Answer:
B
Step-by-step explanation:
Use the Pythagorean theorem, 7^2+24^2=25^2
49+576=625
625=625
All the other answers do not satisfy the Pythagorean theorem (a^2+b^2=c^2)
Answer: A, B
Step-by-step explanation:
A right triangle's sides have a special property that the sum of the squares of the two legs is equal to the square of the hypotenuse. This is also known as the Pythagorean Theorem.
Let's check if this theorem holds true for each triangle.
A[tex]11^2+13^2=(\sqrt{290})^2\\ 121 + 169=290\\ 290 = 290[/tex]
The Pythagorean Theorem holds true, so this is a right triangle.
B[tex]7^2+24^2=25^2\\ 49 + 576 = 625\\ 625=625[/tex]
The Pythagorean Theorem holds true, so this is a right triangle.
C[tex]2^2+5^2=7^2\\ 4+25=49\\ 29 = 49[/tex]
This is a false statement, which doesn't make this triangle a right triangle. We could have use the triangle inequality theorem to prove that this isn't a triangle at all, and therefore not a right triangle, but I encourage you to learn about it and try it yourself.
Find three consecutive integers such as two times the first integer, plus three times the second integer, minus the third integer, is equal to 21.
The three consecutive integers are 5, 6, and 7.
What are consecutive integers?
Whole numbers that follow one another without a gap are known as consecutive integers. A few examples of consecutive integers are 15, 16, and 17, 1,2 and 3, and so on.
Finding the Consecutive Integers
Let the three consecutive integers be a, a + 1, and a + 2.
These three consecutive integers are to be such that two times the first integer when added to three times the second integer minus the third integer, it is equal to 21.
⇒ 2a + 3(a+1) - (a+2) = 21
2a + 3a + 3 - a -2 = 21
5a - a + 3 - 2 = 21
4a + 1 = 21
4a = 20
a = 20/4
a = 5
∴ a+1 = 5+1
a+1 = 6
And, a+2 = 5 + 2
a +2 =7
Hence, the three consecutive integers come out to be 5, 6, and 7
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What is the square root of pi?
Pi is a Greek number that plagues mathematics, physics, and circles to the point where pi-fatigue is actually a thing. Pi is an infinite number, however it will henceforth only be written as 3.14159.
I have two solutions to your problem.
The first, and probably less appealing answer, but most used everywhere, would be to use a calculator.
But if you find yourself without a calculator at the ready, I hope you’re prepared to math quite dubiously.
Finding the square power, inverse of a radical, or whatever is multiplied by itself to equal 3.14159, is the second step. We must start someplace to start our attempt, and that place is 3.14159. Since 1 squared equals 1 and 2 squared equals 4, our result, expressed in decimal form, is larger than 1 but less than 2. After that, we just start divising and multiplying the decimals again until we have calculated the square root of pi.
TL;DR
1.7724531 is the approximate square root of pi.
Answer:
1.77245385091
Step-by-step explanation:
If the measure of angle ø is 3pie/4, which statements are true?
The measure of the reference angle is 45°.
cos (0) = √2
sin (0) = √2
The measure of the reference angle is 60°.
The measure of the reference angle is 30°.
tan (0) = 1
Find 3π/4 in degrees
(3(180))/43(45)135°Referance angle
π-3π/4180-13545° or π/4Option A
TanØ=sinØ/cosØ=√2/√2=1Answer:
The measure of the reference angle is 45°.
[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
Reference Angle: The smallest possible angle made by the terminal side of the given angle and the x-axis. The reference angle is always between 0° and 90° (0 and π/2 radians).
To convert radians to degrees, multiply by 180/π:
[tex]\implies \sf \theta=\dfrac{3\pi}{4} \cdot \dfrac{180}{\pi}=135^{\circ}[/tex]
Positive angles are drawn in a counterclockwise direction from the x-axis.
(See attached for diagram of the angle θ and its reference angle).
Angles on a straight line sum to 180°.
Therefore, to calculate the reference angle, subtract the measure of the angle from 180°:
[tex]\implies \sf Reference\:angle=180^{\circ}-135^{\circ}=45^{\circ}[/tex]
The angle 135° lies between 90° and 180° and so is in Quadrant II.
