Answer:
multiple of 3
Step-by-step explanation:
I think that it will least likely land on a multiple of 3 because none of them are multiples of 3.
4) Amy traveled to the recycling plan
back. It took one hour less time to get
there than it did to get back. The average
speed on the trip there was 50 km/h. The
average speed on the way back was 40
km/h. How many hours did the trip there
take?
The time taken by Amy to travel to the place was t = 4 hours.
What is average speed?A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.
In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.
Let the time taken to get back = t + 1.
Now, it took one hour less time to get there thus time = t.
Now, average speed is given as:
average speed = total distance / total time
Substituting the values:
50 km/h = d / t
d = 50t .........(1)
40 km/h = d / (t + 1)
d = 40(t + 1)......(2)
Setting the value of d as equal we have:
50t = 40(t + 1)
50t = 40t + 40
10t = 40
t = 4
Hence, the time taken by Amy to travel to the place was t = 4 hours.
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A bank account earns 4.1% APR compounded monthly. Find the doubling time of the account.
It would take 211 months for the bank account to double in value at a 4.1% APR compounded monthly.
What is the doubling time of the account?We are going to use the rule of 72 which states that the number of years it takes for an investment to double is approximately equal to 72 divided by the annual interest rate.
The annual interest rate is 4.1% compounded monthly.
Monthly interest rate = 4.1% / 12
Monthly interest rate = 0.0034166667
Now we can use the rule of 72:
Doubling time = 72 / (0.0034166667 x 100)
Doubling time = 210.731705261
Doubling time = 211 months.
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how to plot 4x-5y less than equal to -15
The answer of the given question based on the plotting graph , the steps are given below .
What is Inequality?An inequality is a statement that compares two values or expressions and indicates that one is greater than, less than, or equal to the other. Inequalities can be solved or simplified using various algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides by the same quantity, or factoring and finding the roots of the expressions
To plot the inequality 4x - 5y ≤ -15, you can follow these steps:
First, rearrange the inequality to solve for y:4x - 5y ≤ -15
-5y ≤ -4x - 15
y ≥ (4/5)x + 3
This gives you the equation of the boundary line. Plot this line on a graph by plotting two points and drawing a straight line through them. To plot the line, you can choose any two values of x and find the corresponding values of y using the equation.Let's choose x = 0 and x = 5.
When x = 0: y = (4/5)(0) + 3 = 3, so one point is (0, 3).
When x = 5: y = (4/5)(5) + 3 = 7, so another point is (5, 7).
Plot these two points and draw straight line through them.
Now, to shade the region that satisfies the inequality, choose a point that is not on the boundary line. The easiest point to choose is (0,0). Substitute x and y values of this point into inequality.4x - 5y ≤ -15
4(0) - 5(0) ≤ -15
0 ≤ -15
Since this is not true, the point (0,0) is not in the region that satisfies the inequality. Shade the region above the boundary line to show the region that satisfies the inequality.
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This is untrue since the point (0,0) is not located in the area where the inequality is satisfied. To highlight the area that satisfies the inequality, shade the area above the boundary line.
What is Inequality?An inequality is a comparison that shows that one value or expression is larger than, less than, or equal to another. Different algebraic methods, such as adding, subtracting, multiplying, or dividing both sides by the same amount, or factoring and determining the roots of the equations, can be used to resolve or simplify inequalities.
Plotting the inequality 4x - 5y ≤-15 can be done by doing the following:
To solve for y, rearrange the inequality first:
4x - 5y ≤ -15
-5y ≤ -4x - 15
y ≥ (4/5)x + 3
You are then provided with the boundary line's equation. Plot two points on a graph, then draw a straight line through them to represent this line. You can use the equation to determine the values of y that correspond to any two x values to plot the line.
Let's choose x = 0 and x = 5.
When x = 0: y = (4/5)(0) + 3 = 3, so one point is (0, 3).
When x = 5: y = (4/5)(5) + 3 = 7, so another point is (5, 7).
Plot these two spots and a line should be drawn directly between them.
Now select a point that is not on the border line to shade the area that satisfies the inequality. (0, 0) is the simplest position to select. In the inequality, replace the x and y values of this point.
