According to the given information the mean(MAD) of the data is = 16.
What is the mean mathematical term?The mean is the average of a set of variables in mathematics and statistics. The mean can be calculated in a variety of ways, such as the simple arithmetic mean (add the numbers and divide the sum by the number of observations), geometric mean, and harmonic mean.
According to the given data:(13 ,14 ,14, 16, 16, 16, 16, 18, 18, 19)
adding the numbers together.
(13 + 14 + 14 + 16 + 16 + 16 + 16 + 18 + 18 + 19)
= 160.
Then divide it by the amount of numbers. Which is ten.
160 divided by 10 = 16.
—MAD—
Subtract each value from the mean.
(|13-16| + |14-16| + |14-16| + |16-16| + |16-16| +|16-16| + |16-16| + |18-16| + |18-16| + |19-16|)
Negative numbers are unimportant; everything should be positive.
(3 + 2 + 2 + 0 + 0 + 0 + 0 + 2 + 2 + 3)
= 16.
16 divided by 16 (amount of numbers).
MAD = 1
–IQR—
Separate both sides in half.
(|13 14 14 16 16| ,|16 16 18 18 19|)
Take the middle value of each group.
Group1.
|13 14 (14) 16 16|
This one is 14.
Group 2:
|16 16 (18) 18 19|
This one is 18.
Subtract (number from group 2) 18 from (number from group 1) 14.
18 - 14 = 4
IQR = 4.
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Select all pairs of numbers that have a least common multiple of 30.
Answer:
5 and 6, 3 and 10
Step-by-step explanation:
that's all I can think of
Select the graph of the solution. Click until the correct graph appears.
|x| = 1
Answer:
It's the graph with two dots and no area marked, first image (for me).
Step-by-step explanation:
|x| = 1 means "the distance from x to the 0 point on the axis is exactly 1". There's only 2 numbers x that satisfy that condition: -1 and 1
The second and third image both show an area marked, so it cannot be the right answer, while the first image shows precisely two numbers: -1 and 1
two friends Natasha and Trisha shared a sum of money in the ratio 5:3 respectively. if Trishia share is $ 120 calculate the total amount of money shared
The money shared by Natasha and Trisha is $160.
What is defined as the term ratio?A ratio is a measure of 2 or more numbers which indicates their relative sizes. A ratio compares two amount by dividing them, with the dividend or number divided referred to as the antecedent and thus the divisor or number divided referred to as the consequent.Let the amount paid by the Natasha is 'x'
And the amount Paid by Trisha is 'y';
Their amounts are in the ratio of 5:3
Thus, x/y = 5/3
Trisha shares a amount of $120.
y = $12.
Then, put y = 120 in the ratio.
x/y = 5/3
x = 5y/3
x = (5×12)/3
x = 5×4
x = 40 (amount shared by Natasha)
Total amount = Natash's share + Trisha's share
Total amount = 40 + 120
Total amount = 160
Thus, the total amount of money shared is $160.
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Andrew made an error in determining the polynomial equation of the smallest degree whose roots are 3, 2+2i and 2-2i. review andrew's work, identify the error and correct all work from that point forward that is affected by this error.
The polynomial equation is (x³ - 7x² + 20x - 24) = 0 and the Error that made by Andrew is incorrect factors of the roots.
Polynomial Equation:
The equations formed with variables, exponents and coefficients are called as polynomial equations.
Roots of the Polynomial:
Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.
Given,
Roots of the polynomial are: 3, 2 + 2i, 2 - 2i.
Here we need to find the error he made and the correct form of the equation.
According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is a factor of P(x).
According to this definition:
=> (x - 3) , (x - (2 + 2i)) , (x - (2 - 2i))
are factors of the required polynomial.
Simplifying the brackets, we get:
=> (x - 3), (x - 2 - 2i), (x - 2 + 2i)
are factors of the required polynomial.
This is the step where Andrew made the error.
The factors will always be of the form (x - a) , not (x + a).
Andrew wrote the complex factors in form of (x + a) which resulted in the wrong answer.
So, the polynomial would be:
=> (x - 3)(x - 2 - 2i)(x - 2 + 2i) = 0
=> (x - 3) (x² - 2x + 2xi - 2x + 4 - 4i - 2xi - 4i - 4i²) = 0
When we simplify it, then we get,
=> (x - 3)(x² - 4x + 4 + 4) = 0
=> (x - 3)(x² - 4x + 8) = 0
=> (x³ - 4x² + 8x - 3x² + 12x - 24) =0
=> (x³ - 7x² + 20x - 24) = 0.
