myopenmath.comA CBS News poll involved a nationwide random sample of 651 adults, asked those adults about theirparty affiliation (Democrat, Republican or none) and their opinion of how the US economy waschanging ("getting better," "getting worse" or "about the same"). The results are shown in the tablebelow.betterworsesame1043844RepublicanDemocrat128790137118none21If we randomly select one of the adults who participated in this study, compute the followingprobabilities. (round to four decimal places)a. P (Democrat) =b. P (worse) =C. P (worse Democrat) =d. P (Democrat worse) =e. P(Democrat and worse) =CalculatorScratchwork Area
Answers
Solution:
Given:
The table of the poll results;
The formula for calculating probability is given by;
\(\text{Probability}=\frac{n\text{ umber of required outcomes}}{n\text{ umber of total outcomes}}\)a) The P(Democrat) is;
\(\begin{gathered} \text{P(Democrat)}=\frac{\text{ total number of democrat}}{n\text{ umber of total outcomes}} \\ P(\text{Democrat)}=\frac{236}{651} \\ P(\text{Democrat)}=0.3625 \end{gathered}\)Therefore, the probability that it is a democrat is 0.3625
b) The P(worse) is;
\(\begin{gathered} \text{P(worse)}=\frac{\text{ total number of worse}}{n\text{ umber of total outcomes}} \\ P(\text{worse)}=\frac{299}{651} \\ P(\text{worse)}=0.4593 \end{gathered}\)
Therefore, the probability that it is worse is 0.4593
c) The P(worse|Democrat)- This is a conditional probability.
We use the conditional probability formula to solve this.
Conditional probability is given by;
\(P(A|B)=\frac{P(A\cap B)}{P(B)}\)Hence,
\(\begin{gathered} \text{Probability of worse given democrat=}\frac{P(worse\text{ and democrat)}}{\text{Probability (democrat)}} \\ P(\text{worse}|\text{democrat)}=\frac{137}{651}\text{ /}\frac{236}{651} \\ P(\text{worse}|\text{democrat)}=\frac{137}{651}\times\frac{651}{236} \\ P(\text{worse}|\text{democrat)}=\frac{137}{236} \\ P(\text{worse}|\text{democrat)}=0.5805 \end{gathered}\)Therefore, the probability of worse given democrat is 0.5805
d) The P(Democrat|worse) is;
\(\begin{gathered} \text{Probability of democrat given worse=}\frac{P(democrat\text{ and worse)}}{\text{Probability (worse)}} \\ P(\text{democrat}|\text{worse)}=\frac{137}{651}\text{ /}\frac{299}{651} \\ P(\text{democrat}|\text{worse)}=\frac{137}{651}\times\frac{651}{299} \\ P(\text{democrat}|\text{worse)}=\frac{137}{299} \\ P(\text{democrat}|\text{worse)}=0.4582 \end{gathered}\)Therefore, the probability of democrat given worse is 0.4582
e) The P(Democrat and worse) is;
\(\begin{gathered} P(A|B)=\frac{P(A\cap B)}{P(B)} \\ P(A\cap B)=P(A|B)\times P(B) \\ P(\text{Democrat and worse)=P(Democrat|worse)}\times P(worse) \\ P(\text{Democrat}|\text{worse) calculated in option (d) above = 0.4582} \\ P(\text{worse) calculated in option (b) above = 0.4593} \\ \\ \text{Hence,} \\ P(\text{Democrat and worse)=P(Democrat|worse)}\times P(worse) \\ P(\text{Democrat and worse)=}0.4582\times0.4593 \\ P(\text{Democrat and worse)=}0.2105 \\ \\ \\ \\ \text{Alternatively,} \\ P(\text{Democrat and worse)=}\frac{n\text{ umber of democrat and worse}}{\text{total number}} \\ P(\text{Democrat and worse)=}\frac{137}{651} \\ P(\text{Democrat and worse)=}0.210445 \\ P(\text{Democrat and worse)=}0.2105 \end{gathered}\)Therefore, the probability of democrat and worse is 0.2105
Related Questions
What is the complementary angle of CFB
Answers
Step-by-step explanation:
CFB reads as twenty five degrees
complementary angle will add to it to sum 90 degrees = sixty five degrees
angle CFD is sixty five degrees
Pls help!
