From the given information provided, the probability of P(X ≤ 6), P(X˃ 4) and P(|X- 5| ˃ 1) is 0.6915, 0.6915 and 0.3829 respectively.
(i) To find P(X ≤ 6), we need to standardize the value of 6 using the formula:
Z = (X - μ) / σ
where μ = 5 and σ = 2 (since the standard deviation is the square root of the variance, which is 4).
So, we have:
Z = (6 - 5) / 2
Z = 0.5
We can then look up the probability of Z ≤ 0.5 in a standard normal distribution table, or use a calculator to find:
P(X ≤ 6) = P(Z ≤ 0.5) = 0.6915
(ii) To find P(X > 4), we again need to standardize the value of 4:
Z = (4 - 5) / 2
Z = -0.5
Then, we can use the fact that the total area under a normal distribution curve is 1 to find the probability of X being greater than 4:
P(X > 4) = 1 - P(X ≤ 4) = 1 - P(Z ≤ -0.5)
Using a standard normal distribution table:
P(X > 4) = 0.6915
(iii) To find P(|X - 5| > 1), we first need to transform this inequality into a standard normal distribution by standardizing both sides:
|X - 5| > 1
implies:
X - 5 > 1 or
X - 5 < -1
which gives:
X > 6 or X < 4
We can then standardize each inequality separately. For X > 6, we have:
Z = (6 - 5) / 2
Z = 0.5
and for X < 4, we have:
Z = (4 - 5) / 2 = -0.5
Then, using the fact that the total area under a normal distribution curve is 1, we can find the probability of both events occurring:
P(|X - 5| > 1) = P(X > 6 or X < 4) = P(Z > 0.5 or Z < -0.5)
Since the standard normal distribution is symmetric around 0:
P(Z > 0.5 or Z < -0.5) = 2 × P(Z < -0.5)
Using a standard normal distribution table:
P(|X - 5| > 1) = 0.3829
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OFERING BRAINLIEST! Step by step explanation please!
Answer:
600ft²
Step-by-step explanation:
Volume of a cube V = a³
a³ = 1000
Cube root of both sides
a = 10ft
Surface area A =6a²
A = 6 x 10 x10 ft²
Answer:
600 feet²
Step-by-step explanation:
1) Break down the info
To answer this question we have to figure out the values of the sides. As it is a cube all sides should have the same area and length!
We know that the equation for volume is...
volume = area of cross-section x heightThis means that to simply find the sides, we can cube root 1000
[tex]\sqrt[3]{1000}[/tex] = 10Let's check...
10 x 10 x 10 = 10002) Find the surface area
We now know that the sides are 10 feet each so to find the surface area is [tex]6a^2[/tex] where a is the length of one side!
We can solve the question by plugging our numbers into the equation...
[tex]6[/tex] × [tex]10^{2}[/tex] = [tex]600[/tex]Our surface area is 600 feet!
Hope this helps, have a lovely day! :)
Nick hiked 10 miles up a hill. He is 8 miles east from his starting point. To the nearest degree, at what angle was the incline of the hill?
To the nearest degree, the angle of the incline was approximately 39°.
What is an angle?
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
We can use the inverse tangent function to calculate the angle of the incline. The angle θ is given by:
θ = tan⁻¹(opposite/adjacent)
where opposite is the vertical distance (the height Nick hiked) and adjacent is the horizontal distance (the distance he traveled eastward).
Using the Pythagorean theorem, we can find the height Nick hiked:
height = [tex]\sqrt{(10)^{2} - (8)^2}[/tex]≈ 6
So, the opposite is approximately 6 miles.
Now we can plug in the values to find the angle:
θ = tan⁻¹(6/8)
θ ≈ 38.66°
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A rectangular prism has a height of 1 inch, a width of of an inch, and a 2 1volume of of a cubic inch. What is the length, in inches, of this prism?
The length of the rectangular prism is 1 inch.
The volume of a rectangular prism can be calculated using the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, the volume of the prism is given as 1 cubic inch and the width and height are given as 1 inch and 1 inch, respectively. To solve for the length of the prism, we can rearrange the equation to l = V/wh. Plugging in our given values, we can calculate the length of the prism as l = 1/1 x 1 = 1 inch. Thus, the length of the rectangular prism is 1 inch.Therefore, the length of the rectangular prism is 1 inch.
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mike has these marks on his report card ; english =82% , french=75% , history =78% , science=80% what mark will he need in math if he wants to earn a mean mark of 80% across all these subjects ?is it possible for him to earn a mean mark of 85%
Mike cannot attain a mean grade of 85% for every one of his studies since a grade higher than 100% is not feasible.
