There is a line that includes the point (8,3) and has a slope of 1. What is its equation in slope-intercept form?
Answers
Answer:
y=x-5
Step-by-step explanation:
y-y1=m(x-x1)
y-3=1(x-8)
y-3=x-8
y=x-8+3
y=x-5
Related Questions
Im not the best at word problems A box of jerseys for a pick-up game of basketball contains 10 extra-large jerseys, 7 large jerseys, and 5 medium jerseys. If you are first to the box and grab 3 jerseys, what is the probability that you randomly grab 3 medium jerseys? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
Answers
Given:
The number of extra-large jerseys is 10.
The number of large jerseys is 7.
The number of medium jerseys is 5.
Three jerseys to be taken.
To find the probability that randomly grabs 3 medium jerseys:
The probability is,
\(\begin{gathered} P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} \\ =\frac{^5C_3}{^{22}C_3} \\ =\frac{\frac{5!}{(5-3)!3!}}{\frac{22!}{(22-3)!3!}} \\ =\frac{\frac{5!}{2!3!}}{\frac{22!}{19!3!}} \\ =\frac{5\times4\times3}{22\times21\times20} \\ =\frac{1}{154} \end{gathered}\)Hence, the probability that randomly grabs 3 medium jerseys is,
\(\frac{1}{154}\)Ay 82a25) F C(2a + 2c, 26) The area of a parallelogram is given by the formula A = bh, where A is the area, b is the length of a base, and h is the height perpendicular to the base. ABCD is a parallelogram. E, F, G, and Hare the midpoints of the sides. 7. Show that the area of EFGH is half the area of ABCD. G A(0,0) H D(2c, 0)
Answers
First let's calculate the area of ABCD.
Using AD as the base, the height can be calculated with the difference of y-coordinates of the points B and A, and the base is the difference of x-coordinates of the points D and A:
\(\begin{gathered} h=2b-0=2b \\ base=2c-0=2c \end{gathered}\)So the area of ABCD is:
\(A=2b\cdot2c=4bc\)Now, finding the coordinates of the midpoints E, F, G and H, we have:
\(\begin{gathered} E_x=\frac{2a+0}{2}=a \\ E_y=\frac{2b+0}{2}=b \\ \\ F_x=\frac{2a+2c+2a}{2}=2a+c \\ F_y=\frac{2b+2b}{2}=2b \\ \\ G_x=\frac{2a+2c+2c}{2}=a+2c \\ G_y=\frac{2b+0}{2}=b \\ \\ H_x=\frac{0+2c}{2}=c \\ H_y=\frac{0+0}{2}=0 \end{gathered}\)Using EG as a base of the triangles EGF and EGH, we can calculate the areas of these triangles.
The height of these triangles are the difference in y-coordinates of the point F and E:
\(\begin{gathered} h=2b-b=b \\ \text{base}=a+2c-a=2c_{} \\ \text{Area}=\frac{2c\cdot b}{2}=bc \end{gathered}\)Adding the area of the two triangles, we have the area of EFGH:
\(A=bc+bc=2bc\)So comparing the area of EFGH and ABCD, we have:
\(\frac{2bc}{4bc}=\frac{1}{2}\)Therefore the area of EFGH is half the area of ABCD.
(1 point) if you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
Answers
The largest area that can be enclose in straight wall is 2450 m².
What is meant by the largest area?Having to maximize or decrease a geometric figure's measurements, area, or volume is a special example of a geometry word problem.Let 'x' be the length of rectangle.
Let 'y' be the width rectangle.
Perimeter = 140 meters
2x + y = 140
y = 140 - 2x
Area = xy
Put the value of y in area.
Area = x(-2x + 140)
Area = -2x² + 140x
Differentiating the area with respect to x.
dA/dx = -4x + 140
Put dA/dx = 0 to get the critical point.
-4x + 140 = 0
x = 140/4
x = 35
Largest area at x = 35.
y = 140 - 2x
y = 140 - 2×35
y = 70
Area = xy
Area = 70×35
Area = 2450 m²
Thus, the largest area that can be enclose in straight wall is 2450 m².
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m(x)=4x+15;m(x)=7
Answer?
Answers
Answer:
M=0
Step-by-step explanation:
(M)=4M+15(M)=7
We move all terms to the left:
(M)-(4M+15(M))=0
We add all the numbers together, and all the variables
M-(+19M)=0
We get rid of parentheses
M-19M=0
We add all the numbers together, and all the variables
-18M=0
M=0/-18
M=0
Two athletes Or training over a two week period to increase the number of push-ups each can do consecutively . Athlete a can do 16 push-ups to start and increase his total by each to each day. Athlete b can do 12 push-ups to start an increase he's so tall by three each day. Compare the initial values for each what does the initial value mean in the situation
Answers
Answer:
Initial values of Athlete a and b is 16 and 12 respectively. That means, Athlete a start with more push-ups as compared to athlete b
Step-by-step explanation:
Athlete a perform 16 push-ups to start and increase 1 push-up each day for 14 days
⇒ number of push-ups at the end of x days is for Athlete A is
n = number of push-ups for athlete A= 16 + x
Athlete b perform 12 push-ups to start and increase 3 push-up each day for 14 days
⇒ number of push-ups at the end of x days is for Athlete B is
m = number of push-ups for athlete B = 12 + 3x
where x is the number of days
thus, total number of athletes at the end of 14 day is
n = 16+14 = 30 push-ups for athlete A and m = 12 + 42 = 54 push-ups for athlete B at the end of 14th day
Now similarly for the initial day x = 0
thus, total number of athletes at the starting of 1st day is
n = 16+0 = 16 push-ups for athlete A and m = 12+0 =12 push-ups for athlete B at the starting of 1st day.
That means, Athlete a start with more push-ups as compared to athlete b, But at the end of 14th day Athlete b do more push-ups then athlete a
Answer: The initial value for Athlete A is greater.
Pay attention for the keyword initial value.
I got no explanation D:
Use the graph of the function f to decide whether the value of the given quantity exists. (If an answer does not exist, enter DNE.) WebAssign Plot (a) f(−2) DNE Correct: Your answer is correct. (b) lim x→−2 f(x) DNE Correct: Your answer is correct. (c) f(0) 5 Correct: Your answer is correct. (d) lim x→0 f(x) 3.5 Incorrect: Your answer is incorrect. (e) f(2) DNE Correct: Your answer is correct. (f) lim x→2 f(x) 0.5 Correct: Your answer is correct. (g) f(4) 0 Correct: Your answer is correct. (h) lim x→4 f(x) DNE Correct: Your answer is correct.
Answers
f(-2) and f(2) does not exist. Limit when x tend to -2, 0 and 4 does not exist. f(0) = 5 and f(4) = -1. Limit when x tend to 2 converges to 0.5.
f(-2) does not exist as shown in the figure there is no definite value at -2. Also limit does not exist at x = -2 as right limit approaches positive infinity where left limit approaches negative infinity.
f(0) equals 5 and not 3.5 as we can see that at 3.5 it is a hole implying it is not defined, while at 5 it is a solid dot. Limit does not exist at f(0) as the left limit approaches 3.5 and the right limit approaches 5.
f(2) does not exist as there is a hole at that point in the graph. Limit as x tend to 2 approaches 0.5 as both right and left limit approaches 0.5.
f(4) equals -1 as the solid dot is at that point. As x tend to 4 the limit diverges to positive infinity implying the limit does not exist.
--The question is not readable, answering to the question below and graph attached--
"Use the graph of the function f to decide whether the value of the given quantity exists. (If an answer does not exist, enter DNE.)
(a) f(−2)
(b) lim x→−2 f(x)
(c) f(0)
(d) lim x→0 f(x)
(e) f(2)
(f) lim x→2 f(x) 0.5
(g) f(4)
(h) lim x→4 f(x) "
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Can you please help me with this problem!!
Answers
Answer:
.
Step-by-step explanation:
Compare the budgets of Hong Kong, United States of America, and
Korea based on your definition of a budget, in terms of contents,
formats, advantages, and disadvantages, etc.
Answers
The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.
A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:
Hong Kong Budget:Contents: The Hong Kong budget comprises revenue and expenditure. It provides a detailed analysis of expected sources of income and the allocation of funds.Format: The Hong Kong budget is presented in a clear and concise format, including charts and graphs to aid understanding.Advantages: The budget is easy to understand, and it promotes transparency and accountability.Disadvantages: It does not provide detailed information on tax expenditures and lacks public participation in the budget process.
