Answer:
(a) [tex]\sigma = 7.04[/tex]
(b) [tex]\sigma = 14.1[/tex]
(c) The population standard deviation is multiplied by k
Step-by-step explanation:
Given
[tex]Dataset: 12, 7, 18, 23, 24, 27[/tex]
Solving (a): The population standard deviation
Start by calculating the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{12+7+18+23+24+27}{6}[/tex]
[tex]\mu = \frac{111}{6}[/tex]
[tex]\mu = 18.5[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
This gives:
[tex]\sigma = \sqrt{\frac{(12-18.5)^2 + (7 - 18.5)^2 + (18-18.5)^2 + (23-18.5)^2 + (24 - 18.5)^2 + (27 - 18.5)^2}{6}}[/tex]
[tex]\sigma = \sqrt{\frac{297.5}{6}}[/tex]
[tex]\sigma = \sqrt{49.5833}[/tex]
[tex]\sigma = 7.04[/tex]
Solving (b): Double the dataset and calculate the new population standard deviation
The new dataset is:
[tex]Dataset: 24, 14, 36, 46, 48, 54[/tex]
Start by calculating the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{24+ 14+ 36+ 46+ 48+ 54}{6}[/tex]
[tex]\mu = \frac{222}{6}[/tex]
[tex]\mu = 37[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
This gives:
[tex]\sigma = \sqrt{\frac{(24-37)^2 +(14-37)^2 +(36-37)^2 +(46-37)^2 +(48-37)^2 +(54-37)^2}{6}}[/tex]
[tex]\sigma = \sqrt{\frac{1190}{6}}[/tex]
[tex]\sigma = \sqrt{198.33}[/tex]
[tex]\sigma = 14.1[/tex]
Solving (c): What happens when the dataset is multiplied by k
In (a), we have:
[tex]\sigma = 7.04[/tex]
In (b), when the dataset is doubled,
[tex]\sigma = 14.1[/tex]
This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:
i.e.
[tex]New \sigma = k * \sigma[/tex]
LMNP is a rectangle. Find the value of x and the length of each diagonal.
The value of x is equal to 3.
The length of diagonal LN is equal to 18 units.
The length of diagonal MP is equal to 15 units.
What is a diagonal?In Mathematics, the diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.
This ultimately implies that, the length of each diagonal of a rectangle is always equal to each other. Therefore, the diagonals of any rectangle is always equal to one other.
How to determine the value of x?We would determine the value of x by equating the length of each diagonal as follows;
LN = MP
7x - 3 = 4x + 3.
7x - 4x = 3 + 3
3x = 6
x = 6/2
x = 3.
Next, we would calculate length of each diagonal as follows;
LN = 7x - 3
LN = 7(3) - 3
LN = 21 - 3
LN = 18 units.
MP = 4x + 3.
MP = 4(3) + 3.
MP = 12 + 3
MP = 15 units.
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Complete Question:
LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 7x - 3 and MP = 4x + 3.
3y+2=2x is this a direct variation
The equation 3y + 2 = 2x is not a direct variation
How to determine if the equation is a direct variation
From the question, we have the following parameters that can be used in our computation:
Variation = direct variation
3y + 2 = 2x
A direct variation is represented as
y = kx
Where k is the constant of proportion
When the equations y = kx and 3y + 2 = 2x are compared, we can see that
The equation 3y + 2 = 2x has a constant term
Hence, the equation is not a direct variation
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Find the area. The figure is not drawn to scale.
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
Answer:
[tex](a)\ Area = 28.12cm^2[/tex]
[tex](b)\ Volume = 1437.33cm^3[/tex]
Step-by-step explanation:
Solving (a): The parallelogram
[tex]h = 7.6[/tex] --- height
[tex]b = 3.7[/tex] --- base
The area is calculated usng:
[tex]Area = base * Height[/tex]
[tex]Area = 3.7 * 7.6[/tex]
[tex]Area = 28.12cm^2[/tex]
Solving (b): The sphere
[tex]d = 14cm[/tex]
Required
The volume
First, calculate the radius
[tex]r = d/2[/tex]
[tex]r = 14cm/2 = 7c,[/tex]
The volume is calculated using:
[tex]Volume = \frac{4}{3} \pi r^3[/tex]
This gives:
[tex]Volume = \frac{4}{3} * \frac{22}{7} * 7^3[/tex]
[tex]Volume = \frac{4}{3} * 22 * 7^2[/tex]
[tex]Volume = \frac{4}{3} * 1078[/tex]
[tex]Volume = \frac{4*1078}{3}[/tex]
[tex]Volume = \frac{4312}{3}[/tex]
[tex]Volume = 1437.33[/tex]