Whoever answers in a few minutes with a clear answer will be marked brainiest!!!
Use exponent laws to write each expression with a positive power
Answers
Answer:
a. \(\tt \frac{1}{9}\)
b. \(\frac{1}{16}\)
c. 4
Step-by-step explanation:
\(\tt a. \:3^{-2}\)
We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:
\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)
\(\hrulefill\)
\(\tt b.\: -2^{-4}\)
We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:
\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)
\(\hrulefill\)
\(\tt c. \:(\frac{1}{2})^{-2}\)
We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:
\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)
Answer:
Step-by-step explanation:
(a) 3^-2 = 1/9
(b) (-2)^-4 = 1/(-2)^4 = 1/16
(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4
give an example of a function that is discontinous at one and only one point in its domain but is continous at every other point
Answers
An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function f(x) = x^2.
This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous. At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.
The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.
To learn more about discontinuous check the link below:
https://brainly.com/question/15009884
#SPJ4
Constructed Response
Two skyscrapers are under construction in Atlanta. They will sit on opposite sides of Peachtree St. and
the architect has designed them to be similar. The architect made a sketch of two rectangles to model
the front view of the two buildings and included the following statement: ABCD ~ JKLM. It was also given
that AB = 1600 ft., BC = 200 ft., and JM = 150 ft.. Use the scenario to solve problems (a) through (d)
a.) Which rectangle is being used to model the taller building?
b.) Which line segments could be used to model the height of the smaller building?
c.) What is the height of the taller building? Explain your reasoning.
d.) What is the height of the smaller building? Explain your reasoning.
e.) Would it make sense to say that the scale factor from smaller building to taller building is 3/4?
Explain your reasoning.
Answers
A rectangle is a quadrilateral which has the length of its opposite sides to be equal. Thus, the following are the solutions to the questions:
a) The rectangle used to model the taller building is ABCD.
b) The line segment used to model the height of the smaller building is JM = KL.
c) The height of the taller building is 200 feet.
d) The height of the smaller building is 150 feet.
e) Yes, the scale factor from small to tall building is \(\frac{3}{4}\).
Rectangles have equal length of opposite sides , and the sum of its interior angles to be \(360^{o}\). Since the two given skyscrapers were modeled with respect to rectangles ABCD and JKLM, then the answers to the questions are:
a) The rectangle used to model the taller building is ABCD. Since the length of a rectangle is always greater than its width. So that the height; AD = BC.
b) The line segment that can be used to model the height of the smaller building is; JM = KL. This represent the width of the rectangular model for the small building.
c) The height of the taller building is AD = BC = 200 feet. The width of a rectangle is often smaller than its length, which in this case is the height.
d) The height of the smaller building is JM = KL = 150 feet. The length of a rectangle is usually longer than its width.
e) Yes, it would make sense because:
scale factor = \(\frac{height of the smaller building}{height of the taller building}\)
= \(\frac{150 ft}{200ft}\)
= \(\frac{15}{20}\)
scale factor = \(\frac{3}{4}\)
Visit: https://brainly.com/question/24265754
Find the values of x and y in the diagram.
Answers
Answer:
x = 18
y = 6
Step-by-step explanation:
In triangle UTR, measures of all angles are equal (60°). (given)
Therefore, it is an equilateral triangle.
So, it's sides will also be equal.
In triangle TRS, m angle T = m angle S
So, RT = RS = 11 (sides opposite to the equal angles are equal)
In triangle URT,
UT = RT (sides of equilateral triangle)
x - 7 = 11
x = 11 + 7
x = 18
In triangle TRS,
m angle T = m angle S = 5y°
m angle R = 180° - 60° = 120° (Linear pair angles)
5y° + 5y° + 120° = 180°
10y° = 180° - 120°
10y° = 60°
y = 60/10
y = 6
(Diversifying Portfolios MC)
worth points)
Name of Stock Symbol High Low Close
Stock A
105.19 103.25 103.38
Stock B
145.18 143.28 144.05
A
B
Last year, an investor purchase
difference in overall loss or ga
O The difference in overall gain is $207.00.
