 observations from population 1 and 5151 observations from population 2. The sample means have been calculated to be x¯¯¯1=13.2x¯1=13.2 and x¯¯¯2=11.5x¯2=11.5. From previous experience with these populations, it is known that the variances are σ21=39σ12=39 and σ22=29σ22=29.For the hypothesis test of H0:(μ1−μ2)=1.6H0:(μ1−μ2)=1.6 and Ha:(μ1−μ2)≠1.6Ha:(μ1−μ2)≠1.6 Use α=0.04α=0.04.(a) Compute the test statistic.z=z=(b) Find the approximate p-valuep−value=p−value=The final conclustion isA. There is not sufficient evidence to reject the null hypothesis that (μ1−μ2)=1.6(μ1−μ2)=1.6.B. We can reject the null hypothesis that (μ1−μ2)=1.6(μ1−μ2)=1.6 and accept that (μ1−μ2)≠1.6(μ1−μ2)≠1.6.
a) The test statistic for the two independent samples is 0.7
b) The p-value for the test sample is 0.483 , here p-value is greater than significance level.Thus, there is no sufficient evidence to reject null hypothesis.
Given,
significance level, \alpha = 0.04
From population 1,
Mean, [tex]x_1=13.2[/tex]
variance, [tex]\sigma^2_1=39[/tex]
standard deviation, [tex]\sigma_1 =6.24[/tex]
sample size,[tex]n_1=62[/tex]
From population 2,
Mean, [tex]x_2=11.5[/tex]
variance, [tex]\sigma^2_2 = 29[/tex]
standard deviation, [tex]\sigma_2=4.47[/tex]
Test hypothesis,
[tex]H_0:(\mu_1-\mu_2)=1.6\\\\H_a:(\mu_1-\mu_2)\neq1.6[/tex]
a)
The test statistic can be determined by formula,
[tex]z=\frac{(x_1-x_2)-d}{\sqrt{\frac{S^2_1}{n^2_1}+\frac{S^2_2}{n_2}}}[/tex]
[tex]d=\mu_1-\mu_2=1.6[/tex]
[tex]z=\frac{(13.2-11.5)-1.6}{\sqrt{\frac{6.24^2}{62^2}+\frac{4.47^2}{51}}}\\\\z=\frac{0.1}{\sqrt{0.01+0.007}}\\\\z=\frac{0.1}{0.13}=0.7[/tex]
b)
P-value can be calculated by the z-score table
as z=0.7 then from z-value table
p=0.483
A p-value greater than 0.04 (> 0.04) indicates strong support for the null hypothesis. This means that the null hypothesis is retained and the alternative hypothesis is rejected. It is important to note that you cannot accept the null hypothesis; we can only reject it or fail to reject it.
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The window measures 32 inches wide 48 inches tall to put lights around the window how many inches will I need
Answer: 160 inches
Step-by-step explanation:
To put lights around the window, you will need a total of 32 + 48 + 32 + 48 = <<32+48+32+48=160>>160 inches of lights. You will need this much light to go completely around the window.
You need to compute a 90% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.4? (Use 7.0 as an estimate of the population standard deviation from prior studies.) Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places. Round up your answer to the nearest whole number.)
As per the given confidence interval, the sample size is 102.
The term confidence interval in math is referred as the mean of your estimate plus and minus the variation in that estimate.
Here we have given that you need to compute a 90% confidence interval for the population mean.
And we need to find the sample size.
While we looking into the given question, we have identified the following values,
Confidence interval = 90% = 0.09
mean = 1.4
Then the sample size is calculated as,
In order to find this one we have to find the critical value of z for 90% confidence level is,
=> z = 1.645
Now, we have to calculate the value of n as,
=> z x σ / √n
when we apply the value on it, then we get,
=> 1.645 x 1.4/√n
When we simplify this one then we get the value of n as 102.
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Daniel ran 5 kilometers less then Abhasra last week. Daniel ran 16 kilometers. how many kilometers did Abhasra run?
How do you graph 5x= -50
Answer:
you cannot
Step-by-step explanation:
you cannot graph something like that, it is not a equation of a line nor a point or if you want to solve it it is x = -10
Answer:
Step-by-step explanation:
given in the question that 5x=-50
on solving the equation
we get, x=-10
on the graph on the negative x-axis locate the point x=-10
NO LINKS!! Please help me with this problem. Part 3gg
Answer:
It is a reciprocal function
Step-by-step explanation:
f(x) = x, the reciprocal function is f(x) = 1/x
Age of Senators The average age of senators in the 108" Congress was 57.5 years. If the standard deviation was 11.5 years, find the -scores corresponding to the oldest and youngest senators of age 87 and 44. Round scores to two decimal places. find the z-score corresponding to the oldest senator of age 85 is
The z-scores correspond to the oldest and youngest senators of ages 87 and 44 are 2.57 and -1.17. The z-score corresponding to the oldest senator of age 85 is 2.39.