20. You are buying new car for $24,320. You must put down 17%. How much will you need to finance the car for?
17 percent of 24320 is 4134.4
basically minus that
so
24320 - 4134.4 = 20,185.60
Answer:
24320 - 4134.4 = 20,185.60
Step-by-step explanation:
:)
4. The profit on one share is Rs20.What is the profit on 5000 shares?
Answer:
The profit is: [tex]Rs100000[/tex]
Step-by-step explanation:
Given
[tex]1 \to Rs20[/tex]
Required
Profit on 5000
Repesent this as: x
So, we have:
[tex]1 \to Rs20[/tex]
[tex]5000 \to x[/tex]
Cross Multiply
[tex]x * 1 = Rs20 * 5000[/tex]
[tex]x * 1 = Rs100000[/tex]
The profit is: [tex]Rs100000[/tex]
Please explain step by step I dont get it.
What is a remainder
A remainder is the remaining amount of a number than comes out of a division. I'm not sure how to explain it better, so I'll give you an example:
Let's say you want to divide 5 by 2. We know that 5 can't be divided by 2 evenly, it won't give you a whole number. Instead it will give you a decimal 2.5.
In this case, 1 is the remainder and I will explain why! Do the long division for 5/2. 2 fits into 5 two times, so you multiply 2 * 2, which gives you 4. If you subtract that number from 5, you get 1. We know that 2 can't fit into one, therefore, 1 is the remainder. once you start getting into decimals, you can fit numbers into other numbers, which is why technically you can fit 2 into 5, but you can't fit it in evenly, if that makes sense!
I hope this example helps see what a remainder is. It's just the number in a long division that the divisor (in my example, 2 is the divisor) can't fit in!
Help! Cant figure out math question!
Order from least to greatest √_220 , -10, √_100 , 11.5
Answer: -10, √_100, 11.5, √_220
Step-by-step explanation:
-10 is the least bc it just is and √_100 simplified is 10 and 11.5 is a little greater so duh and √_220 simplified is 14.83
Given:
f(x) = x² + x − 6
g(x) = x + 3
Find: (f/g)(x)
Answer:
x–2, x ≠ -3
Step-by-step explanation:
Solution in the diagram
y=(x+3)(x-2)(x-r) with a y int. of 24. solve for r?
Answer:
Step-by-step explanation:
To solve for r, you need to first find the values of x that make y equal to 24. These values of x are called the roots of the polynomial equation y = (x+3)(x-2)(x-r).
To find the roots of the equation, you can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation y = ax^2 + bx + c.
In this case, the coefficients are:
a = 1
b = -3
c = -24
Substituting these values into the quadratic formula, we get:
x = (3 +/- sqrt(9 - 96)) / 2
= (3 +/- sqrt(-87)) / 2
Since sqrt(-87) is not a real number, there are no real roots for this equation. Therefore, the value of r cannot be determined.
In ΔNOP, the measure of ∠P=90°, the measure of ∠N=26°, and OP = 13 feet. Find the length of PN to the nearest tenth of a foot.
Answer:
b
Step-by-step explanation:
Half of the class of 40 students are absent. How many students are absent today?
Answer:
20 students were absent
Step-by-step explanation:
Half means divide by 2:
40/2 = 20
NO LINKS!!!
A researcher found the average cost of one and two-bedroom apartments for different cities and graphed the data in a scatter plot, with costs of one-bedroom apartments along the x-axis. The variables have a strong linear correlation and the equation for the regression line is yˆ=1.182x+19.096 .
Based on the equation, what should the researcher expect for the average cost of a two-bedroom apartment in a city where the average cost of a one-bedroom apartment is $815?
Answer:
i hope it helps mapriend
Exponential Functions
Determine which of the following exponential formula(s) represents exponential function II in the graph above.
(a) 10(1.2)t (β) 10(1.5)t
(x) 20(1.2)t (8) 30(0.85)t
(8) 30(0.95)t (∅) 30(1.05)t
a. x c. 8
b. a d. ∅
Please select the best answer from the choices provided
Answer:
A. x
Step-by-step explanation:
I calculated it logically
Round 0.265625 to the nearest hundredth
Answer:
0.27 is the answer
I wish you luck in your assignments.
Answer:
Step-by-step explanation:
0.27
WILL MARK BRAINLIEST!
Calculate mF in parallelogram FGDE.
Find the perimeter of the polygon.