4x - 5y ≤ -15
4(0) - 5(0) ≤ -15
0 ≤ -15
Since this is untrue, the point (0,0) is not located in the area where the inequality is satisfied. To highlight the area that satisfies the inequality, shade the area above the boundary line.
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The vertices of a rectangle are plotted in the image shown. A graph with the x-axis and y-axis labeled and starting at negative 8, with tick marks every one unit up to positive 8. There are four points plotted at negative 1, 3, then 3, 3, then negative 1, negative 3, and at 3, negative 3. What is the perimeter of the rectangle created? 20 units 24 units 10 units 16 units
Answer:
To find the perimeter of the rectangle, we need to add up the lengths of all four sides.
The horizontal sides of the rectangle have a length of 3 - (-1) = 4 units.
The vertical sides of the rectangle have a length of 3 - (-3) = 6 units.
Therefore, the perimeter of the rectangle is:
2(4 units) + 2(6 units) = 8 units + 12 units = 20 units.
Therefore, the perimeter of the rectangle is 20 units. Answer: 20 units.
The perimeter of the rectangle is 20 units.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
Using the distance formula, the length of the side between (-1,3) and (3,3).
= √[(3 - (-1))² + (3 - 3)²]
= √16
= 4
Similarly, the length of the side between (3,3) and (3,-3).
= √[(3 - 3)² + (3 - (-3))²]
= √36
= 6
The length of the side between (3,-3) and (-1,-3) is also 4, and the length of the side between (-1,-3) and (-1,3) is 6.
Now,
The perimeter of the rectangle.
= 4 + 6 + 4 + 6
= 20
Thus,
The perimeter of the rectangle is 20 units.
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Your friend is considering how much he should invest in his new IRA. He is debating if he should invest the full $800 he was planning to or just $400 and use the extra money to buy a couple of pairs of sneakers he had been eyeing. What advice would you give? Use math to justify your answer
Answer:
invest full 800$
Step-by-step explanation:
I would advise my friend to invest the full $800 in his new IRA. While buying a couple of pairs of sneakers may provide immediate satisfaction, investing in an IRA can have long-term financial benefits.
If we assume an average annual return of 8% for his IRA, then the $800 investment would grow to approximately $4,536 after 30 years. On the other hand, if he only invests $400 and spends the remaining $400 on sneakers, then the investment would only grow to approximately $2,268 after 30 years.
Thus, by investing the full $800, my friend would have a potential gain of over $2,268 compared to if he only invested $400. Furthermore, investing in an IRA can provide tax benefits and potentially reduce his taxable income, providing additional financial benefits.In summary, while it may be tempting to use some of the money for immediate gratification, investing the full $800 in an IRA can provide long-term financial benefits that outweigh the short-term satisfaction of purchasing a couple of pairs of sneakers.
The length of a rectangurlar frame is 15 inches and the width of the frame is 8 inches what is the length of the frame
the correct length of the frame is 17 inches.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Area of rectangle is A = a*b
Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.
This will be:
d² = 15² + 8²
d² = 225 + 64
d² = 289
d = ✓289
d = 17
Therefore, the correct option is 17 inches.
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A rectangular prism has a surface area is 484 square centimeters and the edge lengths are consecutive integers. Determine the longest segment that can be drawn to connect two vertices.
The longest segment that can be drawn to connect two vertices is 10 cm
Determining the longest segment that can be drawn to connect two vertices.From the question, we have the following parameters that can be used in our computation:
A rectangular prism has a surface area is 484 square centimeters The edge lengths are consecutive integers.Represent the smallest length with x
So, we have
SA = 2 * (x(x + 1) + x(x + 2) + (x + 1)(x + 2))
Substitute the known values in the above equation, so, we have the following representation
2 * (x(x + 1) + x(x + 2) + (x + 1)(x + 2)) = 484
So, we have
(x(x + 1) + x(x + 2) + (x + 1)(x + 2)) = 242
When solved using a graph, we have
x = 8
So, we have
Longest edge = 8 + 2
Longest edge = 10
Hence, the longest segment that can be drawn to connect two vertices is 10 cm
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The function f(x) = 2.75x2 models the packaging costs, in cents, for shipping a book with the side lengths, in inches, shown in the diagram. What are reasonable domain and range values for this function?
A cuboid with base or length x, height 1.5x and width 0.5x.
