The simplified form of (m + 3n + 8)(m + 3n - 8) is m^2 + 3n^2 + 6mn - 64.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, (x+2)(x+3) = x^2+5x+6.
∴ (m + 3n + 8)(m + 3n - 8).
= m^2 + 3mn - 8m + 3mn + 3n^2 - 24n + 8m + 24n - 64.
= m^2 + 3n^2 + 6mn - 64.
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Leah runs 2000 meters in 5 minutes. How may meters can Leah run in one min
meters per minute
Answer:
Leah runs:
400 meters per minute
Step-by-step explanation:
2000 meters ⇒ 5 minutes
A meters ⇒ 1 minute
A = 2000 meters * 1 minute / 5 minute
A = 400 meters
The length of a rectangular poster is 2 more inches than three times its width. The area of the poster is 161 square inches. Solve for the dimensions (length and width) of the poster.
The length and width of the rectangular poster are 23 inches and 7 inches respectively.
Here we have to find the dimensions of the length and width of the rectangular.
Data given:
length of the rectangular poster is 2 more than three times its width.
Let us assume that the width of the rectangular is x.
The area of the poster = is 161 inches²
So by this, we get the length 3x + 2.
width = x
length = 3x + 2
The formula of the area of the rectangular:
Area = length × width
161 = (3x+ 2) × x
161 = 3x² + 2x
3x² + 2x - 161 = 0
3x² + 23x - 21x - 161 = 0
x(3x + 23) - 7( 3x + 23) = 0
(3x + 23) ( x -7)= 0
x = -23/3, 7
As the length cannot be negative so we get the value of x as 7
width = 7 inches
length = 3x + 2
= 3×7 + 2
= 21 + 2
= 23inches
Therefore the length and width are 23 inches and 7 inches respectively.
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1.5(6t+2) i need help with problem let me know if one of yall ppl get the answer so i can finish my homework sheet pls and thank you!!!
The value of the expression illustrated as 1.5(6t+2) is 9t + 3.
What is the value of the expression?Expression is simply used in Mathematics to show the relationship between the variables that are illustrated. In this case, this depicts the information given.
Based on the information, the expression is illustrated as:
1.5(6t+2)
Open the parentheses
(1.5 × 6t) + (1.5 × 2)
= 9t + 3.
The value is 9t + 3.
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Complete question
Find the value of the expression given 1.5(6t+2) i
Cesar danced for 16 minutes on Saturday. On Sunday he danced for 28 minutes more than he did on Saturday. How long has he danced in total
Answer:
60 minutes
Step-by-step explanation:
Saturday = 16 minutes
Sunday = 28 minutes + 16 minutes = 44 minutes
Saturday + Sunday = 44 + 16 = 60 minutes
Which table could be a partial set of values for a linear function?
Responses
x y table 1
0 0
1 1
2 4
3 9
x y 0 0 1 1 2 4 3 9 , , ,
x y table 2
0 0
1 1
2 8
3 27
x y 0 0 1 1 2 8 3 27 , , ,
x y table 3
0 0.0
1 0.5
2 1.0
3 1.5
x y 0 0.0 1 0.5 2 1.0 3 1.5 , , ,
x y table 4
0 0.0
1 0.5
2 2.0
3 4.5
Answer:
table 3
Step-by-step explanation:
As we know that
A Linear function is the one whose graph represents a line OR value of its dependent and independent variable change at a rate which remains constant throughout.
Now in the fourth table the values of x and y are given as show below:
One equation in a linear system is x + y = 1. Is it possible for the system to have a
solution of (0, 0)? (100, -49)? Explain your reasoning.
answer:
no, because 0+0≠1 and 100+-49≠1 so the values are not a part of the system.
step-by-step explanation:
for this question, plug in the x & y values into the equation x+y=1. if the values add up to be 1, then it's possible for the system to have those solutions. hope that helps!
a plane has a cruising speed of 200 miles per hour when there is no wind. at this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind. find the speed of the wind. speedofthewind:miles/hour
The speed of wind is 380 miles per hour.
What is speed?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path.
Here, we have
The plane has a cruising speed of 200 miles per hour when there is no wind. at this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind.
We have to find the speed of the wind.
Time = Distance/speed
Time = 500/200 = 2.5hrs
When the plane moves against the wind its effective speed reduces as it has to overcome the opposing force of the wind since it is given that it cover's a distance of 300 miles at the same time we can write
2.5 = 300/ V(plane) - v(wind)
2.5 = 300/500- v(wind)
v(wind) =380mph
Hence, the speed of the wind is 380mph.
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What is the measure of ZLMQ?
Answer:
97
Step-by-step explanation:
< LMN = 33
The sum of the interior angles equal 180
180 - 92 - 55 = 33
<QM (can't read the last letter 50
180 - 45 - 85 = 50
<LMQ This is a straight angle and straight angles are 180
180 - 33 -50 = 97
8x-2 < 30 help pls im slow
Answer: x < 4
Step-by-step explanation: look at the link attached
Layla is thinking of a positive single digit even number. Luis guesses it was 7. What is the sample space??
The sample space for the single digit even number = {2, 4, 6, 8}
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space.
Events are the subset of possible experiment results. Depending on the experiment, a sample space could contain a variety of results.
Given that,
Layla thinks about a positive single digit even number.
There are four single digit even numbers 2, 4, 6 and 8.
The sample space for the single digit even number = {2, 4, 6, 8}
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a search committee is formed to find a new software engineer. there are 6666 applicants who applied for the position. 1) how many ways are there to select a subset of 1515 for a short list?
The number of ways would be 2.68367259e14 for selecting 15 candidates out of 66 candidates.
What is arrangements ?Generally speaking, an arrangement of objects is just a collection of them. The sequence of the n items has no bearing on the number of "arrangements" that can be made of them (order is significant).
Total Candidates for software engineer = 66
Total Short listed candidates = 15
To find:
Number of 15 Candidates set possible
⁶⁶C₁₅ = [tex]\frac{66!}{51! 15!}[/tex]
After Calculating from calculator we get,
2.68367259e14.
Hence the number of ways would be 2.68367259e14.
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When Angel left his house in the morning, his cell phone battery was partially charged. Let B represent the charge remaining in Angel's battery, as a percentage, t hours since Angel left his house. A graph of B is shown below. Write an equation for B then state the x-intercept of the graph and determine its interpretation in the context of the problem.
The equation of the function is: B = -5x + 30
X-intercept is 6, which means after 6 hours, the battery is totally drained.
What is the X-intercept of a Function?The x-intercept of a function is the point on the x-axis that the line intercepts, which is the value of x when y = 0.
Find the slope of the function (m):
Slope (m) = change in B / change in t = (20 - 10) / (2 - 4)
Slope (m) = 10/-2
Slope (m) = -5
The y-intercept (b) = 30.
Write the equation of the function by substituting m = -5 and b = 30 into B = mt + b:
B = -5x + 30
The x-intercept of the function is 6, which represents the hours it took for the whole battery to drain.
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A park began with a population of 8 rabbits. Every year, the rabbit population triples. How long will it take for the population to reach 1,944 rabbits? choose the equation for the population of rabbits, r, in terms of the number of years that have passed, y, and the correct solution.
When the population starts out with 8 people and triples, it will take 5 years to reach 1,944.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Initial population=8
Final population=1944
Rate of increment=3ˣ
1944=8*3ˣ
1944/8=3ˣ
243=3ˣ
3ˣ=3⁵
x=5
It will take 5 years for the population to reach 1,944 when started with with the population of 8 and increase by 3ˣ.
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if z is a standard normal variable, find the probability. the probability that z lies between -0.56 and 0.56
The normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution.
The usual normal distribution is then followed by the z variable. A value of the x variable's z variable, also known as the z-score of the x variable, indicates how many standard deviations from the mean it is.
The area under the normal distribution curve must be calculated that lies between
z=−1.56 and z=1.56
Using the standard normal table, the area is calculated as:
P(−1.56<z<1.56)
=P(z<1.56)−P(z<−1.56)
=P(z<1.56)−(1−P(z<1.56))
=0.9406−(1−0.9406)
=0.8812
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The complete question is
if z is a standard normal variable, find the probability. the probability that z lies between -1.56 and 1.56 is
Let x and y be some integers. Consider the following statement: If xis odd and y is odd, then xy is odd. Proof. Assume that x is odd and y is odd. Then there exists some k integers such that x=2k+1 and m=2k+1. Then xy=(2k+1)(2k+1)=4k2+4k+1=2(2k2+2k)+1. Since 2k2+2k is an integer because k is an integer then xy is odd. The proof is correct but the statement is incorrect The statement is correct, but the proof is incorrect. The statement and proof are incorrect. The statement and the proof are correct.
hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.
Odd number integers = 2k + 1, where k is integer
Even number integer = 2k
Odd integer + even integer
= 2k + 1 + 2k
= 4k + 1
= 2(2k) + 1
Let 2k = t, where t is integer
= 2t + 1
= Odd integer by definition
If number is 2t + 1 where t belongs to integer, then it is odd integer.
Hence proved.
The question is incomplete. The complete question is :
Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd
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if the null hypothesis is rejected in hypothesis testing, no conclusions can be drawn from the test. the sample size has been too small. the alternative hypothesis is true. the data must have been accumulated incorrectly.
if the null hypothesis is rejected in hypothesis testing the alternative hypothesis is true.
