Answer: 1/3
Step-by-step explanation:
The probability of selecting a chocolate cream pie can be found by dividing the number of chocolate cream pies by the total number of pies:
Probability of selecting a chocolate cream pie = Number of chocolate cream pies / Total number of pies
Probability of selecting a chocolate cream pie = 4 / 12
Simplifying this fraction by dividing the numerator and denominator by 4 gives:
Probability of selecting a chocolate cream pie = 1/3
Therefore, the probability of selecting a chocolate cream pie from Annie's Pie Shop is 1/3.
HELP ASAP!!!
The graph shows two accounts with the same principle and annual interest rate. Use the graph to estimate the anwser to each question.
A) About how much more compound interest than simple interest is earned after 35 years?
B) About how much more compound interest than simple interest is earned after 45 years?
The answers are:
(A) More compound interest than simple interest after 35 years: $260
(B) More compound interest than simple interest after 45 years: $445
What is Compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
The interest you earn on interest is known as compound interest.
Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.
You will wind up with $110.25 at the conclusion of the second year.
Now, calculate according to the given graph as follows:
(A) More compound interest than simple interest after 35 years:
870 - 610 = $260
(B) More compound interest than simple interest after 45 years:
1150 - 705 = $445
Therefore, the answers are:
(A) More compound interest than simple interest after 35 years: $260
(B) More compound interest than simple interest after 45 years: $445
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A cube has a surface area of 24 ft². What is the length of one edge of the cube?
The length of one edge of the cube is 2 feet long whose surface area is 24 ft sq.
What is surface area?Surface area is a measure of the total area that the surface of an object occupies. In geometry, it is the sum of the areas of all the faces or surfaces of a three-dimensional object
According to question:The surface area of a cube is given by the formula 6s², where s is the length of one edge of the cube.
We are given that the surface area of the cube is 24 ft², so we can set up the equation:
6s² = 24
Dividing both sides by 6 gives:
s² = 4
When you square the two sides, you get:
s = ±2
Since the length of a side cannot be negative, the only valid solution is:
s = 2
The cube's one edge is therefore 2 feet long.
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the weyland corporation, owns five offices that it leases to other businesses. the lease per square foot differs by building due to its location and amenities. currently, all buildings are fully leased, and detailed data is given below. calculate the weighted average price per square foot of the five offices owned by weyland corp. round your answer to 2 decimal places (include zero if necessary). price per sq. ft. ($) number of sq. ft. building 1 75 125,000 building 2 85 37,000 building 3 90 77,500 building 4 45 35,000 building 5 50 40,000
The weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.
Building Price per square ft ($) Number of sq. ft Building 1 75 and 125,000, Building 2 85 and 37,000, Building 3 90 and 77,500, Building 4 45 and 35,000, Building 5 50 and 40,000. Now, the formula to calculate weighted average price per square foot is,
Weighted Average Price per square foot = [ (Price per sq. ft of Building 1 * Number of sq. ft of Building 1) + (Price per sq. ft of Building 2 * Number of sq. ft of Building 2) + (Price per sq. ft of Building 3 * Number of sq. ft of Building 3) + (Price per sq. ft of Building 4 * Number of sq. ft of Building 4) + (Price per sq. ft of Building 5 * Number of sq. ft of Building 5) ] / Total sq. ft of all buildings.
Applying the values in the formula,
Weighted Average Price per square foot = [(75 * 125000) + (85 * 37000) + (90 * 77500) + (45 * 35000) + (50 * 40000)] / (125000 + 37000 + 77500 + 35000 + 40000)= [9375000 + 3145000 + 6975000 + 1575000 + 2000000] / 297500= 23092500 / 297500= 77.72
Therefore, the weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.
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James has 27 metres of red wire and 12 metres
of black wire. He needs to cut both wires into
smaller pieces so that all of the smaller pieces are
the same length and there is no wire left over. The
length of each piece must be a whole number of
metres.
What is the longest he can make each smaller
piece of wire? Give your answer in metres (m).
Answer:
3m
Step-by-step explanation:
red wire = 27
black wire= 12
so, we take HCF (highest common factor)
which would be 3 so all the wires would be cut into 3m long.
I hope it helps.