A. domain: 4 ≤ x ≤ 12; range: 6 ≤ f(x) ≤ 18
B. domain: x ≥ 4; range: f(x) ≥ 44
C. domain: 4 ≤ x ≤ 12; range: 44 ≤ f(x) ≤ 396
D. domain: x ≥ 0; range: f(x) > 0
On solving the provided question ,we can say that As a result, option C—domain: 4 x 12; range: 44 f(x) 396—is the proper response.
what is a sequence?A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.
The packing expenses in cents for transporting a book with the specified dimensions are represented by the function f(x) = 2.75x2.
Option B is invalid because the minimal value of x is 0 and the base of the cuboid cannot be negative.
The cuboid's measurements in the diagram also imply that its base length ranges from 4 to 12 inches, hence the function's domain is 4 x 12.
At x = 4, where f(4) = 2.75(4)2 = 44, and x = 12, where f(12) = 2.75(12)2 = 396, f(x) has its minimum and maximum values, respectively. As a result, the function's range is 44 f(x) 396.
As a result, option C—domain: 4 x 12; range: 44 f(x) 396—is the proper response.
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Surface area of the shape
The total surface area of diagram is 119.1 unit
Define rectangular pyramid?A rectangular pyramid is a three-layered strong item that comprises of a rectangular base and four three-sided faces that meet at a typical point, called the summit.
In the figure below is a cuboid and upside is Square Pyramid;
Surface area of cuboid = 2 (l×h + l×w+ h×w)
Surface area of cuboid = 2 (6×3 + 6×3+ 3×3) = 2 (18+18+9)
Surface area of cuboid = 90 unit²
The slant height is the hypotenuse of a right triangle whose height is 3 inches and half the base of the triangular (3/2 = 1.5 inches). Using the Pythagorean theorem,
slant height = [tex]\sqrt{3^2 + 1.5^2}[/tex] [tex]= \sqrt{11.25}[/tex]
slant height = 3.35 unit
Surface Area of a Square Pyramid = base² + 2×base×slant height
Surface Area of a Square Pyramid = 3² + 2×3×3.35
Surface Area of a Square Pyramid = 9 + 20.1
Surface Area of a Square Pyramid = 29.1 unit²
The total area of these two faces = Surface area of cuboid + Surface area of pyramid.
The total Surface area = 90 + 29.1 = 119.1 unit²
Therefore total area of diagram is 119.1 unit²
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Need your help guys
Based on the information, we lack credible evidence to assume an association between a student's academic success and if they are either a boarder or day student at a significance level of 0.05.
How to explain the hypothesisThe statistic for the chi-square test is given as follows:
X² = ∑ [(observed value - expected value)² / expected value]
Through employing a significance level of 0.05, accompanied by 1 degree of freedom (due to two categories and three degrees of performance), the critical value for the chi-square distribution is calculated at 3.84.
The computed chi-square test statistic is measured to be:
X² = [(130-147.43)²/147.43] + [(180-195.57)²/195.57] + [(240-222.57)²/222.57] + [(305-289.43)²/289.43] + [(100-111.43)²/111.43] + [(200-188.57)²/188.57]
X² = 5.61
Given that 5.61 is lower than 3.84, we dismiss the null hypothesis. Ultimately, we lack credible evidence to assume an association between a student's academic success and if they are either a boarder or day student at a significance level of 0.05.
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A group of students interning at WDHS are wanting to reward their loyal listeners with free ice cream. To make it easier on their listeners they rent 6 ice cream trucks to space evenly throughout their coverage area.
Answer:Whats the question like what am I solving I will answer if i have a problem to solve
Step-by-step explanation:
A Sporting goods company makes footballs with an alligator logo. Of the 8,750 footballs produced in one week, 77 were defective
In linear equation, 330 will be defective sporting goods.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Based on the given conditions, formulate = 37500 * 77 ÷ 8750
Simplify fraction(s) = 30 * 11
Calculate the product or quotient: 330
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The complete question is -
A Sporting goods company makes footballs with an alligator logo. Of the 8,750 footballs produced in one week, 77 were defective. If the company produces 37500 footballs in one month , how many do you predict will be defective ?