O The difference in overall loss is $207.00.
O The difference in overall loss is $200.70.
O The difference in overall gain is $200.70.
shares of stock A at $90 per share and 75 shares of stock B at $145 per share. What is the
ween selling at the current day's high price or low price?
Answers
The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.
To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.
Stock A:
High price = $105.19
Low price = $103.25
Close price = $103.38
Stock B:
High price = $145.18
Low price = $143.28
Close price = $144.05
The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.
To calculate the selling prices, we need to multiply the number of shares by the respective selling price.
Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50
Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50
Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50
Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00
Now, let's calculate the difference in overall gain or loss:
Difference in overall gain = Selling price at the high price - Selling price at the low price
= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)
= $16,148.00 - $15,908.50
= $239.50
For similar question on selling stock.
https://brainly.com/question/13454463
#SPJ8
Will give brainliest!! How many ways are there to divide a red bracelet, a yellow bracelet, a green bracelet, and a black bracelet among 4 people if each person must receive exactly 1 of the bracelets?
Answers
After this.....any of the remaining 3 people without a bracelet could receive the yellow bracelet
After this.....either of the remaining 2 people without a bracelet could receive the green bracelet
And, by default, the remianing person without a bracelet will get the black bracelet
4x3x2x1= 24
So the answer is 24
Please mark me as brainliest I really need it :)
) 65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in
i. Swimming and cycling
Answers
Answer:
Step-by-step explanation:
i am working on the assumption that nobody does all three of them
i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.
the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.
so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4
Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary. cos θ = ? A = 22 H = 38
Answers
Answer: To find the angle θ in a right triangle given the cosine value, we can use the inverse cosine function, also known as arccos.
cos θ = A/H = 22/38
θ = arccos (22/38)
Using a table of trigonometric values or a calculator, we can find the value of arccos (22/38) to be approximately 56.3 degrees.
So, θ = 56.3° (rounded to the nearest degree).
Step-by-step explanation:
(b) Suppose CG = 3 in., CH = 2 in. and GE = 5 in. Is it possible to find the length of DH? If so, show how
to find the length. If not, explain why not.
Answers
When CG = 3 in., CH = 2 in. and GE = 5 in. the information made available in the question is not enough to solve for DH
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Examining the figure, shows that lines GH and DE should be parallel to create similar triangles
For similar triangles the sides are proportional and this can be used to solve for DH using the equation below'
CG / CE = CH / CD
Learn more about similar triangles here:
https://brainly.com/question/29333623
#SPJ1
The complete question is attached
Are the expressions
5
(
x
+
2
)
+
10
and
5
x
+
12
equivalent, and why?
Answers
Answer:
Yes it is equivalent
Step-by-step explanation:
Simply 5(x+2)+10 and you will get 5x+12
Show the steps to solve the system of equation. x-2y+3z=-4 , 3x+y-z=0 , 2x+3y-5z=1
Answers
Answer:
x= -1, y = 6, z = 3
Step-by-step explanation:
let me solve it with Gaussian Elimination
Test scores for 26 students in an introductory statistics course are displayed in the stemplot below. The scores range from 72 to 98.
A stemplot titled test scores is incomplete. It has values 72 and 98, and other values are not shown.
The teacher wants to encourage her students by reporting that, overall, the scores were high. Should she use the mean or median to summarize the center of the distribution of scores?
