Answer:
(1,1,36), (1,3,12), (1,2,18), (1,6,6), (1,4,9), (2,3,6), (2,2,9), (3,3,4)
Step-by-step explanation:
, = multiply
Wesley has a grid of six cells. He wants to colour two of the cells black so that the two black cells share a vertex but not a side. In how many ways can he achieve this?
Wesley can color two cells in 5 ways so that the two black cells share a vertex but not a side.
Total number of cell in the grid is 6
Vertex is a point on a polygon where the sides or edges of the object meet.
1st case Wesley can color 1 & 4
2nd case Wesley can color 2 & 3
3rd case Wesley can color 2 & 5
4rt case Wesley can color 3 & 6
5th case Wesley can color 5 & 6
Total 5 cases form in which two cell are colored whose side don't touch each other only vertexes are shared by the cell
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In a study of the effects of stress in rats, 42 rats were randomly divided into two groups. Eighteen rats were placed in a stressful environment and twenty-four rats were in a nonstressful environment. After 21 days, the weight gain (in grams) was measured for each rat. The 18 stressful rats gained an average of 26 grams with standard deviation 3 grams. For the 24 rats, an average weight gain was 32 grams with standard deviation 2 grams.
(a) Conduct a test to determine if rats under a non-stressful environment gain significantly more weights than rats under a stressful environment do. Note: Make sure to show all 5 steps
(b) Use RStudio to find the p-value. Note: See below for RStudio instructions.
ItI > teritical I.p value <0.05, we fail to reject num hypothesis
Test statistic , t= x1-x2/s1.s1/n1+s2.s2/n2
=26-32/3.3/18+2.2/24
=-6/0.815=-7.3484
iti=7.2484
Teritical at >=0.05 I df=n1+n2+n3=40
Static testing is the process of reviewing the code and creating documents and requirements before it is performed to detect errors instead of actually running the code. The major objective is to identify faults early in the development process because it is typically simpler to identify the potential causes of failures in this way.
A sort of testing called static testing is done on a piece of software without running the actual code. We examine and validate the product and its supplementary materials during testing.
Dynamic testing, in contrast, is a sort of testing done on software while the code is being executed.A test statistic is a figure obtained from a statistical analysis. It explains how far your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.
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PLEASE HELP ME I AM GROUNDED AND NEED THIS FINISHED NOWWW
Answer:
x = 8
Step-by-step explanation:
-4x + 10 = -2x - 6
-4x + 2x = -6 - 10 (Calculate)
-2x = -16 (Divide both sides by -2)
x = 8
Have a nice day! :D
Answer:
x=8
Step-by-step explanation:
-4x+10=-2x-6 original equation
-4x+16=-2x add 6 both sides
16=2x add 4 both sides
x=8 divide 2 both sides
two trains running on the same track travel at the rates of 40 and 45 mph, respectively. if the slower train starts an hour earlier, how long will it take the faster train to catch up to the slower train?
It will take the faster train 8 hours to catch up to the slower train.
What is displacement?When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.
In one hour, the slower train travels 40 miles, so after t hours (where t is the time it takes for the faster train to catch up), the slower train will have traveled:
d = 40(t + 1)
The faster train travels at a rate of 45 mph, so in t hours it will have traveled:
d = 45t
We can set these two equations equal to each other, since they both represent the same distance:
40(t + 1) = 45t
Expanding the left side gives:
40t + 40 = 45t
Subtracting 40t from both sides gives:
40 = 5t
Dividing both sides by 5 gives:
t = 8
So it will take the faster train 8 hours to catch up to the slower train.
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the sum of the reciprocals of four positive integers is 1.9. what is the sum of the four positive integers?
the sum of the four positive integers is 20. to define what reciprocals are. Reciprocals are simply the inverse of a number, meaning that if you have a number x, the reciprocal of x is 1/x.
Now, let's use this knowledge to solve the problem. We know that the sum of the reciprocals of four positive integers is 1.9, which can be expressed as:
1/a + 1/b + 1/c + 1/d = 1.9
Where a, b, c, and d are the four positive integers we're looking for.
To solve for the sum of these integers, we need to manipulate this equation to isolate the sum.