What does the math mean?The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from of the median) of a dataset. This central tendency is usually referred to as the "average".
How can you calculate the mean?Just dividing the total amount of information in a data collection even by sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table can be used for the computation.
mean = (sum of all numbers) / (number of numbers)
80% = (82% + 75% + 78% + 80% + m) / 5
85% = m
The another equation is,
85% = (82% + 75% + 78% + 80% + m) / 5
425% = 315% + m
110% = m
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**PLEASE SOMEONE ANSWER IM STRUGGLING** To the nearest hundredth, what is the value x ?
Answer:
A answer that is not yet known.
Step-by-step
For example x is to sub in 21 but you do not know that yet
until you solve the question.
ACTIVITY (EXPERIMENTAL PROBABILITY) 50 trials
The dice i roll: 2, 3, 4, 4, 4, 4, 6, 5, 2, 4, 2
What is the probability of rolling a sum of even number?
What is the probability of rolling a sum of odd number?
What is the probability of rolling a sum of greater than 5?
This is for statistics ok? Ty!U,,w,,U♡
And please answer now thank you!:D
Answer:
1st=3/50
2nd=2/50
3rd=1/50
thats is if the only possible number you can roll are only from 2,6 not 1,6
To approach the runway, a pilot of a small plane must begin a 7 degrees descent starting from a height of 1069 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?
The airplane is approximately 1.7 miles from the runway at the start of the approach.
What is trigonometry?
Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry
To solve this problem, we need to use trigonometry. The angle of descent is 7 degrees, which means that the angle between the horizontal ground and the plane's flight path is 7 degrees. We can use the tangent function to find the distance from the runway:
tangent (7 degrees) = opposite / adjacent
The opposite side is the height of the plane above the ground, which is 1069 feet. The adjacent side is the distance from the plane to the runway, which we need to find.
tangent (7 degrees) = 1069 / adjacent
We can solve for the adjacent side by multiplying both sides by the denominator:
adjacent = 1069 / tangent(7 degrees)
Using a calculator, we get:
adjacent = 1069 / 0.122173048
adjacent = 8743.3 feet
To convert this to miles, we divide by the number of feet in a mile:
adjacent = 8743.3 / 5280
adjacent = 1.655 miles
Rounding to the nearest tenth of a mile, we get:
The airplane is approximately 1.7 miles from the runway at the start of the approach.
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Let S = {-4, 0, 2, 3}. A new sequence of numbers is formed by repeating the numbers in S, IN ORDER from lowest to highest, until 80 numbers have been listed in the new sequence, i. E. , NEW_SEQUENCE = {-4, 0, 2, 3, -4, 0, 2, 3,. }. What is the sum of the first 31 terms in the new sequence?
The sum of the first 31 terms in the new sequence is 5.
Let S = {-4, 0, 2, 3}
New Sequence = {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............}
The four terms are repeatedly separated, as we can see above. Below are some of the first four terms = -4 + 0 + 2 + 3 = 1
Now, first four terms sum = 1
Next four terms sum = 1.
So sum of first 28 terms is given as
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
Now we find sum of first 31 terms = 7 - 4 + 0 + 2 = 5
So, sum of first 31 terms of new sequence {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............} is 5.
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A concrete sidewalk is being put around a square park. If the diagonal line across the center of a square park is 24 feet, what is the exact length of each side?
In a case whereby concrete sidewalk is being put around a square park. If the diagonal line across the center of a square park is 24 feet, the exact length of each side is 12 feet.
How can the exact length of each side be known?Based on the given condition from the question, We know that A diagonal is a line segment that joins two opposing polygonal vertices (or corners). In other terms, a diagonal is a line segment that joins two polygonal vertices that are not next to one another. One type of straight line is the diagonal. There is no straight up, down, or across in a diagonal line. It is a line that joins two shape's corners.
Then we can formulate as 24/2
= 12 feet.
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One side of a rectangle is three yards longer than twice the length of
If the perimeter is 27 yards, then the length of the other side of the rectangle is 3.5 yards.
Let's start by defining our variables. Let x be the length of one side of the rectangle (in yards), and let y be the length of the other side. We know from the problem statement that one side is three yards longer than twice the length of the other side, so we can express this algebraically as:
x = 2y + 3
The perimeter of a rectangle is given by the formula P = 2(x + y), so we can substitute our expression for x into this formula:
P = 2(2y + 3 + y) = 2(3y + 3) = 6y + 6
We are given that the perimeter of the rectangle is 27 yards, so we can set up an equation:
6y + 6 = 27
Solving for y, we can subtract 6 from both sides and then divide by 6:
6y = 21
y = 3.5
To check our answer, we can plug it back into our equation for x:
x = 2y + 3 = 2(3.5) + 3 = 7 + 3 = 10
So the other side of the rectangle is 10 yards long. We can verify that the perimeter is indeed 27 yards:
P = 2(x + y) = 2(10 + 3.5) = 2(13.5) = 27
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Complete question is:
One side of a rectangle is three yards longer than twice the length of the other side. If the perimeter is 27 yards, what is the length of the other side?