Write a quadratic equation for the following graph (i’ll give brainliest)
The quadratic equation which is as represented in the graph and required to be determined is; y = -(x - 1) (x - 5).
Which quadratic equation represents the graph?It follows from the task content that the quadratic equation which correctly represents the given graph is to be determined.
Recall from the graph that the zeroes are at; x = 1 and x = 5.
Therefore, the equation will take the form;
y = a (x - 1) (x - 5)
To determine the value of a, the pair of coordinates; (2, 3) is used, where, x = 2 and y = 3.
Therefore, 3 = a (2-1) (2 - 5)
a = 3 / -3; a = -1.
Ultimately, the quadratic equation as required to be determined is; y = -(x - 1) (x - 5).
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Meghan is spending money at a constant rate. Suppose she initially has $1100, and after 4 months, she has $720.
Express the rate at which Meghan's amount of money is changing.
95$
Step-by-step explanation:
Based on the given conditions, formulate ( 1100 - 720 ) ÷ 4
Calculate the sum or difference = 380/4
Cross out the common factor = 95
Find the surface area
Will give branliest
The surface area of the square base pyramid is 138 inches².
How to find the surface area of a pyramid?The pyramid above is a square base pyramid. The surface area of the pyramid can be calculated as follows:
Therefore,
surface area of the pyramid = base area + 2al
where
a = base lengthl = height of the pyramidTherefore,
a = 6 inches
l = 8.5 inches
Hence,
base area = 6² = 36 inches²
a = 6 inches
l = 8.5 inches
Therefore,
surface area of the pyramid = 36 + 2 × 6 × 8.5
surface area of the pyramid = 36 + 102
surface area of the pyramid = 138 inches²
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Please help me please l don’t understand
Which of the following three dimensional solids would NOT contain a circle?
cylinder
cone
sphere
cube
Answer:
cube.................
Please help with this
Answer:1/10
Step-by-step explanation:
In order to solve this, you need to read the question carefully. If you have 1 whole divided into 10 equal parts you need to divide 1 by 10.
The visualization for this is 1 ÷ 10, which translates to 1/10
A tip to remember is that ÷ looks a bit like a fraction with the numbers replaced with dots!
Natalia paid $40 for 4 t-shirts and a necklace.
If Natalia paid $12 for the necklace, how much did each shirt cost?
If Natalia paid $12 for the necklace, then Each t- shirt cost $7.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.
We are given that Natalia paid $40 for 4 t-shirts and a necklace.
If Natalia paid $12 for the necklace, then;
We need to find the cost of each shirt.
Therefore,
cost of 4 t- shirt + 1 neclace = 40
40 - 12 = 28
Cost of 4 t- shirt = 28
Cost of 1 t- shirt = 28/4 = 7
Hence, the cost of each t shirt is $7.
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Suppose you work for a company that manufactures electronics. The development analysts estimate that 1% of their flagship product will fail within 2 years of the purchase date, with a replacement cost of $ 1300.
A newly hired associate at the company proposes to charge $ 5 for a 2 year warranty.
The company can expect to earn $5 per product sold if they offer a warranty, compared to an expected loss of $13 per product sold if they do not offer a warranty. It is a profitable decision for the company to offer the warranty.
What is binomial distribution?In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value.
Assuming that the failure of the flagship product follows a binomial distribution with a probability of 1% of failure within 2 years of purchase, let's calculate the expected cost to the company without a warranty and with the warranty.
Without the warranty, the expected cost to the company is given by:
Expected cost without warranty = 0.01 x $1300 = $13
With the warranty, the expected cost to the company is given by:
Expected cost with warranty = $5 - (0.99 x $0) = $5
Therefore, the company can expect to earn $5 per product sold if they offer a warranty, compared to an expected loss of $13 per product sold if they do not offer a warranty. It is a profitable decision for the company to offer the warranty.
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r x 24 = 161
what is the answer
Answer:are you trying to solve for R or? sorry if im wrong i have hard time paying attention in math
Step-by-step explanation:
if you are the answer is in exact form its r= 161/24 in decimal form its r=6.7083 and in mixed number form its r= 6 17/24
1. In his closet, John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of
slacks. List all of the possible shirt-and-pant combinations below. -(4 points)
Since he has two shirts, and only 3 pants the possible number of combination would be 2 x 3 = 6
2. John discovered that he also has a pair of boots and a pair of dress shoes in his closet. Make a tree
diagram showing all of the possible shirt, pant, and shoe combinations. (4 points)
3. Jenny has six tlouses, four different skirts, 20 different pairs of socks, and four pairs of shoes in her
closet at the end of the week.