United States Budget:
Contents: The US budget comprises revenue, expenditures, and deficit or surplus. It includes an analysis of taxes, social security, and Medicare.Format: The US budget is presented in a complex and lengthy format, including tables, graphs, and other financial documents.Advantages: The budget provides detailed information on tax expenditures and encourages public participation in the budget process.Disadvantages: The budget can be challenging to understand due to its complexity, and it may not provide an accurate depiction of federal spending.Korean Budget:
Contents: The Korean budget comprises revenue, expenditures, and surplus or deficit. It includes detailed information on taxes, social security, and public welfare.Format: The Korean budget is presented in a clear and concise format, including tables and charts to aid understanding.Advantages: The budget is easy to understand, and it promotes transparency and accountability. It also provides detailed information on social welfare expenditures.Disadvantages: The budget may not provide an accurate depiction of government spending, and it may not include information on hidden expenditures.Learn more about Budget:
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What is the angle of rotational symmetry of the figure
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Rotational symmetry is a property of a shape or a figure that does not change its appearance when rotated by a certain degree about a center. A figure has rotational symmetry if it appears unchanged after being rotated by less than 360 degrees about its center. The degree of rotation at which the figure looks unchanged is called the angle of rotational symmetry of the figure.
Now, let's talk about the angle of rotational symmetry of the figure. The angle of rotational symmetry of a figure is the smallest angle at which the figure looks unchanged after being rotated about its center. For example, if a figure looks the same after being rotated by 60 degrees about its center, it has a rotational symmetry of 60 degrees. If it looks the same after being rotated by 90 degrees, then its rotational symmetry is 90 degrees.There are certain rules that need to be followed to determine the angle of rotational symmetry of a figure. These rules are:
If a figure has rotational symmetry of 360 degrees, then it is said to have infinite rotational symmetry. This is because the figure looks the same after being rotated by any angle about its center.
If a figure has rotational symmetry of 180 degrees, then it is said to have rotational symmetry about a line. This is because the figure looks the same after being rotated by 180 degrees about its center.
If a figure has rotational symmetry of 90 degrees, then it is said to have rotational symmetry about a point. This is because the figure looks the same after being rotated by 90 degrees about its center.
If a figure has rotational symmetry of less than 90 degrees, then it is said to have rotational symmetry about two or more points.
Therefore, we need to see the given figure to determine its rotational symmetry angle.
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Fill in the blanks:- If y = 2 - x + x2 + 8ex is a solution of a homogeneous fourth-order linear differential equation with constant coefficients, then the roots of the auxiliary equation are_________ .
Answers
The roots of the auxiliary equation for a homogeneous fourth-order linear differential equation with constant coefficients, given that the solution is y = 2 - x + x^2 + 8e^x, are -1, -1, -2, and -2.
For a homogeneous linear differential equation with constant coefficients, the auxiliary equation is obtained by replacing the derivatives of y with powers of the variable. In this case, since the given solution is y = 2 - x + x^2 + 8e^x, we differentiate y with respect to x to obtain the derivatives.
The fourth-order linear differential equation corresponds to the fourth power of the variable, which is x. Therefore, the auxiliary equation is a polynomial equation of degree four. To find the roots of the auxiliary equation, we set the polynomial equal to zero and solve for x.
The roots of the auxiliary equation for this particular solution, after solving the polynomial equation, are -1, -1, -2, and -2. These values represent the roots of the characteristic equation and are crucial in determining the form of the general solution of the differential equation.
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Jamie deposits $627 into a savings account.the account has an interest rate of 3.5%, compounded quarterly. Write the function that gives the amount of money in dollars, j(t), in Jamie’s account t years after the initial deposit
Answers
The function that gives the amount of money in dollars, j(n), in Jamie’s account n years after the initial deposit is J(n) = P(1 + (r/3)/100)³ⁿ.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, Jamie deposits $627 into a savings account and the account has an interest rate of 3.5%, compounded quarterly.
P = $627, r = 3.5%.
We know the formula for compound interest compounded quarterly is
A = P(1 + (r/3)/100)³ⁿ.