The relationship between important factors of interest and any apparent connection, according to a competing theory, is most certainly not accidental. The opposite of a null hypothesis is an alternative hypothesis. If we are able to rule out the null hypothesis, it signifies that we have enough data to support the alternative hypothesis. In one test, we cannot rule out both possibilities.
If one is disproven, it indicates that there is evidence to support the other. The opposing view is that a study's potential conclusion will materialize. It claims there is no coincidence in the relationship between important components of interest and the observed connection. As a result, the alternative hypothesis is true if the null hypothesis is disproved during hypothesis testing.
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B
21
31
20
C
G
42
H
16
28
D
instructor number of failures prof. a 13 prof. b 0 prof. c 11 prof. d 16 what is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?
The standard deviation of the sampling distribution is 0.03
Instructor number is calculated as - (failure /100)
Number of failures for instructor A = 13 = 0.13
Number of failures for instructor B = 0 = 0.
Number of failures for instructor C = 11 = 0.11
Number of failures for instructor D = 16 = 0.16
Calculating mean -
Mean(m)
= 0.13 + 0.11 + 0.16) / 3
= 0.4 / 3
= 0.13
Calculating the Standard deviation -
Σ(X - m)² / N - 1
Σ(0.13 - 0.1333)² + (0.11 × 0.1333)² + ( 0.16 - 0.1333)² = 0.001266
= 0.001266 / 2
= 0.00063343
= √0.00063343
= 0.025168
= 0.03
Complete question -
The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: Instructor Number of Failures Prof. A 13 Prof. B 0 Prof. C 11 Prof. D 16 What is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?
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How do I find and interpret the residual?
(Elementary statistics)
Answer:
y value , r i = y i − y i ^
Step-by-step explanation:
Residual = actual y value − predicted y value , r i = y i − y i ^ . Having a negative residual means that the predicted value is too high, similarly if you have a positive residual it means that the predicted value was too low. The aim of a regression line is to minimise the sum of residuals.
write the slope intercept form of the equation of the line through the given points with given slope
The equation of the line passing through the point (-1, -5) with slope = 6 is y = 6x - 1
The coordinates of the point = (-1, -5)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line m = 6
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Substitute the values in the slope intercept form
-5 = 6(-1) + b
-5 = -6 + b
b = -6+5
b = -1
The slope intercept form
y = 6x - 1
Therefore, the equation of the line is y = 6x - 1
I have answered the question in general, as the given question is incomplete
The complete question is:
Write the slope-intercept form of the equation of the line through the given point with the given slope. Through (-1,-5), slope =6
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Describe the relationship between the lines.
1. The lines intersect to form an angle that is 180°
2. The lines intersect to form an angle that is not 90°
3. The lines intersect to form an angle that is 90°
4. he lines do not intersect.
14 on a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. what was the number of men on the sight-seeing tour?
The number of men on the sight - seeing tour was 22 .
In the question ,
it is given that,
the ratio of women to children on the tour is = 5 : 2
let the number of men in the sight seeing tour = m
let the number of women in the sight seeing tour = w
let the number of children in the sight seeing tour = c
So , w/c = 5x/2x
also the ratio of children to men is 5/11 ,
c = 5y and m = 11y
the number of women on the sight seeing tour is less than 30 ,
which is 5x < 30 ,
x < 6
but we have c = 2x and 5y ,
and since c is a multiple of 5 , 2x also has to be a multiple of 5 ,
earlier we got , x < 6 ,
Now using x =5 , we get c = 2*5 = 10
and so , 10 = 5y
y = 2 ,
So , the number of men = 11y = 11*2 = 22 men
Therefore , the number of men are 22 .
The given question is incomplete , the complete question is
On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.
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hat are the zeros of the function: (x) = -x(x+ 2) (x - 6) (x + 4)
Answer:
zero of the function =0,-2,6,-4Step-by-step explanation:
f(x)=-x(x+2)(x-6)(x+4)-x=0 x=0(x+2)=0x=-2(x-6)=0x=6(x+4)=0x=-4Choose the expression that is equivalent to the quantity 9 raised to the negative second power times 9 raised to the seventh power end quantity all raised to the negative third power −99 negative 1 divided by 9 raised to the sixth power 1 divided by 9 raised to the fifteenth power 927
The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power
How to use the Law of Indices?