Part 1: Explain why the methods used in the previous two problems would be inefficient in
determining the number of different outfits Jenny could wear (2 points)
The total number of possible outcomes of shirt and pants are
Red shirt and shorts
Red shirt and jeans
Red shirt and slacks
Blue shirt and shorts
Blue shirt and jeans
Blue shirt and slacks
Given data ,
John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of slacks
Now , total number of possible outcomes of shirt and pants are
A = 2 x 3 = 6 outcomes
Red shirt and shorts
Red shirt and jeans
Red shirt and slacks
Blue shirt and shorts
Blue shirt and jeans
Blue shirt and slacks
Hence , the possible outcomes are solved
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find the area of each parallelogram or rhombus
Answer: 36 m²
Step-by-step explanation:
A = bh
b=4
h=9
A=(4)(9) =36 m²
A box contains 10 balls that each have a dollar amount on them. A person is charged $10 to randomly choose a ball. The person will receive the amount of money that is on the ball. In the box, there are 5 balls with $1, 2 with $2, and 3 balls with $30.
Find the expected value of this game.
$0.10
$0.50
$9.50
$11.00
Answer:
A I'm pretty sure
Step-by-step explanation:
To find the expected value, we need to multiply each possible outcome by its probability and add up the results.The probability of drawing a ball with $1 is 5/10 = 0.5.
The probability of drawing a ball with $2 is 2/10 = 0.2.
The probability of drawing a ball with $30 is 3/10 = 0.3.
The expected value is:
(0.5 * 1) + (0.2 * 2) + (0.3 * 30) = 0.5 + 0.4 + 9 = 9.9
However, the person paid $10 to play, so we need to subtract that from the expected value:9.9 - 10 = -0.1
Therefore, the expected value of this game is -$0.10. Answer choice (A) is correct.
Answer: $9.50
Step-by-step explanation:
Given that -6i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable.
f(x)=x^4-15x³ + 90x² - 540x + 1944
Answer:
Step-by-step explanation:
The Conjugate Roots Theorem states that imaginary roots come in pairs. If -8i is a root of the polynomial, then so is +8i.
If both -8i and +8i are factors, we rewrite them as (x + 8i) and (x - 8i) in factored form. Since imaginary terms aren't accepted, you can FOIL these to get a quadratic with no imaginary terms.
x2 - 8ix + 8ix - 64i2
Simplify. Replace i2 with -1 because √-1 = i
x2 - 64(-1)
x2 + 64
The quadratic x2 + 64 has roots -8i and 8i. You can use the quadratic formula to verify this.
Now, let's tackle the rest of the polynomial. If x2 + 64 is a factor of the polynomial
x4 + 10x3 + 85x2 + 640x + 1344, divide it out to see what is left. I will use long division of polynomials. Note, I am using the square root symbol as a division symbol.
x2 + 10x + 21
x2 + 64 √ (x4 + 10x3 + 85x2 + 640x + 1344)
x4 + 64x2
_____________
10x3 + 21x2
10x3 + 640x
__________
21x2 +1344
21x2 + 1344
___________
0
There is no remainder, meaning x2 + 64 went in evenly. The quotient left when we divide out x2 + 64 from
x4 + 10x3 + 85x2 + 640x + 1344 is x2 + 10x + 21. Factor the quotient to get (x + 7)(x + 3).
x4 + 10x3 + 85x2 + 640x + 1344 = (x2 + 64)(x + 7)(x + 3)
You can check this factored form by FOILing out, and you should get the original polynomial.
Suppose you went to Vegas and you will bet until you are broke. You start with $ 18 and bet $1 each time for the slot machine. The probability of winning is 0.0028 . Once you win, you earn $20 (net earnings are $10 in total considering $1 you paid to bet). Write a loop to simulate this and report the total number of bets you did until you are broke. Before running the loop, set the seed number equals to 77 .
If the random number is less than the winning probability of 0.0028, the player wins $20 and we add that to the amount variable.