Or
J(n) = P(1 + (r/3)/100)³ⁿ. (here t is replaced by n).
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PLEASE HELP ME!!!!! ITS AN EMERGENCY!!! PLEASE!!!
Answers
Answer:
i think G
Step-by-step explanation:
Answer:
G. rational numbers only
Step-by-step explanation:
This part of the question concerns the quadratic equation 5x^2 - 21x + 29 = 0. ii (i) Find the discriminant of the quadratic expression 5x^2 – 21x + 29. What does this discriminant tell you about the number of solutions of the equation? Explain your answer briefly. (iii) What does this discriminant tell you about the graph of y = 5x^2 – 21x + 29?
Answers
(i) the discriminant of the Quadratic expression 5x^2 - 21x + 29, we will use the formula D = b^2 - 4ac is -139
(ii) This is because a negative discriminant means that the quadratic expression doesn't intersect the x-axis, so there are no real x-values that satisfy the equation.
(iii) The negative discriminant also tells us about the graph of y = 5x^2 - 21x + 29. Since the discriminant is negative, the graph will not have any x-intercepts, meaning it does not touch the x-axis.
(i) To find the discriminant of the quadratic expression 5x^2 - 21x + 29, we will use the formula D = b^2 - 4ac, where D is the discriminant, a = 5, b = -21, and c = 29.
D = (-21)^2 - 4(5)(29)
D = 441 - 580
D = -139
(ii) Since the discriminant is negative (D = -139), this tells us that there are no real solutions to the quadratic equation 5x^2 - 21x + 29 = 0. This is because a negative discriminant means that the quadratic expression doesn't intersect the x-axis, so there are no real x-values that satisfy the equation. The discriminant tells us about the number of solutions of the equation because it is related to the nature of the roots. Specifically, if the discriminant is positive, there are two real roots, if it is zero, there is one real root (which is a repeated root), and if it is negative, there are two complex roots.
(iii) The negative discriminant also tells us about the graph of y = 5x^2 - 21x + 29. Since the discriminant is negative, the graph will not have any x-intercepts, meaning it does not touch the x-axis. Also, since the leading coefficient (a = 5) is positive, the graph will open upwards and have a minimum point as its vertex. Since the discriminant of the quadratic expression 5x^2 – 21x + 29 is negative (-139), there are two complex roots. This means that the quadratic equation 5x^2 - 21x + 29 = 0 has no real solutions.
The discriminant also tells us about the graph of y = 5x^2 – 21x + 29. Specifically, because the discriminant is negative, the graph of this quadratic function does not intersect the x-axis (i.e., it does not have any real x-intercepts). Instead, the graph will be a parabola that opens upwards or downwards depending on the sign of the leading coefficient (in this case, positive).
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easy algebra question below first correct answer gets brainliest
Answers
Answer:
y= -5
Step-by-step explanation:
y=2·(-3)+1
y= -5
What is 92 in kg to lbs?
Answers
Answer:
92kg is about 202.8 lbs
Step-by-step explanation:
The value of 92 in kg to lbs is 202.8 lbs
What is Kilo gram ?
Kilo gram can be defined as follows , one kilo gram is equals to thousand grams or one gram is equal to reciprocal of thousand.
Given ,
to find 92 in kg to lbs
So, we know that,
1 kg = 2.204
So, here for 92 kg
we need to multiply with 2.204
we get,
92 kg = 92 * 2.204
= 202.8
So, 92 kg = 202.8 lbs.
Therefore, the value of 92 in kg to lbs is 202.8 lbs
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use the circle unit to evaluate cos(23/6)
Answers
Given
\(\begin{gathered} \cos \text{ }\frac{23\pi}{6} \\ A\text{ complete revolution in a circle is 2}\pi \\ We\text{ have to re-write }\frac{23\pi}{6}\text{ in such a way that it will not be more than 2}\pi\text{ } \\ \text{Hence, } \\ cos\frac{23\pi}{6}\text{ = cos(}\frac{23\pi}{6}-\frac{24\pi}{6}) \\ \cos \text{(}\frac{23\pi}{6})\text{ = cos(}\frac{-\pi}{6}) \end{gathered}\)The representation on the unit circle is shown below
Going round the circle in the negative direction, we realize
\(\cos (\frac{-\pi}{6})\text{ = cos(}\frac{11\pi}{6})\text{ = }\frac{\sqrt[]{3}}{2}\)\(\text{The answer is }\frac{\sqrt[]{3}}{2}\)
help a girl out pls!!!!
