The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.
How to find side of triangle?Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.
In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:
[tex](x+2)^2 = x^2 + (x+1)^2[/tex]
Expanding the squares, we get:
[tex]x^2 + 4x + 4 = x^2 + x^2 + 2x + 1[/tex]
Simplifying and rearranging terms, we get:
[tex]2x^2 - 2x - 3 = 0[/tex]
We can solve this quadratic equation by using the quadratic formula:
x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a
where a = 2, b = -2, and c = -3.
Plugging in these values, we get:
x = (-(-2) ± [tex]\sqrt{((-2)^2 - 4(2)(-3)))[/tex] / 2(2)
x = (2 ± [tex]\sqrt{(4 + 24))[/tex] / 4
x = (2 ± [tex]\sqrt28}[/tex] / 4
x = (2 ± [tex]2\sqrt{7}[/tex]) / 4
x = 1/2 ± [tex]\sqrt{7}[/tex]/2
The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.
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There are two yellow and three green balls in a tub. Ashraf picks a ball without looking. What is his probability that the ball is (i) yellow (ii) green (iii) red
Answer:
Since there are only yellow and green balls in the tub, there is no possibility of picking a red ball. Therefore, the probability of picking a red ball is zero.
(i) The probability of picking a yellow ball can be calculated by dividing the number of yellow balls by the total number of balls. In this case, there are two yellow balls and three green balls, so the total number of balls is 2 + 3 = 5. The probability of picking a yellow ball is 2/5 or 0.4, which is 40%.
(ii) Similarly, the probability of picking a green ball can be calculated by dividing the number of green balls by the total number of balls. In this case, there are three green balls and five total balls. Therefore, the probability of picking a green ball is 3/5 or 0.6, which is 60%.
(iii) As mentioned earlier, there are no red balls in the tub. Hence, the probability of picking a red ball is 0.
I need help with this math
A right triangular pyramid has a height of 14 yards. Its base has a leg that is 8 yd. The volume of the pyramid is 168 cubic yd. The other leg of the base is ___ yd.
Therefore , the solution of the given problem of volume comes out to be the other leg of the right triangular pyramid's base is 3 yards long.
What does volume actually mean?A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.
Here,
Let's use "x" yards to represent the other leg of the right triangle pyramid's base.
A pyramid's volume can be calculated using the following equation: => Volume = (1/3) * Base Area * Height
In this instance, we are informed that the pyramid has a volume of 168 cubic yards and a height of 14 yards.
=> 168 = (1/3) * 14 * base area
The base area can be estimated as (8 * x)/2 = 4x because we know that one leg of the base is 8 yards long and the other leg is designated as "x" yards.
=> 168 = (1/3) * 4x * 14
=> 168 = (4/3)x * 14
=> 168 = (4/3) * 14x
=> 168 = 56x
=> x = 168/56
=> x = 3
Therefore, the other leg of the right triangular pyramid's base is 3 yards long.
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9x7x9x9x7x9 (I tried the answer 9^4 x 7^2 and it’s not correct
Answer:
321489
Step-by-step explanation:
What is the value of r in the equation 3r + 10 − 3r = 15?
Show all the steps by applying inverse operation, then check the answer to get full credit.
Answer:
no solution
Step-by-step explanation:
3r + 10 - 3r = 15 ← collect like terms on left side
10 = 15 ← false statement
this false statement indicates the equation has no solution
2. Fiona opened a retirement account that has an annual yield of 6%. She is planning on retiring in 20 years.
How much must she deposit into that account each year so that she can have a total of $600,000 by the time
she retires?
Answer:
PMT = $52,023.26
Step-by-step explanation:
To calculate how much Fiona must deposit into her retirement account each year, we can use the formula for annuity payments:
PMT = PV x (r / (1 - (1 + r)^(-n)))
Where:
PMT is the periodic payment
PV is the present value (or desired future value) of the annuity
r is the interest rate per period (in this case, the annual yield of 6% divided by the number of periods per year, which is 1)
n is the total number of periods (in this case, 20 years)
We know that Fiona wants to have a total of $600,000 in her retirement account by the time she retires, so PV = $600,000. We also know that the interest rate per period is 6% / 1 = 0.06, and the total number of periods is 20.
