The surface area of the cylinder is 905 square centimeters
Finding the surface area of the cylinderFrom the question, we have the following parameters that can be used in our computation:
Diameter, d = 12 cm
Height, h = 18 m
This means that
Radius, r = 12/2 = 6 cm
Using the above as a guide, we have the following:
Surface area = 2πr(r + h)
Substitute the known values in the above equation, so, we have the following representation
Surface area = 2π * 6 * (6 + 18)
Evaluate
Surface area = 905
Hence, the surface area is 905 square centimeters
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A rectangular park had a dirt path across its diagonal that was 100 yards long the diagonal and the long side of the park formed an angle that measured 30
The expression showing the distance is;
100cos30 + 100sin30 ≅ 137 yards. option B
How to determine the valueUsing the sine identity that is represented as;
sin θ = opposite/hypotenuse
Substitute the values as shown on the diagram, we have that;
sin 30 = y/100
Cross multiply the values, we get;
y= 100(0.5)
Multiply the values
y = 50 yards
Using the cosine identity written as;
cos θ = adjacent/hypotenuse
cos 30 = x/100
cross multiply the values
x = 0.8660(100)
Multiply the values, we get;
x = 86. 6 yards
The total distance = start + end = 86.6 + 50 = 136. 6 yards
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Find the length if the two missing sides in the parallelogram below
The value of the missing sides in the parallelogram are x = 3 and y = 6
Interpreting the parallelogram givenIn other to solve the question posted, we use the law which relates to the sides of a parallelogram which establishes that opposite sides of a parallelogram are of equal length.
This means that the side opposite length of 3 will also be 3 and vice-versa
side x = 3
side y = 6
Therefore, the missing sides of the parallelogram are 3 and 6 for sides x and y respectively.
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16
Select the correct answer.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?
OA.
OB.
O C
OD.
m. All rights reserved.
It is the graph of f(x) translated 3 units up.
It is the graph of f(x) translated 3 units down.
It is the graph of f(x) where the slope is decreased by 3.
It is the graph of f(x) translated 3 units to the left.
Reset
Next
Answer:
Graph translated 3 units down
Step-by-step explanation:
If the sin 60° is square root 3 over 2, then the cos ___° = ___. 30°; one half 60°; square root 2 over 2 30°; square root 3 over 2 60°; 1
If sin 60° = √3/2 then it follows that Cos 30 = √3/2
What is the relationship between the trigonometric ratios of 60 and 30?
Through precise geometric connections found inside a right triangle, the trigonometric ratios of 60 degrees and 30 degrees are connected. These relationships arise due to the specific geometric properties and angles of the right triangle and are frequently linked to the unique angles of 30, 45, and 60 degrees.
Given that;
Sin(30°) = 1/2
Sin(60°) = √3/2
Then;
Cos(30°) = √3/2
Cos(60°) = 1/2
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The table below shows (lifetime) peptic ulcer rates (per 100 population), U, for various family incomes, x, as reported by the 1989 National Health Interview Survey.
Income 4000 6000 8000 12000 16000 20000 30000 45000 60000
Ulcer rate 12.9 12.8 12.4 11.9 12.3 11.1 10.5 8.5 7.2
(a) Find the equation of the regression line.
The equation of the regression line is approximately:
y = -5.347x + 24.405
To find the equation of the regression line, we need to perform linear regression on the given data points.
The equation of a regression line is typically represented as:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
In this case, the independent variable is the family income (x) and the dependent variable is the ulcer rate (y).
We can calculate the slope (m) and y-intercept (b) using the following formulas:
m = (Σ(xy) - (Σx)(Σy) / n(Σx²) - (Σx)²)
b = (Σy - m(Σx)) / n
Let's calculate the slope (m) and y-intercept (b) using the given data points:
Income (x) Ulcer rate (y)
4000 12.9
6000 12.8
8000 12.4
12000 11.9
16000 12.3
20000 11.1
30000 10.5
45000 8.5
60000 7.2
Σx = 4000 + 6000 + 8000 + 12000 + 16000 + 20000 + 30000 + 45000 + 60000 = 224000
Σy = 12.9 + 12.8 + 12.4 + 11.9 + 12.3 + 11.1 + 10.5 + 8.5 + 7.2 = 100.6
Σxy = (4000 * 12.9) + (6000 * 12.8) + (8000 * 12.4) + (12000 * 11.9) + (16000 * 12.3) + (20000 * 11.1) + (30000 * 10.5) + (45000 * 8.5) + (60000 * 7.2) = 2,685,000
Σx² = (4000²) + (6000²) + (8000²) + (12000²) + (16000²) + (20000²) + (30000²) + (45000²) + (60000²) = 8,144,000,000
n = 9 (number of data points)
Now, let's substitute these values into the formulas to find m and b:
m = (Σ(xy) - (Σx)(Σy) / n(Σx²) - (Σx)²)
= (2,685,000 - (224000 * 100.6) / (9 * 8,144,000,000) - (224000)²
≈ -5.347
b = (Σy - m(Σx)) / n
= (100.6 - (-5.347) * 224000) / 9
≈ 24.405
Therefore, the equation of the regression line is approximately:
y = -5.347x + 24.405
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Find the area of the parallelogram
Answer:
1191 cm²
Step-by-step explanation:
Area of parallelogram = base X vertical height.
Call the vertical line h.
h/ sin 80 = 7/ sin 10
h = (7 sin 80) / sin 10
= 39.7.
Area of parallelogram = 30 X 39.7
= 1191 cm²
The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.
Given:
Side length = 30 cm
Using Trigonometry
tan 80 = P / Base
5.6712 = P / 7
P = 39.6984 cm
Using the formula for Area of parallelogram
= Base x height
= 30 x 39.6984
= 1,190.952 square cm.
Therefore, the area is 1,190.952 square cm.
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A family has two cars. During one particular week, the first car consumed 15 gallons of gas and the second consumed 25 gallons of gas. The two cars drove a combined total of 1525miles, and the sum of their fuel efficiencies was 75 miles per gallon. What were the fuel efficiencies of each of the cars that week?
The fuel efficiency of the first car is 35 miles per gallon, and the fuel efficiency of the second car is 40 miles per gallon.
Let's assume the fuel efficiency of the first car is x miles per gallon and the fuel efficiency of the second car is y miles per gallon.
Given that the first car consumed 15 gallons of gas and the second car consumed 25 gallons, we can set up the following equations:
15x + 25y = 1525 -- (Equation 1) (Total miles driven by both cars)
x + y = 75 -- (Equation 2) (Sum of their fuel efficiencies)
To solve this system of equations, we can use substitution or elimination method. Let's solve it using the substitution method:
From Equation 2, we can express y in terms of x:
y = 75 - x
Substituting this value of y into Equation 1:
15x + 25(75 - x) = 1525
Expanding and simplifying:
15x + 1875 - 25x = 1525
-10x = -350
Dividing both sides by -10:
x = 35
Substituting the value of x back into Equation 2 to find y:
y = 75 - x
y = 75 - 35
y = 40
Therefore, the fuel efficiency of the first car is 35 miles per gallon, and the fuel efficiency of the second car is 40 miles per gallon.
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B.
(94)0=
= 9¹
Reason:
Step-by-step explanation:
The exponent you put in the box multiplies the exponent ' 4' to get the exponent '1'
4 * x = 1
x = 1/4 <====this goes in the box
combine like terms
8x+3-5x+9
a. 3x+12
b.-13x-12
c.13x+12
d.3x-6
Answer:
A. 3x+12
Step-by-step explanation:
8x+3-5x+9
8x-5x=3x
3+9=12
then put them together
3x+12
answer= A
Are older men shorter than younger men? According to a national report, the mean height for U.S. men is 69.4 inches. In a sample of 119 men between the ages of 60 and 69 , the mean height was ₓ⁻=69.3 inches. Public health officials want to determine whether the mean height μ for older men is less than the mean height of all adult men. Assume the population standard deviation to be σ=2.58 . Use the α=0.05 level of significance and the P-value method
There is not enough evidence to support the claim that older men are shorter than younger men.
How to explain the hypothesisThe test statistic for this hypothesis test is:
t = (x - μ) / σ / √n
= (69.3 - 69.4) / 2.58 / √119
= -0.13
The p-value for this hypothesis test is:
p-value = P(t < -0.13)
= 0.8944
We cannot conclude that the mean height of older men is less than the mean height of all adult men. The results are not statistically significant.
There is not enough evidence to support the claim that older men are shorter than younger men.
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La asistencia a un juego fue de 250 personas el boleto  de admisión para un adulto fue de 100 y el de los niños de 50 si la recaudación fue de 21,000 ¿cuantos adultos y cuántos niños pagaron el boleto?
The number of adults who paid for the ticket are 170 adults and the number of children who paid for the ticket are 80 children.
How to determine the number of each type of tickets sold?In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of children tickets sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of adult tickets sold.Let the variable y represent the number of children tickets sold.Since 250 people attended the game, a linear equation that models the situation is given by:
x + y = 250 ....equation 1.
Additionally, adult tickets sold for $100 while children tickets sold for $50 each with a total revenue was $21,000, a linear equation that models the situation is given by:
100x + 50y = 21,000 .......equation 2.
By using the substitution method to solve the equations simultaneously, we have:
100x + 50(250 - x) = 21,000
100x + 12,500 - 50x = 21,000
50x = 21,000 - 12,500
x = 8,500/50
x = 170 adults.
For the children tickets sold, we have:
y = 250 - x
y = 250 - 170
y = 80 children.
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Complete Question:
Attendance at a game was 250 people, the admission ticket for an adult was $100 and for children $50, if the collection was $21,000, how many adults and how many children paid for the ticket?
David found a vintage watch his father lost 38 years ago. The watch’s date showed that it had worked for over two years after his father lost it. When David found the watch, it was 3 times as old as when his father lost it. How old was the watch when David’s father lost it?
The age of the watch when David's father lost it was 13. 3 years.
How to find the age ?David found the watch 38 years after his father lost it, and the watch worked for 2 years after it was lost. That means the watch was 40 years old when David found it.
When David found it, the watch was 3 times as old as when his father lost it. This means that :
= Number of years lost / 3
= 40 / 3
= 13. 3 years
In conclusion, the watch was 13. 33 years old when David's father lost it.
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I AM GIVING 45 POINTS IF YOU DO THE WHOLE HOMEWORK CORRECTLY!!!!!!!!!!!!!
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student: Amber / Ben / Carter
Description: Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. / Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. / Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares: f(x) = 3(4)x
Day: Number of Shares:
0 2
1 6
2 18
Carter shared his post with 10 friends, who each share with only 2 people each day.
1. Write an exponential function to represent the spread of Ben's social media post.
2. Write an exponential function to represent the spread of Carter's social media post.
3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
4. Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers.
5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of Amber's photo share?
6. Based on your results, which student's post travels the fastest? How is this shown in the equation form of the functions?
7. If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions.
Answer:
1. The exponential function to represent the spread of Ben's social media post is f(x) = 2(3)^x
2. The exponential function to represent the spread of Carter's social media post is f(x) = 10(2)^x
4. To predict how many shares each student's post will be received on Day 3 and Day 10, substitute the respective values of x into each function:
a) On Day 3, Amber's post will have f(3) = 3(4)^3 = 192 shares. On Day 10, Amber's post will have f(10) = 3(4)^10 = 6,291,456 shares.
b) On Day 3, Ben's post will have f(3) = 2(3)^3 = 54 shares. On Day 10, Ben's post will have f(10) = 2(3)^10 = 196,830 shares.
c) On Day 3, Carter's post will have f(3) = 10(2)^3 = 80 shares. On Day 10, Carter's post will have f(10) = 10(2)^10 = 10240 shares.
5. The graph of Amber's post with copies mailed to the assisted living facility will have the same shape and growth rate as the original function, but it will be shifted upwards by 45 units along the y-axis.
6. Ben's post travels the fastest because it has the largest growth rate of 3 (compared to Amber's 4 and Carter's 2), meaning it triples every day.
7. It depends on the specific purpose of the post. If the goal is to have a widespread influence and viral impact, then Amber's approach of starting with a smaller group of initial shares but a higher growth rate might be more effective. On the other hand, if the goal is to create a more tight-knit network of shares with a smaller number of initial friends, then Carter's approach might be more appropriate.
Identify whether each equation has one solution, no solution, or infinitely many solutions.
9. 3 − x = x − 3
10. 4x − 8 = 4(x − 2)
11. 5(1 − x) = 5 + 5x
12. x + 2(x − 7) = 3x − 7
Answer:
Problem 9: One solution
Problem 10: Infinitely many solutions
Problem 11: One solution
Problem 12: No solution
Step-by-step explanation:
Solving one-variable equations
When solving a one variable equation, there are two steps:
Step 1. Get the variable to show up exactly onceStep 2. Get the variable by itselfDuring Step 1 of that process, usually one will be combining like-terms to take two terms that contain x, and merging them into one term that contains x. However, occasionally, the like terms contain x will completely cancel, leaving an equation with no variable left in it.
At that point, there are one of two possibilities:
Possibility #1: The remaining equation is truePossibility #2: The remaining equation is falseIf the remaining equation is true, it doesn't matter what the value of x is, the equation will be true. This means there are infinitely many solutions (any value of x will make the equation true).
Similarly, if the remaining equation is false, it doesn't matter what the value of x is, the equation will be false. This means there are no solutions (no values of x that will make the equation true).
Problem 9
[tex]3-x=x-3[/tex]
Add "x" to both sides to move the x-term on the left side of the equation from the left, to the right side, and group like terms.
[tex]3=2x-3[/tex]
We were able to combine like terms containing the x into a single term. This equation will have one solution.
The remaining work is unnecessary to answer the question, but shows that there is one solution, the steps to find it, and what it is.
[tex]6=2x[/tex]
[tex]3=x[/tex]
Problem 10
[tex]4x-8=4(x-2)[/tex]
Use the distributive property on the expression on right hand side of the equation ...
[tex]4x-8=4x-8[/tex]
Observe that at this point, the entire left hand side of the equation EXACTLY matches that of the entire right hand side of the equation.
They are not just equal, they are exactly the same.
Attempting to move the term with x on the left hand side to the right hand side will require subtracting 4x from both sides, but combining like terms will cancel all terms with x on both sides....
[tex]-8=-8[/tex]
Since negative eight is ALWAYS equal to negative eight, no matter what value you choose for x, the equation must be true because each side is the same exact expression. This means there are infinitely many solutions.
Problem 11
[tex]5(1-x)=5+5x[/tex]
Apply the distributive property on the expression on left hand side of the equation ...
[tex]5-5x=5+5x[/tex]
Add 5x to both sides of the equation to move the terms with x on the left side to the right side of the equation, and combine like terms...
[tex]5=5+10x[/tex]
Again, we were able to combine like terms containing the x into a single term. This equation will have only one solution:
Subtract 5 from both sides...
[tex]0=10x[/tex]
Divide both sides by 10...
[tex]0=x[/tex]
Problem 12
[tex]x+2(x-7)=3x-7[/tex]
Apply the distributive property on the expression on left hand side of the equation ...
[tex]x+2x-14=3x-7[/tex]
Combine like terms on the left hand side of the equation...
[tex]3x-14=3x-7[/tex]
To move the term with x from the left side to the right side, subtract 3x from both sides, and combine like terms...
[tex]-14=-7[/tex]
Here, when combining like terms, the x all canceled out, and negative 14 is not equal to negative 7. So, there is no solution so this equation.
Let f(x) = 3x^2 + 4x + 5 and let g(h) = (f(3 + h) - f(3))/(h). Determine each of the following
The value of function g(1) is 45, g(0.1) is 22.23, and g(0.01) is 20.22.
To determine the values of g(1), g(0.1), and g(0.01), we need to substitute the given values into the expression for g(h) and evaluate their function them.
First, let's find the expression for g(h):
[tex]g(h) = \frac{(f(3 + h) - f(3))}h[/tex]
Now, substitute the function f(x) into g(h):
[tex]g(h) = \frac{((3(3 + h)^2 + 4(3 + h) + 5) - (3(3)^2 + 4(3) + 5))}h[/tex]
Simplifying further:
[tex]g(h) = \fract{((3(9 + 6h + h^2) + 12 + 4h + 5) - (27 + 12 + 5))}{h}\\\\g(h) = \frac{(27 + 18h + 3h^2 + 12 + 4h + 5 - 27 - 12 - 5)}h\\\\g(h) = \frac{(3h^2 + 22h + 20)}h[/tex]
Now, we can substitute the values of h into the expression to find g(1), g(0.1), and g(0.01):
[tex]g(1) =\frac{ (3(1)^2 + 22(1) + 20)}1 = 3 + 22 + 20 = 45\\\\g(0.1) = \frac{(3(0.1)^2 + 22(0.1) + 20)}{0.1} = 0.03 + 2.2 + 20 = 22.23\\\\g(0.01) = \frac{(3(0.01)^2 + 22(0.01) + 20)}{0.01} = 0.0003 + 0.22 + 20 = 20.22[/tex]
Therefore, the value of function g(1) is 45, g(0.1) is 22.23, and g(0.01) is 20.22.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The exact value of the trigonometric function by half-angle formula is cos 22.5° = √(2 + √2) / 2. (Correct choice: B)
How to determine the exact value of a trigonometric function
In this problem we are asked to determine the exact value of a trigonometric function by means of a trigonometric formula known as half-angle formula:
cos 0.5θ = √[(1 + cos θ) / 2]
If we know that θ = 45°, then the exact value of the half-angle formula:
cos 22.5° = √[(1 + cos 45°) / 2]
cos 22.5° = √[(1 + √2 / 2) / 2]
cos 22.5° = √(2 + √2) / 2
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Right triangle ABC was dilated with a scale factor of 2. How many times larger is the area of triangle DEF than triangle ABC?
The area of triangle DEF is four times larger than the area of triangle ABC.
We have,
Right triangle ABC was dilated with a scale factor of 2.
When a triangle is dilated with a scale factor of 2, the resulting triangle is enlarged by a factor of 2 in each dimension.
Since area is a two-dimensional measure, it will be enlarged by a factor of the square of the scale factor.
In this case, the scale factor is 2, so the area of triangle DEF will be
= 2²
= 4 times larger than the area of triangle ABC.
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4)
Which product is less than ?
10/0
10
>)
Answer: Option A) \frac{7}{10} * \frac{5}{8}
factorise 35 + 5f
No need for explanation if u don't want to type it
Answer: 5(f+7)
Step-by-step explanation: I know you didn't ask for an explanation but here:
First what you want to do is find what both terms have in common, the LCM, (least common multiple), is the only thing common between them, which is 5, so divide 35 by 5, which is 7, and since you divided by 5, you put it outside, and put f and 7 together.
What the meaning of statement this?
The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.
The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.
In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.
The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.
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PLEASE HELP BEGGING YOU PLEASE
EXTRA POINT AND BRIANLY
Answer:
-5, x=2
Step-by-step explanation:
name me brainliest and say thank you and please verify.
how do I understand implicit function
Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.
Step-by-step explanation: To find the implicit derivative,
Differentiate both sides of f(x, y) = 0 with respect to x.
Apply usual derivative formulas to differentiate the x terms.
Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.
Solve the resultant equation for dy/dx (by isolating dy/dx).
A motorboat travels 58 kilometers in 2 hours going upstream. It travels 90 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current? km
b = speed of the boat in still water
c = speed of the current
when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.
We also know it took 2 hours Upstream as well as Downstream, and we also know how far it went, so
[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{km}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&58&b-c&t\\ Downstream&90&b+c&t \end{array}\hspace{5em} \begin{cases} 58=(b-c)(2)\\\\ 90=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{58=(b-c)2}\implies \cfrac{58}{2}=b-c\implies 29=b-c\implies 29+c=b \\\\\\ \stackrel{\textit{using the 2nd equation}}{90=(b+c)2}\implies \cfrac{90}{2}=b+c\implies 45=b+c\implies \stackrel{\textit{substituting}}{45=(29+c)+c} \\\\\\ 45=29+2c\implies 16=2c\implies \cfrac{16}{2}=c\implies \boxed{8=c}~\hfill \stackrel{ 29~~ + ~~8 }{\boxed{b=37}}[/tex]
Can you match the correct expression to its expanded form and type the correct code?
Show Work Please
Expansion is the multiplying of each term in the bracket by the expression outside the bracket. Expansion is also when we multiply to remove the ( ).
How to determine this
Given,
11. [tex](x-8)^{2}[/tex]
By expanding it
= (x-8)(x-8)
Open bracket
= [tex]x^{2} - 8x -8x + 64[/tex]
= [tex]x^{2} - 16x+64[/tex]
Therefore, [tex](x-8)^{2}[/tex] matches with D. [tex]x^{2} - 16x+64[/tex]
12. (x+6)(x-6)
By expansion
Open bracket
= [tex]x^{2} -6x+6x-36[/tex]
= [tex]x^{2} - 36[/tex]
So, (x+6)(x-6) matches with E. [tex]x^{2} - 36[/tex]
13. (2x-5)(2x+5)
By expanding it
Open bracket
= [tex]4x^{2} +10x -10x-25[/tex]
= [tex]4x^{2} - 25[/tex]
So, (2x-5)(2x+5) matches with H. [tex]4x^{2} - 25[/tex]
14.[tex](3x+1)^{2}[/tex]
Expanding this,
= (3x+1)(3x+1)
Open bracket
= [tex]9x^{2} + 3x +3x+1[/tex]
= [tex]9x^{2} +6x+1[/tex]
Therefore, [tex](3x+1)^{2}[/tex] matches with A. [tex]9x^{2} +6x+1[/tex]
15.[tex](x+4)^{2}[/tex]
By expanding it
= (x+4)(x+4)
Open bracket
= [tex]x^{2} + 4x+4x+16[/tex]
= [tex]x^{2} +8x+16[/tex]
Therefore, [tex](x+4)^{2}[/tex] matches with F. [tex]x^{2} +8x+16[/tex]
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Billy has a marble jar that contains 5 orange marbles, and 2 purple marbles. He will draw two marbles from the jar one at a time without replacing the first marble.
What is the probability that Billy gets an orange marble on his first draw and a purple marble on his second draw?
The probability that Billy gets an orange marble on his first draw and a purple marble on his second draw is P ( A ) = 5/21
Given data ,
To find the probability of Billy drawing an orange marble on his first draw and a purple marble on his second draw, we need to calculate the probability of each event and multiply them together.
Billy's marble jar contains 5 orange marbles and 2 purple marbles. Let's calculate the probabilities for each draw:
Probability of drawing an orange marble on the first draw:
Billy has a total of 5 + 2 = 7 marbles in the jar.
The probability of drawing an orange marble on the first draw is 5/7 since there are 5 orange marbles out of the total 7 marbles.
Probability of drawing a purple marble on the second draw:
After the first draw, there will be 6 marbles left in the jar, with 4 orange marbles and 2 purple marbles remaining.
The probability of drawing a purple marble on the second draw is 2/6 since there are 2 purple marbles out of the remaining 6 marbles.
Probability = (5/7) * (2/6)
Probability = 10/42
Probability = 5/21
Hence , the probability that Billy gets an orange marble on his first draw and a purple marble on his second draw is 5/21
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A trawler A is 40km west of another trawler B. A set off at 20kmh travel at 25kmh. What course should trawler B take to intercept trawler A
Trawler B should take a course that is 18 degrees east of north.
How to explain the angleIn order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.
Here are the steps to find the course that Trawler B should take:
Draw a diagram of the situation.
Label the two trawlers A and B.
Draw a line representing the direction that Trawler A is traveling.
Draw a line representing the direction that Trawler B should travel.
Measure the angle between the two lines.
The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.
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Find real numbers a, b, and c so that the graph of the function y=ax^2+bx+c contains the points (-1,4), (3,9) and (0,3)
The values of real numbers a, b, and c are,
a = 3/4
b = - 1/4
c = 3
Since, We have to given that;
The graph of the function y = ax² + bx + c contains the points (-1,4), (3,9) and (0,3).
Now, We can formulate;
The points are satisfy the function.
So, We get;
y = ax² + bx + c
Put x = - 1, y = 4
4 = a (- 1)² + b (- 1) + c
4 = a - b + c ... (i)
y = ax² + bx + c
Put x = 3, y = 9
9 = a (3)² + b (3) + c
9 = 9a + 3b + c .. (ii)
y = ax² + bx + c
Put x = 0, y = 3
3 = a (0)² + b (0) + c
3 = c .. (iii)
In equation (i) put c = 3;
4 = a - b + c
4 = a - b + 3
a - b = 4 - 3
a - b = 1 .. (iv)
In equation (ii) put c = 3;
9 = 9a + 3b + c
9 = 9a + 3b + 3
9a + 3b = 6
3a + b = 2 . (v)
Add (iv) and (v);
4a = 3
a = 3/4
And, a - b = 1
3/4 - b = 1
3/4 - 1 = b
b = - 1/4
Hence, The values of a, b, and c are,
a = 3/4
b = - 1/4
c = 3
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The arrow on each spinner will be spun one time. Which statement about the section each arrow will stop in is true?
A)It is impossible for the arrows on both spinner A and spinner B to stop in a section with the number 3 in it.
B)o The arrows on both spinner A and spinner B are certain to stop in a section with the number 3 in it.
C)o The arrow on spinner A is less likely to stop in a section with the number 3 in it than the arrow on spinner B.
D)o The arrow on spinner A is more likely to stop in a section with the number 3 in it than the arrow on spinner B
Answer:
The answer is D.
Step-by-step explanation:
Determine and state the coordinates of the center and the length of the radius of the
circle whose equation is 17 + y? + 6x = 6y + 63. Do it on a graph also
Answer: The equation of the circle can be rewritten in standard form by completing the square for both x and y terms. The standard form of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
17 + y^2 + 6x = 6y + 63 y^2 - 6y + 6x + 17 = 63 y^2 - 6y + 9 + 6x = 63 + 9 (y - 3)^2 + 6x = 72 (y - 3)^2 + 6(x - (-6)) = 72 (y - 3)^2 + (x + 6)^2 = 72
From this we can see that the center of the circle is (-6,3) and the radius is sqrt(72) = 6sqrt(2).
I’m sorry but I’m unable to draw a graph for you.
pls help e for brainleist
By Using
[tex] \sf \: Exterior \:Angle\: Property \:of\: triangle[/tex]
[tex] \large \sf \: → x = 67° + 90° [/tex]
[tex] \large \bf \: → x = 157° [/tex]
Value of x is = 157°[tex] \underline{ \rule{200pt}{6pt}}[/tex]