Answers
Answer:
Your answer would be D!
Step-by-step explanation:
6. Simplify:
√900+ √0.09+√0.000009
Answers
The simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.
To simplify the given expression, let's evaluate the square roots individually and then perform the addition.
√900 = 30, since the square root of 900 is 30.
√0.09 = 0.3, as the square root of 0.09 is 0.3.
√0.000009 = 0.003, since the square root of 0.000009 is 0.003.
Now, we can add these simplified values together
√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303
Therefore, the simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.
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(q014) how many of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise?
Answers
five out of of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise
If you were to attribute this film, that means you'd say that (something) caused the success of the movie Rocky. This question is basically asking what do you think made this movie a big hit? Personally, I'd say it's because of how the storyline and plot turned out. It's very intriguing and it doesn't just make the movie about boxing. The film adds some love between the protagonist and some other character, and not only that, but the movie teaches you something. Because Rocky lost to Apollo, Rocky didn't care. At least he still had Adrian. So, the movie teaches you that, even if you do lose, at least you still have something and/or someone with you.
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2. Tom bought 500 shares of a company’s stock for $11.06/share. He pays a broker a commission of $12 to buy and sell stock. After one year, Tom sold all his shares, when they were worth $10/share.
(a) How much did it cost Tom to buy the stock? Show your work.
(b) What was Tom’s net gain or loss? Show your work.
(c) What factors would you consider before investing in the stock market? How much money do you think you should be prepared to invest in a stock investment? Explain why you feel that way?
(d) If you were to invest in the stock market, what business would you invest in, why? Would have had the same answer a month ago? Why or why not do you feel your answer did/did not change?
Answers
Step-by-step explanation:
a.)Buying: total cost
Total cost= commission + (price per share× Number of of shares ) ;
Total cost= 10 + (11.06×500)=$5540
b.)Net gain or loss;
First, find cash received from sale of stock and deduct commission;
Cash from sale =10×500= $ 5000
deduct commission= 5000-10= $4990
Gain or loss= sale-cost = 4990-5540 = -$550, meaning there is a loss.
c.) Annual rate of return= (net gain or loss/amount paid)×100%
return= -550/(5540)×100 = -9.92%
pls helpppppppppppppp
Answers
Answer:
-1/36
Step-by-step explanation:
-5/18 - ( -1/4)
Subtracting a negative is like adding
-5/18 + 1/4
Getting a common denominator of 36
-5/18 *2/2 + 1/4 *9/9
-10/36 + 9/36
-1/36
In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate?a. +1b. 0c. Infinityd. -1
Answers
Answer:
In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate b. 0
Step-by-step explanation:
If the plots on a scatter diagram lie on a straight line in a simple linear regression model, it indicates a perfect fit between the predictor variable and the response variable. In this case, the standard error of the estimate would be 0.
The standard error of the estimate represents the average distance between the observed values and the predicted values by the regression model. When the scatter diagram forms a perfect straight line, it means that the regression model can precisely predict the response variable using the predictor variable without any error.
Consequently, the residuals, which are the differences between the observed and predicted values, become zero for all data points, resulting in a standard error of 0. It is important to note that this scenario of a perfect fit on a scatter diagram is rare in real-world data, as there are typically variations and uncertainties in the relationship between variables.
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A map of Long Island has the scale 2.75 cm= 16km. On the map, target Rock is 23.2 cm from Lake Montauk. Find the distance from Target Rock to Lake Montauk. PLEASE HELP ASAP
Answers
Answer:
ytjyhyjhuyjhytujhyuhjnfh
Step-by-step explanation:
solve the following system of equations. if there is no solution, write dne in each coordinate of the ordered triplet. if there are an infinite number of solution, write each coordinate in terms of z . z. x 7
Answers
DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.
Whais the explanation?1.) 2+3 = y + 12
Make y the formula's subject after adding the LHS.