Plugging these values into the formula, we get:
PMT = $600,000 x (0.06 / (1 - (1 + 0.06)^(-20)))
PMT = $600,000 x (0.06 / (1 - 0.312))
PMT = $600,000 x (0.06 / 0.688)
PMT = $52,023.26
Therefore, Fiona would need to deposit approximately $52,023.26 into her retirement account each year for the next 20 years to have a total of $600,000 by the time she retires, assuming the annual yield remains constant at 6%.
In need of assistance! If possible, I'd appreciate it!
Vector a: start at (1, 3) and end at (-4, -2) in blue.
Vector b: start at (-4, -2) and end at (1, 3) in red.
Vector a+b: start at (1, 3) and end at (2, 7) in green.
How do we calculate?To represent a+b using the parallelogram method,
we must draw vectors representing a and b.
The initial point of vector a is (1, 3), and its terminal point is (-4, -2). The initial point of vector b is (-4, -2), and its terminal point is (1, 3).
Using the vector tool, we then draw the vectors a and b. We start at the initial point of each vector and select the terminal point.
Vector a: start at (1, 3) and end at (-4, -2)
Vector b: start at (-4, -2) and end at (1, 3)
We the diagonal, we start at the initial point of vector a, (1, 3), and draw a line parallel to vector b that passes through the initial point of vector b, (-4, -2). This line intersects the line parallel to vector a that passes through the initial point of vector b at point (2, 7). This point is the terminal point of the diagonal vector, which is a+b.
We use the vector tool, we can draw vector a in blue, vector b in red, and vector a+b in green.
Vector a: start at (1, 3) and end at (-4, -2) in blue.
Vector b: start at (-4, -2) and end at (1, 3) in red.
Vector a+b: start at (1, 3) and end at (2, 7) in green.
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Find the surface area of a triangular prism (which has 2 triangular bases and 3 rectangular sides) with the following dimensions:
Base of triangles= 4 in
Height of triangles = 3 in
Length of rectangles = 10 in
Width of rectangles = 5 in
The surface area of the triangular prism is 162 square inches.
What is prism?In geometry, a prism is a three-dimensional solid shape that has two identical, parallel faces (called bases) and rectangular or parallelogram-shaped sides. The sides connect the bases, and their shape determines the type of prism.
To find the surface area of the triangular prism, we need to find the areas of all five faces and add them together.
The area of each triangular base is:
A = (1/2)bh
where b is the length of the base (which is equal to 4 in) and h is the height (which is equal to 3 in).
A = (1/2)(4 in)(3 in) = 6 in²
So the total area of both triangular bases is:
2A = 2(6 in²) = 12 in²
The area of each rectangular side is:
A = lw
where l is the length (which is equal to 10 in) and w is the width (which is equal to 5 in).
A = (10 in)(5 in) = 50 in²
So the total area of all three rectangular sides is:
3A = 3(50 in²) = 150 in²
Therefore, the total surface area of the triangular prism is:
12 in² + 150 in² = 162 in²
Thus, the surface area of the triangular prism is 162 square inches.
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The compliment of an angle is three times the measurement of the angle. Find the measurement of the larger angle
The greater angle has a 67.5° degree measurement. When two angles' measurements add up to 90°degrees, they are said to be complimentary.
How to calculate the larger angle?Call that angle we're looking for "x" for convenience.
The degree that, if added to x, makes x equal 90° degrees is known as the compliment of x.
We now know that 3x, or 3 times x, is the compliment of x.
With this knowledge, we can construct the following equation:
x + 3x = 90°
combining comparable equations;
4x = 90°
x = 22.5°, when both sides are divided by 4.
As a result,
3x = 3(22.5°) = 67.5° degrees is the measurement of the greater angle, which is the complement of x.
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Select all statements that are true.
Answers:
A, B, D, E
Nearly everything except choice C is true.
====================================================
Explanation:
Choice A is true because sine = opposite/hypotenuse.Choice B is true as well because cosine = adjacent/hypotenuseTangent is opposite/adjacent. The 4/9 should be 9/4. Therefore, choice C is false. If beta was theta, then tan(theta) = 4/9 would be true.Choice D is true because of the pythagorean theorem a^2+b^2 = c^2.Choice E is true because tan = opposite/adjacent, and the 9 and 4 are in the correct order (see choice C).What is Bd?
A. 7.5
B. 8.5
C. 9.4
D. 15
Thus, the length of chord BD of the given circle is found to be 8.5 units.
Explain about the chord of circle:A chord is indeed a straight line that connects two points on a circle's circumference. Because it connects to points on the circle's perimeter, the diameter is thought to be the chord with the longest length.
The lengthiest chord in a circle is called the diameter, and the chord's perpendicular distance to the circle's centre is zero.
Given that: From diagram.
CA = AD = 4.5 + 4 = 9.5 (radius of circle)AM = 4Now, in right triangle, MAD, using the Pythagorean theorem:
(AD)² = (AM)² + (MD)²
(9.5)² = (4)² + (MD)²
(MD)² = 9.5² - 4²
(MD)² = 90.25 - 16
(MD)² = 74.25
MD = 8.5
Thus, the length of chord BD of the given circle is found to be 8.5 units.
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4 William and his three friends had lunch at a restaurant. They split the bill
equally. The total bill was $34. They left a 15% tip. How much would each person
pay?
9x
omission for?
Answer:
$9.10 per person
Step-by-step explanation:
34 / 4 is 8.50
15% is 2.40, then divided 2.40 by 4 and get 0.60.
0.60 + 8.50 = 9.10 per person
A cereal box has dimensions of 12 inches, (7)3/4 inches, and 2 inches. A pastry box has a dimensions of (3)2/3 inches, (3)1/2 inches, and (2)1/3 inches. What is the difference in volume, cubic inches, between the two boxes. show your work
The difference in volume between the two boxes would be = 156in³
How to calculate the difference in volume between the boxes?To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;
Volume = length×width×height.
For box 1 = length = 12in, width = 7¾in, height= 2in
Vol = 12×7¾×2 = 186in³
For box 2; length = 3⅔in, width = 3½in, height= 2⅓in
Volume = 3⅔×3½×2⅓ = 30
The difference = 186-30 = 156in³
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18 7/8 + __ = 20 1/5
what is the blank?
Answer:
x = [tex]\frac{53}{40}[/tex]
Step-by-step explanation:
18 7/8 + __ = 20 1/5
18 7/8 = 151/8
20 1/5 = 101/5
[tex]\frac{151}{8}[/tex] + x = [tex]\frac{101}{5}[/tex]
x = [tex]\frac{101}{5}[/tex] - [tex]\frac{151}{8}[/tex]
x = [tex]\frac{53}{40}[/tex]
So, the answer is [tex]\frac{53}{40}[/tex]
The graph of linear function is shown on the grid
The y-intercept of a graph y=-3.
Here, we have,
Given the graph of a function, the y-intercept is defined as the y-coordinate of the point(s) where the graph crosses the y-axis.
There might be more than one y-intercepts or even none.
The graph provided in the question is a line with a negative slope, i.e., a decreasing line.
Carefully looking it can be determined the graph touches the y-axis in the point (0,-3), thus the y-intercept of the graph is y=-3
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complete question:
The graph of the linear function is shown on the coordinate grid. * 910X -10 What is the y intercept of the graph of the linear function?
A certain randomly selected sample of 125 registered voters showed that 20% of them voted in the most recent school board election. How many of these voters actually voted in that election? Construct a 95% confidence interval for the proportion of registered voters who voted in the most recent school board election
There are 25 persons who actually voted, the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07 that is (0.13, 0.27).
What is confidence interval?In statistics, a confidence interval, means the probability which a population parameter will fall between a set of values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. There are various types of confidence interval such as 90%, 95%, 99% etc.
A certain randomly selected sample of 125 registered voters showed that 20% of them voted in the most recent school board election.
So in 125persons the persons who actually voted are
(125×20)/100
= 2500/100
= 25
For 95% confidence interval the z value is 1.96.
If we take p as probability of success that is the persons who actually voted then 1-p denotes the probability of failure.
p= 25/125= 1/5 = 0.2 n= 125
1-p= 1-(1/5)
= 1-0.2= 0.8
The formula for confidence interval is
p± z√{p(1-p)/n}
0.2 ±1.96√{(0.2×0.8)/125}
= 0.2 ± 1.96√(0.16/125)
= 0.2± 1.96 ×0.035777
= 0.2±0.07012
Hence , the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07
that is (0.13, 0.27).
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When we started here, there were 500 employees. Since then, we have added 35% more employees, so we now have a total of _________ employees
The company now has 675 employees after adding 35% more employees to the initial 500 employees.
What is percentage?A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
To calculate the total number of employees after adding 35%, you can multiply the initial number of employees by 1.35:
Total number of employees = 500 x 1.35
Total number of employees = 675
Therefore, the company now has 675 employees after adding 35% more employees to the initial 500 employees.
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Area and perimeter assignment. (9th Grade geometry)
Thus, the perimeter of the shown triangle using the distance formula is found as 13.45 units.
Explain about the perimeter:A path that encircles a region is referred to as a perimeter. Adding the lengths of every one of the sides together is the simplest formula for calculating the perimeter. The word circumference, that only encompasses a circle's perimeter, is used to describe the distance around a circle.
Given that:
coordinates of triangle: A(5,3) , B(1,5) and C(3,0)Perimeter = sum of all sides
Perimeter = AB + BC + CA
Estimate each distance using the distance formula:
d = √(x2 - x1)² + (y2 - y1)²
AB = √(1 - 5)² + (5 - 3)²
AB = √(-4)² + (-2)²
AB = √(16 + 4)
AB = √20
BC = √(3 - 1)² + (0 - 5)²
BC = √(2)² + (-5)²
BC = √(4 + 25)
BC = √29
CA = √(5 - 3)² + (3 - 0)²
CA = √(2)² + (3)²
CA = √(4 + 9)
CA = √13
Perimeter = AB + BC + CA
Perimeter = √20 + √29 + √13
Perimeter = 4.47 + 5.38 + 3.60
Perimeter = 13.45 units.
Thus, the perimeter of the shown triangle using the distance formula is found as 13.45 units.
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look at the picture below
Part a: Ratios of side = 1:3 ; Ratios of Area of base = 1: 9 ; Ratios of volume = 1: 27.
Part b: volume of medium box = 5832 cu. in .
Explain about the shape of cube:A solid shape comprising six square faces is called a cube. Because every square face has the identical side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is called to as a vertex.
Given data:
volume of cubical box = 216 cu. in.Let each side of the box be 'x'.Formula for the volume of cube :
V = side³
216 = x³
x = ∛216
x = 6 in.
Part A: length, with and height of cube is triples.
new side = 3*old side
new side = 3x
Ratios of side:
new side / old side = x / 3x = 1/3
new side : old side = 1:3
Area of base = side²
Ratios of Area of base:
new area / old area = x² / (3x)²
new area / old are = x² / 9x² = 1/9
new area : old are = 1: 9
Ratios of volume:
new vol / old vol = x³ / (3x³)
new vol / old vol = x³ / 27x³ = 1/27
new vol : old vol = 1:27
Part b: volume of medium box:
V = (3x)³
V = (3*6)³
V = (18)³
V = 5832 cu. in
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How are the lines below related
Answer:two lines are parallel if their slopes are equal and they have different y-intercepts
Step-by-step explanation:
Is 285mg more or less than 34.4 mg? My problem is not knowing for sure because of the decimal
Answer: 285 mg is more than 34.4 mg
Step-by-step explanation:
To compare the two quantities, we can simply look at the whole numbers before the decimal point.
285 is a larger whole number than 34, so we can say that 285 mg is more than 34.4 mg.
The decimals after the whole numbers are used to represent the fractions of the numbers.
An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1150, determine the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.
Therefore, the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.9732 or 97.32%.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.
Here,
Let μ be the mean tariff rate of all railroad-car shipments of ethanol, and let x be the mean tariff rate of a random sample of 600 railroad-car shipments of ethanol. We want to find the probability that x will be within $90 of μ.
