The variance of the data sets is 77.7
How to find variance of a data sets?Variance is the average of the squared differences from the Mean.
Therefore, to find the variance we have to find the mean, Then for each number: subtract the Mean and square the result.
Then work out the average of those squared differences.
Hence,
mean = 4 + 16 + 21 + 32 + 11 + 12 / 6 = 96 / 6 = 16
Therefore, lets find the difference and square it.
(4 - 16)² + (16 - 16)² + (21 - 16)² + (32 - 16)² + (11 - 16)²+ (12 - 16)²
144 + 0 + 25 + 256 + 25 + 16 = 466
Therefore,
variance = 466 / 6
variance = 77.6666666667
variance = 77.7
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Find the slope of the line that goes through the points (–4, 1) and (8, –5).
Answer:
[tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
Slope is the change in y over the change in x.
The ordered pair is in the form (x,y). The first number is the x value and the second number is the y value.
for y;
-5 - 1 = -6
for x:
8 - (-4)
8 + 4
12
[tex]\frac{-6}{12}[/tex] Which is the same as [tex]\frac{-1}{2}[/tex] if we divide the top and bottom by 6
The department store sells logo t-shirts at an original price of $12.50. Every month that a t-shirt doesn’t sell, the store reduces the price by 25%. Brianna calculated the price after two reductions:
12 dollars and 50 cents minus (12 dollars and 50 cents) (0.25) minus (12 dollars and 50 cents) (0.25) = 6 dollars and 25 cents
What is Brianna’s error?
Answer:
On the second reduction, she reduced 25% of the original T-Shirt's price. She should have reduced the price of the T-Shirt after one reduction.
Step-by-step explanation:
f(x)=10 x-10 . Find each value.
(f ⁰ f⁻¹)(d)
Function composition exists a mathematical procedure where two functions, f and g, are taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)).
If the function be f(x) = 10x - 10 then the value of (f ⁰ f⁻¹)(d) is 99.
What is meant by composition?Function composition exists a mathematical procedure where two functions, f and g, exists taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)). The function g is used in this operation on the outcome of applying the function f to x.
Let the function be f(x) = 10x -10
We want to find (f ⁰ f⁻¹)(d)
To differentiate with respect to X, then we get
[tex]F^{-1}[/tex](x) = 10
To find the value of (f ⁰ f⁻¹)(d)
F([tex]f^{-1}[/tex](x)) = F(10)
F([tex]f^{-1}[/tex](x)) = 10x - 10
substituting the values in the above equation, then
F([tex]f^{-1}[/tex](x)) = 10(10) - 10
simplifying the above equation, we get
F([tex]f^{-1}[/tex](x)) = 100 -10
F([tex]f^{-1}[/tex](x)) = 99
Therefore, the value of (f ⁰ f⁻¹)(d) = 99
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2(3) 3 as an exponent + 5
Answer: 13
Step-by-step explanation:
The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55.
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.
Work out the cost of
a) 1 kg of turnips.
b) 1 kg of mushrooms.
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Let x represent the cost of on kg of mushroom and y represent the cost of one kg of turnips.
The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. Hence:
2x + 2.5y = 8.55 (1)
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Hence:
3x + 4y = 13.10 (2)
From both equations:
x = 2.9, y = 1.1
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
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The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
Answer:
W = 11/8 or 1 3/8
Step-by-step explanation:
The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
W=(1/4)(L)
width is 1/4 length
if the length is 5 1/2 ft
5 1/2 is equivalent to 11/2
W= (1/4)(11/2)
Multiply across.
W = 11/8 or 1 3/8
8x = 2
Write down the value of x.
(It’s not 2/8 or 0.25)
Answer:
1/4
Step-by-step explanation:
Get x by itself by dividing both sides by 8
x = 2/8
Reduce
1/4
Answer:
8x=2
/8 /8
Step-by-step explanation:
it is 0.25
8x=2
/8 /8
x=0.25
Factor the expression. 8+27 x³
The factored form of the given expression is (3x+2)(9x²-6x+4).
