Answer:
[tex]1[/tex] and [tex]6[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote one of the integers. Since the two integers add up to [tex]7[/tex], the other integer would be [tex](7 - x)[/tex].
The sum of the squares of these integers is [tex]37[/tex]. In other words:
[tex]x^{2} + (7 - x)^{2} = 37[/tex].
Expand [tex](7 - x)^{2}[/tex] using binomial expansion. Simplify and rewrite this equation and solve for [tex]x[/tex].
[tex]2\, x^{2} - 14\, x + 12 = 0[/tex].
[tex]x^{2} - 7\, x + 6 = 0[/tex].
Using the quadratic formula or factorization, [tex]x = 1[/tex] or [tex]x = 6[/tex]. Thus, the two integers are [tex]1[/tex] and [tex]6[/tex].
A parallelogram has a base of 3 inches and a height of 7 inches. What is its area?
Answer:
21 cm square
Step-by-step explanation:
Base x Height = Area
Area = 3 x 7 = 21 cm square.
what is the area of triangle pqr on the grid? a triangle pqr is shown on a grid. the vertex p is on ordered pair 7 and 6, vertex q is on ordered pair 1 and 6, and the vertex r is on ordered pair 4 and 2.
The area of a triangle with the given set of vertices is 12 square units, which is obtained using the concepts of coordinate geometry and the area of triangles.
What is the area of a triangle?
The area of a triangle is defined as the total region bounded by the three sides of a triangle. For a right-angled triangle, the area is given by ½ * (base * height).
Calculation of the area of the given triangle
Given:
P(7,6), Q(1,6), R(4,2) be the three vertices of a triangle PQR
Let PQ be the base parallel to the x-axis
b = 7 - 1 = 6
And altitude is the difference of y coordinates of the point Q and R, h = 6 - 2 = 4
The area of triangle PQR is equal to half the product of base and height
Area = (6 × 4) / 2
= 24 / 2
= 12 square units
Hence, the area of the triangle with given vertices is 12 square units.
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A heap of sand in the form of a square based pyramid is twice as tall as it is wide. If the volume, V, of the sand is 10 m3, find the height, h, of the heap. Give your answer, in metres, correct to two decimal places.
The height of the prism is 4.93 meter with a square base and having a volume of 10 m³
How to solve volumeVolume is the amount of space occupied by a three dimensional shape or object. Examples of shape with volume are cone, cube, cuboid, pyramid, prism and so on.
The volume of a pyramid = (1/3) * base area * height
Let base = b
height = 2 * base = 2b
Since volume is 10 m³, hence:
10 = (1/3) * b * b * 2b
b = 2.47 m, h = 2(2.47) = 4.93 m
The height of the prism is 4.93 meter with a square base and having a volume of 10 m³
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1.5, 21.5, 21.6 d: 20.0, 20.0, 20.0, 20.1, 20.2, 20.5, 20.5, 20.6, 20.7, 20.7, 21.0, 21.2, 21.5, 21.6, 22.1, 22.3 compute the standard deviation of the measurements for each method
Final answer:
The standard deviation from the method A is 2.87
The standard deviation from the method B is 1.35
The standard deviation from the method C is 0.42
The standard deviation from the method D is 0.75
What purposes does standard deviation serve?The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
The statistical concept of standard deviation is used to quantify the variability or dispersion around an average. It is a measure of volatility technically. The discrepancy between the actual and average value is known as the dispersion. The standard deviation increases as the variability or dispersion increases.
A low standard deviation indicates that the data are tightly grouped around the mean, while a high standard deviation indicates that the data are widely dispersed (less dependable) (more reliable)
Explanation:
The highest standard deviation is found in procedure A. Given that it is not based on any actual measurements and is subject to wildly different subjective judgment, one would anticipate that it would be the largest.
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(+7) (–4) Write each multiplication expression as a repeated addition.
We get the repeated addition as ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ).
We are given a multiplication expression:
( + 7 ) ( - 4)
We need to write this expression as a repeated addition
Repeated addition means when we add the same digits many times that is repeatedly.
For example: 3 + 3 + 3 + 3 or 8 + 8 + 8 + 8 or 5 + 5 + 5 +5 etc.
Here, we can see that -4 is multiplied by 7
It means that - 4 will be added 7 times repeatedly to form the expression
So, we get that:
= ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 )
Therefore, we get the repeated addition as ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ).
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patricia will flip the coin 8 times. let a be the event that exactly 4 of the 8 flips are heads, and b be the event that the last two flips are tails. find p(a ∪ b).
The probability of an event of P(A∪B) is 49/128.
In this question,
Patricia will flip the coin 8 times.
The sample space is the flipping of a coin 8 times.
⇒ n(s) = 2⁸
⇒ n(s) = 256
Let A be the event that exactly 4 of the 8 flips are heads
⇒ n(A) = [tex]8C_4[/tex] [∵ [tex]nC_r=\frac{n!}{r!(n-r!)}[/tex]]
⇒ [tex]\frac{8!}{4!4!}[/tex] = 70
Then, P(a) = [tex]\frac{n(a)}{n(s)}[/tex]
⇒ [tex]\frac{70}{256}[/tex]
Let B be the event that the last two flips are tails
⇒ n(B) = [tex]8C_2[/tex]
⇒ [tex]\frac{8!}{2!6!}[/tex] = 28
Then, P(a) = [tex]\frac{n(b)}{n(s)}[/tex]
⇒ [tex]\frac{28}{256}[/tex]
Now, P(A∪B) = P(A) + P(B)
⇒ P(A∪B) = [tex]\frac{70}{256} + \frac{28}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{70+28}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{98}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{49}{128}[/tex]
Hence we can conclude that the probability of an event of P(A∪B) is 49/128.
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The weather report predicted that the low temerature would be 93 degrees farenheit. The weather man said , "The low temperature was 13 degrees warmer than predicted!'' What was the low temperature, in degrees Farenheight?
Answer: 106!
Step-by-step explanation:
Evaluate 4 - 2(a - 3) for a=5
Answer: 0
Step-by-step explanation:
4 - 2(a - 3) =
4 - 2(5 - 3) =
4 - 2(2) =
4-4=0
7 times as long as 3098 kilometers
Answer:21,686
Step-by-step explanation:7*3098=21,686
PLEASE HELP DONT JUST TAKE MY POINTS I DONT KNOW THIS PLEASSE ASAP
explain your reasoning in mathematical terms. Be specific. Draw a picture if you need to.
Question:
Evelyn has some paracord with a total length of 5-½ meters. She needs to cut the cord into 12 equal portions. What is the length of each piece written as a fraction? Is this value rational or irrational; why?
Answer:11/24
Step-by-step explanation:
5 1/2 divided by 12 equals 11/24
Traveling at an average rate of between 40 and 50 miles per hour for 3 to 4 hours, select the best estimate for the distance traveled.
Answer:
Step-by-step explanation:
Take average speed to be (40+50)/ 2 = 45 mph.
Then estimate of distance travelled
= 45 * 3.5
= 160 miles.
Is the question ''how many cars were sold each day this month'' statistical or not?
I need help badly please help
Step-by-step explanation:
these are the answers. ignore the scribbles :)
What is the quotient of the following division problem?
10703 ÷ 25 = ?
OA. 428 r3
OB. 427 r4
OC. 428 r4
O D. 429 r3
Answer is A, 10703 / 25 = 428 r3
Volume of Spheres
Volume of Spheres
Answer:
V ≈ 2,048 ft^3
Hope this helps :)
Step-by-step explanation:
The symbol ^ means raised to a power.
Formula for Volume of Sphere - V = 4/3 π r^3
1. To find the volume of a sphere, first find the radius with the given diameter 16.
16 ÷ 2 = 8
Radius = 8
2. Substitute r for 8 and solve, and 3 will be used for π.
V ≈ 4/3 • 3 • 8^3
V ≈ 4/3 • 3 • 512
V ≈ 4/3 • 1536
V ≈ 6144/3
V ≈ 2,048
Abdoulaye is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he rolls a fair die in the shape of a cube that has six sides labeled 1 to 6 and spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange?
The number of different possible outcomes is 24
How to determine the number of different possible outcomes?The given parameters are:
Fair die = 6 sides
Spinner = 4 sections
The number of different possible outcomes is calculated using
Outcomes = Fair die * Spinner
This gives
Outcomes = 6 * 4
Evaluate
Outcomes = 24
Hence, the number of different possible outcomes is 24
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i don’t know what to do
Answer:
Step-by-step explanation:
If the problem is (-7)^2 then you multiply -7 *-7
If the problem is -(7) ^2 then you multiply -1*7*7
Answer: FALL OUT OF THE TREE
Twelve buckets of water are needed to fill a small swimming pool. there are approximately 3.8 liters in 1 gallon. if each bucket holds 1.5 gallons, what is the volume of water, in liters, the pool holds?
Answer:68.4 liters
Step-by-step explanation: 1.5x12=18 18x3.8=68.4
find the slope-intercept form of the equation of the line that has the given slope and passes through the given point
Answer: you didn't give me any numbers, so I can't give you an answer. But, I can help!
The slope intercept form is Y=mx+b
X and Y are your coordinates
m is the slope
b is the y-intercept.
As long as you know two of those, you can solve for the missing variable.
I hope this helps!!!
2. Ms. B and Ms. D are writing problems for an algebra book. Ms. B started with ten problems already written, and she can write six problems an hour. Ms. D had
no problems written, but she writes ten problems an hour. When will Ms. D have the same number of problems written as Ms. B? How many problems will they
each have written at that time?
The time when they will both have written the same number of problems is 2.5 hours.
The problems they would have written is 25.
When would they have written the same number of problems?The first step is to formulate an equation that represents the number of problems that Ms. B and Ms. D can write in an hour.
Problems Ms. B can write in an hour = 10 + 6h
Problems Ms. D can write in an hour = 10h
Where h represents the number of hours
When Ms. B and Ms. D have written the same number of problems, the two above equations would be equal:
10 + 6h = 10h
In order to determine the value of h, take the following steps:
Combine similar terms : 10 = 10h - 6h
Add similar terms: 10 = 4h
Divide both sides by 4 : 10 / 4
h = 2.5 hours
The number of problems they would have written in 2.5 hours : 10 x 2.5 = 25 problems
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What's 11,000lb in tons
Step-by-step explanation:
What's 11,000lb in tons
it 5.5 us tone
which conversion factors are used to multiply to 18 cm/s to get meters per minute? select each correct answer.
The conversion factor to convert cm/s to m/min is 3 / 5, it is gained by applying the knowledge of conversion of units to the given problem.
What do you mean by conversion of units?
Conversion of units deals with the method of converting a set of values given in a unit to another unit without changing its numerical value. Conversion can take place in both ways, from lower to higher units and vice-versa.
Calculation of the conversion factor to convert cm/s to m/min
We know that,
1 m = 100 cm
1 min = 60 s
To convert cm/s to m/min, we have
= 18 / (100 / 60)
= (18 × 3) / 5
= 54 / 5
= 10.8 m/min
Hence, the conversion factor used to convert cm/s to m/min is 3 / 5.
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the answer is A because to be honest im writing this so it will show me the right naswer but it should be A
what is the volume of a circle with a diameter of 2 inches
Answer:
Volume = 4 πr3 3= 4 ×π×43 3
= 268.08257310633 feet3
Step-by-step explanation: I really hope this helps please let me know if i am wrong hope u have a good day (:
I need help ASAP DUE TODAY Please
Answer:
it's 9 squar feet ;) ........
Consider the number 7,123,456.
a. Approximate the number by rounding to the nearest million.
Approximating 7,123,456 by rounding to the nearest million will be 7,000,000.
What is approximation?Anything similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated. By rounding the values in a computation before carrying out the procedures, an estimated result can be obtained.
If you want to round to one or two decimal places, look at the digit immediately following the decimal point. To the right of the necessary place value digit, draw a vertical line. Observe the following digit. Increase the preceding digit by one if the following digit is 5 or higher.
Therefore, approximating 7,123,456 by rounding to the nearest million will be 7,000,000.
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the hats of n persons are thrown into a box. the persons then pick up their hats at random (i.e., so that every assignment of the hats to the persons is equally likely). what is the probability that (a) every person gets his or her hat back?
The probability that every person gets his or her hat back is 1/n!
What are equally likely function?If each possibility in a sample space S has the same chance of happening, then all of the outcomes are equally likely. The following experiment shows how easy it is to compute the probability of a single result or an event if all outcomes in a sample space S are equally likely.
Think about the sample space for all hat assignments.
This has n! components (n hat picks for the first person, then n - 1 for the second, etc.),
with each occurrence having a chance of 1/n and being equally likely. Calculation is the issue.
The likelihood of a single element occurring, hence the response is 1/n!
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g(x)= x²-x-12/x²-4x+4
find g(2)
Step-by-step explanation:
g(2)=((2)²-2-12)/((2)²-4(2)+4)
=4-2-12/4-8+4
=-10/0=undefined
You invest $2,800 at a 6 nnual interest rate, stated as an apr. interest is compounded monthly. how much will you have in 1 year? in 1.5 years?
If, we invested $2,800 at a 6% annual interest rate. We will have $2972.70 in 1 year and $3063 in 1.5 year of time.
What is interest?In the fields of finance and economics, interest is defined as the payment of a sum over and above the principal amount (the amount borrowed) at a set rate by a borrower or deposit-taking financial institution to a lender or depositor. It is different from a fee that the borrower may pay to the lender or another entity. It also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve, but not at a set rate predetermined beforehand, but rather on a pro rata basis as a portion of the rewards received by risk-taking businesspeople when revenue is earned that exceeds all costs.
Calculations:
The Future value= fv= Pv x [tex](1+r/m)^{mt}[/tex]
R= Rate per period
mt= years x compounding
The Future value in 1 year= 2800x[tex](1+0.06/12)^{1x12}[/tex]
= $2972.70
The Future value in 1.5 years=2800x[tex](1+0.06/12)^{1.5x12}[/tex]
= $3063.00
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2.
To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for
each hour of labor.
y (dollars)
4,000
3,000
2,000
1,000
10
20
30 40 50
x (hours)
1. How much would the painting company charge to paint a house that needs
20 hours of labor? A house that needs 50 hours?
Scom
60
2. Draw a line representing the relationship between x, the number of hours it
takes the painting company to finish the house, and y, the total cost of
painting the house. Label the two points from the earlier question on your
graph.
3. Find the slope of the line. What is the meaning of the slope in this context?
Using a linear function, it is found that:
1. The company would charge $1,500 for 20 hours of labor and $3,000 for 50 hours of labor.
2. The graph is given at the end of the answer.
3. The slope of 50 means that the cost of each additional hour of labor is of $50.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The flat rate is the intercept.The cost per hour is the slope.Hence the charge for x hours of labor is given by the following function:
C(x) = 50x + 500.
Then:
C(20) = 50(20) + 500 = $1500.C(50) = 50(50) + 500 = $3000.The company would charge $1,500 for 20 hours of labor and $3,000 for 50 hours of labor.
The slope of 50 means that the cost of each additional hour of labor is of $50.
The graph with the two points from item a labeled is given at the end of the answer.
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Given y = 6x + 7, what is the value of y when x = -3?
Answer:
y=-11
Step-by-step explanation:
Answer:
y = - 11
Step-by-step explanation:
y=6x+7
y=6*(-3)+7
y=-18+7
y=-11