Therefore, the exact trigonometric ratios for 135° are:
[tex]\sin 135^{\circ}=\dfrac{1}{\sqrt{2}} \textsf{ or }\dfrac{\sqrt{2}}{2}\\\\ \textsf{(Since sine function is positive in the Quadrant II)}[/tex]
[tex]\cos 135^{\circ}=-\dfrac{1}{\sqrt{2}} \textsf{ or }-\dfrac{\sqrt{2}}{2}\\\\\textsf{(Since cosine function is negative in the Quadrant II)}[/tex]
[tex]\tan135^{\circ}=-1\\\\\textsf{(Since tangent function is negative in the Quadrant II)}[/tex]
Therefore, the true statements are:
The measure of the reference angle is 45°.
[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]
If B is the midpoint of AC, and AC = &r - 20 find BC.
The measure of BC from the figure shown is 26
What is a line?A line is the distance between two points. From the given line AC;
AC = AB + BC
Given the following parameters
AC = 8x - 20
AB = 3x - 1
Required
Length BC
Substitute
8x-20 = 3x-1 + BC
BC = 8x-20 -(3x - 1)
BC = 8x - 20 - 3x + 1
BC = 5x - 19
Since B is the midpoint of AC, then;
AB = BC
3x - 1 = 5x - 19
-2x = -18
x = 9
Determine the length of BC
BC = 5(9) - 19
BC = 45 - 19
BC = 26
Hence the measure of BC from the figure shown is 26
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Six numbers from a list of nine integers are $7$, $8$, $3$, $5$, $9$, and $5$. What is the largest possible value of the median of all nine numbers in this list
8 is the largest possible value of the median of all nine numbers in this list.
Lets simplify it,
⇒ The given six numbers are 7,8,3,5,9 and 5.
⇒ Arrange the six numbers in order 3,5,5,7,8,9.
⇒ We have three more numbers to insert into the list, and the median will be the highest 5(and 5 lowest) number on the list. If the three numbers are greater than 9, the median will be the highest it can possible be.
∴ The median is the 5th item of data which is 8.
∴ Median=8
Hence 8 is the largest possible value of the median of all nine numbers in this list.
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A square has side lengths of 9, which of the following is a correct formula for finding the area of a square
Answer:
9 x 9 = 81
Step-by-step explanation:
area = width x height
Since it's a square, width = height
Mr. Omwoyo, the principal of Maili Mbili Secondary would wish to cover the floor of the new administration block using square tiles. The floor is a rectangle of sides 12.8m by 8.4m. Find the area of the largest tiles in cm² which can be used to fit exactly without cutting.
Answer:
hi play truth and dare to with me in g met
You are deciding a social hall that will seat no more than 1600 people. You want at least 500 seats to be priced at $20 each, and at least 800 seats to be priced at $30 each. Those investing in the social hall would also like to bring in at least $2800 in revenue from the ticket sales. Let X represent the number of $20 seats, and let Y represent the number of $30 seats. Which system of inequalities represents this situation?
x ≥ 0
y ≥ 0
x + y ≥ 1600
20x + 30y ≤ 2800
x ≥ 500
y ≥ 800
x + y ≤ 1600
20x + 30y ≥ 2800
x ≥ 800
y ≥ 500
x + y ≤ 1600
20x + 30y ≤ 2800
x ≥ 500
y ≥ 800
x + y ≤ 1600
20x + 30y ≤ 2800
Answer: Option B
Just trust me that its right.
When a person convicted of a crime appeals a conviction, he or she asks a higher court to examine the trial court's decisions to determine whether the proper procedures were followed.
The statement when a person convicted of a crime appeals a conviction, he or she asks a higher court to examine the trial court's decisions to determine whether the proper procedures were followed is True.
What is Appeals?Appeal occur when a person convicted of a crime want another court to reverse a decisions or to examine and re-check the judgement or outcome of a trial court outcome because the convicted person was not satisfied with the outcome or the result of the trial court .
Hence, the statement is true because an offender that was convicted of a crime can tend to files an appeal with a higher court or appellate court so as to examine the trial court's decisions.
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Rank--from first to last--the following steps for finding the bottleneck and capacity in a process with rework.
Steps for finding the bottleneck and capacity in a process with rework:
atevaluateevaluate---What is the bottleneck and capacity in a process with a rework?In production and project management, a bottleneck is a process in a chain of processes whose restricted capacity reduces the capacity of the entire chain. A bottleneck causes production stalls, supply overstock, customer pressure, and low employee morale.To evaluate a reworked process, a weighted average processing time must be calculated. Because the processing time for rework differs from the initial processing time, a weighted average processing time must be computed. The resource's capacity is divided by its weighted average processing time.Steps for determining the bottleneck and capacity in a reworked process:atevaluateevaluate---Therefore, steps for finding the bottleneck and capacity in a process with rework:
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A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 18, 3, 0, 3, 6, 3.
Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?
(
,
)
The largest interval of x-values where the function is increasing is (-1, 1)
How to determine the largest increasing interval?The table of values is added as an attachment
From the table, the function f(x) decreases from x = -3 to x = -1 and x = 1 and x = 2
So, we make use of the intervals
x = -1, 0 and 1
From the table,
From x = -1 to 0, the change is 3
From x = 0 to 1, the change is 3
From x = -1 to 1, the change is 6
Using the above highlights, the largest increasing interval is (-1, 1)
Hence, the largest interval of x-values where the function is increasing is (-1, 1)
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Two cans each hold 750ml by how many ml is their total volume less than 1.8 liters
If two cans hold 750ml ,then their voLume is 0.3 liters less than 1.8 liters.
Given volume of two cans being 750 ml each.
We are required to calculate the quantity in liters of how much the volume of two cans less than 1.8 liters.
Volume is the quantity of substance a container can hold in its capacity.
So volume of cone means quantity of liquid cone can hold if fully filled.
Volume of first cone=750 ml
Volume of second cone=750 ml
Total volume=750+750
=1500 ml
1 liter= 1000 ml
so 1500 ml will be equal to 1500/1000
=1.5 liter
We are required to do comparison with 1.8 liters.
Difference =1.8-1.5
=0.3 liters.
Hence two cans have 0.3 liters less than 1.8 liters.
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What percentage of its total accounts receivable does grainger feel are uncollectible at december 31, 2016?
Using percentage of its total accounts the $50,000 is the amount to be uncollectible. The amount of $50,000 will be reported as an allowance for uncollectible accounts for the Year 2 on December 31 in the balance sheet.
According to the question,
Under the approach of the balance sheet, the ending balance of the allowance for the uncollectible accounts is the percentage (%) of the ending balance of the accounts receivable.
The amount of uncollectible accounts should reflect the aggregate needed ending balance of the allowance which amounts to $50,000.
Hence, using percentage of its total accounts the $50,000 is the amount to be uncollectible.
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A quadrilateral has congruent side lengths. 2 opposite angles have measures of 100 degrees. The other 2 opposite angles have measures of 70 degrees and (5 x) degrees. What is the value of x
Answer: 18
Step-by-step explanation:
Angles of a quadrilateral add to 360 degrees, so
[tex]100+100+70+5x=360\\\\270+5x=360\\\\5x=90\\\\x=18[/tex]
A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}. Find the probability of getting two numbers whose sum is greater than 9. Group of answer choices 6
The probability of getting two numbers whose sum is greater than 9 is [tex]\frac{5}{36}[/tex].
What is probability?Probability is a measure of the possibility that an event will occur in a Random Experiment. Probability is expressed as a number between 0 and 1, where 0 denotes impossibility and 1 denotes certainty. The higher the likelihood of an occurrence, the more probable it will occur.To find the probability of getting two numbers whose sum is greater than 9:
The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Set of numbers greater than 9:
{(5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
Formula:
Favorable event / Total number of events = [tex]\frac{5}{36}[/tex]
Therefore, the probability of getting two numbers whose sum is greater than 9 is [tex]\frac{5}{36}[/tex].
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2. There are 10 pieces of paper, numbered
consecutively from 20 to 29, stuffed in a box.
What is the probability of choosing a prime
numbered paper if one piece is chosen at
random?
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Prime numbers between 20 - 29 = 23 and 29.
There are 2 prime numbers out of these 10.
Therefore,
P(choose prime number) = [tex]\frac{2}{10} \\=\frac{1}{5}[/tex]
A rectangle with a length of x - 4 and a width of 8 has a perimeter of 34. what is the value of x?
Answer:
13
Step-by-step explanation:
2(x-4+8)=34
x-4+8=17
x+4=17
x=13
find the volume of these rctangular prisms l=11.5cm w=2.5mm h=6cm
step by step pls
Answer:
172.5cm^3
Step-by-step explanation:
* = multiply or times
volume = length*width*height
Plug in the numbers: 11.5*2.5*6 = 172.5cm^3
what is the rule for the following sequence:
-1; -4; -9; -16; -25
Answer:
It´s an exponential rule. where one of the factors is negative
Step-by-step explanation:
1 * -1 = -1
2 * -2 = -4
3 * -3 = -9
4 * -4 = -16
5 * -5 = -25
Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
[tex] \frac{y}{x} = \frac{1}{ - 3} \\ - 3y = x[/tex]
[tex] - 3(2) = 6 = x[/tex]
( - 6 , 2 ) Option awrite [tex]sec^{2} x=\frac{1}{cos^2x}[/tex] in two equivalent forms.
write sec²x = 1/cos²x in two equivalent forms
sec²x = 1/cos²x
cos²x/cos²x = 1
sec²x = 1 + tan²x
Which of the following is the MOST accurate definition of standard deviation
The average of a set of scores
The typical amount by which scores differ from the mean of a set of scores
The average of the sum of squared deviations from the mean
The mean absolute deviation of the sum of the squared deviation from the average
The MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average. Option 4
Definition of standard deviation
Standard deviation can be defined as a statistic tool that measures the dispersion of a dataset in relation to its mean and is calculated as the square root of the available variance of the set.
It is calculated as the square root of the given variance.
Thus, the MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average.
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David has kept track of his family’s grocery bills for the past 10 weeks, as shown in the table.
Week 1 2 3 4 5 6 7 8 9 10
Bill ($) 92 106 129 115 100 84 110 156 98 87
Would you choose to use a histogram, a circle graph, or a line graph to display the data? Explain your choice. Then make a display.
The data should be displayed using a line graph, as shown in the attached figure.
Definition of a Line Graph
In a line graph, also known as a line plot or a line chart, each data point is connected by its own line. A line graph displays numerical values across a chosen time span.
Why is a line graph the best choice in this situation?
A line graph would be the best option for showing the data for David's family's grocery spending over the previous 10 weeks because it would show us the trend in the data. This graph tells us of how we can recognize instances where there were significant expenses by analyzing the trend from the line graph.
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At a coffee shop, the manager recorded the number of customers who visited the store at the end of each hour. The graph shows the recordings for a 24-hour period. The function describing this graph is a transformation of the parent sine function, y=sin(x)
Which value is closest to the amplitude of the transformed function?
O 83 customers
O 27 customers
O 54 customers
O 30 customers
Based on the transformed function of y = sin(x) and the given parameters, the value that is closest to the amplitude of the transformed function is 54
Which value is closest to the amplitude of the transformed function?The amplitude of the function is calculated
Amplitude = Highest - Lowest
From the graph, we have the following points
Highest = 84
Lowest = 30
Substitute the known values in the above equation
Amplitude = 84 - 30
Evaluate the difference
Amplitude = 54
Based on the transformed function of y = sin(x) and the given parameters, the value that is closest to the amplitude of the transformed function is 54
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Assuming a level of significance of 0.01, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines
Answer: Yes, there is
Step-by-step explanation:
Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k > 0. Are Rectangle 1 and Rectangle 2 similar? Why or why not? Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1. Write a paragraph proof to show that the area of Rectangle 2 is times the area of Rectangle 1. Answer:
Yes, the two rectangles are similar, because rectangle 2 is a dilation of rectangle 1.
Are the two rectangles similar?
We know that rectangle 1 has dimensions L and W.
And rectangle 2 is made by multiplying the dimensions of rectangle 1 by a factor k > 0.
Then, rectangle 2 is just a dilation of rectangle 1, this means that in fact, the two rectangles are similar by definition.
Then:
Dimensions of rectangle 1:
Length = LWidth = W.Perimeter = 2*(W + L)Area = W*LFor rectangle 2:
Length = k*LWidth = k*WPerimeter = 2*(k*L + k*W) = k*(2*(L + W))Area = (k*L)*(k*W) = k²(L*W)Above we can see that the perimeter of rectangle 2 is k times the perimeter of rectangle 1, and the area of rectangle 2 is k squared times the area of the rectangle 1.
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The more novel a new product or service design is, the more forecasters have to rely on:_______
a) smoothed variation.
b) historical data.
c) seasonality.
d) cyclicality.
e) subjective estimates.
The more on these factors forecasters must rely, the more innovative a new product or service design is: Subjective Estimates.
Option (e) is correct.
A subjective estimate is a specific type of estimate that is founded on a person's subjective evaluation or in-depth comprehension of the possibility of a specific outcome.
A subjective estimate only takes into account the subject's ideas and prior experiences rather than employing data or exact calculations.
Individual subjective evaluations are highly biased and differ from person to person.
Contrarily, a subjective estimate is incredibly prone to revision, even when only one person's viewpoint is taken into account.
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A rectangle has a width of 2.45 feet and a length of 6.5 feet. how will the area of the rectangle change if each side is increased by a factor of 5? the area will be one-fifth the original. the area will be startfraction 1 over 25 endfraction the original. the area will be 25 times the original. the area will be 5 times the original.
The area of the new rectangle will be 25 times that of the original
Area of a rectangleA rectangle is a 2D shape that has 4 sides and equal interior angles
If rectangle has a width of 2.45 feet and a length of 6.5 feet, then;
Width = 2.45 feet
Length = 6.5feet
A = 2.45 * 6.5
A = 15.925 square feet
If each side of the rectangle is increased by a factor of 5, hence;
W1 = 5(2.45) = 12.25feet
L1 = 5(6.5) = 32.5 feet
Determine the area of the new rectangle
A = 12.25 * 32.5
A = 398.125 square feet
Ratio of the area
A1/A = 398.125/15.925
A1 = 25A
Hence the area of the new rectangle will be 25 times that of the original
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If the term of arthematic progression decrease in magnitude then common difference must be
We can say that if the term of arithmetic progression decrease in magnitude then the common difference must be negative.
An arithmetic progression is a sequence where every term is a sum of the previous term and a common difference.
If we suppose the first term of an arithmetic progression to be a, and the common difference to be d, then the arithmetic progression goes like this:
The first term, a₁ = a,
Second term, a₂ = a₁ + d = a + d,
Third term, a₃ = a₂ + d = a + 2d,
Fourth term, a₄ = a₃ + d = a + 3d, and it goes so on up to,
The n-th term, aₙ = aₙ₋₁ + d = a + (n - 1)d.
In the question, we are asked if the term of arithmetic progression decrease in magnitude then what can we say about the common difference.
As the magnitude of the term decreases, we can show that as:
The n-th term < The first term,
or, aₙ < a₁,
or, a + (n - 1)d < a,
or, a + (n - 1)d - a < a - a {Subtracting a from both sides},
or, (n - 1)d < 0.
Since, n > 1, (n - 1) > 0, thus we get the common difference, d < 0, that is, the common difference is negative.
Thus, we can say that if the term of arithmetic progression decrease in magnitude then the common difference must be negative.
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What is the domain of the function represented by the graph? A graph shows an upward parabola on a coordinate plane vertex at (minus 4, minus 4) which intercepts axis at (minus 5, 0), and (minus 3, 0) passes through (minus 3, 1), and (minus 2.5, minus 5). all real numbers x ≤ -2 x ≥ -6 x ≥ 4
Using it's concept, the domain of the function represented by the graph is all real numbers.
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
In this problem, a parabola is used, which has no restriction such as an even root or a fraction, hence the domain is all real values.
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