Answer:2m
Step-by-step explanation:
as the factors of 12 are:1, 2, 3, 4, 6 and 12
and the factors of 26 are:1, 2, 13 and 26
so if you are talking meters 2 would be the longest
i hope you get this right x
I need some help with this
Answer:
27+2.25π
Step-by-step explanation:
Cube's volume is 3x3x3 = 27
The radius of the hemisphere is 3/2 = 1.5
Volume of a sphere is 4/3 π r^3
Plug in: 4/3 π 1.5^3 = 4.5π
Divide by 2: 2.25π
Total volume: 27+2.25π
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently (a) What is the probability that all of the sprinklers will operate correctly in a fire? Round your answer to three decimal places (e.g. 98.765) (b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire? Round your answer to two decimal places (e.g. 98.76), (c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98?
The probability that all 10 sprinklers will operate correctly in a fire is approximately 0.028, probability that at least 7 of the sprinklers will operate correctly in a fire is approximately 0.95 and the probability of at least one sprinkler operating correctly in a fire is at least 0.98, we need to have at least 7 sprinklers in the ballroom.
The sprinklers activate correctly or not independently can be found by:
(A) If the probability if all the sprinklers will operate correctly in fire is:
P(all 10 sprinklers operate correctly) = (0.7)¹⁰= 0.028247 (rounded to 3 decimal places)
Therefore, the probability that all 10 sprinklers will operate correctly in a fire is approximately 0.028.
(b) The probability that at least 7 of the sprinklers will operate correctly can be calculated using the binomial distribution with n = 10 and p = 0.7:
P(at least 7 sprinklers operate correctly) = P(X >= 7) = 1 - P(X < 7)
where X is the number of sprinklers that operate correctly.
Using a binomial calculator or table, we can find that:
P(X < 7) = 0.0518 (rounded to 4 decimal places)
Therefore:
P(at least 7 sprinklers operate correctly) = 1 - P(X < 7) = 1 - 0.0518 = 0.9482 (rounded to 2 decimal places)
So, the probability that at least 7 of the sprinklers will operate correctly in a fire is approximately 0.95.
(c) We need to find the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98. This is equivalent to finding the smallest value of n such that:
P(at least one sprinkler operates correctly) >= 0.98
Using the complement rule, we can rewrite this as:
P(no sprinkler operates correctly) <= 1 - 0.98 = 0.02
The probability that no sprinkler operates correctly in a fire is:
P(no sprinkler operates correctly) = (0.3)¹⁰
So we need to solve for n in the inequality:
(0.3)ⁿ <= 0.02
Taking the natural logarithm of both sides and using the logarithmic rule for inequalities, we get:
n >=ln(0.02) / ln(0.3) ≈ 6.52
Therefore, we need at least 7 sprinklers to ensure that the probability that at least one operates correctly is at least 0.98.
Therefore, The probability that all 10 sprinklers will operate correctly in a fire is approximately 0.028, probability that at least 7 of the sprinklers will operate correctly in a fire is approximately 0.95 and the probability of at least one sprinkler operating correctly in a fire is at least 0.98, we need to have at least 7 sprinklers in the ballroom.
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Calculator Q15. y is directly proportional to x.
When x = 500, y = 50
b) Calcualte the value of y when x = 60.
If y is directly proportional to x, when x = 60, y = 6.
What is proportional?Proportional refers to a relationship between two quantities in which one quantity is a constant multiple of the other. In other words, if one quantity increases or decreases by a certain factor, the other quantity will also increase or decrease by the same factor.
What is directly proportional?Directly proportional is a specific type of proportionality where two quantities increase or decrease by the same factor. In other words, if one quantity doubles, the other quantity also doubles. If one quantity triples, the other quantity also triples, and so on.
In the given question,
If y is directly proportional to x, we can use the formula:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the given values:
y = kx
50 = k(500)
Solving for k:
k = 50/500
k = 0.1
Now that we know the value of k, we can use the formula to find the value of y when x = 60:
y = kxy = 0.1(60)
y = 6
Therefore, when x = 60, y = 6.
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Match the description with its mathematical expression. Residual from an estimated regression equation Choose the correct answer below. obo Oba o O y o bo +61 oy
We have that, the correct match of the description with its mathematical expression is provided with the mathematical expression "or".
What is the correct expression?Correct matching of the description to its mathematical expression is given as follows: The residual of an estimated regression equation is compared to the mathematical expression "or".
Explanation: A residual is the difference between the actual value of a variable and the predicted value of that variable. The residuals are denoted as "or". Therefore, the Residual of an estimated regression equation is compared to the mathematical expression "or".
Other options are incorrect as follows: Oba does not match any description given in the question. Therefore, it is a wrong option. Obo doesn't match any description given in the question. Therefore, it is a wrong option. Oy+ 61 does not match any description given in the question. Therefore, it is a wrong option.
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Can someone help me out?
The probability of a. rolling an even or 3 is 2/3. b. Rolling an even or a number greater than 2 is 5/6. c. Rolling an odd or a number less than 6 is 5/6. d. Rolling a 2 and a 4 is 0.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. A sample space is made up of all potential results of an experiment. Tossing a coin, for instance, has two possible outcomes: head or tail. An experiment is a trial or procedure carried out to generate a result.
Given that, you roll a single fair 6 sided die.
a. Rolling an even or 3:
P(even or 3) = P(even) + P(3) - P(even and 3)
P(even or 3) = 1/2 + 1/6 - 0
P(even or 3) = 2/3
b. Rolling an even or a number greater than 2:
P(even or >2) = P(even) + P(>2) - P(even and >2)
P(even or >2) = 1/2 + 4/6 - 1/3
P(even or >2) = 5/6
c. Rolling an odd or a number less than 6:
P(odd or <6) = P(odd) + P(<6) - P(odd and <6)
P(odd or <6) = 3/6 + 5/6 - 1/3
P(odd or <6) = 5/6
d. Rolling a 2 and a 4:
P(Rolling a 2 and a 4) = 0.
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use the y-and -x intercept to write the equation of the line y intercept (0,6), x intercept (-2,0)
Answer:
3x -y = -6
Step-by-step explanation:
You want the equation of the line with intercepts (0, 6) and (-2, 0).
Intercept formThe equation of the line with x-intercept 'a' and y-intercept 'b' is ...
x/a +y/b = 1
For the given intercepts, the equation is ...
x/(-2) +y/6 = 1
Standard formIn standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:
3x -y = -6
__
Additional comment
You can get slope-intercept form by solving for y, or you can recognize that ...
slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3
Since you already know the y-intercept, you can write the slope-intercept equation as ...
y = 3x +6
There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.
PLS HELP ME ASAP I WILL MARK THE BRAINLIEST
Answer:
The formula for the nth term of a geometric sequence is given by an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.
In this case, a1 = -8 and r = -2. Therefore, we have:
a2 = a1 * r = (-8) * (-2) = 16
a3 = a2 * r = 16 * (-2) = -32
a4 = a3 * r = (-32) * (-2) = 64
So, the next three terms of the sequence are 16, -32, and 64.
Answer:
a₂ = 16
a₃ = -32
a₄ = 64
Step-by-step explanation:
The general formula for a geometric sequence is:
[tex]a_n=a_1 \cdot r^{n-1}[/tex]
where:
a₁ is the initial term.r is the common ratio.Substitute the given values of a₁ and r into the formula to create an equation for the nth term:
[tex]\implies a_n=(-8) \cdot (-2)^{n-1}[/tex]
To find the values of a₂, a₃ and a₄, substitute n = 2, n = 3 and n = 4 into the equation.
[tex]\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{2-1}\\&=(-8) \cdot (-2)^{1}\\&=(-8) \cdot (-2)\\&=16\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_3&=(-8) \cdot (-2)^{3-1}\\&=(-8) \cdot (-2)^{2}\\&=(-8) \cdot (4)\\&=-32\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{4-1}\\&=(-8) \cdot (-2)^{3}\\&=(-8) \cdot (-8)\\&=64\end{aligned}[/tex]
find the inverse of the function
F(x) = x² + 2x₁ [-1, 00]
The lowest temperature ever recorded on earth was -89.2°C recorded in Antarctica in 1983.How many degrees Fahrenheit was that,to the nearest degree
The lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit.
To convert the temperature of -89.2°C to Fahrenheit, we can use the formula:
[tex]F = (C * 1.8) + 32[/tex]
Substituting:
°F = (-89.2 × 1.8) + 32
°F = -128.56 + 32
°F = -97
Therefore, the lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit. It's important to note that this is just an approximation as we rounded the result to the nearest degree. However, it gives us a good idea of how extremely cold the temperature was. It's worth mentioning that at such low temperatures, it's important to take appropriate precautions to avoid any adverse health effects.
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Subtract the given equation
3x-(4x-11)
Answer:
3x - (4x - 11) = 3x - 4x + 11 = -x + 11
Step-by-step explanation:
Gerard wrote down the sum of squares of two (23?)2 + (1?2)² = 7133029 numbers, as shown. Unfortunately some of the digits cannot be seen because they are covered in ink. What is the last digit of the first number? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
Answer:
We know that (23x)² + (1y)² = 7133029. From the right hand side of the equation, we can see that the last digit of 7133029 is 9. Using this information, we can deduce that the last digit of (23x)² must be 9, because (1y)² can only end in 1, 4, 5, 6 or 9.
Now we know that the last digit of (23x)² is 9 and the last digit of 23x is 3. Therefore the last digit of x is 3.
So, the last digit of the first number is 3. And the answer is (A) 3
andrew is buying a cell phone that has a regular price of $485. the cell phone is on sale for 35% off the regular price. what will be the sale price?
4. Alice is creating a pyramid with toy rectangular-prism-shaped blocks
that measure 1 inch by 2 inches by 2 inches. She places 8 blocks in
the first row. Then she places 6 blocks on top of the first row and 4
blocks on top of the second row. If she continues the pattern until
the top row has 2 blocks, what is the volume of the final pyramid?
The final pyramid has a volume of 16 cubic inches. To find this, first multiply the number of blocks in each row together. 8 blocks in row 1 = 8 x 2 x 2 = 32; 6 blocks in row 2 = 6 x 2 x 2 = 24; 4 blocks in row 3 = 4 x 2 x 2 = 16; and 2 blocks in row 4 = 2 x 2 x 2 = 8. Then add all these numbers together to get 32 + 24 + 16 + 8 = 80. Finally, divide this number by 3 to get the volume, 80/3 = 16.
3/4 divided by 1/3 as a fraction
Answer:
[tex]\frac{9}{4}[/tex]
Step-by-step explanation:
Answer:
[tex]\frac{9}{4}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{3}[/tex]
[tex]\frac{3}{4}[/tex] × [tex]\frac{3}{1}[/tex] = [tex]\frac{9}{4}[/tex] ( to divide we make the other fraction reciprocal)
[tex]\frac{9}{4}[/tex] as mixed fraction= [tex]\frac{1}{4}{2}[/tex]
GEOMETRY
determine whether each pair of triangles is similar. give details about each set of sides or angles. give the theory used. write a similarity statement.
The triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.
What is the Angle Side Angle Congruence Theorem?The Angle-Side-Angle (ASA) Congruence Theorem is a postulate in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.
Triangle YXZ is formed from a reflection and then a dilation of the triangle WVZ, then the relations between the angles are given as follows:
m < W = m < Z.m < V = m < Y.The side lengths WV and YZ, which are the side lengths between these two angles, form a proportional relationship, hence the triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.
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Transversals of Parallel lines: corresponding angles
The required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.
What are corresponding angles?In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.
In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.
Angles that are equal in size and are found on the same side as the transversal line are called corresponding angles.
Either both are acute or both are obtuse.
By creating an F shape, we can typically identify comparable angles.
So, now after reading the description we know exactly what are corresponding angles.
Now, we can easily tell that the pair of corresponding is:
∠HIK and ∠EFI
Therefore, the required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.
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Match each integer with one that divides it.
18
matches
Choice
9
-14
matches
Choice
7
11
matches
Choice
11
65
matches
Choice
13
Integers are a type of number used in mathematics that represent whole numbers. They are typically denoted by the symbol Z, and can be positive, negative, or zero.
Integers do not include fractions or decimal points, so they are distinct from real numbers.
In Mathematics, integers are the collection of whole numbers and negative numbers.
18 matches 9
-14 matches 7
11 matches - 65
13 matches 65
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b) There are x number of books that worth Rs. 35 each and 5 books worth Rs. 30 each in a parcel prepared as a gift. The value of two such parcels is Rs. 580. i. Build up an equation using the above information. ii. Find the value of x by solving the equation.
Answer:
Equation: 2(357+30×5) = 580
x=4
Step-by-step explanation:
In one package, there is such a relationship:
357+30X5 = y
(Y is the price of a package)
The price of two parcels is 580:
then. 24=580
y= 290
x=4, so: equation: 2(35x+150) =580
Step-by-step explanation:
A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount each book would have cost Rs. 1 less. How many books did he buy?
A
8
B
16
Correct Answer
C
24
D
28
Medium
Open in App
Updated on : 2022-09-05
Solution

Verified by Toppr
Correct option is B)
Let the shopkeeper buy x number of books.
According to the given condition cost of x books =Rs80
Therefore cost of each book =x80
Again when he had brought 4 more books
Then total books in this case =x+4
So cost of each book in this case =x+480
According to Question,
x80−x+480=1
x(x+4)80(x+4)−80x=1
x2+20x−16x−320=0
(x−16)(x+20)=0
x=16orx=−20
Hence the shopkeeper brought 16 books
The probability density function of X, the lifetime of a certain type of device (measured in months) is given by f(x) = 0 if x < 2121/x^2 if x > 21 f(x) Find the following: P(X > 48) = The cumulative distribution function of X: f(x)= if x < 21if x > 21 The probability that at least one out of 7 devices of this type will function for at least 44 months:
The probability that at least one out of 7 devices of this type will function for at least 44 months is 1 - 0.9779167, or 0.0220833.
The probability density function of X, the lifetime of a certain type of device, is given by [tex]f(x) = 0 if x < 21; 1/x^2 if x > 21.[/tex]To find the probability that X > 48
we can use the cumulative distribution function of[tex]X: f(x) = 0 if x < 21; 1 - 1/x^2 if x > 21[/tex]. Therefore, the probability that[tex]X > 48[/tex] is 1 - 1/48^2, or 0.9609375.To find the probability that at least one out of 7 devices of this type will function for at least 44 months
we can use the binomial distribution formula.
The probability is given by [tex]P(X ≥ 1) = 1 - P(X = 0)[/tex]. Using the cumulative distribution function.
The probability that X = 0 is given by [tex]1 - 1/44^2, or 0.9779167.[/tex]
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Difference between 6z and z to the power of 6
Answer:
[tex]6z \: = 6 + z \: \\ z {}^{6} = z \times z \times z \times z \times z \times z \\ [/tex]
The mathematical statement in the form of expression can be written as 15625z⁶.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is to find the mathematical statement -
"Difference between 6z and z to the power of 6"
We can write the given mathematical statement in the form of expression as -
(6z - z)⁶
(5z)⁶
5⁶ x z⁶
125 x 125 x z⁶
15625z⁶
Therefore, the mathematical statement in the form of expression can be written as 15625z⁶.
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in a school of hundred students, 40 are in the hockey team and 70 are in the football team.
Each student is in at least one team. Find the number of students who are in both teams.
Answer: There are 10 students who are in both the hockey and football teams.
Step-by-step explanation: We can use the principle of inclusion-exclusion to find the number of students who are in both the hockey and football teams.
The total number of students in both teams is the sum of the number of students in the hockey team and the number of students in the football team, minus the number of students who are in both teams (to avoid double-counting):
Total = Hockey + Football - Both
Substituting the given values, we get:
100 = 40 + 70 - Both
Simplifying, we get:
Both = 40 + 70 - 100
Both = 10
Therefore, there are 10 students who are in both the hockey and football teams.
Una pelota es lanzada horizontalmente desde la azotea de un edificio de 54 m de altura y Llega al suelo a 32 m de la base. Cuál fue la rapidez inicial de la pelota?
The initial speed of a ball thrown horizontally from the roof of a building at a height of 54 m and hitting the ground at a height of 32 m from the bottom is equal to 9.64 m/sec.
A ball throws horizontally from the roof of a building. This is where we have to take horizontal movement into account.
Height of building = 54 m
Height of ground from base = 32 m Calculates the initial speed of the ball.
Since the ball is thrown horizontally, its initial velocity has no vertical component. When released, the ball is subject to gravity and accelerates downward until it hits the bottom. To determine how long the ball stayed in the air before hitting the ground, use the following formula,
d = 1/2×g×t²
where g --> acceleration due to gravity
t --> time
d --> the distance covered by ball before hitting the ground, g= 9.81 m/s².
So, 54 m = (1/2) × 9,81 m/s² × t²
=> t² = 54/4.90
=> t² = 540/49
=> t² = 11.02 sec²
=> t = 3.31963 ~ 3.32 sec
So the ball will stay in the air for about 3.32 seconds. Let v₀ₓ be the horizontal component of the initial velocity. According to the information of the problem, the ball landed 32 m from the bottom of the building. Let's make the initial position x₀ = 0. Then, the final horizontal displacement of a ball will be equals to 32 metres. Using the distance velocity relation, x = x₀ + v₀ₓt and substituting all known values in it,
=> 32 m = 0 + v₀ₓ × 3.32 sec
=> v₀ₓ = 32/3.32
=> v₀ₓ = 9.6385 ≈ 9.64 m/sec
Hence, required value is 9.64 m/sec.
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Complete question:
A ball is thrown horizontally from the roof of a building 54 m high and hits the ground 32 m from the base. What was the initial speed of the ball?
A baseball is thrown straight upwards from the ground and undergoes a free fall motion as it rises towards its highest point. What changes, if any, would be observed of the velocity and the acceleration of the baseball as it rises towards its highest point? Pick two answers.
The velocity increases.
The velocity decreases.
The velocity remains a constant value.
The acceleration increases.
The acceleration decreases.
The acceleration remains a constant value
The baseball thrown upwards will experience a change in its velocity while its acceleration will be constant.
A type of motion known as upward motion involves an item moving up against the pull of gravity.
The opposing force of gravity causes an object to go upward with a decreasing vertical velocity as it does so. When the item reaches its maximum height, its velocity ultimately zeroes out. The velocity starts to rise as the object starts to descend and eventually reaches its highest point just before impact with the ground.
The object's acceleration during its upward motion is constant and always points downward. Hence, it follows that an item moving upwards will experience a change in velocity but not in acceleration.
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why is the probability that a continuous random variable is equal to a single number zero? (i.e. why is P(X=a)=0 for any number a)
The probability that a continuous random variable takes on a single specific value is zero because the continuous random variable can take on any value within a range or interval, and there are an infinite number of values that it can take on within that interval.
The probability that a continuous random variable is equal to a single number is zero. The explanation is that a continuous random variable has an infinite number of possible values. As a result, the probability of any single value, including the one you're interested in, is always 0.
To put it another way, it's almost impossible for a continuous random variable to equal a specific value. Consider the following example:
Suppose you're attempting to hit a target on a wall. If the target is the size of a pinpoint, the probability of striking it is virtually zero. In the same way, with continuous random variables, the probability of landing on a single point is practically zero because there are an infinite number of possible outcomes. As a result, the probability of any one of them occurring is tiny.
A continuous random variable may be defined over any interval of real numbers, which is one of its distinguishing features. The amount of time it takes to finish a marathon, the height of a randomly chosen person in a group, and the length of a telephone conversation are all examples of continuous random variables.
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in the same distribution (mean is 70 and the standard deviation is 8. at least what fraction are between the following pairs
At least 68% of the data falls between 62 and 78, and at least 95% of the data falls between 54 and 86.
How to find the minimum fraction of the data?To answer this question, we can use the empirical rule, also known as the 68-95-99.7 rule, which tells us that for a normal distribution:
About 68% of the data falls within one standard deviation of the meanAbout 95% of the data falls within two standard deviations of the meanAbout 99.7% of the data falls within three standard deviations of the meanUsing this rule, we can estimate the fraction of the data that falls between the following pairs:
Between 54 and 86:
To find the range of values that is within two standard deviations of the mean, we can subtract and add two standard deviations from the mean:
Lower bound: 70 - 2*8 = 54
Upper bound: 70 + 2*8 = 86
So, about 95% of the data falls between 54 and 86.
Between 62 and 78:
To find the range of values that is within one standard deviation of the mean, we can subtract and add one standard deviation from the mean:
Lower bound: 70 - 8 = 62
Upper bound: 70 + 8 = 78
So, about 68% of the data falls between 62 and 78.
Therefore, we can conclude that at least 68% of the data falls between 62 and 78, and at least 95% of the data falls between 54 and 86.
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A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the
function S=18.95 +0.60 M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I=4.90 +0.25 M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
C =
Hi. The terms of the standard charge and insurance charge equations are a little garbled, but it is possible to think that these are the right equations:
Standard charge, S = 18.95 + 0.60M, where 18.95 is the initial fee and 0.60 is the charge for each mile driven.
Insurance charge, I = 4.90 + 0.25M, where 4.90 also represents an initial fee and 0.25 a charge for each mile driven.
Then, the total cos, C = S + I =>
C = (18.95 + 0.60M) + (4.90 + 0.25M) which you can rearrange to show the like terms one next to each other =>
C = (18.95 + 4.90) + (0.60M + 0.25M), now add up the like terms=>
C = 23.85 + 0.85M which is the equation is the most simplified form
Answer: C = 23.85 + 0.85M