First, we can multiply both sides by abcd to get rid of the denominators:
bcd + acd + abd + abc = 1.9abcd
Next, we can group the terms with the sum of the four integers together:
(a+b+c+d)(bcd) = 1.9abcd
Now we can solve for (a+b+c+d):
a+b+c+d = 1.9abcd/bcd
Simplifying this expression, we get:
a+b+c+d = 1.9/1 + 1/10
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Solve the separable differential equation for u du/dt = e^5u + 3t. Use the following initial condition: u(0) = 5. U =
By solving differential equation for [tex]du/dt = e^5u + 3t.[/tex] The u =[tex](-1/5) ln[25t + e^{-5u} - 26].[/tex]
How to solve the equation?We have to separate variables first:
[tex]du/e^5u = dt + 3t/e^{5} u du[/tex]
Now, we will integrate sides to their variables:
∫ du/[tex]e^{5u}[/tex]= ∫ (dt + 3t/[tex]e^{5u}[/tex]) du
Using substitution:
let w = 5u, then du = dw/5:
1/5 ∫ dw = [tex]e^{-w}[/tex]∫ (dt + 3t/[tex]e^w[/tex] (du/5)
Integrating both sides:
-1/5 [tex]e^{-w}[/tex]= t + (1/25) [tex]e^{-w}[/tex] + C
Substituting back w = 5u:
-1/5 [tex]e^{-5u}[/tex]= t + (1/25) [tex]e^{-5u}[/tex] + C
Using initial condition, u(0) = 5:
-1/5 [tex]e^{-25}[/tex] = 0 + (1/25) [tex]e^{-25}[/tex] + C
C = -26/25
The solution to differential equation with initial condition is:
-1/5 [tex]e^{-5u}[/tex] = t + (1/25) [tex]e^{-5u}[/tex]- 26/25
When we solve for u, we have:
u = (-1/5) ln[25t + [tex]e^{-5u}[/tex]- 26].
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A rectangle has a perimeter of 68 ft. The length and width are scaled by a factor of 3.5.
What is the perimeter of the resulting rectangle?
Enter your answer in the box.
ft
Answer:
2l + 2w = 68, so l + w = 34
3.5(l + w) = 3.5(34) = 119, so the perimeter of the new rectangle is 2(119) = 238.
Step-by-step explanation:
at similsrity the perimer ratio and the side ratio are the same so equale to K.
P1/P2 = k .... but u don't explain which one is P1 of P2
so i can work u by both and u will check
and take the correct 1.
1. If P1=68ft
68ft/P2 = 3.5P2 ×3.5 = 68ft P2= 68ft/3.5 P2 = 19.42 ft2. If P2=68ft
P1/68ft = 3.5P1 = 3.5 × 68ftP1 = 238ftso if ur give is p1 take the 1st one and if ur given is p2 take the 2nd one.
the perimeter of a rectangular street sign is 28 inches. the area is 40 square inches. what are the dimensions of the sign?
The dimensions of the street sign are 10 inches by 4 inches.
What is the perimeter?
The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.
Let's assume that the length of the rectangular street sign is L, and the width is W.
We know that the perimeter of the sign is 28 inches, which can be expressed as:
2L + 2W = 28
Simplifying this equation, we get:
L + W = 14 (dividing both sides by 2)
We also know that the area of the sign is 40 square inches, which can be expressed as:
L * W = 40
Now we have two equations with two unknowns (L and W). We can use substitution or elimination to solve for the dimensions.
Using substitution, we can rearrange the first equation to solve for one variable in terms of the other:
L = 14 - W
Then we can substitute this expression for L in the second equation:
(14 - W) * W = 40
Expanding and rearranging terms, we get:
W² - 14W + 40 = 0
This is a quadratic equation that we can solve using the quadratic formula:
W = (-(-14) ± √((-14)² - 4(1)(40))) / 2(1)
W = (14 ± √(36)) / 2
W = 7 ± 3
We can reject the negative value of W since it doesn't make sense for a length or width. Therefore, we have:
W = 10 or W = 4
If W = 10, then L = 14 - W = 4, which gives us a perimeter of 28 inches, but an area of only 40 square inches, so this solution doesn't work.
If W = 4, then L = 14 - W = 10, which gives us a perimeter of 28 inches and an area of 40 square inches, so this is the correct solution.
Therefore, the dimensions of the street sign are 10 inches by 4 inches.
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You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as ____________.
The relevant hypotheses for this question would be:Null hypothesis (H0): The incidence of smoking among women is not significantly higher than among men in the neighborhood (μ1 ≤ μ2).