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. The formula to calculate this score [tex]z=\frac{x-\mu}{\sigma}[/tex]. Where z is the z-score, x is the observed value, μ is the sample mean, and σ is the sample standard deviation.
Given μ = 57.5 and σ = 11.5.
When x = 87, the z-score value is,
[tex]\begin{aligned}z&=\frac{87-57.5}{11.5}\\&=2.57\end{aligned}[/tex]
When x = 44, the z-score value is,
[tex]\begin{aligned}z&=\frac{44-57.5}{11.5}\\&=-1.17\end{aligned}[/tex]
When x = 85, the z-score value is,
[tex]\begin{aligned}z&=\frac{85-57.5}{11.5}\\&=2.39\end{aligned}[/tex]
The required answers are 2.57, -1.17, and 2.39.
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A company has computed a seasonal index for its quarterly sales. Which of the following statements is not correct?
Multiple Choice
The sum of the four quarterly seasonal index numbers is 4.
The index for any quarter must be between 0 and 2.
The average index is 1.
An index of 0.75 for quarter-one sales indicates that sales were 25 percent lower than average sales.
An index of 1.10 indicates sales 10% above the norm.
The option b "The index for any quarter must be between 0 and 2" is correct.
In the given question, we have to find the incorrect statement about a company has computed a seasonal index for its quarterly sales.
For its quarterly sales, the corporation has created a seasonal indicator.
Consequently, it is correct that the four quarterly seasonal index figures add up to 4.
True, the average index is 1.
In this situation, an index of 0.75 for the first quarter's sales implies that they were 25% below average, while an index of 1.10 shows that they were 10% over average.
Hence, the incorrect statement of the option b "The index for any quarter must be between 0 and 2" is correct.
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What is the angle of Q?
66°
Step-by-step explanation:
X=22°
3x= 3*22=66°
to find value of x:
(2x+3)+3x+67=180°
5x+70=180°
x=22°
A mom mixes 9 ounces of juice with 3 ounces of water. What percent of the drink is juice?
6th math percent proportions 6.5B
8p 85%
Step-by-step explanation:
cause it's more juice then water
Which two triangles are congruent by the AAS theorem? Complete the congruence statement.
Answer:
Step-by-step explanation:
w
If it were the case that an increase in inflation permanently reduced unemployment, then that would mean
a. money would not be neutral and the long-run Phillips curve would slope upward.
b. money would not be neutral and the long-run Phillips curve would slope downward.
c. money would be neutral and the long-run Phillips curve would slope upward.
d. money would be neutral and the long-run Phillips curve would slope downward.
If it were the case that an increase in inflation permanently reduced unemployment, then that would mean: b. money would not be neutral and the long-run Phillips curve would slope downward.
What happens when inflation increases and unemployment decreases?Theoretically, when unemployment rates decline, inflation rates should climb. The Phillips Curve, which has been codified, is used to describe this. Less unemployment, according to the Phillips Curve, equals more spending by consumers, which puts greater pressure on pricing.
A graph showing that, over the long term, there is no correlation between the unemployment rate and inflation; the LRPC is vertical at the natural rate of unemployment.
In comparison to the long-run Philips curve, the short-run Philips curve slopes downward. The unemployment rate and inflation rate are depicted on the X and Y axes, respectively, of the Philips curve.
Correct option: b
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Ann-Marie can order 5 fewer pounds of cheese
so that her order of 75 pounds of cheese and
50 boxes of crackers will make exactly 25 gift
baskets.
Answer:
Below
Step-by-step explanation:
Divide each quantity by 25 to find the amount in each basket
cheese = 75 lb / 25 bask = 3 lb per basket
crackers = 50 box / 25 bask = 2 boxes per basket
Find the value of each of these quantities a) P(6,3) c) P(8,1) e) P(8,8) b) P(6,5) d) P(8,5) f) P(10,9)
The values for the given data set is as follows 120 , 720 , 8 ,40320 , 6720 ,3628800 respectively.
The formula to calculate the permutation is , P = n! / ( n - r )!. Using this formula we get the result as,
P(6,3) = 6! / (6−3)!
= 6! / 3!
= 120
P(8,1) = 8! / (8 - 1)!
= 8! / 7!
= 8
P(6,5) = 6! / (6-5)!
6! / 1!