5 = y + 12
Y = 5 - 12
Y = - 7
The answer to the equation is -7
2.) 2 + 13 = 1 +8
The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).
3.) y - 7 = 2 - 11
RHS is added, and y is become the formula's subject.
Y - 7 = -9
Y = -9 + 7
Y = -2
The equation's answer is -2.
The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12
2 + 13 = 1 +8
y - 7 = 2 - 11
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The perimeter of a train ticket is 60 centimeters. It is 17 centimeters long. How tall is it?
Answers
If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter
What is perimeter of a rectangle?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;
P = l+l+w+w
P= 2(l+w)
60 = 2( 17+w)
60 = 2( 17+w)
17+w= 60/2
17+ w = 30
w = 30-17
w = 13cm
Therefore the height of the train ticket is 13cm
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suppose that the value of a stock varies each day from $8.82 to $16.17 with a uniform distribution. find the third quartile, i.e., 75% of all days the stock is below what value?
Answers
The third quartile is $10.6575, which means that 75% of all days the stock is below this value.
The range of the stock price is from $8.82 to $16.17, and the distribution is uniform, which means that the probability of the stock price being any value between the minimum and maximum is the same.
To find the third quartile, we need to find the value x such that 75% of the observations are less than or equal to x, and 25% of the observations are greater than or equal to x.
Since the distribution is uniform, we can find x by finding the value that separates the bottom 25% of the distribution from the top 75% of the distribution.
The bottom 25% of the distribution spans from $8.82 to some value x. Since the distribution is uniform, we can find x by setting the probability of the stock price being less than or equal to x to 0.25, which gives:
(x - 8.82) / (16.17 - 8.82) = 0.25
Solving for x, we get:
x - 8.82 = 0.25 * (16.17 - 8.82)
x - 8.82 = 1.8375
x = 10.6575
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Write the absolute value equations in the form |X-B|=C (where B is a number and C can be either number or an expression) that have the following solution sets X=15
Answers
Answer:
|x - 15| = 0Step-by-step explanation:
|x - 15| = 0 ⇔ x - 15 = 0 ⇔ x = 15
A special deck of cards has 12 cards. four are green, three are blue, and five are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? 12 B. Let A be the event that a green card is picked first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal number rounded to two decimal places of accuracy. C. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive?(Yes or No) D. Let B be the event that a blue or red is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? (Yes or No)
Answers
Answer:
A. Sample space = 6
B. 0.17
C. No
D. Yes
Step-by-step explanation:
A. The sample space of an experiment is the set of all possible outcomes of that experiment.
since there are three colours and 2 outcomes for a coin toss,
sample space = 3 * 2 = 6
B. Probability of picking a green first = 4/12 = 1/3
probability of a tail = 1/2
Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17
C. No.
Considering the two events;
A; green card is picked first
C ; a green or red card is picked
There is an intersection point for the two events. Therefore, they are not mutually exclusive.
D. Yes.
Considering the two events;
A; green card is picked first
B ; a blue or red card is picked
There is no intersection point for the two events. Therefore, they are mutually exclusive.
Find the area of a square with sides of length 1/3 yard.
A. 1/3 sq yd
B. 14 sq yd
C. 1/9 sq yd
D. 2/9 sq yd
Answers
Answer:
C
Step-by-step explanation:
Area of a square is:
\(A = a^{2}\) where a is the side
\((\frac{1}{3}^{2} ) = \frac{1}{9}\)
Answer:
c
Step-by-step explanation:
as x approaches infinity, for which function does f(x) approach negative infinity? select all that apply.
Answers
Both \(f(x) = -x^2\) and \(f(x) = -2x^3 + 5x^2 - 3x + 7\) approach negative infinity as x approaches infinity.
As x approaches infinity, the dominant term of the function determines its behavior. In the case of \(f(x) = -x^2\), the term \(x^2\) becomes infinitely large and negative, causing the entire function to approach negative infinity. Similarly, in the case of \(f(x) = -2x^3 + 5x^2 - 3x + 7\), the term \(-2x^3\) dominates and becomes infinitely negative as x approaches infinity, causing the entire function to approach negative infinity. This is because the negative exponent on \(x^3\) causes the value of the term to become increasingly negative as x increases without bound.
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