Answer:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Step-by-step explanation:
For this case we have the following info given:
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
We can find the sample mean and deviations with the the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s =\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}[/tex]
And repaplacing we got:
[tex] \bar X_T = 17.714[/tex] the sample mean for treatment
[tex] \bar X_C = 28.714[/tex] the sample mean for treatment
[tex] s_T= 4.461[/tex] the sample deviation for treatment
[tex] s_C= 7.387[/tex] the sample deviation for control
[tex]n_T= n_C= 7[/tex] the sample size for each sample
The degrees of freedom are given by:
[tex] df= 7+7-2= 12[/tex]
The confidence interval for the difference of means is given by:
[tex] (\bar X_T -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_T}{n_T} +\frac{s^2_C}{n_C}}[/tex]
The confidence is 98% so then the significance is [tex]\alpha=0.02[/tex] and [tex] \alpha/2 =0.01[/tex]. Then the critical value would be:
[tex] t_{\alpha/2}=2.681[/tex]
And replacing we got:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
Answer:
Option (2). 14 m
Step-by-step explanation:
Formula to get the area of a circle 'A' = [tex]\pi r^{2}[/tex]
where r = radius of the circle
Given in the question,
Area of the circle = 153.86 square meters
By putting the values in the formula,
153.86 = πr²
r = [tex]\sqrt{\frac{153.86}{\pi } }[/tex]
r = [tex]\sqrt{49}[/tex]
r = 7 meters
Diameter of circle = 2 × (radius of the circle)
= 2 × 7
= 14 meters
Therefore, diameter of the circle is 14 meters.
Option (2) is the answer.
Answer:
14m
Step-by-step explanation:
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
-1, 1
13, 15
Step-by-step explanation:
x and x+2 are the integers
x*(x+2)= 7(x+x+2) -1x²+2x= 14x+14-1x² - 12x -13= 0Roots of the quadratic equation are: -1 and 13.
So the integers pairs are: -1, 1 and 13, 15
A line intersects the point (-11, 4) and has
a slope of -2. What are the inputs to the
point-slope formula?
y - [?] = [ ](x-[])
Answer: Point slope form is y-y1=m(x-x1)
Step-by-step explanation:
Here y1=4
x1=-11
m i.e slope=-2
And there you go.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of points scored during a basketball game b. The number of free dash throw attempts before the first shot is made c. The response to the survey question "Did you smoke in the last week question mark " d. The number of people in a restaurant that has a capacity of 150 e. The time it takes for a light bulb to burn out f. The height of a randomly selected giraffe a. Is the number of points scored during a basketball game a discrete random variable, a continuous random variable, or not a random variable?
Answer:
a. Discrete random variable
b. Discrete random variable
c. Discrete random variable
d. Discrete random variable
e. Continous random variable
f. Continous random variable
Step-by-step explanation:
a. The number of points scored during a basketball game.
This is a random variable, that only takes integer values, so it is a discrete random variable.
b. The number of free dash throw attempts before the first shot is made.
This is a count, so it is a discrete random variable.
c. The response to the survey question "Did you smoke in the last week question mark".
This is a boolean random variable (only two values), and can be considered discrete.
d. The number of people in a restaurant that has a capacity of 150.
This is a count of people, so it is a discrete random variable.
e. The time it takes for a light bulb to burn out.
Time is continous, so it is a continous random variable.
f. The height of a randomly selected giraffe.
Height, as it is a distance, is also a continous variable, so it is a continous random variable.
WRITING BOOK
Personal Writing
AD 1
NUMBERS
Which of the following cannot be an integer?
A. 0.8
B. -3
C. 4
D. 25
Answer:
A
Step-by-step explanation:
Integers are negative and positive whole numbers
Answer: A. 0.8
Step-by-step explanation:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14
Given that y = 1.5 at x = -2. Find the function y = f(x) such that
dy/dx=√(4y+3)/x²
Answer:
[tex]y=\frac{(-\frac{4}{x}+1)^2-3 }{4}[/tex]
Step-by-step explanation:
We are given the following information. y have the point [tex](-2,\frac{3}{2} )[/tex] and [tex]\frac{dy}{dx} =\frac{\sqrt{4y+3} }{x^2}[/tex]
First, we need to separate the variables to their respective sides
[tex]\frac{1}{\sqrt{4y+3} } dy=\frac{1}{x^2} dx[/tex]
Now, we need to integrate each side
[tex]\int \frac{1}{\sqrt{4y+3} } dy=\int\frac{1}{x^2} dx[/tex]
But first, let us rewrite these functions
[tex]\int (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]
Before we can integrate, we need to have the hook for the first function. When we integrate [tex](4y+3)^{-\frac{1}{2} }[/tex], we must have a lone 4 within the integral as well.
[tex]\frac{1}{4} \int4 (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]
Now we can integrate each side to get
[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + c[/tex]
Now is the best time to use the given point in order to find the value of c.
[tex]\frac{1}{4} \sqrt{4(\frac{3}{2}) +3} =-\frac{1}{-2} + c\\\\\frac{1}{4}\sqrt{6+3} =\frac{1}{2} +c \\\\\frac{3}{4}=\frac{1}{2} +c\\ \\c=\frac{1}{4}[/tex]
Now we can plug in our value for c and then solve for y
[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + \frac{1}{4} \\\\\sqrt{4y+3}=-\frac{4}{x} +1\\ \\4y+3=(-\frac{4}{x} +1)^2\\\\4y=(-\frac{4}{x} +1)^2-3\\\\y=\frac{(-\frac{4}{x} +1)^2-3}{4}[/tex]
Jack buys a bag of 5 apples, each
equal in size. He eats of 1/2 of one apple.
What fraction of the bag of
apples did he eat?
Answer:
4 1/2
Step-by-step explanation:
5 apples - 1/2 apple =
4 1/2 apple
or
9/2
How do I find the value of x for which line a is parallel to line b?
Answer:
x = 20
Step-by-step explanation:
3x + 6x = 180, if you make them supplementary then they will be parallel
9x = 180
x = 20
Write the point slope form of an equation of the line through the points (-2,6) and (3,-3)
Answer:
A.
Step-by-step explanation:
So first you need to find the slope:
[tex]\frac{-2-6}{3+2} =-\frac{8}{5}[/tex]
Since it's point slope, you have to use a point:
It's either:
[tex](y - 6)=-\frac{8}{5}(x+2)[/tex]
or
[tex](y+2)=-\frac{8}{5}(x-3)[/tex]
Check which answer has those:
A.
The solution is Option A.
The equation of line is y - 6 = ( -8/5 ) ( x + 2 ) where the slope is -8/5
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -2 , 6 )
Let the second point be Q ( 3 , -2 )
The slope of the line between the point is given by m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - ( - 2 ) ) / ( -2 - 3 )
On simplifying the equation , we get
Slope m = ( 8 / -5 ) = -8/5
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 6 = ( -8/5 ) ( x - ( -2 ) )
On simplifying the equation , we get
y - 6 = ( -8/5 ) ( x + 2 )
Hence , the equation of line is y - 6 = ( -8/5 ) ( x + 2 )
To learn more about equation of line click :
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Which formula can be used to describe the sequence? - 2/3, -4, -24, -144
Answer:
They are all multiplied by 6
Answer:
Geometric sequence.
Step-by-step explanation:
Here are the terms :
-2/3, -4, -24, -144
Now the first term T1 = -2/3
The second Term T2 = -4
But T2/T1 = -4÷ -2/3 = -4 x -3/2 = 6
Similarly Term 3, T3 = -24
T3/T2 = -24/-4= 6
Hence the expression is a geometric sequence.
a×r^(n-1); a is the first term
r is the common ratio 6
n is the number of terms.
In order to understand reasons why consumers visit their store, a local business conducts a survey by asking the next 100 people who visit their store to fill out a short survey. The business finds that 40 of the 100 people state that the main reason they visited the store was because the store is running a sale on coats that week. A confidence interval is constructed for the population proportion of consumers who would visit the store because of the coat sale. Which confidence interval would be the narrowest?
a. 90%
b. 99%
c. 95%
d. 85%
Answer:
d. 85%
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The higher the confidence level, the higher the value of z, which means that the margin of error will be higher and the interval will be wider,
Which confidence interval would be the narrowest?
The one with the lowest confidence level. So the answer is d.
A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is this distance?
Answer:
150
Step-by-step explanation:
If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 90. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.
90^2 + 120^2 = c^2
c=150
what is the value sin(?)= cos 28
Answer: 62
Step-by-step explanation:
Using the fact that cos(90-x)=sin(x) we get that 90-x=28, so x=62 and the answer is simply 62.
Hope that helped,
-sirswagger21
What is the slope of the line given by the equation below?
y-20 = 5(x-2)
Answer:
5
Step-by-step explanation:
first you need to simplify this equation and put it in slope intercept form which is y = mx + b
after simplifying you will get y = 5x + 10
since the slope is m , the answer will be 5
Solve: 4x^-2 – 3x^-1– 1 = 0
Answer:
1, -4
Step-by-step explanation:
4x^-2 – 3x^-1– 1 = 0Let x^-1 = 1/x = y
4y^2 - 3y - 1 = 04y^2 - 4y + y - 1 = 0(y - 1) (4y + 1) = 01. Root 1
y - 1 = 0 y = 11/x= 1x = 12. Root 2
4y + 1 = 04y = -1y = -1/41/x = - 1/4x = -4Please help meee
Which number line model represents the expression -2/5 + 4/5:
The number line model that represents the expression -2/5 + 4/5 is: Option B
How to solve Inequality on number line?
To plot an inequality, such as x > 2, on a number line, first draw a circle over the number (e.g., 2). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.
Now, in this case, the operation to solve is:
-2/5 + 4/5
Solving this gives 2/5
Now, since the operation shows a negative and positive fraction with the solution being positive, then we can easily say that Option B is the correct answer to the problem
Read more about Inequality on number line at: https://brainly.com/question/24372553
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Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Answer:
The answer is 13
Step-by-step explanation:
Two positive and consecutive old numbers are x and x - 2.
=> x(x - 2) = 143
=> x^2 - 2x - 143 = 0
=> x^2 + 11x - 13x - 143 = 0
=> x(x + 11) - 13(x + 11) = 0
=> (x + 11)(x - 13) = 0
=> x = -11 (invalid)
or x = 13 (valid), the remaining number is 13 - 2 = 11
=> The two numbers are 11 and 13, and the greater number is 13.
Hope this helps!
:)
Answer:
top: 2
bottom: 13
Step-by-step explanation:
step
by
step
explanation
we choose a sample of size 100 from a population of monthly cable bills having standard deviation $20 If we assume the population mean bill is $65, what is the probability mean of our sample is greater than $70.
Answer:
0.0062
Step-by-step explanation:
Find the standard error.
σ = 20 / √100
σ = 2
Find the z-score.
z = (x − μ) / σ
z = (70 − 65) / 2
z = 2.5
Find the probability.
P(Z > 2.5) = 1 − 0.9938
P(Z > 2.5) = 0.0062
A farmer knows that every 50 eggs his chickens lay, only 45 will be marketable. If his
chickens lay 1000 eggs in a week, how many of them will be marketable?
Answer:
900 eggs
Step-by-step explanation:
45/50 are marketable
divide the top and bottom by 5
9/10
Multiply this fraction by the 1000 eggs laid
9/10 *1000
900 eggs will be marketable
Answer:
900
Step-by-step explanation:
Find the value of x:
Find five consecutive integers such that the sum of the first and 5 times the third is equal to 41 less than 3 times the sum of the second fourth and fifth
Answer:
see below
Step-by-step explanation:
We'll cal the first integer x and then the rest of them will be x + 1, x + 2, x + 3 and x + 4. We can write x + 5(x + 2) = 3(x + 1 + x + 3 + x + 4) - 41.
x + 5x + 10 = 3(3x + 8) - 41
6x + 10 = 9x + 24 - 41
6x + 10 = 9x - 17
3x = 27
x = 9
The numbers are 9, 10, 11, 12, 13.
What is the answer to this question?
Answer:it is b
Step-by-step explanation:
A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on 5? A. 1 over 13 B.1 over 8 C.5 over 13 D.5 over 8 PLEASE HURRY!!!!!!!!!!!!!!!!!
Answer:
B. 1 over 8
Step-by-step explanation:
To determine the probability of the spinner landing on 5, we need to first know what probability is,
probability = required outcome/all possible outcome
since the spinner is divided into 8 equal sections and each section contains number from 1-8, this implies there are total of 64 numbers on the spinner. This implies that all possible outcome = 64
In each section there is 5, since there are 8 sections on the spinner, the number of 5's on the spinner are 8.
This implies that the required outcome = 8
but
probability = required outcome/all possible outcome
probability (of the spinner landing on 5) = 8/64 =1/8
Answer:
b
Step-by-step explanation:
The first digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9 because we do not write numbers such as 15 as 015. While it is reasonable to think that for most real-life data each digit occurs with equal frequency so that each digit 1, 2, ..., 9 has probability 1/9 of being the first digit, this is not true. It is a surprising phenomenon that in many naturally occurring numbers and web-based data the first digit has a probability distribution known as Benford's law.
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.
Specifically, for d = 1, 2, 3, 4, 5, 6, 7, 8, 9, Benford's law states P(first digit is d) = log_10(1+(1/d)) . The distribution of the first digit according to Benford's law, calculated to 3 decimal places, is shown in the table below.
Benford's law
First Digit X 1 2 3 4 5 6 7 8 9
Probability .301 .176 .125 .097 .079 .067 .058 .051 .046
Benford's Law and the Equally Likely Model benford equally likely
The law is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881. A surprising variety of data from the natural sciences, social affairs, and business obeys Benford's law.
This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature).
Numbers that are assigned, such as social security numbers and zip codes, or data with a fixed maximum, such as deductible contributions to individual retirement accounts, or randomly generated numbers, do not follow Benford's law.
The figure below shows how the distribution of the first digit of various naturally occurring and web-based data compares with Benford's law.
benford natural data web data
Figure information. Earthquakes: depth in km of 248,915 quakes, 1989-2009; source National Earthquake Information Center, United States Geological Survey. Minnesota lakes: size in acres of approx. 1100 lakes; source Wikipedia. Births: number of births in each county of the United States (approximately 3200), 2010; source: US Census Bureau. Diggs: total number of diggs for each of the top 1000 diggers at digg.com; source: socialblade.com.
Question 1:
(1a). What is the expected value of the first digit when the first digit follows Benford's law?
expected value (Use 3 decimal places).
(1b). What is the expected value of the first digit when the possible first digits are equally likely?
expected value (Use 3 decimal places).
(1c). What is the standard deviation of the first digit when the first digit follows Benford's Law?
Answer:
0.699
Step-by-step explanation:
got it on khan academy, should get brainliest thanks
ASAP
What is the sum of 16.87 + (–98.35)?
–115.22
–81.48
81.48
115.22
Solution,
16.87+(-98.35)
=16.87-98.35
= -81.48
Hope it helps
Good luck on your assignment
Answer:-81.48
Step-by-step explanation:
16.87 + (–98.35)
-81.48
If you stumble in other questions like there you can use a calculator or ask me. :D hope that helps
Does this graph represent a function? Why or why not?
A
B
C
D
Answer:
B
Step-by-step explanation:
As said in B, use the vertical line test. For any vertical line, does it hit the graph in two points? No. Therefore, the answer is B.
This particular function is f(x)=x^2.
Hope that helped,
-sirswagger21
Answer:
Yes is passes the vertical line test
Step-by-step explanation:
This parabola is a function. it has a one to one correspondence and passes the vertical line test
Solve for a.
ab +c= d.
Answer:
a = (d -c)/b
Step-by-step explanation:
Undo the addition of c, by subtracting c.
ab +c -c = d -c
ab = d - c
Undo the multiplication by b, by dividing by b.
ab/b = (d -c)/b
a = (d -c)/b
g A cannonball is shot with an initial speed of 62 meters per second at a launch angle of 25 degrees toward a castle wall that is 260 meters away. If the wall is 20 meters tall, how high off the ground will the cannonball hit
Answer:
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Step-by-step explanation:
Given;
Initial speed v = 62m/s
Angle ∅ = 25°
Horizontal distance d = 260 m
Height of wall y = 20
Resolving the initial speed to vertical and horizontal components;
Horizontal vx = vcos∅ = 62cos25°
Vertical vy = vsin∅ = 62cos25°
The time taken for the cannon ball to reach the wall is;
Time t = horizontal distance/horizontal speed
t = d/vx (since horizontal speed is constant)
t = 260/(62cos25°)
t = 4.627 seconds.
Applying the equation of motion;
The height of the cannonball at time t is;
h = (vy)t - 0.5gt^2
Acceleration due to gravity g = 9.81 m/s
Substituting the given values;
h = 62sin25×4.627 - 0.5×9.81×4.627^2
h = 16.2264134736
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Charlotte is creating a triangular pennant with geometry software.
The base measure of the pennant on screen is 550 pixels. The height
is 275 pixels. Charlotte resizes the pennant, keeping the aspect ratio
constant, so the height is 165 pixels. What is the scale factor of the
dilation? What is the base of the pennant?
~~~~~~~~~~~~~~
pls help T-T
Answer:
Base of the Pennant = 330 pixels
Scale Factor =0.6
Step-by-step explanation:
The base measure of the pennant on screen is 550 pixels.
The height is 275 pixels.
[tex]A$spect Ratio=\dfrac{Base}{Height}=\dfrac{550}{275} =2:1[/tex]
If Charlotte resizes the pennant, keeping the aspect ratio constant.
Height = 165 pixels
Therefore:
[tex]\dfrac{Base}{165}=\dfrac{2}{1} \\\\$Base= 2 *165 =330[/tex]
Therefore, the scale factor of the dilation [tex]=\dfrac{330}{550}= \dfrac{165}{275}=0.6[/tex]
Base of the Pennant = 330 pixels
Scale Factor =0.6
If f(x)=7+4c and g(x) = 1/2x what is the value of (f/g)(5)
Answer: 270
Step-by-step explanation:
The notation [tex](\frac{f}{g})(5)[/tex] means to divide [tex]\frac{f(5)}{g(5)}[/tex]. Now that we know we have to divide, we can plug them into this equation.
[tex]\frac{7+4(5)}{\frac{1}{2(5)} }=\frac{27}{\frac{1}{10} }[/tex]. We know that dividing by a fraction means to multiply by its reciprocal, so we'll do that.
[tex]27*10=270[/tex]