Given the expression is 27x³+8.
In order to be factor out any polynomial expression, we want to identify firstly the method of factoring to be used in the given expression. We also need to simplify the factors.
We are given the expression 27x³+8.
We want to factor out the given expression.
Applying the sum of two cubes formula x³+y³=(x+y)(x²-xy+y²), we have:
27x³+8=(3x)³+(2)³
27x³+8=(3x+2)(3²x²-3x·2+2²)
27x³+8=(3x+2)(9x²-6x+4)
Hence, the factored form of the given expression 27x³+8 is (3x+2)(9x²-6x+4).
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Simplify each expression. (-8x³)⁻⁴/₃
The solution for the expression ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴
Given expression is ( -8x³) ⁻ ⁴/₃
= ( -8x³) ⁻ ⁴/₃
It can be written as
We know that 8 = 2³ then
= ((-2x)³) ⁻ ⁴/₃
= ((-2x)³* ⁻ ⁴/₃
On the exponents '3' will be canceled then we get
= (-2x) ⁻ ⁴
We know that x ⁻ ¹ can be written as 1/x, then
= 1/(-2x)⁴
= 1 / 16x⁴
∴ ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴
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Iggy bought the refrigerator on a payment plan.He paid $150 when he bought it and he agreed to pay $28.50 each month for the next 24 months.
Answer:834$
Step-by-step:150+28.24=834$
Question 10: Neil writes down four numbers with a sum of 50.
All the numbers have two decimal places and no two numbers are the same.
Write down four possible numbers Neil could have written down.
Answer:
15-10-11-14
Step-by-step explanation:
15+10= 25
25+11= 36
36+14= 50
Lola went to the hardware store and bought 6 yellow ropes. The total length of the ropes was 8.1 meters. How long was each rope?
The length of each rope is 1.35 meters
How to calculate the length of each rope ?Lola went to the hardware store and bought 6 yellow ropes
The total length of the rope was 8.1 meters
Therefore the length of each rope can be calculated as follows
= 8.1/6
= 1.35
Hence the length of each rope at the hardware store is 1.35 meters
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What is each expression written as a single natural logarithm?
(c) 3 ln x+2 ln y+ln 5
According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.
Therefore, the given expression is [tex]3 ln x+2 ln y = ln5[/tex]
The values get multiplied in addition. Therefore, the above expression can be written as: [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Expression = [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Using logarithmic definition, we can write:
[tex]ln(x^{3} )+ln(y^{2} )+ln5\\ln(5x^{3} y^{2} )[/tex]
The solution for the given expression is [tex]ln(5x^{3}y^{2} )[/tex]
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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SOLVE FOR BRAINLIEST
The equation of the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) = 0.5 + √x + 2.25
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse function?The function f(x) is given as
f(x) = x^2 - x - 2
Start by expressing the above function in vertex form
Using a graphing calculator, we have
f(x) = (x - 0.5)^2 - 2.25
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = (x - 0.5)^2 - 2.25
The next step is to switch/swap the positions of x and y in the above equation y = (x - 0.5)^2 - 2.25
The equation becomes
x = (y - 0.5)^2 - 2.25
Add 2.25 to both sides
So, we have
(y - 0.5)^2 = x + 2.25
Take the square root of both sides
y - 0.5 = √x + 2.25
Add 0.5 to both sides
So, we have
y = 0.5 + √x + 2.25
Express as an inverse function
f'1(x) = 0.5 + √x + 2.25
Hence, the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) = 0.5 + √x + 2.25
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if a one time deposit of $1000 in invested at age 25 with 12% annual interest rate, how much will be in the account at age 65 (40 years later)?
The amount in the account after 40 years will be $5800.