Null hypothesis (H₀): The incidence of smoking among women (population 1) is equal to the incidence of smoking among men (population 2), or p₁ = p₂.
Alternative hypothesis (H₁): The incidence of smoking among women (population 1) is greater than the incidence of smoking among men (population 2), or p₁ > p₂.
You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as relevant hypothesis .
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What is the result of the math formula: =2*10+4^2
Answer:
36
Step-by-step explanation:
2(10)+4^2
20+4^2
20+16
36
Answer: The result of the math formula =2*10+4^2 is 28.
To calculate this formula, you first need to perform the exponentiation operation of 4^2, which is 16. Then, you multiply 2 by 10, which gives you 20. Finally, you add 20 to 16, which gives you the final answer of 28.
How many 5 number license plates can be made using the digits 0,1,2,3,4,5,if repeatitions are allowed?
There are 7776 possible 5-number license plate combinations utilizing the numbers 0, 1, 2, 3, 4, and 5, with repetitions allowed.
The number of 5-number license plates that can be made using the digits 0, 1, 2, 3, 4, and 5, with repetitions allowed, can be found by using the multiplication principle. Since there are 6 digits to choose from for each of the 5 positions, the total number of possible license plates is:
6 x 6 x 6 x 6 x 6 = 6⁵
= 7776
Therefore, there are 7776 possible 5-number license plate combinations utilizing the numbers 0, 1, 2, 3, 4, and 5, with repetitions allowed.
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What is 9.4 x 103 in standard form?
The given number which is in scientific notation that is 9.4 x 10³ is equivalent to 9400 in standard form.
9.4 x 10³ is a number in scientific notation, which is a way of writing numbers that makes them easier to read and work with, especially when dealing with very large or very small numbers.
To convert this number to standard form, we need to move the decimal point three places to the right, since 10³ is equivalent to 1,000 (10 to the power of 3). This gives us:
9.4 x 10³ = 9,400
Therefore, the standard form of 9.4 x 10³ is simply 9,400.
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If integral from negative 2 to 3 of the quantity 2 times f of x plus 2 end quantity dx equals 18 and integral from 1 to negative 2 of f of x dx equals negative 10 comma then integral from 1 to 3 of f of x dx is equal to which of the following? a 4b 0c −6d −8
For an integral value of [tex]I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ [/tex] and
[tex]I_2 = \int_{ 1}^{-2} f(x)dx = -10 \\ [/tex], the computed value of integral [tex]\int_{ 1}^{3} f(x)dx[/tex] is equals to the -6. So, option(c) is right one.
In mathematics, an integral is the continuous process of a sum, which is used to calculate areas, volumes, and their properties. Integration is a way to sum up parts to the whole.
We have an integral say [tex]I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ [/tex]
[tex]I_2 = \int_{ 1}^{-2} f(x)dx = 10 \\ [/tex]
We have to determine value of [tex]\int_{ 1}^{3} f(x)dx[/tex].
Using the properties of integral, consider integral [tex]I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18\\ [/tex]
from distribution property, [tex]I_1 = \int_{ -2}^{3} 2f(x) dx + \int_{ -2}^{3} 2 dx = 18 \\ [/tex]
[tex]2 \int_{ -2}^{3} f(x) dx + [ 2x]_{ -2}^{3} = 18[/tex]
[tex]2 \int_{ -2}^{3} f(x) dx + 10 = 18[/tex]
[tex]2 \int_{ -2}^{3} f(x) dx = 8[/tex]
[tex]\int_{ -2}^{3} f(x) dx = 4[/tex]
Now, consider the required integral and rewrite, [tex]\int_{ 1}^{3} f(x)dx = \int_{ 1}^{-2} f(x)dx + \int_{ -2}^{3} f(x)dx \\ [/tex]
Substitute all known values of integrals
[tex]\int_{ 1}^{3} f(x)dx = 10 + 4 = 14 [/tex]
Hence, required value is 14.
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Weights of females have approximately a normal distribution with mean 135 lbs. and standard deviation 20 lbs. Allison weighs 145 lbs. What is the z-score for her weight?
After using the formula: z = (x - μ) / σ , the z-score for Allison's weight is 0.5.So, the z-score for Allison's weight is 0.5.