The standard error of the mean (SE) can be calculated as:
SE = σ / √(n)
where σ is the standard deviation of the population, n is the sample size.
Substituting the given values, we get:
SE = 1150 / √(600)
≈ 47.03
The probability that x will be within $90 of μ can be calculated by standardizing x using the standard error and the z-score formula:
z = (x - μ) / SE
z = ($90) / 47.03
≈ 1.915
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.915 is approximately 0.9732.
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The equation -4x + y = 0 relates the
number of pages in a photo album y to
the number of pictures in the album x.
Tell whether the relationship is a direct
variation. Explain your answer.
Recall the general equation for a line in slope-intercept form:
[tex]y=mx+b[/tex]
where:
[tex]\text{y = y-coordinate}[/tex]
[tex]\text{m}=\bold{slope}[/tex]
[tex]\text{x = x-coordinate}[/tex]
[tex]\text{b = y-intercept}[/tex]
In this equation, if you isolate for [tex]y[/tex], you end up with an equation that looks like this:
[tex]-4x+y=0[/tex]
[tex]-4x +4x+y=0+4x[/tex]
[tex]\implies y=4x+0[/tex]
Recall that in direct variation, the graph goes through the origin, (0,0). Since the y-intercept of this equation is 0, this means the graph intersects the origin. Thus, this graph represents direct variation.
If you were to graph the line, you would see the intersection at (0,0):
graph[tex]\{y=4x [-12.66, 12.65, -6.33, 6.33]\}[/tex]
Please help me. Giving brainliest to whoever answers it!!!
The algebraic expression that represents the age of Ethan's dad is 4a - 5
How to represent the situation as an algebraic expression?Let's start by defining a variable to represent Ethan's age. We'll call this variable "a".
According to the problem, Ethan's dad is five years younger than four times Ethan's age. So, if we multiply Ethan's age by 4 and then subtract 5 years, we'll have the age of Ethan's dad.
Algebraically, we can represent this as:
4a - 5
Therefore, the algebraic expression that represents the age of Ethan's dad is 4a - 5.
Solve the equation [tex]3\frac{2}{3} x=2\frac{2}{5}[/tex]?Solve for x by simplifying both sides of the equation and isolating the variable.
[tex]3\frac{2}{3}x=2\frac{2}{5}[/tex]
Convert mixed numbers to improper fraction :
[tex]3\frac{2}{3} =\frac{11}{3}[/tex]
[tex]\frac{11}{3}x=2\frac{2}{5}[/tex]
Convert mixed numbers to improper fractions:
[tex]2\frac{2}{5} = \frac{12}{5}[/tex]
[tex]\frac{11}{3}x=\frac{12}{5}[/tex]
Multiply both sides by 3
[tex]11x=\frac{36}{5}[/tex]
Divide both sides by 11
[tex]x=\frac{36}{55}[/tex]
Therefore, [tex]3\frac{2}{3} x=2\frac{2}{5}[/tex] = [tex]x=\frac{36}{55}[/tex]
Steve sold 252 fruit baskets for the fundraiser. Therefore, we can find how many baskets Evie sold by using the ratio of her sales to Steve's sales, which is given as 25 baskets for each 100 baskets Steve sold.
We can set up a proportion to solve for the number of baskets Evie sold:
25/100 = x/252
Here, x represents the number of fruit baskets Evie sold.
To solve for x, we can cross-multiply and simplify:
25 * 252 = 100 * x
6300 = 100x
x = 63
Therefore, Evie sold 63 fruit baskets for the fundraiser.
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I saw this problem somewhere and tried to solve it, but it didn't work. Here is the problem; Suppose you have a ruler whose length is infinite, to measure a line of length: 3x + 15y = 12y - 45
Write a function and call it ω, and get the line length per ruler with the function
The function ω that gives the length per ruler for the line 3x + 15y = 12y - 45 is:
ω(x) = √(2)
How do we calculate?rewrite the equation of the line as:
3x - 3y = -45
The line has a slope of:
m = 3/3 = 1
We choose two points on the line with integer coordinates:
Point 1: (0, 15)
Point 2: (15, 30)
d = √t((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of the two points, we get:
d = √((15 - 0)^2 + (30 - 15)^2)
d = √(225 + 225)
d = √t(450)
d = 15√(2)
Length per ruler = (distance between points) / (total length of line)
3x + 15((3/2)x + 15) = 12((3/2)x + 15) - 45
we simplify this equation, we get:
3x + (45/2)x + 225 = (18/2)x + 180 - 45
Combining like terms, we get:
(57/2)x = 0
Solving for x, we get:
x = 0
Substituting this value of x into the expression for the total length of the line, we get:
y = (3/2)x + 15
y = 15
Length per ruler = (15√(2)) / 15
Length per ruler = √(2)
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The diameter of a circle is 6 centimeters. What is the circle's area?
Use 3.14 for .
Answer: The area of circle is 28.26 cm^2
Step-by-step explanation: As the diameter of the given circle is 6 cm, the radius of the same would be 3 cm.
Area of circle = pi r^2
And the value of pi is to be taken 3.14
The area of the given circle is 28.26cm^2.
answer ASAP pls with as as much detail in how to complete it as possible :))
Susan has a part-time job. The table below shows her earnings based on the number of hours worked.
Hours Worked, x
Earnings, E
Which equation best models this set of data?
An equation that best models this set of data is: D. y = 9.74x - 0.06
How to determine the line of best?In this scenario, the hours worked would be plotted on the x-axis (x-coordinate) of the scatter plot while the earnings would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the hours worked and earnings, an equation for the line of best fit is given by:
y = 9.74x - 0.06
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Identify the coordinate of any local and absolute extreme points and inflection points. Graph the function.
Y=5x+5 sin x, 0
The inflection occurs at x = n*pi, while the absolute extreme points, while the critical points can be found with the expression 5 + 5cos(x) = 0.
What are the extreme and inflection points?To find local extreme points, absolute extreme points, and inflection points, we will first take the first and second derivatives of the function.
y = 5x + 5sin(x)
y' = 5 + 5cos(x)
y'' = -5sin(x)
To find critical points, we set the first derivative equal to zero.
5 + 5cos(x) = 0
cos(x) = -1
x = pi
This is the only critical point, so we only need to evaluate the function at x = pi to find any extreme points.
y(pi) = 5pi - 5
So the absolute minimum occurs at (pi, -5).
To find inflection points, we set the second derivative equal to zero.
-5sin(x) = 0
sin(x) = 0
x = k*pi, where k is an integer.
So the inflection points occur at x = n*pi, where n is an integer.
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Suppose you roll a special 11-sided die. What is the probability that the number rolled is a "1" OR a "2"?
The probability of rolling a "1" OR a "2" on an 11-sided die is 2/11, or approximately 0.1818.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. Usually, it is stated as a number between 0 and 1, where 0 denotes that an event is impossible and 1 denotes that it is certain to happen.
According to question:The probability of rolling a "1" or a "2" on an 11-sided die can be calculated by adding the probabilities of rolling a "1" and rolling a "2".
Assuming the die is fair (i.e., each face has an equal chance of landing face up), the probability of rolling any particular number is 1/11. Therefore, the probability of rolling a "1" is 1/11, and the probability of rolling a "2" is also 1/11.
To find the probability of rolling a "1" OR a "2", we add the probabilities:
P(rolling a "1" OR a "2") = P(rolling a "1") + P(rolling a "2")
P(rolling a "1" OR a "2") = 1/11 + 1/11
P(rolling a "1" OR a "2") = 2/11
Therefore, the probability of rolling a "1" OR a "2" on an 11-sided die is 2/11, or approximately 0.1818 (rounded to four decimal places).
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a plumber has 6 1/3 feet of piping she needs 75 inches of piping does she have enough
Answer:
We need to convert both measurements to the same unit in order to compare them. Let's convert 6 1/3 feet to inches:
1 foot = 12 inches
6 feet = 6 x 12 = 72 inches
1/3 foot = (1/3) x 12 = 4 inches
6 1/3 feet = 72 + 4 + (1/3) x 12 = 76 inches
Therefore, the plumber has 76 inches of piping.
Since the plumber needs 75 inches of piping, we can see that she does have enough piping.
Step-by-step explanation: