PLEASE HELP!!!!! Lines BC and EF meet at A. Set up an equation to find the value of x. Find the measurements of EAH and HAC
Answers
Answer:
Value of X = 21
EAH = 63
HAC = 84
Step-by-step explanation:
Related Questions
ly| ≤3
Are the lines on graph at 3 and -3 also part of the answer?
Answers
Answer:
Yes, the lines on the graph at 3 and -3 a part of the solution,
Step-by-step explanation:
The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.
Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.
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In circle I, IJ=4 and mJIK∠=90∘ Find the area of shaded sector. Express your answer as a fraction times π.
Answers
The area of the shaded sector is 4π square units.
To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.
Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.
Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.
The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.
Plugging in the values, we have A = (90/360) * π * 4².
Simplifying, A = (1/4) * π * 16.
Further simplifying, A = (1/4) * π * 16.
Canceling out the common factors, A = π * 4.
Hence, the area of the shaded sector is 4π square units.
Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.
In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.
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{(x, y)|6 = x = 12, 8 = y = 12}
Use a Riemann sum with m = 3, n = 2, and take the sample point to be the upper right corner of each square.
V =
(b) Use the Midpoint Rule to estimate the volume of the solid in part (a).
V =
Answers
A) V = 2 B) Midpoint of each subdivision to use as the sample point: For the x-values: 7, 9, 11 For the y-values: 9, 11 To estimate the volume of the solid using the Midpoint Rule, we need to divide the given region into smaller rectangular boxes and calculate the volume of each box.
The Midpoint Rule considers the midpoint of each box as the sample point for calculating the volume. Given: m = 3 (number of subdivisions along the x-axis) n = 2 (number of subdivisions along the y-axis)
The width of each subdivision along the x-axis is Δx = (12 - 6) / 3 = 2. The width of each subdivision along the y-axis is Δy = (12 - 8) / 2 = 2. Now, let's calculate the volume of each rectangular box and sum them up to estimate the total volume of the solid.
First, we calculate the volume of each rectangular box: Volume of each box = Δx * Δy * height Since the height of the solid is not given in the problem, we need additional information to calculate the exact volume. Without the height information, we cannot provide a precise numerical value for the volume of the Riemann sum.
However, we can still explain the steps involved in using the Midpoint Rule to estimate the volume. Next, we calculate the midpoint of each subdivision to use as the sample point: For the x-values: 7, 9, 11 For the y-values: 9, 11
Using the midpoint and the dimensions of each subdivision, we can calculate the volume of each rectangular box. Finally, we sum up the volumes of all the rectangular boxes to estimate the total volume of the solid.
Please note that without the height information or further specifications about the solid, we cannot provide a numerical value for the volume using the Midpoint Rule in this case.
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Consider the following scenario to understand the relationship between marginal and average values. Suppose Lorenzo is a professional b. player, and his game log for free throws can be summarized in the following table.
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The missing points from the Column is:
Game Free-Throw Percentage: 60 20 60 80
Average Free-Throw Percentage: 70 60 55 56.67
Game Game Total Game Average
Result Free-Throw Free-Throw
Percentage Percentage
1 8/10 8/10 80 80
2 6/10 14/20 60 70
3 1/5 15/25 20 60
4 3/5 18/30 60 55
5 8/10 26/40 80 56.67
In the "Total" column, we keep track of the cumulative number of successful free throws out of the total attempts.In the "Game Free-Throw Percentage" column, we calculate the percentage of successful free throws made in each game.In the "Average Free-Throw Percentage" column, we calculate the average free-throw percentage up to that game by dividing the cumulative successful free throws by the cumulative total attempts and multiplying by 100.Learn more about Cumulative Frequency here:
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The question attached here seems to be incomplete, the complete question is
Fill in the columns with Dmitri's free-throw percentage for each game and his overall free-throw average after each game.
Game Game Result Total Game Free-Throw Percentage Average Free-Throw Percentage
1 8/10 8/10 80 80
2 6/10 14/20
3 1/5 15/25
4 3/5 18/30
5 8/10 26/40
Find the quotient 5/28 divided by 1/7
Answers
The answer is: 1.25
Remember: Keep the first fraction, Change the Sign, Flip the second fraction.
KEEP - 5/28
CHANGE - division to multiplication
FLIP - 7/1
Answer:
5/4 or 1 1/4 or 1.25
(5/28) / (1/7) =
5/28 * 7 =
5/4
PLEASE HELP MEEEEEEEEEEEEE
Answers
Answer:
1 no ans is 13
2no. ans is 28
3 no. ans is 4
4no.ans is 2
we get all these by simplifying them....
can someone help me with algebra 2 with an explanation?
Answers
Answer: This took me a long time to type, hope you read it and find it helpful and easy to understand...
1. \(x=1\)
2. \(x=\frac{3}{2}\)
3. \(x=1\)
4. \(x=\frac{6}{5}\)
Step-by-step explanation:
1.
\(\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}\)
To make it easier to add / subtract fractions, we are looking for common denominators. I can see that if I move the fraction on the left with a denominator 3x to the right, I'll be able to add two equations with like denominator.
Let's add \(\frac{x-2}{3x}\)
\(\frac{1}{x}=\frac{4}{3x}+\frac{x-2}{3x}\)
Add the numerators and keep the same denominator.
\(\frac{1}{x}=\frac{4+x-2}{3x}\)
\(\frac{1}{x}=\frac{2+x}{3x}\)
To get rid of the denominator x on the left side, we can multiply by x.
\((x)\frac{1}{x}=\frac{2+x}{3x}(x)\)
\(1=\frac{2+x}{3}\)
Now multiply by 3.
\((3)1=\frac{2+x}{3}(3)\)
\(3=2+x\)
Subtract 2.
\(3-2=x\\1=x\)
The value of x is 1.
Proof.
\(\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}\)
\(\frac{1}{1}-\frac{1-2}{3(1)}=\frac{4}{3(1)}\)
\(1-\frac{-1}{3}=\frac{4}{3}\)
\(1+\frac{1}{3}=\frac{4}{3}\)
\(\frac{1*3+1}{3} =\frac{4}{3}\\\frac{4}{3}=\frac{4}{3}\)
I can't show the proof to the following problems because I have a 5000 character limit.
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2.
\(\frac{5x-5}{x^2-4x} -\frac{5}{x^2-4x}=\frac{1}{x}\)
Again, we have like denominators, therefore, we can simply subtract the numerators and keep the same denominator.
\(\frac{5x-5-5}{x^2-4x}=\frac{1}{x}\)
\(\frac{5x-10}{x^2-4x}=\frac{1}{x}\)
Again, we can multiply by x to get rid of the x in the denominator.
\((x)\frac{5x-10}{x^2-4x}=\frac{1}{x}(x)\)
Do not distribute the x in the numerator yet because we're gonna eliminate it later.
\(\frac{(x)(5x-10)}{x^2-4x}=1\)
Factor the denominator.
\(\frac{(x)(5x-10)}{(x)(x-4)}=1\)
Simplify x's.
\(\frac{5x-10}{x-4} =1\)
Multiply by x-4 to get rid of the denominator.
\((x-4)\frac{5x-10}{x-4} =1(x-4)\)
\(5x-10=x-4\)
Add 10
\(5x=x-4+10\)
Subtract x
\(5x-x=-4+10\)
Combine like terms;
\(4x=6\)
Divide by 4.
\(\frac{4x}{4}=\frac{6}{4}\)
\(x=\frac{6}{4}\)
Simplify by 2.
6/2 = 3
4/2 = 2
\(x=\frac{3}{2}\)
-----------------------------------------------------------------------
3.
\(\frac{x^2-7x+10}{x}+\frac{1}{x}=x+4\)
Same denominator, add numerators.
\(\frac{x^2-7x+10+1}{x}=x+4\)
\(\frac{x^2-7x+11}{x}=x+4\)
Multiply by x to get rid of the x.
\((x)\frac{x^2-7x+11}{x}=(x+4)(x)\)
\(x^2-7x+11=x^2+4x\)
Subtract \(-x^2-4x\)
\(x^2-7x+11-x^2-4x=0\)
Combine like terms;
\(-11x+11=0\)
Subtract 11.
\(-11x=-11\)
Divide by -11
\(x=\frac{-11}{-11} \\x=1\)
-------------------------------------------------------------------------
4.
\(\frac{x^2+7x+10}{5x-30}+\frac{x}{x-6}=\frac{x^2-13x+40}{5x-30}\)
It's easier if you move the operation with denominator x+6 to the right side with negative sign and bring the operation on the right side to the left side with negative sign as well.
\(\frac{x^2+7x+10}{5x-30}-\frac{x^2-13x+40}{5x-30}=-\frac{x}{x-6}\)
Now, since we have the same denominators, we can simply subtract numerators.
\(\frac{x^2+7x+10-(x^2-13x+40)}{5x-30} =-\frac{x}{x-6}\)
Distribute the negative sign.
\(\frac{x^2+7x+10-x^2+13x-40}{5x-30} =-\frac{x}{x-6}\)
Combine like terms;
\(\frac{20x-30}{5x-30}=-\frac{x}{x-6}\)
Factor.
I can see that I can factor a 5 on both numerator and numerator. This will allow me to simplify them.
\(\frac{(5)(4x-6)}{(5)(x-6)} =-\frac{x}{x-6}\)
Simplify.
\(\frac{4x-6}{x-6}=-\frac{x}{x-6}\)
Multiply by x-6
\((x-6)\frac{4x-6}{x-6}=-\frac{x}{x-6}(x-6)\)
This will simplify the denominators.
\(4x-6=-x\)
Add x and 6.
\(4x+x=6\\\)
Combine like terms;
\(5x=6\)
Divide by 5.
\(x=\frac{6}{5}\)
n cattle, the allele for red coat color (r) shows incomplete dominance over the allele for white (r’) coat color. the hybrid (rr’) is a roan coat color,
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When cattle with the red coat allele (r) and white coat allele (r') are crossed, the resulting offspring will have a roan coat color, representing an example of incomplete dominance.
In cattle, the allele for red coat color (r) exhibits incomplete dominance over the allele for white coat color (r'). In incomplete dominance, the heterozygous condition (rr') results in an intermediate phenotype that is different from both homozygous conditions.
When a red-coated individual (rr) is crossed with a white-coated individual (r'r'), the resulting offspring will have the genotype rr'. In terms of coat color, the offspring will exhibit a roan coat color, which is a mixture of red and white hairs. This is because neither the red allele (r) nor the white allele (r') is completely dominant over the other. Instead, they interact and blend to produce the roan phenotype.
In roan cattle, the red and white hairs are evenly interspersed, creating a mottled or speckled appearance. The extent of the roan phenotype may vary among individuals, with some displaying a more balanced mixture of red and white, while others may have a more dominant color.
It's important to note that incomplete dominance is different from complete dominance, where one allele completely masks the expression of the other. In the case of incomplete dominance, the heterozygous genotype results in an intermediate phenotype, showcasing a blending of traits.
In conclusion, the progeny of calves having the red coat gene (r) and white coat allele (r') will have a roan coat colour, illustrating an instance of incomplete dominance.
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If you are to
evaluate your life now using polynomial functions , how will you
look at it?
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For the linear regression y = ẞ1 + ẞ2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 +681 +382 + 18ẞ1ẞ2
Derive the partial derivatives of SSE with respect to B1 and B2 and solve the optimal values of these parameters.
a. B₁ = B1
b. B₂ =
Answers
The optimal values of these parameters are:
a. β₁ = 0
b. β₂ = 0
The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 + 681 + 382 + 18β1β2
Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.
Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0
Now, we need to find the partial derivative of SSE with respect to β1.
∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0
Therefore, we obtain the optimal value of β2 as 0.
Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0
Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.
Thus, the optimal values of β1 and β2 are 0 and 0, respectively.
Therefore, the answers are: a. β₁ = 0 b. β₂ = 0
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ignore the top but please help. will ignore brainliest
Answers
Answer:
the in's are 6 7 and the outs are 12 and 0.2
Step-by-step explanation:
Factor the expression
49x^5 - 63x^3
Answers
Answer:
7x³(7x² - 9)
Step-by-step explanation:
Hope this helps!
Answer:
\(7x^3(7x^2-9 )\)
Step-by-step explanation:
To factor, you have to find the GCF of 49 and 63 and the GCF of \(x^{5}\) and \(x^3\)
Factor 49: 1,7, and 49
Factor 63: 1, 3, 7, 9, 21, 63
Factor \(x^{5}\): \(x*x*x*x*x\)
Factor \(x^3\): \(x*x*x\)
So the GCF of 49 and 63 is 7
The GCF of \(x^{5}\) and \(x^{3}\) is \(x^3\)
We multiply 7 by \(x^{3}\) to get \(7x^3\)
So now we start to factor out the GCF of \(49x^5-63x^3\)
\(7x^3(\frac{49x^5}{7x^3}+ \frac{63x^3}{7x^3} )\)
\(\frac{49}{7} =7\\x^5-x^3=x^2\)
\(\frac{63}{7} =9\\x^3-x^3=x^0\) because \(x^{0}\) can't be written as an exponent we don't write \(9x^0\)
When we factor we get \(7x^3(7x^2-9 )\)
can you please help me
Answers
We have to calculate the area and perimeter of ABC.
Area:
We can calculate the area by substracting from the area of the big triangle ABD the area of the little triangle BCD. Both are right triangles.
The area of ABD is:
\(A_{\text{ABD}}=\frac{b\cdot h}{2}=\frac{(15+5)\cdot12}{2}=\frac{20\cdot12}{2}=\frac{240}{2}=120\)The area of BCD is:
\(A_{\text{BCD}}=\frac{b\cdot h}{2}=\frac{5\cdot12}{2}=\frac{60}{2}=30\)Then, the area of ABC is:
\(A_{\text{ABC}}=A_{\text{ABD}}-A_{\text{BCD}}=120-30=90\)The area of ABC is 90 cm^2.
Perimeter:
We calculate the perimeter by adding the length of the three sides. We know only 2 of the sides, so we have to calculate the other one (BC).
The length of BC can be calculated using Pythagorean theorem for the triangle BCD, so we can write:
\(\begin{gathered} BC^2=CD^2+BD^2=5^2+12^2=25+144=169 \\ BC=\sqrt[]{169}=13 \end{gathered}\)Now, we can calculate the perimeter as:
\(P_{\text{ABC}}=AB+BC+AC=25+13+15=53\)The perimeter is 53 cm.
A five question multiple choice quiz has five choices for each answer. Use the random number table provided, with O's representing incorrect answers, and 1's
representing correct answers to answer the following question: What is the experimental probability of correctly guessing at random exactly one correct answer?
Answers
Answer:
You will need to count the amount of 0's and total them left to right = per question and total them top to bottom for answering a total
answering b total answering c total etc..
This creates line of 5 totals at the bottom of table and other totals per question = amount of questions x total.
The experimental probability is setting all 1/5 (1 answered question and multiplying it by the inverse of 4/5 non answered questions = 1/5 = 1/25
p) 1/5 x 1/5 = 1/25
Step-by-step explanation:
Question Progress
Homework Progress
a)
45%
y is inversely proportional to the square of x.
b)
х
1
2
3
4
A table of values for x and y is shown.
y
4
1
4
9
1
4
a) Express y in terms of x.
b) Work out the positive value of x when y = 25
Answers
An inscribed angle is an angle whose vertex is a point on a circle and whose sides are two _____ of the circle
Answers
An inscribed angle is formed by two chords of a circle that intersect at a vertex located on the circle.
The angle itself is formed by the two sides of the angle, which are the line segments connecting the vertex to the endpoints of the chords. The property that makes inscribed angles interesting is that the measure of an inscribed angle is half the measure of the intercepted arc on the circle.
This relationship holds true for any inscribed angle in a circle, making it a useful concept in geometry for solving problems involving angles, arcs, and circles.
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The Faulty Combination Lock
A combination lock with three dials, each numbered 1 through 8, is defective in that you only need to get two of the numbers right to open the lock. (For example, suppose the true combination is 4-2-7. Then 4-2-7 would open th lock but so would 4-2-5, 4-2-2 , 8-2-7 or 4-6-7. But not 2-4-7)
What is the minimum number of (Three-number) combinations you need to try in order to be sure of opening the lock?
Answers
============================================
Explanation:
Let's go with the example given to us. Let's say the correct lock combo is 4-2-7.
If we get the first two digits right, then we have 8 choices for the third digit since we pick from between 1 and 8 inclusive. There are 8 combos of the form 4-2-x.
The same goes for stuff of the form 4-x-7 and x-2-7.
There appear to be 8+8+8 = 24 different combos that will open this faulty lock. However, we must subtract off 2 because we've triple counted "4-2-7" when adding up those 8's.
In reality there are 24-2 = 22 different combos that will open the faulty lock.
There are 8^3 = 512 different combos total. That gives 512-22 = 490 combos that do not open the lock.
If the person is very unlucky, with the worst luck possible, then they would randomly try all of the 490 combos that don't work.
Attempt number 491 is when they'll land on one of the 22 combos that do work.
Linear equation in slope intercept form
Answers
Given:
The table of values of a linear function.
To find:
The equation of linear function in slope intercept form.
Solution:
The slope intercept form of a linear function is:
\(y=mx+b\)
Where, m is the slope and b is the y-intercept.
If a linear function passes through two point, then the equation of the linear function is:
\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)
Consider any two points from the given table. Let the two points are (-6,12) and (-5,14). So, the equation of the linear function is:
\(y-12=\dfrac{14-12}{-5-(-6)}(x-(-6))\)
\(y-12=\dfrac{2}{-5+6}(x+6)\)
\(y-12=\dfrac{2}{1}(x+6)\)
\(y-12=2x+12\)
Adding 12 on both sides, we get
\(y-12+12=2x+12+12\)
\(y=2x+24\)
Therefore, the slope intercept form for the given linear function is \(y=2x+24\).
Harry and Olivia are planning to buy a bedroom furniture set that costs $4,100 plus 6% taxes. They would like to apply for a 0% APR store credit card on purchases for 10 months. How much money do they need to pay in equal installments monthly for the next 10 months such that they will be able to pay off the bedroom furniture set before the 0% APR offer expires?
Answers
Answer:
434.60
Step-by-step explanation:
The total stopplng bistance T of a vehicle is shown befow, where T is in feet and x is the speed in mifes per hour: T=2.5x+0.5x 2
Approximate the change and percent change in total stopping distance as speed changes frem x=25 to x=26 miles per hour. (flound your ancwers to one decimal place.
Answers
The percent change in the total stopping distance is approximately 7.5%.
The percent change in the total stopping distance is approximately 7.5%. The total stopping distance of a vehicle is given by the equation T = 2.5x + 0.5x^2, where T represents the stopping distance in feet and x is the speed in miles per hour.
To approximate the change and percent change in the total stopping distance as the speed changes from x = 25 to x = 26 miles per hour, we can substitute these values into the equation.
For x = 25 miles per hour, the stopping distance is calculated as
T = 2.5(25) + 0.5(25)^2 = 375 feet.
For x = 26 miles per hour, the stopping distance is calculated as
T = 2.5(26) + 0.5(26)^2 = 403 feet.
The change in the total stopping distance is obtained by subtracting the initial stopping distance from the final stopping distance:
Change = 403 - 375 = 28 feet.
To calculate the percent change, we divide the change by the initial stopping distance and multiply by 100:
Percent Change = (Change / T(initial)) * 100
Therefore, the percent change in the total stopping distance is approximately 7.5%.
In conclusion, as the speed increases from 25 to 26 miles per hour, the total stopping distance of the vehicle increases by approximately 28 feet, resulting in a percent change of around 7.5%.
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Will give brainliest answer!!
Answers
Answer:
least possible is -9 and greatest is 0
Directions: State whether or not (3, -2) is a solution to the following systems.
1. x-2y = 7 and 2x + 3y = 0
2.- x - y = -5 and 3x - 4y = 17
3. x + y = 1 and x - y = 6
Answers
(3, -2) is a solution to the system of equations x - 2y = 7 and 2x + 3y = 0, (3, -2) is not a solution to the system of equations -x - y = -5 and 3x - 4y = 17 and (3, -2) is not a solution to the system of equations x + y = 1 and x - y = 6
How to determine the whether or not (3, -2) is a solution to the following systems?The systems of equations are given as:
1. x - 2y = 7 and 2x + 3y = 0
2. -x - y = -5 and 3x - 4y = 17
3. x + y = 1 and x - y = 6
Next, we substitute (3, -2) for (x, y) in the system of equations.
So, we have:
1. x - 2y = 7 and 2x + 3y = 0
3 - 2 * -2 = 7 and 2 * 3 + 3 * -2 = 0
Evaluate
7 = 7 and 0 = 0
The above equation is true
Hence, (3, -2) is a solution to the system of equations x - 2y = 7 and 2x + 3y = 0
2.- x - y = -5 and 3x - 4y = 17
-3 + 2 = -5 and 3 * 3 + 4 * 2 = 17
Evaluate
- 1 = - 5 and 1 7 = 1 7
The above equation is false
Hence, (3, -2) is not a solution to the system of equations -x - y = -5 and 3x - 4y = 17
3. x + y = 1 and x - y = 6
3 - 2 = 1 and 3 + 2 = 6
Evaluate
1 = 1 and 5 = 6
The above equation is false
Hence, (3, -2) is not a solution to the system of equations x + y = 1 and x - y = 6
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solve for x. 7(x-3)+3(4-x)=-8
Answers
Answer:
x=1/4
Step-by-step explanation:
1.distribute the 7 and 3 into parentheses
2. combine like terms
3. add 9 on both sides
4. divide both sides by 4
x=1/4
hope this helped!
Answer:
x = \(\frac{1}{4}\)
Step-by-step explanation:
7(x-3)+3(4-x)= -8
Expand 7(x-3) and 3(4-x)
i.e. 7x-21+12-3x= -8
4x-9=-8
Collect like terms
4x= -8+9
4x= 1
x = \(\frac{1}{4}\)
Hope this helps!!!
Destiny places the letters in the word October into a bag what is the probability of destiny selecting a B and then 80 without replacement
Answers
The probability of selecting a B and then a O without replacement is 1/21
Probability conceptProbability measures the chances of an event occurring from a group of events based on certain conditions.
Given word : OCTOBER
PROBABILITY OF SELECTING BProbability is the ratio of required outcome to the total possible outcomes
Number of B's
P(B) = 1/7
Since selection is done without replacement ; Number of letters left after first selection is 7-1=6
P(O) = 2/6 = 1/3
Hence, the probability of selecting a B and then a O is :
(1/7 × 1/3) = 1/21
Therefore, the probability of selecting a B and then a O is 1/21
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Bryan’s golf coach suggested he take some golf lessons. The pro at windy fairways charges $20.00 per month plus $10.00 per lesson. The pro at sunny sands charges $100.00 per month for unlimited classes. How many classes does he have to take for both pros be the same price?
Answers
Answer:
8
Step-by-step explanation:
(100 - 20) / 10 = 8
Answer: He has to take a class per month from the both pros
Step-by-step explanation:
What is the inverse of:
If a = b and b = c, then a = c
1) a = b and b = c if, and only if, a = c
2) If a ≠ c then a ≠ b or b ≠ c
3) If a ≠ b or b ≠ c, then a ≠ c
4) If a = c, then a = b and b = c
Answers
Answer:
1
Step-by-step explanation:
Is the correct way to do it
John surfs the website on a regular basis. Suppose the time he spent surfing the website per day is normally distributed, µ = 8 minutes and σ = 2 minutes. If you select a random sample of 4 sessions,
a. What is the probability that the sample mean is less than 8 minutes? Explain
b. What is the probability that the sample mean is between 8 and 10 minutes?
Answers
Given that John surfs the website on a regular basis. The time he spent surfing the website per day is normally distributed, µ = 8 minutes and σ = 2 minutes. If you select a random sample of 4 sessions. We are to find the probability of sample mean.a.
The probability that the sample mean is less than 8 minutes sample size(n) = 4μ = 8 minutesσ = 2 minutes
As we know, the sample means follow a normal distribution with mean, μ and standard deviation, σ / sqrt(n).
Therefore, the sample mean will follow a normal distribution with a mean of μ and standard deviation of σ/√n=2/√4=1
So the Z-score for the given data can be calculated as: Z= X−μ/σ/√nZ= 8−8/2/√4=0Thus, the probability that the sample mean is less than 8 minutes is P(Z < 0).
Since the Z distribution is normal, the area to the left of 0 is 0.5.
Therefore, the probability that the sample mean is less than 8 minutes is 0.5.b. The probability that the sample mean is between 8 and 10 minutes sample size(n) = 4μ = 8 minutesσ = 2 minutes
The Z-scores corresponding to X1=8 and X2=10 can be calculated as: Z1= X1−μ/σ/√n= 8−8/2/√4=0Z2= X2−μ/σ/√n= 10−8/2/√4=1
Thus, the probability that the sample mean is between 8 and 10 minutes is the area under the standard normal curve between Z1 and Z2, which is P(0
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Chapter 1:Qua
END-OF-CHAPTER REVIEW EXERCISE 1
1
A curve has equation y = 2xy + 5 and a line has equation 2x + 5y = 1.
The curve and the line intersect at the points A and B. Find the coordinates of the midpoint
of the line AB
Answers
Answer:
(¹/₂, 0)Step-by-step explanation:
2x + 5y = 1 ⇒ 2x = 1 - 5y
y = 2xy + 5
y = (1 - 5y)y + 5
y = y - 5y² + 5
5y² = 5
y² = 1
y₁ = 1 ∨ y₂ = -1
2x₁ = 1 -5(1) 2x₂ = 1 - 5(-1)
2x₁ = 1 - 5 2x₂ = 1 + 5
2x₁ = -4 2x₂ = 6
x₁ = -2 x₂ = 3
Midpoint:
\(M=\left(\frac{x_1+x_2}2\ ,\ \frac{y_1+y_2}2\right)=\left(\frac{-2+3}2\ ,\ \frac{1+(-1)}2\right)=\left(\frac12\ ,\ 0\right)\)
The coordinates of the midpoint of the line AB is (0, 1/2).
The equation of the curve is given by y = 2xy + 5.
The equation of the line is given by 2x + 5y = 1.
We have to first find the point of intersection between the curve and the line and then find the coordinates of the midpoint of line AB where A and B is the point of intersection between the curve and the line.
What is the formula for finding the coordinates of a point that divides a given line in the ratio m:n?If C(x, y) divides a line AB in m:n then we have,
\(x = \frac{mx_2 +nx_1}{m+n},~~~y =\frac{my_2+ny_1}{m+n}\)
And if C(x,y) is the midpoint then m = n.
we have,
\(x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}\)
Where x and y are the coordinates of the midpoint o the line AB.
Find the point of intersection between the line and the curve.
y = 2xy + 5............(1)
2x + 5y = 1..............(2)
From (2) we have,
2x = 1 - 5yx = (1-5y) / 2..........(3)
Substituting (3) in (1).
\(y =2\frac{(1-5y)}{2}y + 5\\\\y =\frac{2y-10y^2}{2} + 5\\\\2y = 2y - 10y^2 + 10\\\\10y^2 = 10\\\\y^2 = 1\)
So we have,
y = 1 and y = -1
Puttin y = 1 in (3) we get,
x = (1 - 5) / 2 = - 4 / 2 = -2
Puttin y = -1 in (3) we get,
x = {1-5(-1)} / 2 = (1+5) / 2 = 6 / 2 = 3
Now we have two points of intersection A( 1, -2 ) and B( -1, 3 ).
Finding the coordinates of the midpoint of the line AB.
we have,
\(A(1, -2) = A (x_1, y_1)~~and~~B(-1, 3) = B(x_2, y_2)\)
Substituting in the given equation.
\(x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}\\\\x = \frac{-1 +1}{2},~~~y =\frac{3+(-2)}{2}\\\\x = 0,~~~y=\frac{1}{2}\)
So the coordinates of the midpoint is (x,y) = ( 0, 1/2 ).
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A patient is given 0.050 mg of tecgnetium -99m ( where m means mestastable- an unstable but long-lived state) a radioactive isotope with a half-life of about 6.0 hours. How long until the radioactive isotope decays to 7.8×10^-4 mg ?
Answers
Answer:
36 hrs
Step-by-step explanation:
It will need to decay 6 half-lives, which is 36 hrs
0.050/2 = 0.025 (6 hrs)
0.025/2 = 0.0125 (6 hrs)
0.0125/2 = 0.00625 (6 hrs)
0.00625/2 = 0.003125 (6 hrs)
0.003125/2 = 0.0015625 (6 hrs)
0.0015625/2 = 0.00078 = 7.8 x 10^-4 (6 hrs)
Find the area of polygon with A(-5,-2) ,B (4,-2), C (4,-7) , D (-5,-7))?
Answers
Answer:
A=45
Step-by-step explanation:
Area of a rectangle equation: A=L*W
A=9*5=45