Mr. champion storage container is 4 feet long 3 feet wide and 7 feet tall can fit 88 boxes that each has a volume of 1 ft.³ in his container explain your answer
Answer:
because 7*3*4 is 88 ft^3
A serving of skinny popcorn has 4 grams of fiber. This is about 16% of the recommended daily amount of fiber. How many grams of fiber are in the recommended daily amount?
A serving of skinny popcorn has 4 grams of fiber, which is about 16% of the recommended daily amount of fiber. The recommended daily amount of fiber is 25 grams.
If a serving of skinny popcorn has 4 grams of fibre and provides 16% of the necessary daily fibre intake, we can apply a proportion to calculate the entire recommended daily fibre intake:
If x is the required daily fibre intake in grams, we may calculate the following proportion:
4 / x = 16 / 100
We may cross-multiply and simplify to find x:
4 × 100 = 16 × x
400 = 16x
x = 25
As a result, the daily fibre recommendation is 25 grams.
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hi i don't get this question pls HELP! calculate the monthly repayments for the house loan(total cost divided by number of months) so for example i got my total cost that is 15,393,86 and i divided by the per month which is 12 so basically i did this and here is the answer:
(15,393,86 ÷ 12= 128282.1667) is this correct?
pls correct me and guid me
Yeah, it seems fine so you're doing great so far! ^^
Ruby sold art supplies but it's on her website she bought the art supplies bundles of drawing paper and utensils for $75 each and included 70% markup to get the selling price what's the retail price including the marker for the art supply bundles
The retail price of each art supply bundle, including the markup, would be $127.50.
What is a markup, and how is it calculated?The gross or whole profit on a certain item or service is what is meant by markup. Moreover, it can be shown as a % of the cost price. For instance, if a product costs Rs. 100 and is sold for Rs. 150, the markup in this case will be 50%.
In studying the fundamentals of business, students come across the words selling price and cost price. A commodity's cost price is the amount paid when buying it from a retailer. The selling price, however, is the cost at which it is offered for sale.
Given that, the products were marked them up by 70%, then the selling price would be:
Selling price = $75 + 70% of $75
Selling price = $75 + $52.50
Selling price = $127.50
Therefore, the retail price of each art supply bundle, including the markup, would be $127.50.
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Without graphing, tell whether the slope of a line that models the linear relationship is positive, negative, zero, or undefined. Then find the slope.
A laptop battery has 85% power after 1 hour of use and 40% after after 4 hours of use
Answer:
its a negative slope because the battery is going down, not staying the same, or going up
Step-by-step explanation:
22. At a wedding, guests are given cone-
shaped cups filled with flower petals. The cups
have a radius of 5 centimeters and a height of
10 centimeters. If there are 150 cups, what is
the total volume of petals that all the cones will
hold? Round to the nearest whole number.
Answer:
The volume of one cone-shaped cup can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height. Substituting the given values, we get:
V = (1/3)π(5 cm)^2(10 cm)
V ≈ 261.8 cm^3
Therefore, one cup can hold approximately 261.8 cubic centimeters of flower petals.
To find the total volume of petals that all 150 cups will hold, we can multiply the volume of one cup by the total number of cups:
Total volume = 150 cups × 261.8 cm^3/cup
Total volume ≈ 39,270 cm^3
Rounding to the nearest whole number, we get that the total volume of petals that all the cones will hold is approximately 39,270 cubic centimeters.
Answer:
I forgot how to do this sorry
The cost of 4 chairs is the same as the cost of 3 tables. If the
cost of one chair is Rs. 48, find the cost of one table.
Answer: 64 Rs
Step-by-step explanation:
Let x be the number of tables
4 x 48 = 3x
192 = 3x
x = 64
Factorise. 15(k+g)² - 20 (k+g)
Answer:Factorise. 15(k+g)² - 20 (k+g)
Step-by-step explanation:=[15(k+g)-20] (k+g)
=15 k²+15kg-20k+15kg+15g²-20g
=15k²+15g²+30kg-20k-20g
is this statement true sometimes always or never ??
The statement: If ∠F is a 60° angle, then cos (F) = sin (F), is never true.