S cm
6 cm
6 cm
8 cm
a. 25 cm
b. 20 cm
C. 30 cm
d. 28 cm
Please select the best answer from the choices provided
Ο Α
Answer:
A. 25 cm
Step-by-step explanation:
Perimeter of a polygon = the sum of all sides of the polygon
Therefore,
Perimeter of the given polygon = 5 + 6 + 8 + 6
Perimeter = 25 cm
if you earn 3250 over the 10 year period, how much will be in the account at the end of the 10 year period?
If earning 3250 per month over 10year period, At the end of 10th year, the amount on the account will be 390,000
What is multiplication?To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.
The amount earned In a month is 3250.
There are 12 months In a year.
The total month in 10 years = 10× 12 = 120 months
The total amount in the account for 10years = 120×3250 = 390,000
Therefore there will be 390000 in the account at the end of 10th year.
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Please help on both!!!!!
Answer:
[tex]14\pi[/tex] and [tex]16\pi[/tex]
Step-by-step explanation:
The equation for the circumference of circles is either [tex]d\pi[/tex] or [tex]2r\pi[/tex], with r being the radius and d being the diameter.
Question A
The diameter is stated as 14. Plug into the equation to get:
[tex]14\pi[/tex]
This is your answer in exact form.
Question B
The radius is stated as 8. Plug into the equation to get:
[tex]2(8)\pi[/tex]
[tex]16\pi[/tex]
This is your answer in exact form.
Answer:
1) 43.98
2) 50.27
Step-by-step explanation:
I hope this helps!
b) Express of 8000 cm³ of milk as a percentage of 16 litres of milk
Answer:
50%
Step-by-step explanation:
16 litres = (16 x 1000) cm^3
= 16000 cm^3
Hence,
Percentage = 8000/16000 x 100%
= 1/2 x 100%
= 50%
10 gallons 4 quarts = ____ quarts
Please help
Find the sum of all solutions to the equation $4x(x-3) = 23$.
I NEED THIS ASAP
The sum of the solutions of the equation 4x(x - 3) = 23 is 3.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, An equation 4x(x - 3) = 23.
Now, Distributing the terms in the LHS we have,
4x² - 12x = 23.
4x² - 12x - 23 = 0.
By applying Sridhar acharya's formula we have,
[tex]x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\left(-23\right)}}{2\cdot \:4}[/tex].
[tex]x=\frac{3+4\sqrt{2}}{2},\:x=\frac{3-4\sqrt{2}}{2}[/tex].
Therefore, The sum of the solutions of the equation is,
x + x = (3 + 4√2)/2 + (3 - 4√2)/2.
= (3 + 4√2 + 3 - 4√2)/2.
= 6/2.
= 3.
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mark is thinking of two numbers
his two numbers have a positive sum but a negative product
give an example of what hi numbers could be ?
9514 1404 393
Answer:
-2, 3
Step-by-step explanation:
For the product to be negative, exactly one of the two numbers must be negative. For the sum to be positive, the positive number must be larger than the absolute value of the negative number.
One such pair of numbers is -2 and 3.
__
Their product is -6; their sum is +1.
without using a calculator
cos² 43° - sin² 74° + cos² 47 - Sin16°
Answer:
100
Step-by-step explanation:
because if you add it all up you will find the sum
PLEASE HELP ME! There are 2 Images below!!!
Answer:
A
Step-by-step explanation:
The slop formula is [tex]\frac{rise}{run}[/tex] and in the first one the rise increase per y (x) is 2 units and the run (y) is 1 as we calculated the run as how many units x rises per y and A is the answer due to it being the one which follows the rule.
What is the axis of symmetry for a parabola expressed by the quadratic equation? y=x^2+10x-25
Answer:
the axis of symmetry is: x=-5
100 POINTSSSSS!!!!!!!!!!!!!!!!!
What is the solution to the equation 1 over 5 multiplied by n equals 3 ? (5 points)
n = 8
n = 15
n = 25
n = 125
Answer:
n=15
Step-by-step explanation:
Answer:
n = 15
Step-by-step explanation:
1/5 * 15 = 3
This is 100% correct, if you don't believe me go to a new tab and type 1/5*15
It will say 3.
The weight of the square is 10 grams. How much heavier is the circle than the square?
The weight of the circle is heavier than the weight of the square by the weight of the triangle
How to find how much weightier is the circle as compared with the squareExamining the weights, can lead to a linear equation, the equation will have the follows parameters
let t represent triangle
let c represent circle
let s represent square
6s + 3t = 3s + 3c
6s - 3s + 3t = 3s + 3c
3s + 3t = 3c
divide through by 3
s + t = c
10 + t = c
From the equation 10 + t = c we can say that the weight of the circle is a triangle weight more than the square
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Write an explicit formula for An, the nth term of the sequence 16, -8,4, ....
Answer:16(-1/2)^n-1
Step-by-step explanation: