The standard deviation for the number of people with the genetic mutation in such groups is 3.1305.
Standard DeviationIn statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Let X be the number of people with genetic mutation is a group of 500,
The formula of standard deviation is given as
[tex]SD=\sqrt{n*p(1-p)} \\SD=\sqrt{500*0.02*0.98} \\SD=3.1305[/tex]
The standard deviation of the given sample is 3.1305
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I have to find out at which points the lines intersectY= .5x+3 & Y= 2x-9
SOLUTION
We want to find out at which points the lines
[tex]\begin{gathered} y=0.5x+3\text{ and } \\ y=2x-9 \end{gathered}[/tex]intersect.
To do this, we have to solve the equations simultaneously and look for the values of x and y.
This becomes
[tex]\begin{gathered} y=0.5x+3\ldots\ldots\ldots\text{.}\mathrm{}eq\text{ 1} \\ y=2x-9\ldots\ldots\ldots\ldots\text{.}\mathrm{}eq\text{ 2} \\ \text{subtracting equation 2 from 1, we have } \\ y-y=(0.5x-2x)+(3-(-9) \\ 0=-1.5x+(3+9) \\ 1.5x=(3+9) \\ 1.5x=12 \end{gathered}[/tex]Dividing both sides by 1.5, we get x, this becomes
[tex]\begin{gathered} \frac{1.5x}{1.5}=\frac{12}{1.5} \\ x=8 \end{gathered}[/tex]To get y, we substitute the x for 8 into equation 1 or 2. Let us use equation 1, we have
[tex]undefined[/tex]Find the slope of the line:
Answer:
20
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
Choose any two points on the line. For this, I will use (0, 5) and (1, 25):
[tex]\frac{25-5}{1-0}=\frac{20}{1} = 20[/tex]
Find the sum. 2 3/6 + 4 1/6
Answer:
6 4/6
Explanation:
To sum 2 3/6 and 4 1/6, we first need to convert the mixed numbers to fractions as follows
[tex]\begin{gathered} 2\frac{3}{6}=\frac{(2\times6)+3}{6}=\frac{12+3}{6}=\frac{15}{6} \\ 4\frac{1}{6}=\frac{(4\times6)+1}{6}=\frac{24+1}{6}=\frac{25}{6} \end{gathered}[/tex]Now, we can add the numbers as
[tex]\frac{15}{6}+\frac{25}{6}=\frac{15+25}{6}=\frac{40}{6}[/tex]Finally, when we divide 40 by 6, we get 6 as a quotient and 4 as a remainder, so 40/6 is equivalent to
[tex]6\frac{4}{6}[/tex]Therefore, the answer is 6 4/6
Use the rate and the amount of water pumped after 13 minutes to find how much will have been pumped into pool after 14.5 minutes? The unit rate is 24 gal/min so 1.5 minutes after 13 minutes, an additional gallons will be pumped in
An additional 36 gallons of water will be pumped into the pool past 13 minutes
Constant rate of flow: The definition of a constant rate of flow rate shows how fluid of a certain volume moves through a segment in a specified amount of time. Instead of measuring how quickly a fluid moves from point A to point B, the motion of fluids is examined by figuring out its flow rate. Specifically, how much fluid volume moves from point A to point B in a given amount of time.
Time for which water has been pumped into the pool = 13 minutes
Rate of flow of water = 24 gal/min
So, water pumped in 1.5 minutes = 24*1.5 = 36 gallons
Total water pumped in the pool in 14.5 minutes = 24*14.5 = 348 gallons
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I will give brainliest, like and rating if u solve this right
Which of the following statements is not true?
Answer:
Answer C
This statement is not true
Step-by-step explanation:
Logarithms result in real values only for positive values of the argument i.e. log(x) results in a real value only for x > 0 So A is correct
Range is set of all real numbers -∞ < x < ∞ So B is correct
D is also correct. At x = 0, log is not defined
Only C is incorrect. If 0 < a < 1 the graph actually shows a downward trend ie logarithmic decline instead of growth
Cross out the unnecessary information. Then solve the problem.Pedro had a very busy Saturday. After a 6:00 a.m. tennis match, he hadbreakfast with his grandmother, stopped at the corner store to get an icecream cone, hurried to his Spanish lesson, stopped by the swimming poolfor a quick dip, and then ate lunch with his buddies. At 2:00p.m. he wentto a movie and finally stopped at the soccer match to cheer for the team.Just on time he met his family for pizza. When he arrived home he fell intobed and slept 14 hours. His clock showed 10:00 a.m. when he opened hiseyes the next morning. What time did Pedro fall into his bed?Yes
Pedro went to bed and slept 14 hours, when he woke up next day it was 10 am, it means he went to sleep 14 hours before 10am, it means he went to sleep at 8 pm
help meeeeeee
Write the verbal sentence as an equation or an inequality:
Four is greater than six times a number t.
Answer:
four is greater than six times a number t in an inequality sentence is 4 › 6 * t
Write the following expression using a single exponent. 7^(4))^(3) x7^(7)
Answer:
7⁷¹
Step-by-step explanation:
Let's do it this way
7⁴^³ × 7⁷
Let's firstly apply indices since the base is the same
7⁴^³+ (⁷)
(4³ = 4×4×4 can be rewrite)
7⁴×⁴×⁴ + ⁷
7⁶⁴+⁷
= 7⁷¹
#AllonGod
Answer:
Raise 7 to the power of 4
Step-by-step explanation:
2401
PLEASE CAN SOMEONE HELP ME PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Fill in the gap in the equation below by
completing the square.
2
x² +14x+55= (x + 7)² +
The correct value of the equation that's illustrated will be x² + 14x + 55= (x + 7)² + 6
How to illustrate the information?It should be noted that an equation can be used in order to show the relationship between the variables.
It should be noted that (x + 7)² will be:
= (x + 7)(x + 7)
= x² + 7x + 7x + 49
= x² + 14x + 49
Therefore, x² 14x + 55 - (x² + 14x + 49) = 6
In conclusion, the answer in the box is 6.
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What are the coordinates of the point that lies of the way along directed line segment AB with A(2,5) and B(14,9)?
1/4 of the distance between points A(2,5) and B(14,9) is given by the formula:
[tex]\begin{gathered} \frac{1}{4}AB=\frac{1}{4}\sqrt[]{(x_2-x_1)^2+(y_2}-y_1)^2 \\ \frac{1}{4}AB=\frac{1}{4}\sqrt[]{(14-2)^2+(9-5)^2} \\ \frac{1}{4}AB=\frac{1}{4}\sqrt[]{12^2+4^2}\text{ = }\frac{1}{4}\sqrt[]{144+16} \\ \frac{1}{4}AB=\frac{1}{4}\text{ }\sqrt[]{160}=\frac{1}{4}\times12.649=3.162 \end{gathered}[/tex]Please help me with all I’ll mark you brainly
Answer:
am pretty sure am correct i hope it helps you
2. Let S = R - {0}, with the wacky definitions of vector addition and scalar multiplication given below.
Verify or disprove that S is a Vector Space.
For x, y in S, the definition:
Vector Addition: x + y = xy
• Scalar Multiplication: c*x = x^C.
(ie. 2+5= 2*5 = 10)
Hint: First identify the additive identity
A vector space, also known as a linear space, is a set whose elements, frequently termed vectors, can be added to and multiplied ("scaled") by figures known as scalars. Real numbers make up scalars most of the time, but they can also be complex numbers or, more broadly, components of any field.
Varied SpacesEvery vector space has a scalar field F at its foundation (to be specified shortly).
Real and complex numbers are two examples of scalar fields.
Real numbers R:
C: Complex numbers.
We only utilize these fields in this context.
Definition : A group of objects in a vector space V have a (vector)
scalar multiplication defined as closed under both addition and multiplication
also satisfying the following axioms:
I For any x V and, F, ( + )x = x + x
(ii) α(βx)=(αβ)x
(iii) For all x, y V, x + y = y + x
(iv) For any x, y, and z > V, x + (y + z)=(x + y) + z.
(v) α(x + y) = αx + αy
(vi) O V z 0 + x = x, where 0 is commonly referred to as the origin
Since V cannot be left using vector addition or scalar multiplication, the "closed" criterion described above states that for any, F and x, y V x + y V. Additionally, the "+" is in the field when we write for, F and x V ( + )x, but it is in the vector space when we write for x + y for x, y V. This symbol has a variety of uses.
Examples.(1) R2 is equal to the two-dimensional space (a1, a2) | a1, a2 R.
(2) In an n-dimensional space, Rn = (a1, a2,..., an) | a1, a2,..., an.
An "n-tuple" is (a1, a2,...,an).
(3) C, the field of complex numbers, to C2 and Cn, respectively, to R2 and Rn.
Pn = l n j = 0 ajxj | a0,
The polynomial space of all polynomials of degree n is denoted as Pn = l n j=0 ajxj | a0, a1,...,an R M. Be aware that this covers polynomials of all degrees, not only those with n degrees exactly.
(5) fp = (ai,...) | ai p, |ai| R. Vectors in the form of infinite-tuples of numbers make up this space. To properly designate the field, we would write fp(R) or fp(C).
Trigonometric polynomials TN = F N n=1 a sin nx | a1,...,an R k are included in the list.
Typical vecs in Rn e1 = (1, 0,... , 0)
e2 = (0, 1, 0,... , 0) (0, 1, 0,... , 0)
e3 = (0, 0, 1, 0,... , 0) (0, 0, 1, 0,... , 0)
.\s.\s.\sen = (0, 0,... , 0, 1) (0, 0,... , 0, 1)
The unit vectors that point in the n orthogonal directions are those.
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40 POINTS!
1. Find the missing angle.
2. What is the measure of Angle 1?
3. What is the measure of Angle 2?
4. Can the measure of an exterior angle of a triangle ever equal the measure of its adjacent interior angle? Explain in 2-3 sentences.
Answer:
43 for the first one
Step-by-step explanation:
108+29=
43
PLEASE HURRY!
Write the following expression using the fewest possible terms.
(−4x − 15) + (17 + 7x)
3x + (−2)
3x + 2
11x + (−2)
11x + 32
The simplified expression of (−4x − 15) + (17 + 7x) is - 11x + 2.
How to simplify expression?The expression can be simplified as follows:
(−4x − 15) + (17 + 7x)
we have to open the brackets of the expression
(−4x − 15) + (17 + 7x)
−4x − 15 + 17 + 7x
Combine like terms
−4x − 15 + 17 + 7x
- 4x + 7x - 15 + 17
Do the arithmetic of the like terms
- 4x + 7x - 15 + 17
Therefore, the simplified expression is as follows:
- 11x + 2
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Answer: 3x+2
Ex:
(-4x-15)+(17+7x)
-4x-15+17+7x Remove unnecessary parentheses
3x-15+17 Add like terms
3x+2
A wheel on Amanda's bicycle is 0.3 m in diameter. Amanda races the bicycle for 35 m. How many times does the wheel turn as the bicycle travels this distance?
Use the value 3.14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answer: 37.2
Step-by-step explanation:
The circumference of the bike is [tex]0.3\pi \approx 0.3(3.14)=0.942[/tex] m.
Dividing this by the 35 m traveled, we get the bike turned [tex]\frac{35}{0.942} \approx 37.2[/tex]
(a) Give an example of an angle which is coterminal with 260°.
(b) State the reference angle associated with 260°.
(b) Convert 260° to radians. Leave the answer in terms of
π .
a) 620° is an angle coterminal to 360°. The reference angle associated with 260° is 260°.
b) The measure of 260° in radian system equals to 13π / 9 radians.
How to analyze coterminal angles
Two angles are coterminal when they share the same initial and terminal sides. Two consecutive coterminal angles have a difference of 360° (2π radians). Then, we can find any angle of a family of coterminal angles by using this formula:
θ' = θ + i · 360°
Where:
θ - Reference angle, in degrees.i - Angle index.a) If we know that θ = 260° and i = 1, then the measure of an example of coterminal angle is:
θ' = 260° + 1 · 360°
θ' = 620°
620° is an angle coterminal to 360°.
The reference angle is the angle whose measure is equal to or greater than 0° and equal to or less than 360°. Thus, the reference angle associated with 260° is 260°.
b) According to radian system, 2π radians are equal to 360°. Thus, the measure of 260° is found by the following simple rule of three:
x = 260° × 2π / 360°
x = 13π / 9 rad
The measure of 260° in radian system equals to 13π / 9 radians.
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Think about your answers to these questions. Then write a summary of your findings below.1. How do you decide which of two numbers is greater when...a. both numbers are positive?b. both numbers are negative?c. one number is positive and one number is negative?
1. a)
Given:
Both numbers are positive.
Aim:
We need to find which one of the two numbers is greater than the other.
Explanation:
On a number line, numbers always increase so numbers to the right are greater than numbers to the left.
Mark the given points on the number line and find which number is right of another. numbers to the right are greater than numbers to the left.
For example.
The positive numbers are 17 and 20.
20 to the right are greater than 17 to the left
20 is greater than 17.
1. b)
Given:
Both numbers are negative.
Aim:
We need to find which one of the two numbers is greater than the other.
Explanation:
On a number line, numbers always increase so numbers to the right are greater than numbers to the left.
If both numbers are negative, the number closer to zero is the bigger number.
For example.
The negative numbers are -10 and -5.
-5 is closer to zero.
-5 is greater than -10.
1, c).
Given:
one number is positive and one number is negative
Aim:
We need to find which one of the two numbers is greater than the other.
Explanation:
On a number line, numbers always increase so numbers to the right are greater than numbers to the left.
The positive numbers are always to the right are greater than the negative numbers to the left.
Positive numbers are greater than negative numbers.
For example.
The positive number is 5 and the negative number is -8.
5 is greater than -8.
If ABC is reflected across the z-axis to get the AA'B'C', what is the y-coordinate of C'? Enter the answer in the box.
The horizontal and vertical axes are the two axes of the coordinate plane.
The origin is the location where these two axes come together. What is the y-coordinate of C' if ABC is mirrored across the z-axis to produce AA'B'C'?
Answer :
(-3,2)
Detailed explanation:
The right response is C (-3,2). The bold line moving up and down in the middle of the page is the y axis. If you could take up the triangle and turn it on its side, you could. In Point C's landing zone (-3,2).
Point C is situated two spaces to the right of the y-axis, as you can also see. The x axis is still three spaces below it.
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Find the zeros of each function by using a graph and a table f(x)=x^2+3x-18.
1) Finding the zeros of this function f(x) =x² +3x -18
f(x) = x²+3x-18 Factoring this equation, and rewriting it
Which two numbers whose sum is equal to 3 and their product is equal to 18?
6 -3 = 3 and 6 *-3 = -18
So we can rewrite as (x +6) (x-3)
(x+6)(x-3)=0 Applying the Zero product rule, to find the roots
x+6=0,
x=-6
x-3=0,
x=3
S={3,-6}
2) Setting a table, plugging in the values of x into the factored form: (x-6)(x-3)
x | y |
1 | -14 (1 +6)(1-3) =-14
2 | -8 (2 +6)(2-3) =-8
3 | 0
4 | 10
-5 | -8
-6 | 0
3) Plotting the function:
Use your calculator on the following data X1=3, Y1=7, X2=4, Y2=8, X3=5, Y3=10.
Determine (1) correlation, (2) slope of the regression line, (3) y-intercept of the regression line:
From the given data-set, we have that:
The correlation coefficient is of: r = 0.982.The slope of the regression line is of: 1.5.The intercept of the regression line is of: 2.33. How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
To find the correlation coefficient, we find the same strategy, inserting these points into a calculator of correlation coefficients.
From the data, the points are given as follows:
(3, 7), (4, 8), (5, 10).
Hence the correlation coefficient is of:
r = 0.982.
The line of best-fit is given by:
y = 1.5x + 2.33.
Which has a slope of 1.5 and an intercept of 2.33.
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Please help me with my calculus homework :)
Given
Answer
Let the side of square be s
s = 10 ft
[tex]\Delta s=\pm0.1ft[/tex][tex]\begin{gathered} A=s^2 \\ \frac{dA}{ds}=2s \\ \text{ now error in area is} \\ dA=\frac{dA}{ds}\Delta s \\ dA=(2s)\pm0.1 \\ dA=2(10)(\pm0.1)=\pm2ft^2 \end{gathered}[/tex]the volume of a volleyball is 288 cubic inches. What is the radius of the volleyball, to the nearest tenth of an inch?
The radius of the volleyball to the nearest tenth of an inch is 8.3
How to calculate the radius of the volleyball ?The formula is
= √ 3v/4π
volume(v) = 288
π = 3.142
= √ 3×288/4×3.142
= √ 864/12.6
Next step is to get the square root of 68.6
= √ 68.6
= 8.29
Hence the radius of the volley ball is 8.3 inches
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Find the equation of the line passing through points (6,0) and (-1,14).
Oy = 6x
y = -2x + 12
y = -2x + 14
y = 2x + 10
Answer:
y = - 2x + 12
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 0 ) and (x₂, y₂ ) = (- 1, 14 )
m = [tex]\frac{14-0}{-1-6}[/tex] = [tex]\frac{14}{-7}[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 0 )
0 = - 12 + c ⇒ c = 0 + 12 = 12
y = - 2x + 12 ← equation of line
lim
x→ pi/4
(sec x)/(4x^2 -5x)
The correct answer for the limit expression is √2 (π/4)(π - 5).
What is limit?
In mathematics, the value of the limit of a function always approaches as input and finally it approach to some value. It is used for the calculation of the continuity function, derivatives or calculus.
According to the question, the value of the variable 'x' should be substituted in the limit expression.
Now, the required expression will be:
[tex]\lim_{x \to \\pi /4} (secx)(4x^{2} -5x) = sec(\pi/4)(4(\pi /4)^{2} -5(\pi /4))[/tex]
Now, the value of the sec(pi/4) is √2
⇒ √2((π²/4)-5(π/4)) = √2 (π/4)(π - 5)
Hence, the correct answer for the limit expression is √2 (π/4)(π - 5).
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A system of inequalities is shown.Which system is represented in the graph? y > –x2 – x + 1y < 2x2 + 3 y ≤ x2 – x + 1y < 2x2 + 3 y ≥ x2 – x + 1y ≤ 2x2 + 3 y ≥ –x2 – x + 1y > 2x2 + 3
The system of inequatilies that is represented in the graph is:
y ≥ –x² – x + 1
y > 2x² + 3
We can confirm this statement since the first equation implies that the system doesn't include any point bellow the parabola y = -x² - x + 1, and the second equation implies that the system must include only points above the parabola y = 2x² + 3
Convert the measurement as indicated.
11 ft=_yd_ft
Answer:
3 yards, 2 feet
Step-by-step explanation:
Convert the measurement as indicated. 11 ft=_yd_ft
There are 3 feet in a yard so 3 yards (equal to 9 feet) and a remainder of 2 feet equal 11 feet so:
11 feet = 3 yards, 2 feet
There are 5 more girls than boys in MS, Rabu's class of 31 students, What is the ratio of number of girls to the number of boys in her class?
Answer: The answer is 18 Girls and 13 Boys. (18 + 13 = 31)
The ratio for girls to boys would 18:13
Step-by-step explanation: Confirmed correct.
On a piece of paper, graph y ≥ 2x – 3. Then determine which answer choice matches the graph you drew.
Answer:
Step-by-step explanation:
We are asked to graph an inequality . y≥2x - 3
The boundary line of our given inequality will be a solid line as we have greater than or equal to ≥ sign.
The boundary line of our given inequality would be .y=2x - 3
Now, we will test point (0,0) to shade in the correct region as:
0≥2(0)-3
0≥0-3
0≥-3
It should look something like this:
Fully factorise w² - 144
Answer:
(w-12)(w+12)
Step-by-step explanation:
Using the identity
a^2-b^2=(a-b)(a+b)
now,
w^2-144=(w)^2-(12)^2=(w-12)(w+12)
Select all the intervals where h is increasing A:-1.5< x < -0.5B: 0 < x <1c: 3.5 < x <4D none of the above
So,
We can identify that the function is increasing when it goes up.
In this graph, we can notice that the graph goes up in the intervals:
[tex]-1.5As the function increases in that whole interval, the correct answers are A and B.