Otherwise, the player loses $1 and we subtract that from the amount variable.
To simulate this scenario in Python.
Here's a possible implementation:
import random
# Set the seed number
random.seed(77)
# Initialize the starting amount and the number of bets
amount = 18
num_bets = 0
# Loop until the player runs out of money
while amount >= 1:
# Increment the number of bets
num_bets += 1
# Check if the player wins
if random.random() < 0.0028:
amount += 20 - 1 # The net earnings are $10
# Otherwise, the player loses $1
else:
amount -= 1
# Report the total number of bets
print(f"Total number of bets: {num_bets}")
In this implementation, we use the random module in Python to simulate the outcome of each bet.
We set the seed number to 77 to ensure that the results are reproducible.
We initialize the starting amount to $18 and the number of bets to 0. We then loop until the player runs out of money (i.e., the amount variable is less than $1).
Inside the loop, we increment the number of bets by 1 and simulate the outcome of the bet using random.
random() which returns a random float between 0 and 1.
If the random number is less than the winning probability of 0.0028, the player wins $20 and we add that to the amount variable.
Otherwise, the player loses $1 and we subtract that from the amount variable.
After the loop ends, we print the total number of bets.
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Which is the graph of f(x) = -(x+3)(x + 1)?
Using functions, we can find that the given equation is a quadratic equation so, the graph will be a parabola.
Option B is correct.
How to graph a function?Simple functions like linear and quadratic functions are simple to graph. The fundamental concept behind graphing functions is to locate the shape, if at all possible. A line would be the graph of a linear function of the type f(x) = axe + b, for instance; a parabola would be the graph of a quadratic function of the form f(x) = ax² + bx + c.
By replacing some random x values into the function, one can locate some spots on it by determining the corresponding y values for each value.
Here in the question,
Given equation will be:
-(x+3)(x + 1)
Solving it we get:
= -x² -x + 3x + 3
= -x² + 2x + 3
So, graph for this function will be a parabola as the function is a quadratic function.
Therefore, the graph of the function will be the 2nd graph. Option B is correct.
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Please help me with this due tomorrow
Answer:
Step-by-step explanation:
you have to match the numbers on the lines of the plane, they have to match up with each other it goes (x,y) the x line is the one going to the side, and the y is the one going up to down
The plane region is revolved completely about the x-axis to sweep out a solid of revolution. Find its volume in terms of PI .
The correct answer is C. 320×pi
How to solveWhat occurs when something is rotated around a pole? What kind of shape is the point closest to the pole making?
Obviously, a circle.
that means rotating the rectangle around the x-axis creates a round object (with the bottom area being a circle).
so, all answers about a prism (rectangular bottom shape) are automatically wrong.
again, just imagine to rotate a small sheet of paper around a pole (the x-axis acts like one in this scenario).
the result is solid with a circular bottom area, and it maintains this shape all the way to the top.
it is a cylinder!
and what is its radius?
well, the outermost point of the rectangle is 8 points away from the x-axis. when we rotate this rectangle, that attribute remains, of course. and every point on the side surface of the resulting cylinder has the same distance from the central x-axis : 8.
so, the radius is 8.
and the volume of a cylinder is
ground area × height = pi×r² × height
in our case
pi×8² × 5 (the width or "height" of the rectangle) = pi×64 × 5 = 320×pi
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IQ test scores are normally distributed with a mean of 99 and a standard deviation of 11. An individual's IQ score is found to be 128. Find the z-score corresponding to this value.
According to the given data the z-score corresponding to an IQ score is [tex]2.64[/tex].
What do you mean by z-score?A z-score (or standard score) is a measure of how many standard deviations an observation or data point is away from the mean of its distribution.
It is calculated by subtracting the mean of the distribution from the observed value, and then dividing the difference by the standard deviation of the distribution.
Given ; Data in the problem
∴μ[tex]= 99[/tex] , σ[tex]= 11[/tex] , [tex]x = 128[/tex]
so, z - score =( [tex]x -[/tex]μ)/σ
[tex]\frac{(128-99)}{11} \\=\frac{29}{11} \\= 2.64[/tex]
Therefore the z-score corresponding to an IQ score of [tex]128[/tex] is approximately [tex]2.64[/tex]
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