Can l get some help please
The probability of obtaining at least 1 six in 5 throws of the die is 1 - (1-p)⁵.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
The probability of obtaining a six on one throw of the die is given as a fraction, say p.
We are not given the value of p, but we know that the die is biased so that the probability of obtaining a six is greater than 1/6.
The probability of not obtaining a six on one throw of the die is (1-p), since the sum of the probabilities of all possible outcomes must be 1.
To find the probability of obtaining at least 1 six in 5 throws of the die, we can use the complement rule.
This states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
So, the probability of not obtaining any sixes in 5 throws of the die is:
(1-p)⁵
The probability of obtaining at least 1 six in 5 throws of the die is therefore:
1 - (1-p)⁵
This formula gives the probability of obtaining at least one six in any 5 throws of the die, regardless of the order in which the throws occur.
Note that we cannot determine the exact value of the probability without knowing the value of p, but we can use the given information that the die is biased so that the probability of obtaining a six is greater than 1/6 to conclude that the probability of obtaining at least one six in 5 throws of the die is also greater than 1/6.
Therefore, The probability of obtaining at least 1 six in 5 throws of the die is 1 - (1-p)⁵.
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Determine the slope of the line passing through the points (9, 4) and (-6, -7).
Answer:
slope = [tex]\frac{11}{15}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-x_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 4 ) and (x₂, y₂ ) = (- 6, - 7 )
m = [tex]\frac{-7-4}{-6-9}[/tex] = [tex]\frac{-11}{-15}[/tex] = [tex]\frac{11}{15}[/tex]
can someone help me with this
The other leg measures 4 centimetres in length.
The right triangle in the illustration has a hypotenuse that is 5 cm long and a leg that is 3 cm long. The length of the other leg must be determined.
Applying the Pythagorean theorem, which asserts that the square of the hypotenuse's length is equal to the sum of the squares of the two legs of a right triangle, we may write:
[tex]a^2 + 3^2 = 5^2[/tex]
When we simplify this equation, we obtain:
[tex]a^2[/tex] + 9 = 25
By taking 9 away from both sides, we arrive at:
[tex]a^2[/tex] = 16
By multiplying both sides by their square roots and keeping in mind that a must be positive, we arrive at:
a = 4
Hence, the other leg is 4 cm long.
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Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places.
x y
2 8.18
6.5 12.816
11 16.768
15.5 21.222
20 26.462
24.5 31.36
29 34.584
y
=
x
+
By using the data in the given table, the missing coefficients should be filled as followed;
y = x + 6.128.
How to construct and plot the data in a scatter plot?In this scenario, the x-values would be plotted on the x-axis (x-coordinate) of the scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the line of best fit is given by
y = x + 6.128
In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.
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2) You are given the following time line; CFs are at the end of the year. Years: 0 1 2 3 4 5 CF $s 0 1500 1500 3000 4500 5000 Rate: 12.00% bgs a) Calculate the PV of the CFs
According the question given above the present value of the cash flows is $12,114.36.
What is Algebraic expressiοn ?
Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.
Tο calculate the present value (PV) οf the cash flοws (CFs), we need tο discοunt each cash flοw tο its present value using the given rate οf 12%. The fοrmula tο calculate the present value οf a cash flοw is:
[tex]PV = CF / (1 + r)^n[/tex]
where:
PV = present value οf the cash flοw
CF = cash flοw amοunt
r = discοunt rate
n = number οf periοds (in this case, the number οf years)
Using this fοrmula, we can calculate the present value οf each cash flοw as fοllοws:
[tex]PV(CF0) = 0 / (1 + 0.12)^0 = 0[/tex]
[tex]PV(CF1) = 1500 / (1 + 0.12)^1 = 1339.29[/tex]
[tex]PV(CF2) = 1500 / (1 + 0.12)^2 = 1191.08[/tex]
[tex]PV(CF3) = 3000 / (1 + 0.12)^3 = 2382.16[/tex]
[tex]PV(CF4) = 4500 / (1 + 0.12)^4 = 3221.56[/tex]
[tex]PV(CF5) = 5000 / (1 + 0.12)^5 = 3080.27[/tex]
Tο find the present value οf all the cash flοws, we simply add up the present values οf each cash flοw:
PV = PV(CF0) + PV(CF1) + PV(CF2) + PV(CF3) + PV(CF4) + PV(CF5)
= 0 + 1339.29 +1191.08 + 2382.16 + 3221.56 + 3080.27
= 12114.36
Therefοre, the present value οf the cash flοws is $12,114.36.
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Find the indicated terms of the geometric sequence with the given description.
The fourth term is 18 and the seventh term is (16/3). Find the first and nth terms.
Answer: Let's denote the first term of the geometric sequence as "a", and the common ratio as "r". Then, we can use the given information to set up a system of equations:
a * r^3 = 18 (the fourth term is 18, so ar^3 is the fourth term)
a * r^6 = 16/3 (the seventh term is 16/3, so ar^6 is the seventh term)
To solve for "a" and "r", we can divide the second equation by the first equation:
(a * r^6) / (a * r^3) = (16/3) / 18
Simplifying this expression, we get:
r^3 = (16/3) / 18 = 16/54 = 8/27
Taking the cube root of both sides, we get:
r = 2/3
Substituting this value of "r" into the first equation, we can solve for "a":
a * (2/3)^3 = 18
a = 18 / (2/3)^3
a = 27
Therefore, the first term of the geometric sequence is 27, and the nth term is given by:
a * r^(n-1) = 27 * (2/3)^(n-1)
Step-by-step explanation:
The combination of your locker contains 3 non-repeating digits from the numbers 0-9.
What would the answer be to the question above if you absolutely choose 9 as your first digit?
There are total 56 combination of your locker contains 3 non-repeating digits from the numbers 0-9.
Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.
Moreover, there are two other kinds of combinations (the specific sequence is not relevant at this time): It's acceptable to repeat phrases like "coins in your pocket" (5,5,5,10,10) In the same way, lottery numbers (2,14,15,27,30,33)
Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.
Permutations and combinations are compatible.
As the first digit is fixed i.e. 9,
So, there are 2 non-repeating digits left,
Using permutations,
we are left with 8 × 7 = 56 ways.
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12 people sit down for dinner at gullo's. 1/6 order a shrimp poboy. 1/2 order a cheese burger . The rest order a salad
What expression would you use to determine how many people ordered the salad
What expression would you use to determine how many people did not order the
How many people order a salad
We may take the number of people who ordered a salad out of the total to find the number of individuals who did not order one:
12 - 4 = 8 people did not order a salad.
The expression to use to estimate the number of persons that ordered the salad would be
(1/3) x 12 = 4 people ordered a salad
what is an expression?Every mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Everything with a variable value is anything whose value changes over time. Typically, alphabetical letters like a, b, c, m, n, p, x, y, and z are used to denote expression variables. A combination of several variables and integers can be used to create a variety of expressions.
from the question:
We can utilize the information that 1/6 of customers ordered a shrimp po'boy and 1/2 ordered a cheeseburger to estimate how many individuals ordered the salad. Hence, the proportion of customers that choose a salad is:
1 - (1/6 + 1/2) = 1 - 2/3 = 1/3
Hence, to count how many people ordered the salad, the statement would be:
4 individuals (1/3) x 12 ordered salads.
We may take the number of people who ordered a salad out of the total to find the number of individuals who did not order one:
Those who did not order a salad were 12 - 4 = 8.
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what is the answer to this ?
Answer:
-f(x+3) and -2f(x)+4
Step-by-step explanation:
it is all the ones with a negative in front of the function, so that is -f(x+3) and -2f(x)+4.
Which value must be added to the expression x^2 + 12x to make it a perfect-squared trinormal?
Find the diameter. Round to the nearest whole number.
Answer : 14
Explanation : Divide The Circumference By π, Or 3.14 For The Answer.
Answer: 14
Step-by-step explanation:
To find the diameter, divide your circumference by pi "3.14".
43.9/3.14 = 13.9808917197
Rounded to the nearest whole number is: 14
Have a good day!
At the end of the spring semester, the dean of students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year.
The average was a gain of µ = 15 pounds with a standard deviation of
= 6. The distribution of scores was approximately normal.
A sample of n = 4 students is selected, and the average weight change is computed for the sample.
What is the probability that the sample mean will be greater than M = 10 pounds? In symbols, what is p (M > 10) (four decimals)
The probability that the sample mean weight change is greater than 10 pounds is p(M > 10) = 0.9088.
What is the probability?To find the probability that the sample mean will be greater than M = 10 pounds, we need to standardize the sample mean using the formula for z-score:
z = (M - µ) / (σ / √n)
Substituting the given values, we get:
z = (10 - 15) / (6 / √4)
z = -1.33
Using a standard normal distribution table or calculator, we can find the probability that z is greater than -1.33, which is approximately 0.9088.
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what should be added to 6x²+9x-8 to obtain 4x²-8x+6 ?
Hence, in answering the stated questiοn, we may say that As a result, we equatiοn must add (2x - 1)2 + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.
What is equatiοn?A algebraic equatiοn is a strategy fοr linking twο prοpοsitiοns and expressing equivalence using the equals symbοl (=). A mathematical sentence that shοws the equivalency οf twο fοrmulas is knοwn as an equatiοn in algebra. In the calculatiοn 3x + 5 = 14, fοr example, the equal sign puts a space between the values 3x + 5 and 14. Tο describe the relatiοnship between the twο sentences printed alοng either side οf a letter, a mathematical fοrmula can be utilised. Usually, the insignia and the prοgramme are the same. 2x - 4 = 2, fοr example.
Tο identify what shοuld be added tο 6x² + 9x - 8 tο create 4x² - 8x + 6, we need tο undertake a methοd called "cοmpleting the square".
We can cοnclude frοm cοmparing the twο fοrmulas that a = 4, b = -8, and c = 6.
Sο we must "finish the square" by adding and remοving a term equal tο (b/2a)2. In this instance, we have:
(b/2a)² = (-8/2(4))
a² = 1
4x² - 8x + 6 + 1 - 1
(4x² - 8x + 1) + (6 - 1) (6 - 1)
(4x² - 8x + 1) is a perfect square trinοmial, which may be factοred as (2x - 1)².
As a result, the ultimate sοlutiοn is:
6x² + 9x - 8 + 1 - 1 + (2x - 1) (2x - 1)
a² + 5
As a result, we must add (2x - 1)² + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.
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sion Problems
How you solve each problem.
Yuki and Jake made 52 snowballs if they wanted to
share them evenly with 2 other friends, how many
snowbalis would each of the 4 of them get?
The answer is each of the 4 friends would get 13 snowballs.
52 divided by 4 = 13
Answer: 52 divided by 4 is 13 each of them would get 13 snowballlllsssssss!!!!
Step-by-step explanation:
CAN SOMEONE HELPP WITH THIS QUESTION?✨
The angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.
How to calculate for the angle of elevation θ in degreeThe angle of elevation is the angle θ between the horizontal line given as 2000 feet and the line of sight which is above the horizontal line.
The angle θ in degree is calculated, and then converted to radian as follows:
since the camera and the rocket is 4255 feet apart, then;
θ = tan⁻¹(4255/2000)
θ = 64.82482°
To convert 64.82482° to radian, we multiply by π/180
θ' = 64.82482° × π/180
θ' = 1.13186 approximately to 5 decimal place.
Therefore, the angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.
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The list below shows the scores for each of Sarah’s homework assignments.
100, 95, 47, 83, 87, 89, 89
If the score 47 is removed from the list, which of the following statements is true?
Group of answer choices
The mean will decrease.
The mean will increase by about 6.
The mean will increase by 47.
The mean will remain the same.
Answer:
i think it will decrease
Step-by-step explanation:
A more clear view of the graph.
Answer:
Hi! The slope is -3/2
Y intercept 2.5
(0,2.5)
Step-by-step explanation:
I hope this helps!
Answer:
The slope is [tex]\frac{-3}{2}[/tex]
The y - intercept is 2 1/2
The y-intercept point is (0, 2 1/2)
Step-by-step explanation:
If you start at the point on the left to get to the lower point on the right, you need to go down 3 units and to the right 2 units. This is the slope. Going down represents a negative number and going right represents a positive number. The slope is [tex]\frac{-3}{2}[/tex]
The y -intercpet is where the graph is cross the y axis. It looks like it is crossing between 2 and 3. So, 2 1/2 is a good estimate. Actually, I did calculate the y-intercept and it is in fact 2 1/2.
The point of the y-intercept is when x = 0
(0, 2 1/2)
Helping in the name of Jesus.
Choose ALL answers that describe the polygon.
Answer:
ParallelogramQuadrilateralRectangleStep-by-step explanation:
You want to know the names of a 4-sided figure with opposite sides congruent and adjacent sides perpendicular.
Congruent sidesA 4-sided figure is a quadrilateral.
When opposite sides are the same length, the quadrilateral is a parallelogram.
When corners of a parallelogram are right angles, it is a rectangle.
__
Additional comment
A rhombus also has congruent adjacent sides, as does a square. We are not told that is the case here. A trapezoid is not a parallelogram.
Which is a solution to the equation StartAbsoluteValue StartFraction y Over 4 EndFraction minus 2 EndAbsoluteValue = 22?
y = negative 6
y = negative 5
y = 80
y = 96
Answer:see answer
Step-by-step explanation:see answer
Answer:
y=96
..........................................................................
If C(x, y) = 500 − 5xy + 12x2y, find
∂C
∂x
and
∂C
∂y
.
If
q =
6p1 + 4p2
p1 + p2
,
find
∂q
∂p1
and
∂q
∂p2
.
The answers are, For C(x, y) = 500−5xy + 12x2y, ∂C/∂x = -5y + 24xy and ∂C/∂y = -5x + 12x².
For q = 6p₁ + 4p₂ / (p₁ + p₂), ∂q/∂p₁ = -2(p₁ - p₂)/(p₁ + p₂)² and ∂q/∂p₂ = 2(p₁ - p₂)/(p₁ + p₂)².
What is functions?A function is a mathematical object that accepts one or more inputs, processes those inputs according to a predetermined procedure, and then generates an output.
The domain and range of a function are its inputs and outputs, respectively.
An equation, a graph, or a table can all be used to depict a function.
To find ∂C/∂x and ∂C/∂y for C(x, y) = 500 − 5xy + 12x²y, we differentiate C with respect to x and y, respectively, while treating the other variable as a constant:
∂C/∂x = -5y + 24xy
∂C/∂y = -5x + 12x²
To find ∂q/∂p₁ and ∂q/∂p₂ for q = 6p₁ + 4p₂ / (p₁ + p₂), we differentiate q with respect to p₁ and p₂, respectively, while treating the other variable as a constant:
∂q/∂p₁ = (4p₂ - 2p₁ - 4p₂) / (p₁ + p₂)² = -2(p₁ - p₂)/(p₁ + p₂)²
∂q/∂p₂ = (6 - 2p₁/(p₁ + p₂)) / (p₁ + p₂) - (6p₁ + 4p₂)/(p₁ + p₂)²
= 2(p₁ - p₂)/(p₁ + p₂)²
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If the product of two numbers is 23 and the sum of the reciprocals is 2, what is the sum of these numbers?
Answer:
Let the two numbers be x and y. We know that:
xy = 23
We also know that:
1/x + 1/y = 2
Multiplying both sides of the second equation by xy, we get:
y + x = 2xy
Substituting the value of xy from the first equation, we get:
y + x = 2(23)
y + x = 46
Therefore, the sum of the two numbers is 46.
Step-by-step explanation:
5 On a scale drawing, the height of a tree is 3.75 inches.
Part A
If the scale of the drawing is 1 in.: 50 ft, how tall is the tree?
A
13.3 in.
B
13.3 ft
C 187.5 in.
D 187.5 ft
Part B
If the same tree is shown as 6 inches tall in a new scale drawing, mademulov ort
what is the new scale?
1 in.:.what about part b
Part A:
We are given that the height of a tree in a scale drawing is 3.75 inches. The scale of the drawing is 1 inch: 50 feet.
To find the height of the actual tree, we can use the ratio of the drawing scale to the real-life scale. For every 1 inch on the drawing, there are 50 feet in real life.
Therefore, we can set up a proportion:
[tex]$\frac{1 \ \text{inch}}{50 \ \text{feet}} = \frac{3.75 \ \text{inches}}{x \ \text{feet}}$where $x$ is the height of the actual tree in feet.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot x = 3.75 \ \text{inches} \cdot 50 \ \text{feet}$$x = \frac{3.75 \ \text{inches} \cdot 50 \ \text{feet}}{1 \ \text{inch}} = 187.5 \ \text{feet}$Therefore, the height of the tree is $\boxed{D \ 187.5 \ \text{ft}}$.[/tex]
[tex]Part B:We are now given a new scale drawing where the height of the same tree is 6 inches. We need to find the new scale.Since the tree's height in the new drawing is different, we can use a new proportion to find the new scale.Let the new scale be $1$ inch to $x$ feet. We can set up a proportion:[/tex]
[tex]$\frac{1 \ \text{inch}}{x \ \text{feet}} = \frac{6 \ \text{inches}}{187.5 \ \text{feet}}$where $187.5$ feet is the height of the tree in real life.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot 187.5 \ \text{feet} = 6 \ \text{inches} \cdot x \ \text{feet}$$x = \frac{1 \ \text{inch} \cdot 187.5 \ \text{feet}}{6 \ \text{inches}} = 31.25 \ \text{ft}$Therefore, the new scale is $\boxed{1 \ \text{inch} : 31.25 \ \text{ft}}$.[/tex]
Answer:
Step-by-step explanation:
Part A:
We can use a proportion to solve for the height of the tree:
1 inch on the drawing represents 50 feet in real life.
So, 3.75 inches on the drawing would represent:
3.75 inches * (50 feet/1 inch) = 187.5 feet
Therefore, the height of the tree is 187.5 feet.
The answer is D) 187.5 ft.
Part B:
The ratio of the height of the tree on the new scale drawing to its actual height must be the same as the ratio of the height of the tree on the original scale drawing to its actual height.
Let the new scale be 1 in. : x feet.
Then, we have the proportion:
1 in. / 50 ft. = 6 in. / (x) ft.
Solving for x, we get:
x = (6 in. * 50 ft.) / 1 in.
x = 300 ft.
Therefore, the new scale is 1 in. : 300 ft.
The answer is 1 in. : 300 ft.
One side of a parallelogram is 30cm, and its area is 540cm². Find the height corresponding to the given side.
The height corresponding to the given side is 18cm
How to determine the heightSome of the properties of a parallelogram are given below as;
The opposite sides of a parallelogram are equal.The opposite angles of a parallelogram are congruent or equal.The measure of the sum of the interior angles are 360 degrees.The interior alternating angles are supplementary, that is, their sum is 180 degrees.The formula for calculating the area of a parallelogram is expressed as;
Area = bh
Given that;
b is the base side of the parallelogram and h is the height
Substitute the values
540 = 30h
Divide by the coefficient of h
h = 18 cm
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Johnathan is using a hose to fill his pool with water. The pool already had 2,000 gallons of water in it before he started, and the hose puts water into the pool at a rate of 360 gallons per hour. Let g represent the number of gallons that the hose has put into the pool after a given number of hours. Let h represent the number of hours that the hose has put water into the pool. Let w represent the total number of gallons of water in the pool. Complete the equations so that: Equation 1 shows the relationship between g and h. Equation 2 shows the relationship between g and w.
Therefore, Equations 1 and 2 are: Equation 1: g = 360h
Equation 2: w = 2,000 + 360h.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to find the value of the variable that makes the equation true. Equations are used extensively in mathematics and science to model real-world phenomena and solve problems.
by the question.
We know that the hose puts water into the pool at a rate of 360 gallons per hour. Therefore, after h hours, the hose has put g gallons of water into the pool. We can express this relationship using the following equation:
Equation 1: g = 360h
We also know that the pool already had 2,000 gallons of water in it before Johnathan started filling it with the hose. Therefore, the total number of gallons of water in the pool after h hours is given by:
w = 2,000 + g
We can substitute the expression for g from Equation 1 into this equation to obtain an equation that relates g and w:
Equation 2: w = 2,000 + 360h
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hii
what is meant by corrosion
Answer:
Corrosion is a natural process which converts refined metal to their more stable oxide.It is the gradual destruction of materials {usually metals} by chemical reaction with their environment.In the most common use of the world, this means electrochemical oxidation of metals in reaction with an oxidant such as oxygen.
Find all the remaining zeros if 1-2i is a zero. f(x)=4x^(4)+17x^(2)+14x+65
Answer:
Step-by-step explanation:
If 1-2i is a zero of the polynomial, then its conjugate 1+2i is also a zero. This is because complex zeros of a polynomial with real coefficients always occur in conjugate pairs.
Let's use synthetic division to factor out the polynomial with the given zeros:
1-2i | 4 0 17 14 65
| 4 -8i -9+2i -12
-------------------
4 4 -8i -9+2i 53
So we have factored the polynomial as:
f(x) = (x - 1 + 2i)(x - 1 - 2i)(4x^2 + 4x - 53)
Now we need to find the zeros of the quadratic factor:
4x^2 + 4x - 53 = 0
Using the quadratic formula, we get:
x = (-4 ± sqrt(16 + 4453)) / 8
x = (-4 ± sqrt(848)) / 8
x = (-4 ± 4sqrt(53)) / 8
x = (-1 ± sqrt(53)) / 2
So the remaining zeros are (-1 + sqrt(53))/2 and (-1 - sqrt(53))/2.
Members of a charity organization are interested in finding ways to make it easier for individuals to donate money to their cause.
They analyze the data from their last fiscal year of donations and find that 75% of their money came from online sources. Of the 60% of donations that came from regular donors (repeat donors), approximately 95% were submitted through the organization’s website.
Is the method of donation (online vs. not online) independent from the type of donor (regular vs. new) in this sample?
We cannot determine whether the method of donation is independent from the type of donor in this sample based on the information given in the question.
Define the term statistical analysis?Statistical analysis is the process of collecting, cleaning, analyzing, and interpreting data using statistical methods and techniques. It involves summarizing and describing data, identifying patterns and relationships, testing hypotheses, and making predictions based on the data.
We cannot determine whether the method of donation (online vs. not online) is independent from the type of donor (regular vs. new) in this sample based on the information given in the question.
To determine whether two categorical variables (in this case, method of donation and type of donor) are independent, we would need to conduct a chi-square test of independence. This would involve comparing the observed frequencies of each combination of the two variables to the expected frequencies if the two variables were independent.
However, the question only provides information on the percentage of donations from online sources and the percentage of donations from regular donors that were submitted through the organization's website. It does not provide information on the percentage of donations from new donors that were submitted through the website, or the percentage of donations from regular donors that were not submitted through the website. Therefore, we cannot determine whether the method of donation is independent from the type of donor in this sample.
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The road from A to E and the road from C and D are perpendicular and intersect at point F. Theresa's house is at C, 500 feet from the intersection. Ray's house is at D, 750 feet from the intersection. Ivy's house is at E, 750 feet from the intersection.
Zanas house is at A, 500 feet from the intersection, and Tan's house is at B, 750 feet from F. Which distance is longer, the distance from Zana's house to Tan's house or the distance from Theresa's house to Is house? Show how you know.
Step-by-step explanation:
what is meant by "distance" ?
ground distance (using the roads to get there), or air distance (line of sight) ?
I have to assume we mean air distance, as the ground distance is the same in both cases (500 ft + 750 ft = 1250 ft).
for the air distance we need to use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), and a and b being the legs.
Zana to Tan = AB
FB² = FA² + AB²
750² = 500² + AB²
562,500 = 250,000 + AB²
312,500 = AB²
AB = 559.0169944... ft
Theresa to Ivy = CE
CE² = CF² + FE²
CE² = 500² + 750² = 250,000 + 562,500 =
= 812,500
CE = 901.3878189...
so, the distance from Theresa to Ivy is longer.
1.) The following two arguments are Invalid arguments, so each breaks at least 1 of the rules. Tell which
of the rules are broken in the following and briefly explain:
ALL P are Q
NO Q are S
Some Pare R
All A are B
All B are C
All Care A
The rule broken in the first argument is of undistributed middle.
The rule broken in the second argument is of exclusive middle.
What is Converse?
In logic and mathematics, converse of statement is formed by switching hypothesis and conclusion of original statement. For example, converse of the statement "If it rains, the streets get wet" is "If the streets get wet, it is raining."
The first argument violates the rule of the undistributed middle. The argument appears to be the fallacy of the converse of the inverse. This is a form of invalid reasoning where the contrapositive of a true statement is used as evidence for the original statement. The argument could be stated in syllogistic form as:
Premise 1: All P are Q.
Premise 2: No Q are S.
Conclusion: Some P are not S.
This argument is invalid because it violates the rule of the undistributed middle. The middle term Q is not distributed in either premise, which means that we cannot logically conclude anything about the relationship between P and S.
The second argument violates the rule of the exclusive middle. The argument appears to be the fallacy of the illicit conversion. This is a form of invalid reasoning where the subject and predicate terms of a statement are switched without changing the truth value of the statement. The argument could be stated in syllogistic form as:
Premise 1: All A are B.
Premise 2: All B are C.
Conclusion: All C are A.
This argument is invalid because it violates the rule of the exclusive middle. The argument assumes that there are only three categories of things: A, B, and C. However, this assumption is not justified, and there may be other categories that are not included in the argument.
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Which inequality is true when the value of x is -5?
The true inequality from the list of options is (c) -x - 6 > -3.5
How to determine the true inequalityTo determine which inequality is true when x is -5, we need to substitute -5 for x in each inequality and simplify.
a) -x – 6 < -3.5
Substituting x = -5, we get:
-(-5) - 6 < -3.5
5 - 6 < -3.5
-1 < -3.5
This is false, so option a) is not true.
b) -x – 6 > 3.5
Substituting x = -5, we get:
-(-5) - 6 > 3.5
5 - 6 > 3.5
-1 > 3.5
This is false, so option b) is not true.
c) -x - 6 > -3.5
Substituting x = -5, we get:
-(-5) - 6 > -3.5
5 - 6 > -3.5
-1 > -3.5
This is true, so option c) is true.
Hence, the correct option is (c) -x - 6 > -3.5
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Complete question
Which inequality is true when the value of x is -5?
a) -x – 6 < -3.5
b) -x – 6 > 3.5
c) -x - 6 > -3.5
d) x - 6 > -3.5