The population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8
For given question,
We need to find the population variance of the following set of numbers: 3, 5, 8, 9, 10
The formula for the Population variance is,
[tex]\sigma = \frac{\sum (x-\bar x)^2}{N}[/tex]
Here,
[tex]\bar x[/tex] = sample average
x = individual values in sample
N = count of values in the sample.
For given question,
[tex]\bar x=\frac{3+ 5+ 8+ 9+ 10}{5} \\\\\bar x=7[/tex]
Using the formula for variance,
[tex]\sigma = \frac{1}{5} [(3-7)^2 + (5 - 7)^2 + (8 - 7)^2 + (9 - 7)^2 + (10 - 7)^2]\\\\\sigma = \frac{1}{5} \times 34\\\\\sigma = 6.8[/tex]
Therefore, the population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8
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The distance from the sun to mercury is approximately 36,270,000 miles. the distance from the sun to saturn is 8 x 108miles. about how many times larger is the distance from the sun to saturn than the distance from the sun to mercury? about 20 times about 20 times about 4.5 times
If the distance from the sun to mercury is 36270000 miles and the distance from sun to Saturn is 8×[tex]10^{8}[/tex] miles, then it is about 22 times larger is the distance from the sun to Saturn than the distance from the sun to mercury
Given,
The distance from the sun to mercury = 36270000 miles
The distance from the sun to Saturn = 8×[tex]10^{8}[/tex] miles
Then,
The number of times larger is the distance from the sun to Saturn than the distance from the sun to mercury
[tex]\frac{8*10^{8} }{36270000} =22.05[/tex]
≈22 times
Hence, if the distance from the sun to mercury is 36270000 miles and the distance from sun to Saturn is 8×[tex]10^{8}[/tex] miles, then it is about 22 times larger is the distance from the sun to Saturn than the distance from the sun to mercury
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Pre-Calculus question
The Interpret (N · T)(t) is [tex]N[T(t)] = 20t^{2}+92t+205.[/tex]
The number of bacteria after 5 hours will be 1165.
It will take for the bacteria count to reach 2221.
As per the question statement, the number of bacteria "N" in a refrigerated food is given by [N(T) = (5T² - 4T +100)], where "T" is the temperature of the food in degrees Celsius,
And when the food is removed from the refrigerator, the temperature of the food is given by [T(t) = (2t+5)].
First we are required to find out (N · T)(t), which is N[T(t)] which can be expressed as
[tex]N[T(t)] = 5[T(t)]^{2} - 4T +100\\or, N[T(t)] = 5(2t+5)^{2} -4(2t+5)+100\\or, N[T(t)] = 5(4t^{2}+25+20t)-8t-20+100\\ or, N[T(t)] = 20t^{2} +125+100t-8t+80\\ or, N[T(t)] = 20t^{2}+92t+205.[/tex]
Then, the number of bacteria after 5 hours will be N[T(5)], i.e.,
[tex]N[T(5)] = 20(5^{2})+(92*5)+205\\or, N[T(5)] = (20*25)+460+205\\or, N[T(5)] = 500+665\\or, N[T(5)]=1165[/tex]
And finally, the time required for the bacteria count to reach 2221 can be calculated by solving the quadratic equation [tex][2221 = 20t^{2}+92t+205][/tex], i.e.,
[tex][20t^{2}+92t+205 = 2221]\\or, 20t^{2}+92t+(205-2221)=0\\or,20t^{2}+92t-2016=0\\or, 5t^{2}+23t+504=0[/tex]
And the formula to calculate the solutions of a standard quadratic equation [ax² + bx +c = 0] goes as
[tex]x=\frac{-b+\sqrt{(b^{2}-4ac) } }{2a}, \frac{-b-\sqrt{(b^{2}-4ac) } }{2a}[/tex]
Comparing [ax² + bx +c = 0] with [5t² + 23t + 504=0], we get
(a = 5), (b = 23) and (c = -504), and using these values in the above mentioned formula to calculate the solutions of quadratic equations, we get, [t = 8, (-12.6)].
Since time (t) cannot be negative, thus [t ≠ (-12.6)].
Hence, (t = 8) or, the time required for the bacteria count to reach 2221 is 8 hours.
Quadratic Equation: In algebra, any polynomial equation whose highest degree is two and can be rearranged to the standard form of [ax² + bx + c = 0], where (a ≠ 0), is known as a quadratic equation.To learn about Quadratic Equations, click on the link below.
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Skylar drives 18 miles in 12 minutes. If she drove one hour in total at the same rate, how far did she go?
Answer:
90 miles
Step-by-step explanation:
18/12 = ?/60
12*5=60
18*5=90
90/60
Hope that helps :)
The rise-over-run formula for the slope of a straight line is the basis of _____
The rise-over-run formula for the slope of a straight line is the basis of the high-low method.
What is slope of a straight line?
The slope of a straight line by joining two points is the rise over run formula. The subtraction between the two points of the y-coordinates is called the rise. And the subtraction between the two points of the x-coordinates is called the run. The slope can be calculated by dividing the rise by run.
The slope of a line either goes in the upward direction or in the downward direction or left direction or right direction. It determines the direction of the line. When the straight line goes in the upward direction, it means the rising line and slope is positive. When it goes in the downward direction, it means a falling line and slope is negative.
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please help me quick! easy points
Answer: x=138 degrees
Step-by-step explanation:
x+42=180 ==> Angle x and the supplementary angle of 42 are congruent angles, meaning that x and 42 add up to 180 degrees.
x-42+42=180-42
x=180-42
x=138 degrees
Joe is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges an initial fee of 50 and an additional 50 cents for every mile driven.
Company B charges an initial fee of 35 and an additional 75 cents for every mile driven.
For what mileages will Company A charge no more than Company B?
Write your answer as an inequality, using m for the number of miles driven.
If the mileage is more than or equal to 60 miles Company A will charge no more than Company B.
The inequality is: 50 + 0.50m ≤ 35 + 0.75m.
What are inequalities?When both sides of a mathematical expression are not equal, an inequality exists. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.Inequality simply means that two things aren't equal. One of the items might be inferior to, superior to, greater than, or equivalent to the other things.Given:
m = number of miles driven.
initial fee of Company A = $50
initial fee of Company B = $35
additional fee of Company A = 50 cents = $0.50
additional fee of Company B = 75 cents = $0.75
then the inequality will be,
⇒ 50 + 0.50m ≤ 35 + 0.75m
⇒ 50 - 35 ≤ 0.75m - 0.50m
⇒ 15 ≤ 0.25m
⇒ m ≥ 15 /0.25
⇒ m ≥ 60
Therefore, if the mileage is more than or equal to 60 Company A will charge no more than Company B.
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One year, the population of a city was 117,000. Several years later it was 136,890. Find the percent increase.
The percent increase in population of the city is 17%.
A percentage in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). A percentage lacks dimensions and has no associated unit of measurement.
For instance, 45% (written as "forty-five percent") equates to the fraction [tex]\frac{45}{100}[/tex] .
The percentage increase is calculated by the ratio of the increase to the original value. So to calculate the percent increase in the population of a city we have to find the ratio of the increase in population to the original population.
The population of the city is given as 117,000 .
The population increased to 136890.
Increase in population=136890-117000=19890
percentage increase in population
[tex]=\frac{19890}{117000} \times 100\%[/tex]
= 0.17×100%
=17%
The percent increase in the population of the city is 17%.
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Which of the following is most likely the next step in the series ?
Option c. The next in series is blue picture with 7 lines.
The series is following the trend, Red, Blue, Red…. So, the next in this series should be blue.
Next is the pattern of picture. Straight line, 45 degree to both lines from center, 45 degree from preceding lines. So, next should be 45 degree from both the preceding lines.
Next is the number of lines. This follows the pattern as 1 line, 3 line, 5 line. From this it's clear that here follows the odd number pattern. So the next should be picture with 7 lines.
Finally we cam conclude that the next in this series is option c, the blue picture with 7 lines.
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Use the diagram to answer the questions.
*Will give brainliest*
6: Which angle forms a vertical pair with
A:
B:
C:
D:
7: Which type of angle pair are
A: Adjacent angles
B: Linear pair
C: Complimentary angles
D: Vertical angles
8: Which angle is supplementary to
A:
B:
C:
D:
Answer:
opcation a
Step-by-step explanation:
can someone help me really quick
Answer:
-2(5y-3)= -10y-6 should instead be -10y+6 because two negatives multiplied together is a positive integer which is why you have +6 and not -6 so it'll be the second bullet point: he should have subtracted (-2x3) resulting in the expression -10y+6
María debe repartir los alimentos del convivio para elaborar los almuer-
zos de sus 22 alumnos y que cada uno reciba la misma cantidad. Tiene
kg de jamón, 3 kg de uvas, 6 litros de jugo de manzana, 25 bolillos
y 2 kg de queso. ¿Cuánto le toca a cada niño?
When Maria distribute the lunches to the 22 students equally, each person gets 1.6 of the meal.
How to calculate the value?It should be noted that from the information, Maria must distribute the lunches to the 22 students equally.
Therefore, the total foods will be:
= (3 + 6 + 25 + 2) / 22
= 36 / 22
= 1.6
Therefore each person gets 1.6 of the meal.
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Hurry I really need the answer for this
1 question answers:
Angle B=70
Angle C=70
Step-by-step explanation:
2 question:
Angle B= 90
Angle C=50
Given that line k bisects BD at point C and that BC=9x−13 and BD=118, find CD.
Applying the definition of a segment bisector, the length of CD is: 59 units.
What is a Segment Bisector?A line segment that bisects a line segment is known as a segment bisector. It divides the line segment into two smaller segments that are equal in length to each other.
Since line k bisects BD at point C, therefore, based on the definition of a segment bisector, we have the following equation:
2(BC) = BD
BC = 9x - 13
BD = 118
Substitute the values
2(9x - 13) = 118
18x - 26 = 118
18x = 118 + 26
18x = 144
18x/18 = 144/18
x = 8
CD = BC = 9x - 13
CD = 9x - 13 = 9(8) - 13
CD = 59 units
Therefore, applying the definition of a segment bisector, the length of CD is: 59 units.
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The map shows the length of two trails used for a race around a lake. What is the total distance of the race?
A trail race map. One part of the race is 3.21 miles and the other part of the race is 5.7 miles.
What are the steps you would follow to solve this problem?
The total distance of the race = 8.91 miles
Solution :
Miles :
There are 5,280 feet in one mile. Simply divide 5,280 feet by your average stride length to learn how many steps it will take to walk a mile. If your average stride length is 2 feet, for example, it will take 2,640 steps to walk a mile.
One part of the race is 3.21 miles
another part of the race is 5.7 miles
Total :
add of both trails
= 3.21+5.7
= 8.91
The total distance of the race = 8.91 miles
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Use the rational function below to find the following f(x)= 2x-7/3x-4
Answer:
i think its x=-12
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace f(x) with 0 and solve for x.
x = −12
Dana bought 1.8 ounces of flour and she used 0.81 ounces of it to make biscuits. How much is left?
−6(6p−9)−10p please respond quick this is Simplify Expressions with Distribution
Answer:
[tex]-46p+54[/tex]
Step-by-step explanation:
First, distribute -6 to both 6p and -9. That gives you -36p + 54-10p
Add like terms:
-46p+54
Hi pls help me my teacher is currently yelling Lol
Answer:
Dear bro not to use this brainly is app that's why do not search answer on brainly do yourself cause you are the better one
Solve the system of linear equations by graphing
Y=x+3
Y=-2x-3
The graph for the system of linear equation is attached
What is a linear equation?An equation is said to be linear if the variables are of power not greater than one. This is to say the power of the variables should be one. It is a norm in math not to write the power when the power is one
For the equation given the the powers of both y and x are all 1. Linear equations also have a straight line graph hence have the equation of straight line represented as
y = mx + c
where:
m is the slope
c is the y intercept
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HELP ASAP What are the zeros of the polynomial function?
Select all correct zeros of each function.
The zeros of the polynomial function
1.0,3,-1
2.3,-2,+1
3.2,-3,0
The zeros of a polynomial are the x values that satisfy the equation f(x) = 0. In this case, f(x) is a function of x, and the polynomial zeros are the x values for which the f(x) value is zero. The number of zeros in a polynomial is determined by the degree of the equation f(x) = 0. The polynomial zeros are all domain values of the function whose range is equal to zero.
The polynomial zeros are the points on the graph where y = f(x) touches the x-axis. More on this in the page below on expressing polynomial zeros on a graph.
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8x – 2 – 5x + 7 =
x +
Answer:
x=− 2/5
Alternative Form
x=−2.5
Step-by-step explanation:
PLEASE HELP ASAP!!! DON'T ANSWER IF YOU DON'T HAVE THE ANSWER!
1) Converting all to scientific notation gives;
J a p a n = 1.3718 * 10⁸
B r a z i l = 2.75 * 10⁸
G e r m a n y = 8.5619 * 10⁷
United Kingdom = 6.3706 * 10⁷
N i g e r i a = 1.43615 * 10⁸
B a n g l a d e s h = 1.8251 * 10⁰
I n d i a = 1.589143847902 * 10¹²
2) Arranging the populations from least to greatest is;
1.8251 * 10⁰ < 6.3706 * 10⁷ < 8.5619 * 10⁷ < 1.3718 * 10⁸ < 1.43615 * 10⁸ < 2.75 * 10⁸ < 1.589143847902 * 10¹²
How to write in Scientific Notation?
The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one.
We are given countries and their populations as;
J a p a n = 1.3718 * 10⁸
B r a z i l = 2.75 * 10⁸
G e r m a n y = 8.5619 * 10⁷
United Kingdom = 6.3706 * 10⁷
N i g e r i a = 1.43615 * 10⁸
B a n g l a d e s h = 1.8251 * 10⁰
I n d i a = 1.589143847902 * 10¹²
1) Converting all to scientific notation gives;
Japan = 1.3718 * 10⁸
B r a z i l = 2.75 * 10⁸
Germany = 8.5619 * 10⁷
United Kingdom = 6.3706 * 10⁷
N i g e r i a = 1.43615 * 10⁸
Ban glad e s h = 1.8251 * 10⁰
India = 1.589143847902 * 10¹²
2) Arranging the populations from least to greatest is;
1.8251 * 10⁰ < 6.3706 * 10⁷ < 8.5619 * 10⁷ < 1.3718 * 10⁸ < 1.43615 * 10⁸ < 2.75 * 10⁸ < 1.589143847902 * 10¹²
3) The way it was solved was to change all numbers first to scientific notation
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A coastline decreases by 3 cm each year for a total of 8 years. Which integer represents the total loss of coastline?
-2.66...
2.66...
24
-24
There are two more questions in the screenshot
If a coastline decreases by 3 cm each year for a total of 8 years. the integer that represents the total loss of coastline is: -24. The integer that can be use to represent the decrease is -3 and the expression that represent the total loss of coastline over 8 years is 8 (-3).
IntegerGiven:
Decrease in coastline=-3
Total number of years=8 years
Hence,
a. Integer that represent the total loss of coastline is:
Integer=8(-3)
Integer=-24 (Total loss)
b. The integer that can be use to represent the decrease is:
Decrease in coastline= -3
c. The expression that represent the total loss of coastline over 8 years is:
Expression= 8(-3)
Therefore If a coastline decreases by 3 cm each year for a total of 8 years. the integer that represents the total loss of coastline is: -24. The integer that can be use to represent the decrease is -3 and the expression that represent the total loss of coastline over 8 years is 8 (-3).
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9b (b+3) -6 when b=2
12y +4 when y= 6
6r -3 when r=10
please help out w those 3 questions
Answer:
84, 76 , 57
Step-by-step explanation:
substitute b = 2 into the expression
9(2)(2 + 3) - 6 = 18(5) - 6 = 90 - 6 = 84
substitute y = 6 into the expression
12(6) + 4 = 72 + 4 = 76
substitute r = 10 into the expression
6(10) - 3 = 60 - 3 = 57
Answer: 84, 76, 57
Step-by-step explanation:
1. 9b (b+3) -6 b=2
9(2) (2+3) -6
18 (2+3) -6
18 (5) -6
90 -6
84
2. 12y + 4 y=6
12(6) + 4
72 + 4
76
3. 6r - 3 r=10
6(10) - 3
60 - 3
57
Simplify quantity x squared plus 3 x plus 2 end quantity over quantity x plus 1. x + 2 x − 2 x2 + 1 x2 − 1
Simplifying quantity x squared plus 3 x plus 2 end quantity over quantity x will give x+2.
How to calculate the value?It should be noted that the expression given is illustrated as:
(x² + 3x + 2) / (x + 1)
(x² + x + 2x + 2) / (x + 1)
x(x + 2) 1)2(x+1) / (x + 1)
= (x + 2)(x + 1) / (x + 1)
= x + 2.
Therefore, the correct value is x + 2.
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Ann needs to make a total of 80 deliveries this week. So far she has completed 8 of them. What percentage of her total deliveries has Ann completed
Answer:
10%
Step-by-step explanation:
Find the moment of inertia about the x-axis of a thin plate with density bounded by the circle . then use your result to find =5
The lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].
What is a moment of inertia?The tendency of a body to withstand an object's angular acceleration is known as its moment of inertia. Inertia can be calculated by multiplying the mass by the orthogonal distance.Given:
Density - [tex]\delta=d(x, y)=5[/tex]Circle - [tex]x^2+y^2=16[/tex]Find the moment of inertia [tex]I_y[/tex] and [tex]I_0[/tex].
The lamina's moment of inertia about the x-axis is:
[tex]I_x=\iint_D y^2 d(x, y) d A[/tex]In the above equation, substitute the given value:
[tex]I_x=\iint_D 5 y^2 d A[/tex]Make use of polar coordinates:
[tex]\begin{aligned}x &=r \cos \theta \\y &=r \sin \theta \\d A &=d x d y=r d r d \theta \\D &=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]
As we all know, the general equation of a circle is:
[tex]x^2+y^2=r^2[/tex]The given circle equation is:
[tex]x^2+y^2=4^2[/tex]As a result, r ranges from 0 to 4.
And ranges from 0 to 2[tex]\pi[/tex].
As a result, the integral is shown below; simply enter all of the values and then integrate.
[tex]\begin{aligned}&I_x=\iint_D 5 y^2 d A \\&I_x=\int_0^{2 \pi} \int_0^4 5(r \sin \theta)^2 r d r d \theta \\&I_x=\int_0^{2 \pi} \int_0^4 5 r^3 \sin ^2 \theta d r d \theta \\&I_x=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi} \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_x=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_x=320\left(\frac{2 \pi}{2}\right) \\&I_x=320 \pi\end{aligned}[/tex]
Now, calculate [tex]I_y[/tex] and [tex]I_0[/tex].
Make use of polar coordinates.
[tex]\begin{aligned}&x=r \cos \theta \\&y=r \sin \theta \\&d A=d x d y=r d r d \theta \\&D=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]
As we all know, the general equation of a circle is:
[tex]x^2+y^2=r^2[/tex]The given circle equation is:
[tex]x^2+y^2=4^2[/tex]As a result, r ranges from 0 to 4.
And ranges from 0 to 2[tex]\pi[/tex].
As a result, the integral is shown below; simply enter all of the values and then integrate.
[tex]\begin{aligned}&I_y=\iint_D 5 x^2 d A \\&I_y=\int_0^{2 \pi} \int_0^4 5(r \cos \theta)^2 r d r d \theta \\&I_y=\int_0^{2 \pi} \int_0^4 5 r^3 \cos ^2 \theta d r d \theta \\&I_y=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi} \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_y=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_y=320\left(\frac{2 \pi}{2}\right) \\&I_y=320 \pi\end{aligned}[/tex]
The lamina's moment of inertia about the origin is given by:
[tex]\begin{aligned}&I_0=\iint_D\left(x^2+y^2\right) d(x, y) d A \\&I_0=\iint_D 5 r^2 r d r d \theta \\&I_0=5 \int_0^{2 \pi} \int_0^4\left(\frac{r^4}{4}\right)_0^4 d \theta \\&I_0=320 \int_0^{2 \pi} d \theta \\&I_0=320(\theta)_0^{2 \pi} \\&I_0=640 \pi\end{aligned}[/tex]
So, the moment of inertia is [tex]I_x=320 \pi[/tex].
The worth of, [tex]I_y=320 \pi[/tex].
Therefore, the lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].
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The correct question is given below:
Find the moment of inertia about the x-axis of a thin plate with density δ=5 bounded by the circle x2+y2=16. Then use your result to find Iy and Io.
Which integer is greater, -5 or -7 ?
Answer:-5
Step-by-step explanation:
PLEASE HURRY!!!! Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Based on the figure on the graph, match the described transformations with the transformed figures.
reflected across the x-axis
rotated 180° clockwise
translated 9 units to the
right and 2 units down
reflected across the y-axis
Answer:
translated 9 units to the right and 2 units down
Answer:The first one is translated 9 units to the right and 2 units down.The second is reflected across the x-axis and the last i reflected across the y-axis.
Step-by-step explanation:Please give brainliest if correct.
HELP QUICK!!
write the sentence as an equation.
172 is f more than 245
Answer:
f+245=172
Step-by-step explanation: