a. The mean of X is 1.7549 and the standard deviation is 0.3536.
b. To calculate the proportion of washing machines that will last for more than 15 years, we need to use the standard normal distribution table. The z-score for 15 years is (15-14)/0.3536 = 2.822. Using the table, we find that the proportion of washing machines that will last for more than 15 years is 0.9968.
c. To calculate the proportion of washing machines that will last for less than 10 years, we need to use the standard normal distribution table. The z-score for 10 years is (10-14)/0.3536 = -2.822. Using the table, we find that the proportion of washing machines that will last for less than 10 years is 0.0032.
d. To calculate the 90th percentile of the life of the washing machines, we need to use the standard normal distribution table. The z-score for the 90th percentile is 1.28. Using the table, we find that the 90th percentile is 17 years.
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If a certain apple tree grew 2 feet and then tripled its height, it would become 4 feet
shorter than the pine tree that grows on the other end of the street. Which
of the formulas below describes the relation between the height of the apple tree a
and the height of the pine tree p?
A) P-4=3a+2
B) P=2(a+3)+4
C) P=3(a+2)-4
D) P=3a+10
Answer:
Step-by-step explanation:
C.) P = 3(a+2)-4
The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Growth of apple tree= 2feet
Now,
Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:
3(h+2) - 4 = p
Simplifying, we get:
3h + 2 = p
Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.
Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:
P = 3a + 6
This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:
P = 2a + 10
This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:
P = 3a + 2
Therefore, by equation the answer will be P=3(a+2)-4.
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Write 735 as the product of its prime factor.
Answer:
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
Step-by-step explanation:
[tex]735 = 7 \times 105[/tex]
[tex]735 = 7 \times 3 \times 35[/tex]
[tex]735 = 7 \times 3 \times 5 \times 7[/tex]
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
Determine wheter the given vale of the varible is a soultion of the equatiom1/3 h=6 h=2
No, the given value of h=2 is not a solution of the equation 1/3h=6.
Write the first four terms of the sequence defined by a n = 5
{5, if n=1
a n -1 -5, if n>1
Answer:
The sequence is defined as follows:
a1 = 5
an = an-1 - 5, for n > 1
Using this definition, we can find the first four terms of the sequence as follows:
a1 = 5
a2 = a1 - 5 = 5 - 5 = 0
a3 = a2 - 5 = 0 - 5 = -5
a4 = a3 - 5 = -5 - 5 = -10
Therefore, the first four terms of the sequence are: 5, 0, -5, -10.
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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In order to make the same amount of money, they would have to each sell ______ bicycles. They would both make $______.
In order to make the same amount of money, they would have to each sell 5 bicycles. They would both make $500
How many bicycle would they sell to make the same amount of money?To find the number of bicycles they would need to sell to make the same amount of money,
We can set Jim's and Tom's weekly earnings equal to each other and solve for the number of bicycles:
250 + 50x = 400 + 20x
30x = 150
x = 5
So they would need to sell 5 bicycles to make the same amount of money.
How much would they make for selling that amountTo find out how much money they would make for selling 5 bicycles, we can substitute x = 5 into either equation.
Let's use Jim's equation:
250 + 50(5) = 500
So they would make $500 for selling 5 bicycles.
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Xavier buys a dog collar that costs $6.79. He pays for the dog collar
with a $10 bill.
How much change does Xavier receive?
Answer: Xavier will receive $3.21 in change.
Step-by-step explanation:
To find the change Xavier receives, we need to subtract the cost of the dog collar from the amount he paid with his $10 bill:
Change = $10 - $6.79 = $3.21
Therefore, Xavier will receive $3.21 in change.
A car travelling at a constant speed travels 60 km 30 minutes .how far will it travel in 2hrs,if it continues at the same constant speed
Answer: 240 miles in 2 hours
Step-by-step explanation:
we know the car is traveling 60 km per half hour (30 minutes)
so to find km per hour, multiply both by 2.
the rate of speed is 120 miles per 60 minutes (1 hour)
multiply 120 mph by the 2 hours given = 240 miles in 2 hours
Answer:
240 km in 2 hours
Step-by-step explanation:
If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:
Speed = distance ÷ time
Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour
Since the car is traveling at a constant speed, we can use the formula:
Distance = Speed × Time
To find how far the car will travel in 2 hours, we can substitute the values we have found:
Distance = Speed × Time
Distance = 120 km/hour × 2 hours
Distance = 240 km
Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.
Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
HELP DUE TODAY!!!!!!!!!
. Write the (x, y) coordinates for P in terms of cosine and sin.
6. Using the image above, if cos(Θ) = 0.6, what are the coordinates of P? Explain your reasoning.
Explanation:
Use the pythagorean trig identity to determine sine based on cos(theta) = 0.6
[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\sin^2(\theta)=1-\cos^2(\theta)\\\\\sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}\\\\\sin(\theta)=-\sqrt{1-\cos^2(\theta)} \ \ \text{....sine is negative in quadrant Q4}\\\\\sin(\theta)=-\sqrt{1-(0.6)^2}\\\\\sin(\theta)=-\sqrt{1-0.36}\\\\\sin(\theta)=-\sqrt{0.64}\\\\\sin(\theta)=-0.8\\\\[/tex]
Since [tex]\cos(\theta)=0.6 \text{ and } \sin(\theta)=-0.8[/tex], the location of point P is (0.6, -0.8)
Recall that for any point (x,y) on the unit circle, we have:
[tex]\text{x}=\cos(\theta)\\\\\text{y}=\sin(\theta)[/tex]
meaning cosine is listed first in any (x,y) pairing.
A surfboard is in the shape of a rectangle and semicircle. The perimeter is to be 4m. Find the maximum area of the surfboard correct to 2 places.
The maximum area of the surfboard correct to 2 places is 0.67 m².
Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.
Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)
Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)
We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)
Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.
To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),
we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.
Area of surfboard =
[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]
[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]
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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
Work out the fraction and ratio that
complete the equations below.
Give each answer in its simplest form.
a) h:k=5:6
h =
k
b) 2x=9y
x:y
=
:
The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.
What is the fraction and ratio that complete the equations?h : k = 5 : 6
h/k = 5/6
cross product
h × 6 = k × 5
6h = 5k
divide both sides by 6
h = 5/6k
Then,
2x = 9y
2/9 = x/y
2 : 9 = x : y
Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.
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how does the graph of the function g(x) = 2x – 3 differ from the graph of f(x) = 2x?
Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)
A simplified carbon cycle with aerobic and anaerobic processes is depicted here. Although much of the emphasis on global climate change has been on increasing carbon dioxide levels, methane is also a greenhouse gas whose levels are increasing due to human and other activity. Which of these actions would increase methane levels in the atmosphere and potentially affect global climate change? Select ALL that apply.
--------------------------------------------------------------------------------------------------------------------------------
A Agricultural practices in rice cultivation releases methane.Agricultural practices in rice cultivation releases methane.
B Anaerobic digestion of cellulose by cows produces methane.Anaerobic digestion of cellulose by cows produces methane.
C Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.
D Industrial combustion of fossil fuels releases methane into the atmosphere.Industrial combustion of fossil fuels releases methane into the atmosphere.
E Anaerobic decomposition of landfill material releases methane into the atmosphere.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
what is equation ?A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.
given
A) Rice farming operations release methane into the atmosphere.
B) Methane is created when cows break down cellulose anaerobically.
E) Methane is released into the atmosphere when landfill material decomposes anaerobically.
Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.
Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.
It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
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A triangle has two sides of length 3 and 16. What is the largest possible whole-number length for the third side
The largest possible whole-number length for the third side is 18, which satisfies all three inequalities.
What is inequality theorem?The triangle inequality theorem explains the relationship between the three sides of a triangle. This theorem states that for any triangle, the sum of the lengths of the first two sides is always larger than the length of the third side.
According to question:Let x be the length of the third side. By the triangle inequality, we have:
3 + 16 > x and 16 + x > 3 and 3 + x > 16
Simplifying, we get:
19 > x and x > 13 and x < 19
The largest possible whole-number length for the third side is 18, which satisfies all three inequalities.
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the product of 2 rational numbers is 16/3.If one of the rational number is -26/3,find the other rational number
Answer:
- [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
let n be the other rational number , then
- [tex]\frac{26}{3}[/tex] n = [tex]\frac{16}{3}[/tex]
[a number × its reciprocal = 1 ]
multiply both sides by the reciprocal - [tex]\frac{3}{26}[/tex]
n = [tex]\frac{16}{3}[/tex] × - [tex]\frac{3}{26}[/tex] ( cancel the 3 on numerator/ denominator )
n = - [tex]\frac{16}{26}[/tex] = - [tex]\frac{8}{13}[/tex]
For each growth rate, find the associated growth factor.
1. 30% increase
2. 30% decrease
3. 2% increase
4. 2% decrease
5. 0.04% increase
6. 0.04% decrease
7. 100% increase
Answer:
The associated growth factor for a 30% increase is 1 + 0.30 = 1.30.
The associated growth factor for a 30% decrease is 1 - 0.30 = 0.70.
The associated growth factor for a 2% increase is 1 + 0.02 = 1.02.
The associated growth factor for a 2% decrease is 1 - 0.02 = 0.98.
The associated growth factor for a 0.04% increase is 1 + 0.0004 = 1.0004.
The associated growth factor for a 0.04% decrease is 1 - 0.0004 = 0.9996.
The associated growth factor for a 100% increase is 1 + 1 = 2.
Step-by-step explanation:
A growth factor is a multiplier that represents the amount by which a quantity changes as a result of a growth rate or percentage change. It is calculated by adding 1 to the decimal form of the growth rate. For example, if the growth rate is 30%, the decimal form is 0.30, and the growth factor is 1 + 0.30 = 1.30.
In case of a decrease, the growth factor is calculated by subtracting the decimal form of the decrease rate from 1. For example, if the decrease rate is 30%, the decimal form is 0.30, and the growth factor is 1 - 0.30 = 0.70.
In cases where the growth rate is a small percentage, it is important to convert it into a decimal by dividing the percentage by 100 before calculating the growth factor.
In the case of a 100% increase, the quantity doubles, so the growth factor is 2 (i.e., 1 + 1).
BRAINLY AND 20 POINTS IF ANSWERED!!!!!! roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds
[ ] meters per second
1.4m/s is the rate that Roberto is walking. We know the formula for calculating the time i.e. t= d/r.
The term "distance" refers to how far we move. The rate is a measurement of our trip speed. Time is measured by how far we travel. The distance an object will travel over time and at a specific average rate is the subject of rate problems.
Given,
Distance = D
D= 1.4t
Rate= ?
Substituting the given values in the formula t= d/r
where,
t= time in seconds
d= distance
r= rate
We get,
t= 1.4t/r
t/1.4t= 1/r
t gets cancelled
so we have,
1/1.4= 1/r
r= 1.4m/s
Therefore, 1.4m/s is the rate at which Roberto is walking.
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The complete question is as follows:
Roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds.
What is the rate that Roberto's walking in meters per second?
Jayden evaluated the expression a + (2 + 1. 5) for a = 14. He said that the value of the expression was 8. 5. Select all the statements that are true. Jayden's solution is incorrect. Jayden added inside the parentheses before dividing. Jayden substituted the wrong value for a. Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.
It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
1) The correct solution is
Given,
a ÷ (2 + 1. 5)
Substituting the value of a which is 14
= 14 ÷ (2 + 1. 5)
= 14 ÷ 3.5
= 4
2) As there is no term which needs to be divided so, the second statement is false.
3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.
4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
i.e. a ÷ (2 + 1. 5)
14 ÷ 2 + 1. 5
7+1.5
8.5
This is the way Jayden solved the equation due to which he arrived at the wrong solution.
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The Correct question is as below
Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.
1. Jayden's solution is incorrect.
2. Jayden added in the parentheses before dividing.
3. Jayden substituted the wrong value for a.
4. Jayden divided 14 by 2 and added 1.5
some rate functions require algebraic manipulation or simplification to set the stage for undoing the chain rule or other antiderivative techniques. find an equivalent closed form for each function.a. S π / π /4 5t+4 / t² + 1 dtHint : begin by writing as a sum of two functions ____ previewb. S π/t 4tan (t) dt Hint : begin by using a trig identity to change the form of the rate function___ preview
the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)
Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt
Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C
a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt
Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.
Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,
we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:
S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)
dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change
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If n(Ax B) = 72 and n(A) = 24, find n(B).
Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.
What is Cartesian product?The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.
In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.
For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.
By the question.
We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.
Using the formula for the size of the Cartesian product, we have:
n (Ax B) = n(A) x n(B)
Substituting the given values, we get: 72 = 24 x n(B)
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Write an equation for the line on a graph below.
Check the picture below.
Answer:
x=-3
Step-by-step explanation:
Pablo needs to memorize words on a vocabulary list for Latin class he has 12 words to memorize and he is 3/4 done how many words has Pablo memorized so far
Answer:
9 words
Step-by-step explanation:
We know
He has 12 words to memorize, and he is 3/4 done.
How many words has Pablo memorized so far?
We Take
12 x 3/4 = 9 words
So, Pable has memorized 9 words.
Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) P(Z < 0.79) = Х 5 ? (b) P(Z > 0.75) (c) P(-1.06 < Z< 2.17) =
The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).
The probability of Z > 0.75 is 1 - 0.77337 = 0.22663
The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968
Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).
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An amount of money is divided among A, B and C in the ratio 4: 7:9 A receives R500 less than C. Calculate the amount that is divided.
Answer:
We know that A receives R500 less than C, so we can write:
4x = 9x - 500
Solving for x, we get:
5x = 500
x = 100
Now we can calculate the amounts received by each person:
A = 4x = 4(100) = R400
B = 7x = 7(100) = R700
C = 9x = 9(100) = R900
To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:
A:B = 400:700 = 4:7
B:C = 700:900 = 7:9
Therefore, the total amount divided is:
400 + 700 + 900 = R2000
So the amount that is divided is R2000.
Step-by-step explanation:
The total amount of money divided is R2000.
What is the ratio?Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
The ratio of A, B and C= 4:7:9
Now,
Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:
4x + 500 = C's share
We can also write an equation to represent the fact that the three shares add up to the total amount:
4x + 7x + 9x = T
Simplifying this equation, we get:
20x = T
Now we can substitute the first equation into the second equation and solve for x:
4x + 7x + (4x + 500) = 20x
15x + 500 = 20x
500 = 5x
x = 100
Now we can find the individual shares by multiplying x by the appropriate ratio factor:
A's share = 4x = 400
B's share = 7x = 700
C's share = 9x = 900
Finally, we can check that these add up to the total amount:
400 + 700 + 900 = 2000
Therefore, by the given ratio the answer will be R2000.
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Aamena buys a business costing $23000
She pays part of this cost with $12000 of her own money
Calculate what percentage of the $23000 this is
Show your calculations
Answer:
52.17%
Step-by-step explanation
[tex]\frac{12000}{23000}[/tex] ×100%
[tex]\frac{1200}{23}[/tex]
52.17
The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function F(x)= {1−kx^−3 for x>44000 {0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. a)Find the constant k here and provide its natural logarithm to three decimal places. b)Calculate the mean salary given by the model.
a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.
b) The mean salary of the given model by using the probability density function is approximately $270.86.
a) The cumulative distribution function of the given random variable is provided as follows:
F(x) = {1−kx^−3 if x>44000, and 0 otherwise
The cumulative distribution function is given as
F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)
We need to check the value of the cumulative distribution function at 44000
We have, F(44000) = 0
0 = 1−k(44000)^−3
⇒ 1 = k(44000)^−3
⇒ k = 1/(44000)^−3
⇒ 5.427 x 10^−12
Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)
Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68
b) The probability density function is given as,
f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise
The mean or expected value of the random variable is given as
E(X) = ∫[−∞,∞]xf(x)dx
= ∫[44000,∞]x(3kx^−4)dx
= 3k∫[44000,∞]x^−3dx
= 3k[(−1/2)x^−2] [∞,44000]
= (3k/2)(44000)^−2
= 270.86 (approx.)
Therefore, the mean salary given by the model is $270.86 (approx.)
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Question 4(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Order √50,-7.1.3-7 from least to greatest.
0 -7.1.-7. √50,23
O
0-71.-7.7.23,√50
O
0 -7.1.-723√50
0-7-7.1,√50,23
Answer:
D
Step-by-step explanation:
The square root of 50 is approximately equal to 7.07
-7.1111… can be rounded to -7.11
23/3 is equal to approximately 7.67
-7 1/5 is equal to -7.2
please help me with this savvas question!
Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:
">" which means "greater than"
"<" which means "less than"
"≥" which means "greater than or equal to"
"≤" which means "less than or equal to"
Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.
Here,
The formula for the circumference of a circle in terms of its diameter is:
C = πd
where π (pi) is approximately 3.14.
We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:
9.9 ≤ 3.14d ≤ 10.2
Dividing all sides of the inequality by 3.14, we obtain:
3.15 ≤ d ≤ 3.24
Rounding to three decimal places, the corresponding interval for the diameters of the washers is:
3.150 ≤ d ≤ 3.240
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