What are sine and cosine functions?Two of the six trigonometric functions used to connect angles to the sides of a right triangle are sine and cosine. The length of the opposite side of an angle divided by the length of the hypotenuse of a right triangle is known as the sine function. The length of the adjacent side of an angle divided by the length of the hypotenuse of a right triangle is known as the cosine function.
We know that,
If angle F is 60 degrees, then the value of cos F = 1/2 and sin F = sqrt(3)/2.
Therefore, cos F is not equal to sin F and the statement is never true.
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Determine if 32,48,80and 150 are in proportion
Answer:
No , they are not
Step-by-step explanation:
Checking the ratios:
32/48 = 0.67
48/80 = 0.6
80/150 = 0.53
Since the values are not equal, they are not in proportion.
Answer:
32, 48, 80, and 150 are not in proportion.
Step-by-step explanation:
To determine if 32, 48, 80, and 150 are in proportion, we need to check if the ratio of any two numbers is equal to the ratio of any other two numbers in the set.
Let's check:
Ratio of 32 to 48: 32/48 = 2/3
Ratio of 48 to 80: 48/80 = 3/5
Ratio of 80 to 150: 80/150 = 8/15
Since the ratios are not equal, 32, 48, 80, and 150 are not in proportion.
The lenght of a rectangle is twice its breath. if the perimeter of a rectangle is 60cm, find the dimension of the rectangle.
Answer:
L = 20 , B = 10
Step-by-step explanation:
L = 2B
we know perimeter of rectangle = 2( L + B )
By substitution , 2( 2B+ B) =60
4B + 2B = 60
6B = 60
B= 10
L = 2 * B = 2 * 10 = 20
A city is building a new pool. A scale drawing of the pool is shown below.
Scale,
1 in: 3 ft
What is the area, in square feet, of the pool?
4 in.
A.16n
B.24n
C.48n
D.144n
After answering the provided question, we can conclude that As a result, expression the answer is D. 144n.
what is expression ?In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators. Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.
According to the scale, 1 inch on the drawing equals 3 feet in real life. As a result, the pool's length is 4 inches x 3 feet/inch = 12 feet. Similarly, the pool's width is 4 inches x 3 feet/inch = 12 feet.
As a result, the pool's area equals the length multiplied by the width, which is:
144 square feet = 12 feet x 12 feet.
As a result, the answer is D. 144n.
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where would [-8,-6] be graphed on a coordinate grid
The point [-8,-6] would be graphed 8 units left and 6 units down from the origin (0,0) on a coordinate grid.
What is a coordinate grid?A coordinate grid, also called a Cartesian plane, is a two-dimensional plane formed by a horizontal x-axis and a vertical y-axis that intersect at the origin (0,0). It is used to graph and locate points in a two-dimensional space by their x- and y-coordinates.
The coordinate grid is formed by two perpendicular lines, the horizontal x-axis and the vertical y-axis.
The point [-8,-6] represents an ordered pair where -8 is the x-coordinate and -6 is the y-coordinate.
To graph this point on a coordinate grid, start at the origin (0,0), which is where the x-axis and y-axis intersect. Then, move 8 units to the left along the x-axis since the x-coordinate is negative.
After that, move 6 units down along the y-axis since the y-coordinate is negative. The point where you end up after moving left 8 units and down 6 units is the point (-8,-6).
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Greatest common factor of 14b with a exponent of 3 and 5b with a exponent of 2
The only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]
Define common factor.The term "common" means "same for both." The two numbers' common factor is one that applies to both numbers.
The common factor between [tex]6[/tex] and [tex]10[/tex] is [tex]2[/tex], for instance. Although it is not the sole quality shared by each number, it is a trait that they both have in common.
To find the GCF of [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] we need to find the largest factor for both
[tex]14b^{3}[/tex] = 2*7*[tex]b^{2}[/tex]*[tex]b[/tex]
[tex]5b^{2}[/tex] = [tex]5*b^{2}[/tex]
Therefore the only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]
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You pay $3.00 to play. The dealer deals you one card. If it is a spade, you get $10. If it is anything else,
you lose your money. Is this game fair?
The game is fair in the sense that the expected value is not negative.
What is expected value?The expected value serves as a gauge for a random variable's typical value. It is determined by multiplying each of the variables' potential outcomes by its corresponding probability, then adding the resulting products. In order to comprehend the typical outcome of a random process and determine if a given course of action is likely to be lucrative or not, the expected value is a valuable tool in decision-making.
The probability of getting a spade is 13/52 or 1/4.
The probability of getting anything else is 3/4.
he expected value of playing the game can be calculated as:
Expected value = (probability of winning x amount won) - (probability of losing x amount lost)
Expected value = (1/4 x $10) - (3/4 x $3)
Expected value = $2.50 - $2.25
Expected value = $0.25
Since the expected value is positive, this means that on average, you can expect to win $0.25 for every time you play the game.
Hence, game is fair in the sense that the expected value is not negative.
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FORM 3A4
MATHS PROJECT
Get into groups of no more than 4 persons. Select a family size of 4/6/10 persons based on the greatest number of persons in the family in your group.
Calculate for the family size selected (allowing 24 inches for each person) the minimum diameter of a circular table to seat all members the minimum length of the side of a square table.
Calculate the area of the top of the circular table and the square table, and explain which is most appropriate for the family.
Assuming the family size selected is 6 persons,
The area of the top of the circular table would be: 1,660.51 In²; and The area of the top of the square table would be: 10,404 In²What is the explanation for the above response?Assuming the family size selected is 6 persons, the minimum diameter of a circular table to seat all members would be:
Minimum diameter = (Number of persons x Minimum distance between two persons) / π
= (6 x 24) / 3.14
= 45.86 inches (rounded up to 46 inches)
The minimum length of the side of a square table to seat all members would be:
Minimum length of side = (Number of persons x Minimum distance between two persons) / √2
= (6 x 24) / 1.41
= 101.41 inches
The area of the top of the circular table would be:
Area = π x (Diameter / 2)²
= π x (46 / 2)²
= 1,660.51 In²
The area of the top of the square table would be:
Area = (Length of side)²
= 102²
= 10,404 In²
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Find product of face values of all digits in
the number 91250
To find the product of the face values (the values of the digits as they appear in the number) of all digits in 91250, we can simply multiply the face values of each digit together.
The face value of a digit is simply the value of the digit itself, regardless of its position in the number.
So, we have:
9 * 1 * 2 * 5 * 0 = 0
Note that the face value of the digit 0 is 0, so any product that includes a 0 will also be 0.
Therefore, the product of the face values of all digits in 91250 is 0.
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y=x^2-8x-8 quadratic function in vertex form
Answer:
[tex]y=(x+4)^2-8[/tex]
Step-by-step explanation:
[tex]y=x^2-8x-8[/tex]
complete the square.
[tex](x+4)^2-8[/tex]
set y equal to the new right side.
[tex]y=(x+4)^2-8[/tex]
Hope this helps!
Brainliest is much appreciated!
Answer:
Answer is Below!Step-by-step explanation:
a = 1
c = -8
b= -8
the formula of vertex form is a(x-h)^2 +k = y
First find H and k using the formula -b/2a = h
h = 4
so, k = -24
y =1(x-4)^2 -24
Find the value of x, y, and z. (Round to the 3rd decimal place if possible)
Addressing issue hand, we state that Therefore, the linear equation solution to the system of equations is: x = 0.5, y = 0.1667, z = -0.5 and x = 0.500, y = 0.167, z = -0.500
What is a linear equation?In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.
values of x, y, and z, we can use the system of equations
3x - 2y + z = 1
2x + y - z = 0
x + 2y + 3z = -1
We can use Gaussian elimination or any other suitable method to solve the system. Here's one way to do it:
3x - 2y + z = 1 (eq. 1)
2x + y - z = 0 (eq. 2)
x + 2y + 3z = -1 (eq. 3)
3x - 2y + z = 1 (eq. 1)
0.6667x + 1.3333y - 1.3333z = -0.6667 (eq. 2')
-0.3333y + 2.3333z = -1.3333 (eq. 3')
3.3333x - 0.3333z = 0.1667 (eq. 1')
0.6667x + 1.3333y - 1.3333z = -0.6667 (eq. 2')
2.1667z = -1.0833 (eq. 3')
z = -0.5
y = 0.1667
x = 0.5
Therefore, the solution to the system of equations is:
x = 0.5, y = 0.1667, z = -0.5
x = 0.500, y = 0.167, z = -0.500
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What is the median of the following data values? 10, 14, 15, 17, 20, 21, 22, 25
Answer:
The median of the data set is 18.5
Step-by-step explanation:
To find the median of this set of data values, we need to first arrange them in numerical order:
10, 14, 15, 17, 20, 21, 22, 25
The middle value is the median. If there is an odd number of values, there will be exactly one middle value, and if there is an even number of values, the median will be the average of the two middle values.
In this case, there are 8 values, which is an even number. So, we take the average of the sum of the 2 middle numbers:
Median of Data Set = (17 + 20)/2 = 18.5
Therefore, the median of the data set is 18.5.