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What lines would you use to solve –3x – 2 = 2x + 8? Graph the line for the left side of the equation. Graph the line for the right side of the equation.
Answer:
See attached graph for lines
Left side line is y = -3x-2
Right side line is y = 2x + 8
Point of intersection is at (-2,4)
Step-by-step explanation:
The line graphs are attached
The solution for (x, y) is the point of intersection of the two lines
This is at point (2,4)
We can also solve this algebraically by solving first for x and then y
–3x – 2 = 2x + 8
The two line equations are
y = -3x - 2 and y = 2x+8
3x – 2 = 2x + 8
==> 3x -2x - 2 = 2x-2x + 8 (subtract 2x on both sides)
==> -5x -2 = 8
==> -5x -2 + 2 = 8 + 2 (add 2 on both sides to isolate the x term)
==> -5x = 10==> -5x/5 = 10/5 (divide by 5 both sides)
==> x = -2
Plug this value of x into the RHS giving
y = 2(-2) + 8 ==> y = -4 + 8 ==> y = 4
So (-2,4) is the point of intersection of the two lines and is consistent with the point of intersection on the graph
Rory has 3 pounds of ground turkey to make meatballs.He uses 3/8 pound per to make 6 meatballs. How many 1/8 pound meatballs can Rory make with the remaining turkey?
He can make 2 meat balls from the remaining turkey.
Total pounds of ground turkey available = 3 pounds.
Turkey used to make 6 meat ball = 3 / 8 of 3 pounds = 9 / 8 pounds
Turkey used to make 1 meat ball = 9 / 8 ÷ 6 = 3 / 16
1 / 8 meat = 1/ 8 of 3 = 3 / 8 pound of meat.
Number of meatballs made = 3 / 8 × 16 / 3 = 2
Therefore, he can make 2 meat balls from the remaining turkey.
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Evaluate the expression −x^2 + 2x-7 when X=-4
what is the estimate of 3,182x5
Step-by-step explanation:
15,910 like what said of calculator
What is an explicit formula for the sequence 0,3,8,15,24,...? What is the 20th term?
Answer:
the most logical answer is
n^2-1
20th term is then 399
Step-by-step explanation:
The rule behind the sequence could be anything, but it is very likely that we're supposed to notice that the terms are all squares minus 1
0 = 1*1 - 1
3 = 2*2 - 1
8 = 3*3 - 1
15 = 4*4 - 1
24 = 5*5 - 1
So we expect that the explicit formula is n^2-1 and the 20th term is 399
The kinetic energy k of an object varies jointly with its mass m and its velocity v. The formula to kinetic energy is K = 1/2mv^2. Rearrange the formula to write the mass m in terms of K and v, where v is not equal to 0.
(I will rate brainliest if only right)
The mass m in terms of K and v is expressed as m= 2K/v^2
Subject of formulaThe subject of formula is a way of representing a variable in terms of other variables.
Given the equation below;
K = 1/2mv^2
Make m the subject of the formula
2K = mv^2
Divide both sides by v^22K/v^2 = mv^2/v^2
2K/v^2 = m
Swap
m= 2K/v^2
Hence the mass m in terms of K and v is expressed as m= 2K/v^2
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56) The length of a rectangle is 1 inch more than 4 times its width. The area of the rectangle is 3 square
inches. What is the perimeter of the rectangle?
Perimeter of rectangle is 9.5 inches
If the length of the rectangle is l and its width is w,
l = 4w + 1, and
lw = (4w+1)×w = 3.
This yields 4w² + 1w -3= 0, which can be solved in the normal way for quadratic equations.
Solving the equation we get as
w=0.75 or w=-1
as it an not be negative value hence w=0.75
l=4
Perimeter of rectangle is 2*(l+w)= 9.5 inches.
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Directions: Use the distributive property to multiply the following binomials. Write your answer in standard form!
a.) (x+5)(x-2)
Answer:
x^2 +3x -10
Step-by-step explanation:
(x+5)(x-2)
x^2 +5x -2x -10
x^2 +3x -10
PLEASE HELPPPP. WILL GIVE BRAINLIEST AND 5 STR RATINGGG
which function has an inverse that is also a function? {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}
The correct option is A. {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}.
The function which also has an inverse that is also a function is {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}.
What is termed as a inverse function?An inverse in mathematics is a function which serves to "undo" another function. That is, if f(x) yields y, then placing y into the inverse of f yields x.
A function is a type of relationship that binds inputs to primarily one output.The machine will only acknowledge inputs which are primary criterion as part of a function's domain and will only generate one output for each input.In some other words, the function is the nature of the relationship between variables.In response to the given question
We understand that such a function is really only one that has a unique y value that corresponds to x.
An inverse function is only a function is if function being inversed is also a function.
Thus, option (A) has all x corresponding to y values that are different, but all remaining options have the values repeating, so that will not be a function because only (A) has to inverse.
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The complete question is -
Which function has an inverse that is also a function?
A. {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}
B. {(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)}
C. {(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)}
D. {(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}
PLS ANSWER ALL OF THE QUESTIONS IN ORDER
The the required value of function of the expression when x equal to 5 i.e f(5) is 167.
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given:
The given expression is
f(x) =[tex]7x^{2} -8[/tex]
We have to find the value of f(5).
According to given question we have
f(x) =[tex]7x^{2} -8[/tex]
Put the value of x= 5 in the given function we get,
f(x) =[tex]7x^{2} -8[/tex]
f(5) =[tex]7(5)^{2} -8[/tex]
After simplifying we get
f(5)=167
Therefore, the required value of function of the expression when x equal to 5 i.e f(5) is 167.
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Chad will have new carpet put on the rectangular floors of two rooms in his house. One floor is 12 1/2 feet long, and
the other floor is 15 3/4 feet long. Each floor has a width of 10 feet.
What is the total area in square feet of the new carpet?
A 125 ft²
B 157.5 ft²
©282.5 ft²
96.5 ft²
Answer:
c) 282.5 ft²
Step-by-step explanation:
Formula we use,
A = L × W
The area of one floor will be,
→ 12 1/2 × 10
→ 25/2 × 10
→ 250/2
→ 125 ft²
The area of another floor will be,
→ 15 3/4 × 10
→ 63/4 × 10
→ 630/4
→ 157.5 ft²
Total area of the new carpet is,
→ 125 + 157.5
→ 282.5 ft²
Hence, the total area is 282.5 ft².
If One floor is 12 1/2 feet long, and the other floor is 15 3/4 feet long. Each floor has a width of 10 feet. Then total area of new carpet is 282.5 ft²
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that new carpet put on the rectangular floors of two rooms in his house.
One floor is 12 1/2 feet long
Second floor is 15 3/4 feet long.
Width is given by 10 feet.
We know that area of rectangle is
Area = Length × Width
The area of one floor will be,
12 1/2 × 10
25/2 × 10
250/2
125 ft²
The area of another floor will be,
15 3/4 × 10
63/4 × 10
630/4
157.5 ft²
Total area of the new carpet is,
125 + 157.5
282.5 ft²
Hence, the total area of new carpet is 282.5 ft².
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Jackson and Flora both have bank accounts, and they use credit cards.
Use the number line to determine if they can pay off the credit card bill.
A. Jackson has $20 in his account. He uses a credit card to spend $30 on a
coat and $10 on a movie. Jackson then deposits $50 into his account.
How much will Jackson have left after he pays the credit card bill?
is five less than a number an equation or expressions
it hard to tell what you are saying, but if we know what the other number is, then expression.
I need help on this one question, anyone know the answer?
A mother wants to invest $15,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $900.00, how much money was invested in the CD account?
The total interest earned after one year is $900.00.
How much money was invested in the CD account? $
(Round to the nearest cent, if necessary.)
From the analysis of the above math, the amount she invested in the CD account is 5,000. See the analysis below.
What is the analysis showing the above answer?Let A be the amount invested in the CD.
Let B be the amount invested in the savings bond.
A + B = 15, 000
.04A + .07B = 900
Multiply the first equation by -.04 and add it to the second equation to get rid of the A term.
-.04A-.04B = -600 add this equation to the second equation.
.03B = 300 multiplying by 100. 3B = 30,000
dividing by 3 on both sides: B = 10,000. So A = 5,000
So she invested 5,000 in the CD account
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Long division 1,755 divided by 27
Answer:
65
Step-by-step explanation:
In a shipment of 62 vials, only 14 do not have hairline cracks. if you randomly select 3 vials from the shipment, what is the probability that all 3 of the selected vials have hairline cracks?
The probability that all three of the selected vials have hairline cracks = 0.096
Total number of vials in the shipment = 62
Number of vials with hairline cracks = 14
Number of vials without hairline cracks = 48
Three from 62 vials are selected.
So total outcomes = 62C3
Number of possible outcomes for all 3 of selected vials have hairline cracks = 14C3, which is the number of favorable outcomes
Probability that all three of the selected vials have hairline cracks = Number of favorable outcomes/Total outcomes = 14C3/62C3 = 0.096
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David has 10 yd. Of material that he wiil cut into 15in. Thick mats. How many mats can David make?
Step-by-step explanation:
10 yards is equal to 360 inches. If you divided 360 inches by 15 inches, the answer will be 24. So the answer is 24 mats.
Some Math i can’t helppp
Annually The amount after 10 years = $ 7247.295
quarterly compound after 10 years = $7393.5
Continuously interest =$7,419
Given:
P = the principal amount
r = rate of interest
t = time in years
n = number of times the amount is compounding.
Principal = $4500
time= 10 year
Rate = 5%
To find: The amount after 10 years.
The principal amount is, P = $4500
The rate of interest is, r = 5% =5/100 = 0.05.
The time in years is, t = 10.
Using the quarterly compound interest formula:
A = P (1 + r / 4)4 t
A= 4500(1+.05/4)40
A= 4500(4.05/4)40
A= 4500(1.643)
Answer: The amount after 10 years = $7393.5
Using the Annually compound interest formula:
A = P (1 + r / 100) t
A= 4500(1+5/100)10
A= 4500(105/100)10
Answer: The amount after 10 years = $ 7247.295
Using the Continuously compound interest formula:
e stands for Napier’s number, which is approximately 2.7183
[tex]A=Pex^{rt} \\A=4500(e)^{.5} \\A= 4500(2.71)^{.5}[/tex]
A= $2,919
Answer: The amount after 10 years = $4500+$2,919=$7,419
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is 9.02 x 10-8 larger than 9.02 x 10-6
Answer:Yes 90.2 x 10-8 is greater then 90.2 x 10-6
Step-by-step explanation:
Is √35 rational or irrational
Answer:
Irrational
Step-by-step explanation:
It can not be square rooted, the closest squared number to 35 is 36. The square root of 36 is 6 as 6x6= 3.
Therefore it is irrational.
Answer:
see below
Step-by-step explanation:
sqrt35 is irrational since by the definition of rational: able to be expressed as a whole number or a fraction.
sqrt35 is approximatly 5.91607978. which is not able to be a whole number or a fraction
thus sqrt35 is irrational
What's the Gcf of 16,44, and 28 (greatest common factor)
Answer:
4
16 / 4 = 4
44 / 4 = 11
28 / 4 = 3
easy
There were 127 birds on the endangered species list in some year. This is more than twice the number of reptiles on the list. How many reptiles were on the endangered species list in this year?
r = number of reptiles on the endangered species list
2r = twice that number
2r < 127 since the 127 is more than twice the number of reptiles
Solve for r by dividing both sides by 2
2r < 127
r < 127/2
r < 63.5
If r is a positive whole number, then r could be anything from this set: {1, 2, 3, ..., 62, 63}
Unfortunately there isn't enough information to fully pin down what r is.
I would ask your teacher for further clarification.
-2x(-3)=
(-3x4)÷(-8)=
(-2x(-3))x(-4)=
Answer:
61,5-24Step-by-step explanation:
[tex]1. \: \: - 2 \times - 3 = \\ = 6[/tex]
[tex]2. \: \: ( - 3 \times 4) \div ( - 8) = \\ = ( - 12) \div ( - 8)\\ = ( - 6 )\div ( - 4) \\ = ( - 3 )\div ( - 2 )\\ = 1.5[/tex]
[tex]3. \: \: ( - 2) \times ( - 3) \times ( - 4) = \\ = 6 \times ( - 4) \\ = - 24[/tex]
distance between points -10,6 and 2, -3
Answer:
15 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 10, 6 ) and (x₂, y₂ ) = (2, - 3 )
d = [tex]\sqrt{(2-(-10))^2+(-3-6)^2}[/tex]
= [tex]\sqrt{(2+10)^2+(-9)^2}[/tex]
= [tex]\sqrt{12^2+81}[/tex]
= [tex]\sqrt{144+81}[/tex]
= [tex]\sqrt{225}[/tex]
= 15 units