To find the z-score for Allison's weight, we use the formula:
z = (x - μ) / σ
where x is Allison's weight (145 lbs), μ is the mean weight of females (135 lbs), and σ is the standard deviation (20 lbs).
Substituting the values, we get:
z = (145 - 135) / 20
z = 0.5
Therefore, the z-score for Allison's weight is 0.5.
To calculate the z-score for Allison's weight, we can use the following formula:
z-score = (Allison's weight - mean weight) / standard deviation
Plugging in the given values:
z-score = (145 lbs - 135 lbs) / 20 lbs = 10 lbs / 20 lbs = 0.5
So, the z-score for Allison's weight is 0.5.
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Given the function
What is the domain of the function?
The domain of the function f(x) = 5x+3 is (-∞, +∞), which means that any real number can be substituted for x in the function.
The domain of a function is the set of all possible values of the independent variable, x, for which the function is defined. In this case, f(x) = 5x+3 is a linear function with a coefficient of 5 and an intercept of 3. Since there are no restrictions or limitations on the value of x that can be input into the function, the domain of f(x) is all real numbers or (-∞, +∞).
This means that any real number can be substituted for x in the function, and a corresponding value of f(x) will be produced. For example, if x = 0, then f(x) = 5(0) + 3 = 3. If x = -2, then f(x) = 5(-2) + 3 = -7.
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Complete question is:
Given the function f(x) = 5x+3
What is the domain of the function?
Suppose that the function g is defined, for all real numbers, as follows.
1x²-5 ifx#-2
g(x)=-
4
if x = -2
Find g (-5), g (-2), and g (5).
8 (-5) = 0
8 (-2) = 0
8 (5) = 0
8
X
Ś
The value of g(-5) is 7.5, g(-2) is 4, and g(5) is 7.5 if the value of function g(x) = 1/2x²-5 if x≠-2 and g(x) = 4 if x = -2.
A function is a rule that associates each element in a set (called the domain) with a unique element in another set (called the range). A function takes an input from the domain and produces an output in the range.
To find the value of g(-5), substitute the value in given function
g(-5) = 1/2×(-5)² - 5
= 1/2×25 - 5
= 12.5 - 5 = 7.5
The value of g(-2) is 4 as it is defined in the question only.
To find the value of g(5), substitute the value in given function
g(5) = 1/2×(5)² - 5
= 1/2×25 - 5
= 12.5 - 5 = 7.5
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What’s the answer to this problem?
Answer:
can you tell me the options please so I can answer it thank you
A survey found that the american family generates an average of 17. 2 pounds of glass garbage each year. Assume the standard deviation of the distriution is 2. 5 pounds. Find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds
The probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.
How to solve for the probabilityσ_sample = σ / sqrt(n)
σ_sample = 2.5 / sqrt(55)
σ_sample ≈ 0.336
Now, we can standardize the values of 17 and 18 pounds using the Z-score formula. This will tell us how many standard deviations away from the population mean these values are:
Z = (X - μ) / σ_sample
Z_17 = (17 - 17.2) / 0.336 ≈ -0.595
Z_18 = (18 - 17.2) / 0.336 ≈ 2.381
Now we will use the standard normal distribution (Z-distribution) to find the probabilities corresponding to these Z-scores. You can use a Z-table, statistical software, or an online calculator to find these probabilities.
P(Z < -0.595) = 0.2760
P(Z < 2.381) = 0.9915
To find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds, we will find the difference between the probabilities corresponding to the two Z-scores:
P(17 < X < 18) = P(Z < 2.381) - P(Z < -0.595)
P(17 < X < 18) = 0.9915 - 0.2760
P(17 < X < 18) ≈ 0.7155
So, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.
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Help pls and thank you
The exact value of y is [tex]\sqrt{3}[/tex]
The correct answer is an option (c)
Let us assume that in the attached diagram of right triangle the angle A measures 45 degrees.
Here, the hypotenuse measures [tex]\sqrt{6}[/tex]
We know that in right triangle, the sine of angle θ is nothing but the ratio of opposite side of angle θ to the hypotenuse.
Consider the sine of angle A
sin(A) = opposite side of angle A / hypotenuse
sin(45°) = y / ( [tex]\sqrt{6}[/tex])
We know that from the standard trigonometric table the value of sin(45°) is [tex]\frac{1}{\sqrt{2} }[/tex]
Substitute this value in above equation we get,
[tex]\frac{1}{\sqrt{2} }[/tex] = y / ( [tex]\sqrt{6}[/tex])
We solve this equation to find the value of y.
y = [tex]\sqrt{6}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex]
y = [tex]\frac{\sqrt{3}\sqrt{2} }{\sqrt{2} }[/tex]
y = [tex]\sqrt{3}[/tex]
Therefore, the correct answer is an option (c)
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a card is drawn from a standard deck of 52 cards. find the probability that a king or a club is selected
The probability of selecting a King of Clubs from a standard deck of 52 cards is 1/52, or 0.019.
This is so because there is just one King of Clubs—the lone card with that particular suit and rank—in the regular deck.
No of the card's suit or rank, there is always a 1/52 chance that it will be drawn from a normal deck.
This is due to the fact that every card has an equal chance of being chosen, and as a normal deck contains 52 cards, the likelihood of any card being chosen is 1/52.
In summary, the likelihood of drawing a King of Clubs from a conventional 52-card deck is 1/52, or 0.019.
Complete Question:
A card is drawn from a standard deck of 52 cards. What is the probability of selecting a King of Clubs?
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What number should be added to both sides of the equation to complete the square? x2 + 3x = 6
a. (StartFraction 3 Over 2 EndFraction)
b. squared 3/2
c. 3
d. 6^2
The equation to complete the square for x² + 3x = 6 is 3/2 (option a)
To complete the square for the equation x² + 3x = 6, we need to add a specific number to both sides of the equation. The number we need to add is half of the coefficient of x, squared. In other words, we need to find (b/2)², where b is the coefficient of x.
In this equation, b is 3, so (b/2)² is (3/2)², which simplifies to 9/4. Therefore, to complete the square, we need to add 9/4 to both sides of the equation:
x² + 3x + 9/4 = 6 + 9/4
Now, we can rewrite the left side of the equation as a perfect square:
(x + 3/2)² = 33/4
Finally, we can solve for x by taking the square root of both sides of the equation:
x + 3/2 = ± √(33/4)
x = -3/2 ± √(33/4)
Therefore, the answer to the question is a) 3/2.
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9. Need sum help with this ASAP
The value of the missing side lengths such as b and d would be = 3.5 and 11.3
How to calculate the value of the missing side lengths of the given triangle?To calculate the side length of the given triangle, the sine rule must be obeyed. That is;
a/sinA= b/sin B
For the first triangle;
b = ?
B = 30°
a = 6
A = 60°
That is ;
b/ sin30° = 6/sin60°
Make b the subject of formula;
b = sin30×6/sin60
= 0.5×6/0.866025403
= 3.5
For second triangle:
a/sinA= d/sin D
where;
a = 8
A = 45°
d = ?
D = 90°
That is;
8/sin45° = d/sin90°
d =8×1/0.707106781
= 11.3
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Create the equation of a circle that has a center at (-7, 10) and has a radius of 11 units.
What is the equation of this circle in Standard Form?
A. (x – 10)2 + (y + 7)2 = 11
B. (x + 10)2 + (y – 7)2 = 121
C. (x – 7)2 + (y + 10)2 = 11
D. (x + 7)2 + (y – 10)2 = 121
The equation of this circle in standard form include the following: D. (x + 7)² + (y - 10)² = 11².
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Based on the information provided, we have the following parameters:
Radius, r = 11 units.Center, (h, k) = (-7, 10).By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - (-7))² + (y - 10)² = 11²
(x + 7)² + (y - 10)² = 11²
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if a wave has a length of 30 feet, what is the depth? question 2 options: a) 20 feet b) 15 feet c) 10 feet d) 5 feet
The length of a wave does not directly determine its depth. The depth of a wave is influenced by various factors, including the shape and size of the seafloor,
The temperature and salinity of the water, and the strength and direction of the current. Therefore, without additional information about these factors, it is impossible to accurately determine the depth of a wave based solely on its length. I suggest seeking the advice of an expert in oceanography or physics for a more comprehensive explanation.
The length of a wave is the distance between two successive points in the same phase, such as from crest to crest or trough to trough. In your case, the wave length is given as 30 feet. However, without additional information about the wave, we cannot determine its depth solely based on its length.
Depth refers to the vertical distance from the surface to the lowest point of a wave (trough), and it's not directly related to the wave length. Therefore, we cannot accurately choose an option (a, b, c, or d) for the depth based on the provided information.
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How do you find the solutions to a system of equations involving quadratic functions
Solution of a system of equations involving quadratic functions, required to calculate the values of the variables that satisfy both equations simultaneously.
Write down the equations in standard form.
A quadratic equation can be written in the form ax² + bx + c = 0, where a, b, and c are constants.
Similarly, a system of quadratic equations can be written in the form.
a₁x² + b₁x + c₁= 0
a₂x² + b₂ x + c₂ = 0
Rearrange one of the equations so that one of the variables is expressed in terms of the other.
Then substitute this expression into the other equation to obtain a single quadratic equation in one variable.
Solve the resulting quadratic equation using any of the available methods.
Such as factoring, completing the square, or using the quadratic formula.
Once you have found the values of the variables.
Substitute them back into one of the original equations to find the corresponding values of the other variables.
Check the solutions by plugging them into both equations and verifying that they satisfy both equations.
If the two equations do not have any real solutions, then the system has no real solutions.
If the two equations have infinitely many solutions, then the system is dependent.
And one of the equations is a multiple of the other.
Here, the solution set is given by the equation of the dependent line.
If the two equations have a unique solution, then the system is independent.
And the solution set is given by the coordinates of the intersection point of the two graphs.
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All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions. )P(x) = x3 + 3x2 − 25x + 21x = ?Write the polynomial in factored form. P(x) = ?
The graph is attached, from the graph the zeros are
x = -7, 1 and 3
The polynomial in factored form. P(x) = (x + 7) (x - 1) (x - 3)
How to find the zeros of the polynomial functionThe zeros of the polynomial function given as P(x) = x³ + 3x² − 25x + 21 is solved using graphical method
From the graph are deduced to be
x = -7, x = 1 and x = 3
From the zeros the factored form of the equation is written as
x = -7, x + 7 = 0
x = 1, x - 1 = 0
x = 3, x - 3 = 0
hence factored form of the polynomial is, P(x) = (x + 7) (x - 1) (x - 3)
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kindergarten class has four left-handed children and nine right-handed children. Two children are selected without replacement for a shoe-tying lesson. Let X = the number who are left-handed.
(a) The simple events in the sample space are {RR, RL, LR, LL}. For instance, one simple event is RL, indicating that the first child is right-handed and the second one is left-handed. Find the probability for each of the simple events in the sample space. (Hint: A tree diagram may help you solve this.)
p rr
p rl
p lr
p ll
(b) Find the probability distribution function for X.
So the probability distribution function for X is:
- P(X = 0) = 0.46
- P(X = 1) = 0.46
- P(X = 2) = 0.08
What is probability?Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty.
(a) Using the tree diagram:
- P(RR) = (9/13) * (8/12) = 0.46
- P(RL) = (9/13) * (4/12) = 0.23
- P(LR) = (4/13) * (9/12) = 0.23
- P(LL) = (4/13) * (3/12) = 0.08
So the probabilities for the simple events are:
- P(RR) = 0.46
- P(RL) = 0.23
- P(LR) = 0.23
- P(LL) = 0.08
(b) The possible values for X are 0, 1, or 2.
- P(X = 0) = P(RR) = 0.46
- P(X = 1) = P(RL) + P(LR) = 0.23 + 0.23 = 0.46
- P(X = 2) = P(LL) = 0.08
So the probability distribution function for X is:
- P(X = 0) = 0.46
- P(X = 1) = 0.46
- P(X = 2) = 0.08
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Monique collects data from a random sample of seventh graders in her school and finds that 12 out of 20 seventh graders barticipate in after-school activities. Write and solve a proportion to estimate the number of seventh graders n who barticipate in after-school activities if 165 seventh graders attend Monique's
The proportion is 12/20 = n/165 and we can estimate that 99 seventh graders out of the 165 attending Monique's school participate in after-school activities.
To estimate the number of seventh graders who participate in after-school activities, we can set up a proportion using the given data. Let n be the number of seventh graders who participate in after-school activities out of the total number of seventh graders attending Monique's school, which is 165.
The proportion can be written as:
12/20 = n/165
To solve for n, we can cross-multiply and simplify:
12 × 165 = 20n
1980 = 20n
n = 1980/20
n = 99
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a. Determine whether the descriptions of the figure in Step 4 and Step 15 are true or false.
8
Step 1 Step 2
Step 3
Step 4 is a 5-by-5 array of squares with the lower left corner square moved to the upper right corner. Select Choice
Step 15 is a 15-by-15 array of squares with the lower left corner square moved to the upper right corner. Select Choice
b. How many small squares will there be in each of these steps?
Step 4: Select Choice
Step 15: Select Choice
c. Does the equation y = n²-1 represent the relationship between the step number, and the number of small squares, y, in each step? Select Choice
d. Complete the following to explain how the equation that represents the relationship between n and y relates to the pattern.
If you move the small square in the upper right corner to the lower left comer, it makes an Select Choice
array of small squares, which gives ².
Step-by-step explanation:
a)
with step 1 to 3 we see that the numbers of squares serving the length of the sidelines is following the step number 1:1.
so, step 1 has a side length of 1 square.
step 2 has a side length of 2 squares.
step 3 has a side length of 3 squares.
so, we expect step 4 to have a side length of 4 squares.
but the first statement says "5-by-5", so, the side length is 5.
therefore, this statement is false.
and yes, we expect step 15 to have a side length of 15.
and the shift of the single square from the bottom left to the top right is also correct.
therefore, the statement is true.
b)
step 4 = 4×4 = 16 squares
step 15 = 15×15 = 225 squares
c)
no.
just look at step 1.
y = 1² - 1 = 1 - 1 = 0.
but I can clearly see that there is 1 square.
d)
it makes an n×n array. which is the same as n².
Effect of consumption of chocolate is perhaps the most misrepresented news in traditional media outlets, with claims from "eating chocolate once every day decreases the risk of liver cancer" to "eating chocolate once every day increases the risk of liver cancer" and everything in between. However, statistical studies are much more focused and particular research questions and outcomes often go unnoticed in media.
A group of researchers are interested in studying whether consumption of Belgian chocolate with 14gms of added sugar every day can be linked to increased palpitation in adults of ages 25-50. They performed a randomised trial concerning 10 adults over 2 days. They were given a normal breakfast on the first day, and on the second day, they were given chocolates with breakfast. Each day, their pulse rate was measured and the difference in pulse rates were recorded.
Please use this setup for the next 4 questions.
Let C be the change in the recorded pulse rates from eating the belgian chocolate. c = u after - u before
State the null and alternative hypotheses for this study.
State the null and alternative hypotheses for this study.
Question 1 options:
a) H0: The average pulse rate does not change after the consumption of chocolates (C = 0 beats / min)
Ha: The average pulse rate is higher after the consumption of chocolate (C > 0 beats / min).
b) H0: The average pulse rate does not change after the consumption of chocolates (C = 0 beats / min)
Ha: The average pulse rate changed after the consumption of chocolate(�≠0 beats/min).
c) H0: The average pulse rate will increase after the consumption of chocolates (C > 0 beats / min)
Ha: The average pulse rate decreased after the consumption of chocolate (C ≤0 beats / min).
d) H0: The average pulse rate reduced after the consumption of chocolates (C < 0 beats / min)
Ha: The average pulse rate is higher after the consumption of chocolate (C ≥0 beats / min).
Question 2 (1 point)
The change in heart rate for the 10 individuals are as follows
(1.8, -0.4, -0.6, 0.4, 0.2, -1.0, 1.6, 0.8, 2.0, -2.0).
Please calculate the mean change in heart rate and round to 2 decimal places.
The mean change in heart rate is 0.28 , around to 2 decimal places.
What is mean?
In statistics, the mean is nothing but the measures of central tendency, apart from the mode and median. Mean is the average of the given set of values or data. It denotes the equivalent distribution of values for a given data set. To calculate the mean of given data, we need to add the total values given in a datasheet and then divide the sum by the total number of values.
The change in heart rate for the 10 individuals are as follows
(1.8, -0.4, -0.6, 0.4, 0.2, -1.0, 1.6, 0.8, 2.0, -2.0).
So the data is given by,
(1.8, -0.4, -0.6, 0.4, 0.2, -1.0, 1.6, 0.8, 2.0, -2.0).
Mean of the given data = sum of all data/ number of data
Mean = (1.8-0.4 -0.6+0.4+ 0.2 -1.0+1.6+ 0.8+2.0-2.0)/10
= 2.8/10
=0.28
Hence, the mean change in heart rate is 0.28 , around to 2 decimal places.
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