How to illustrate the information?It should be noted that the interest is calculated as:
= (Principal × Rate × Time) / 100
= ($1000 × 12 × 40) / 100
= $480000 / 100
= $4800
Therefore, the amount in the account after 40 years will be:
= Principal + Interest
= $1000 + $4800
= $5800
Therefore, the amount in the account after 40 years will be $5800.
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Multiply and simplify. √8 x² . √2 x²
The simplest form of the expression is 4 x² .
Expressions in science are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by degree operator in between.Simplifying expressions mean editing an analogous math expression with no like terms and through a compact manner.To change expressions, we tend to tend to combine all kind terms and solve all the given brackets, if any, and then inside the simplified expression, we tend to are about to be alone left with not like terms that cannot be reduced any.We have given an expression √8 x² . √2 x² . .....(1)
On multiplying , we get
√8 x² . √2 x² = √16 x⁴
On simplifying , we get
√16 x⁴ = √ 4 × 4 × x² × x²
= 4 x²
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Please help fast thank you!
Answer:
-3.78= (-1.2y)+(-4.2y)
y= 0.7
Step-by-step explanation:
-3.78= (-1.2y)+(-4.2y)
-3.78= -5.4y
/-5.4 /-5.4
y=0.7
Please help me calculate the value of y with steps
The value of y in the triangle is 7.5
How to calculate the value of y?The given parameter is the triangle
On the triangle, we have the following equivalent ratio
y : 8 = y + 15 : 20
Express as fraction
y/8 = y + 15/20
Cross multiply
20y = 8y + 90
Collect the like terms
20y - 8y = 90
Evaluate
12y = 90
Divide by 12
y = 7.5
Hence, the value of y in the triangle is 7.5
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the table shows a proportional relationship between the millilitres (ml) of red paint and millilitres of yellow paint to make a certain shade of orange.
Motorcycle A can reach a top speed of 140 miles per hour motorcycle B can reach a top speed of 200 feet per second which motorcycle has a greater top speed
Motorcycle A has a greater top speed.
What unit conversion?A unit conversion expresses the same property as a different unit of measurement.
given:
Motorcycle A can reach a top speed of 140 miles per hour.
Motorcycle B can reach a top speed of 200 feet per second
Now,
1 miles/h = 1.46667 feet/sec
140 miles/h = 140*
= 205.333 feet/sec
So, Motorcycle A can reach a top speed of 205.333 feet/sec.
Hence, Motorcycle A has a greater top speed
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Doy muchos puntos pls ayuda
Answer:
5. 18%
6. 5.25% o 5.3 o 5
7. 33.33%
8. 2005-2010
Which of the following vertices would minimize the objective function N = 7x + 2y?
A. (4,0)
B. (6,3)
C. (3,9)
D. (0,12)
Check the picture below.
Let g(x)=5 x-2 and h(x)=x²+1 . Find the value of each expression. (h⁰g)(0)
The value of the expression ( h o g)(0) is 5.
When two functions say f and g, are composed in such a way that h(x) = g(f(x)), a new function, h, is created. In this case, the function of g is being applied to the function of x. So, in essence, the output of one function is applied to the result of another.
Consider the two functions,
g(x) = 5x - 2 and h(x) = x² + 1
So,
( h o g)(x) = h(g(x))
( h o g)(x) = ( 5x - 2 )² + 1
( h o g)(x) = 25x² - 20x + 4 + 1
( h o g)(x) = 25x² - 20x + 5
( h o g)(0) = 25 × (0)² - 20 × (0) + 4 + 1
( h o g)(0) = 0 - 0 + 4 + 1
( h o g)(0) = 5
The value of the expression ( h o g)(0) is 5.
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In ΔJKL, m ∠ L=71°, j=11 m , and m ∠ K=46° . Find k .
Step-by-step explanation:
first : the sum of all angles in a triangle is always 180°.
second : the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides, A, B, C are the the corresponding opposite angles.
therefore,
angle J = 180 - 71 - 46 = 63°
j/sin(J) = k/sin(K)
11/sin(63) = k/sin(46)
k = 11×sin(46)/sin(63) = 8.880673249... m
Can some one help me it’s too difficult
EVERY ONE PLEASE GO ON MY PAGE AND HELP ME, PLEASE
Answer:With what?
Step-by-step explanation:there is no page
Answer:
I helped you on your first question, I wasn't too sure about the others because their answer options are mostly inaccurate from what I know.
Your sports drink bottle is 56 full. After practice, the bottle is 38 full. Write the difference of the amounts after practice and before practice. Write your answer as a fraction in simplest form.
The difference of the amounts after practice and before practice is 18 full.
The difference as a fraction in simplest form will be 9/28.
How to calculate the value?The sports drink bottle is 56 full and after practice, the bottle is 38 full, the difference of the amounts after practice and before practice will be:
= 56 - 38
= 18
The difference as a fraction in simplest form will be:
= Difference / Original value
= 18 / 56
= 9 / 28
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The midpoint of \overline{\text{AB}} AB is M(-4, -3)M(−4,−3). If the coordinates of AA are (-1, -2)(−1,−2), what are the coordinates of BB?
The midpoint of AB is M(-4, -3). If the coordinates of A are (−1,−2), then B has coordinates of (-2, -7/3)
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
Line AB has a midpoint, M.
A is (-1, -2)
B is unknown, M is(−4,−3)
Let's assume straight line of the form y=mx+b, where m is the slope.
Rise = (-3-(-2))= -1
Run = (-4-(-1)) = -3
Slope = (Rise/Run) = (1/3)
The line becomes y=(1/3)x+b
Calculate b, the y-intercept (the value of y when x is 0)
y=(1/3)x+b
-2 = (1/3)(-1)+b
b = -2 + (1/3)
b = -5/3
The equation becomes:
y=(1/3)x - -5/3
Find the value of y for x=-2:
y=(1/3)x - -5/3
y=(1/3)(-2) - 5/3
y= -7/3
B has coordinates of (-2, -7/3)
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Row a in a certain section in a football stadium has 10 seats. each row behind row a is labeled alphabetically (b, c, d, and so on) and has 6 more seats than the row immediately in front of it.how many seats are in row g of this section of the stadium?
The total number of seats in row g is 224.
Number of seats in a row a = 10
Number of seats in row b = 16
Number of seats in row c = 22
The common difference is d.
d = (22-16) = 6
The first term is a.
a = 10
The total number of rows is n.
n = 7
[tex]a _{n} = a + (n - 1)d[/tex]
[tex]a _{n} = 10 + (7 - 1)6[/tex]
= 46
The total number of seats in row g is,
[tex]S _{n} = \frac{n}{2} (a + a _{n})[/tex]
[tex]S _{n} = \frac{8}{2} (10 + 46)[/tex]
= 224
Therefore, the total number of seats in row g is 224.
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A farmer has 30 boxes of eggs.
6 There are 6 eggs in each box.
Write, as a ratio, the number of eggs in three boxes to the total number of eggs.
Give your answer in its simplest form
Answer: 1:15
Step-by-step explanation:
we know that the total number of eggs is the same as the number of eggs in 30 boxes. Hence the ratio will be 2 : 30, and then divide both sides by 2 to get 1 : 15 as the ratio in its simplest terms.
The ratio of the number of eggs in three boxes to the total number of eggs is 1 : 10.
We have,
To find the ratio of the number of eggs in three boxes to the total number of eggs, first, let's calculate the number of eggs in three boxes:
Number of eggs in three boxes
= 3 boxes * 6 eggs per box
= 18 eggs
Now, the ratio of the number of eggs in three boxes to the total number of eggs is:
18 eggs : 30 boxes x 6 eggs per box
18 eggs : 180 eggs
Cancel out the common factors.
1 egg : 10 eggs
So, the simplified ratio is:
1 egg : 10 boxes
Therefore,
The ratio of the number of eggs in three boxes to the total number of eggs is 1 : 10.
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