We want to find the expression that is equivalent to the quantity nine raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power. Indices display the results of multiples of a number, such as squared or cubed, or they display the roots of numbers, such as the square root. The laws of indices can be used to condense some indexed terms.This is written as;
(9⁻² * 3⁵)⁻²
According to laws of indices, we know that;
(a²)³ = a²*³ = a⁶
Thus;
(9⁻² * 3⁵)⁻²= (9⁻²)⁻² * (3⁵)⁻²
⇒ 9⁴ * 1/3¹⁰
⇒ 9⁴/3¹⁰
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Answer:The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power
Drag numbers to use a negative factor to factor the expression –5g + 15h – 25. Numbers may be used once, more than once, or not at all.
–1 –2 –3 –4 –5 1 2 3 4 5
(___-5__g –____3_ h +___5__)
The expression -5g + 15h - 25 can be simplified as -5(g + 3h - 5)
ExpressionExpressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
In the question given, the expression is -5g + 15h - 25;
We have to simplify this to by factoring the expression.
-5g + 15h - 25 = -5(g + 3h - 5)
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Which number sentence shows the best way to estimate 64.12÷7.4 ? A. 60 ÷ 10 = 6 60÷10=6
B. 63 ÷ 7 = 9 63÷7=9
C. 56 ÷ 7 = 8 56÷7=8
D. 100 ÷ 10 = 10
Answer:
B
Step-by-step explanation:
Round 64.12 and 7.4 to whole numbers that divide nicely, and are CLOSE to the original numbers.
what is the minimum number of students required in a school to be sure that at least 17 students will be in the same class, assuming the school only has grade 1 to grade 6 and each grade has only one class?
The minimum number of students required in a school are 102 , it can be calculated by multiplying the 2 quantities.
What is arithmetic?
Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main body:
Total grades = 1 to 6 = 6
minimum students in each grade required = 17
total students required = 6*17
= 102
hence total minimum number of students required in a school are 102.
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a newsletter publisher believes that less than 49% of their readers own a personal computer. for marketing purposes, a potential advertiser wants to confirm this claim. after performing a test at the 0.05 level of significance, the advertiser decides to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
The proportion should be sufficiently demonstrated to be lower than 49% at the 0.05 level.
Given,
Less than 49% of a newsletter publisher's subscribers, in their estimation, own a personal computer.
A potential advertiser wants to verify this claim for marketing purposes.
The marketer chooses to reject the null hypothesis after running a test with a 0.05 level of significance.
We have to determine the conclusion regarding the publisher's claim;
Here,
Null and Alternative hypothesis;
H₀ = P ≥ 0.49
H₁ = P < 0.49 (Left tailed test)
The significance level is 0.05
So,
0.05 < 0.49
Then,
At the defined meaning level, it is chosen to reject the null hypothesis.
Therefore,
There should be sufficient evidence that the proportion is lower than 49% at the 0.05 level.
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the number of disintegrations per minute (dsm) of a sample of iodine-133 is measured at 5.5 x 102 dsm. when the sample is measured 295 minutes later, the number of disintegrations has decreased to 4.7 x 102 dsm. what is the half-life of iodine-133
Half-life of iodine-133 is 21.7 hours .
FR = 0.5n (fraction remaining)
n = number of half lives that have elapsed.
FR = 4.7x102 / 5.5x102 = 0.8545
n = to find
0.8545 = 0.5n
log 0.8545 = n log 0.5
-0.0683 = -0.301 n
n = 0.227 half lives have elapsed
Since this is equal to 295 minutes, we can easily find what 1 half life is
0.227 / 295 = 1 / x
x = 1300 min = 21.7 hours
The amount of time it takes for the concentration of a given reactant to reach half of its initial concentration is known as the half-life of a chemical reaction (i.e. the time taken for the reactant concentration to reach half of its initial value).
It is commonly expressed in seconds and is represented by the sign t1/2 .
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A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15°, from a height of 2. 2 feet. How far away does the ball land in feet?use x=(v * cos [theta])*ty=h+(v * sin [theta]t-16t^2Solve T in the second equation using the quadratic formula, then solve x
The ball will land 67.381 feet away.
Thus, option (B) is correct.
Given:
v = 62 feet / second
[tex]\theta[/tex] = 15
h = 2.2 feet
Using the formula
Horizontal range = [tex]\dfrac{v \;cos\; \theta\; [v \;sin\;\theta + \sqrt{v^2\;sin\;\theta + 2gh]}}{g}[/tex]
Substituting the value back into the formula as
Horizontal range = [tex]\dfrac{62 \;cos\; (15)\; [62 \;sin\;(15)+ \sqrt{(62\;sin\;(15))^2 + 2g*2.2]}}{g}[/tex]
= 67.381 feet
Therefore, the distance is 67.381 feet.
Thus, option (B) is correct.
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The question attached here seems to be incomplete, the complete question is:
A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15", from a height of 2.2 feet. How far away does the ball land in feet? (5 points)
56.372 feet
67.381 feet
60.646 feet
47.293 feet