720
Similarly ,
P(8,8)= 40320
P(8,5) = 6720
P(10,9) = 3628800
A permutation is a specific arrangement of items. Set members or elements are arranged in a sequence or linear order here.
For example, the permutation of set A=1,6 is 2, as in 1,6,1.
There are no alternative ways to arrange the items in set A, as you can see.
In permutation, the elements must be organised in a specific sequence, whereas in combination, the order of the elements is irrelevant. Read also: Permutation And Combination
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You are given the statement: Vertical angles are equal in measure.
A. Rewrite the statement as an if-then statement.
B. Write the converse of the implication.
The if-then statement is:
If angles are vertical angles then their measure is equal.
and converse of the implication is:
If the measure of angles is equal then they are vertical angles.
What is the Converse Statement?
That sort of reversal is called a converse. Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry, the conditional statement is referred to as p → q. The Converse is referred to as q → p.
We have given the statement:
Vertical angles are equal in measure.
A). Rewrite the statement as an if-then statement.
If angles are vertical angles then their measure is equal.
B). Write the converse of the implication
If the measure of angles is equal then they are vertical angles.
Hence, the if-then statement is:
If angles are vertical angles then their measure is equal.
and converse of the implication is:
If the measure of angles is equal then they are vertical angles.
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-3x ≤ -36 What is the solution?
Answer:
x≤12
Step-by-step explanation:
-3x≥36
÷-3 ÷-3
Which property justifies the statement below? X(y+5)=xy+5x
Find the product. Write fractions in simplest form.
-2/7 x 7/4=
The product of -2/7 x 7/4 to the simplest form in fraction is -1/2.
FractionIn arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
[tex]\frac{-2}{7} x \frac{7}{4}[/tex]
Solving this we multiply the fraction by multiply the numerator by numerator and also Denominator by Denominator
= [tex]\frac{-14}{28}[/tex]
Simplify further by dividing the numerator by denominator we have:
= [tex]\frac{-1}{2}[/tex]
Therefore, the the product of the fraction to the simplest form is -1/2 and this can also be written in decimal; -0.5
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interpret r(t) as the position of a moving object at a time t. use the following information to find the curvature of the path
If the position of a moving object at a time t the curvature of the earth would be 1/4t.
A curved path having various radii of curvature is known as a variable-curvature path. from: 2020 Control Systems Design of Bio-Robotics and Bio-mechatronics with Advanced Applications.
A straight line has zero curvature. In contrast to the tangent, which is a vector quantity, the curvature at a point is often a scalar quantity or one that can be described by a single real integer.
|| r (t) || = 3[tex]t^{2}[/tex], || r' (t) || = 2t, || T (t) || = 1
|| T' || = 1/2
Curvature K = || T' (t) || / || r' (t) || = (1/2) / 2t
K = 1/4t
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PLEASE HELP ME THIS IS MY LAST QUESTION.
Answer:
A
Step-by-step explanation:
as the graphic suggests : reflect (mirror) ABD across the line BD, and CBD is a mirrored but otherwise equal copy of ABD, which also makes angle C equal to angle A.
all the other answer options are creating new triangle that do not map to CBD.
what a literal ratio
Answer: The relationship in quantity, amount, or size between two or more things: proportion.
Wei Jing has between 70 and 150 baseball
cards in his collection. When he arranges them
in groups of 10, he has 3 left over. When he
arranges them in groups of 9, he has 5 left
over. If he arranges them in groups of 8, how
many will he have left over?
The number of baseballs which Wei Jing would have left if he arranged them in groups of 8 as required is; 1.
What is the number of baseballs left if the arrangement is in groups of 8?According to the task content;
Since the number of baseballs available is between; 70 and 150 and
When he arranges them in groups of 10, he has 3 left over.
The possible numbers are; (70 + 3), (80 + 3), (90 + 3), (100 + 3), (110 + 3), (120 + 3), (130 + 3), (140 + 3).
Therefore, the possible numbers according to the first condition are; 73, 83, 93, 103, 113, 123, 133, 143.
Also, When he arranges them in groups of 9, he has 5 left over, the possible numbers are; ( 72 + 5 ), ( 81 + 5 ), ( 90 + 5 ), ( 99 + 5 ), ( 108 + 5 ), ( 117 + 5 ), ( 126 + 5 ), ( 135 + 5 ), ( 144 + 5 ).
Therefore, the possible numbers according to the second condition are; 77, 86, 95, 104, 113, 122, 131, 140, 149.
On this note, by comparison; Only 113 is common to the both sets of numbers.
Hence, the number in discuss is; 113.
Ultimately, if the arrangement is in groups of 8; it follows that the remainder would be; 1 since; 113 / 8 = 14 ⅛.
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