Answers
what is 7/9 of 1 1/14
Answers
Answer:
1.5555556
1 5/9
14/9
Step-by-step explanation:
. A marketing company reviewing the length of television commercials monitored a random sample of commercials over several days. They found that a 95% confidence interval for the mean length in seconds) of commercials aired daily was (23, 27). Which is true? 1. The interval (23,27) contains 95% of the population. II. The interval is narrower than a 98% confidence interval would be. III. 95% of all samples would show mean commercial length between 23 and 27 seconds. IV. Were 95% sure that the mean commercial length is between 23 and 27 seconds. (a) I only (b) IV only (e) I and II only (d) II and III only (e) II and IV only
Answers
The option II "The interval is narrower than a 98% confidence interval would be" and III "95% of all samples would show mean commercial length between 23 and 27 seconds" is the true about the question. So the option d is correct.
If all possible samples are taken and confidence intervals are calculated, 95% of them will include the true population mean somewhere within their range.
Because of the large margin of error, a 98 percent confidence interval would be wider than a 95 percent confidence interval. So, here we are. The confidence interval is narrower than a 98% confidence interval.
Furthermore, 95% of all samples would have a mean commercial length of 23 to 27 seconds. As a result, the correct answer is II and III (d).
To learn more about margin of error link is here
brainly.com/question/29101642
#SPJ4
a) A car is purchased for $30000 and is depreciating at a rate of 12% per
year. Write an equation to represent this situation.
b) What is the car worth in 10 years?
c) How many years does it take for the car to be worth $1000
Answers
Answer: 187.5 gallons of gas
Step-by-step explanation:
He travels 30000 miles per year, and each gallon lets him travel 16 miles. Divide 30000 by 16 to get the amount of gas he uses in a year, which amounts to 187.5 gallons of gas.
NO LINKS!! URGENT HELP PLEASE!!!
NOT MULTIPLE CHOICE!!
8. a. Finish the table
b. Name the type of sequence
c. Find the equation for the following sequence
Answers
Answer:
7: 63
8: 73
arithmetic sequence
y = 10x - 7
or f(n) = 10x -7
or
\(a_{n}\) = 3 + (n-1)10
Step-by-step explanation:
the output increases by 10 every time that the input increases by 1. That gives us our common difference or slope. The y intercept is -7. That is the value is you worked backwards until you get to n = 0. The initial value is 3. That is when n is 1.
When n is 3, f(n) is 23
When n is 2, f(n) is 13
When n is 1, f(n) is 3
When n is 0, f(n) is -7
I am not sure if this is clear. I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence. If my explanation is confusing it is me and not you.
Answer:
a. 63,73
b. Arithmetic sequence
c.t(n)=10n-7
Explanation:
a. Here is the completed table:
n | t(n)
4 | 33
5 | 43
6 | 53
7 | 63
8 | 73
b.
The type of sequence is arithmetic.
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.
In this case, the difference between any two consecutive terms is 10.
c.
The equation for the arithmetic sequence is:
t(n)=a+(n-1)d
where:
t(n) is the nth term in the sequencen is the term numberd is the common differencea is the first termFor Question:
d=43-33=10a=?Now
equation becomes:
t(4) = a+(4-1)10
33=a+30
a=33-30
a=3
Now, the Equation becomes
t(n) = 3+(n-1)10
t(n) = 3+10n-10
t(n)=10n-7
If f(x) =3x^3+10x^2-13x-20 and f(-4)=0, then find all of the zeros of f(x) algebraically
Answers
Answer:
If f(x) =3x^3+10x^2-13x-20 and f(-4)=0, then find all of the zeros of f(x) algebraically
Two researchers make a test concerning standardized exam performance among senior high school students in one of two local communities. Researcher A tests performance from the population in the northern community, where the standard deviation of test scores is 110 ( ); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 ( ). All other things being equal, which researcher has more power to detect an effect? Explain.
Answers
Answer:
Researcher B
Step-by-step explanation:
Normally, when all other things being equal, we usually say that power is higher when the standard deviation is small than when it is large.
Now, from researcher A, standard deviation is 110 while from researcher B, standard deviation is 60.
We can see that the standard deviation for researcher B is smaller than that of researcher A.
Therefore, we can conclude that since the standard deviation for researcher B is lesser than that of researcher A, it means that Researcher B will have more power to detect an effect.
Solve for m/CDF.
E
66°
D
с
Answers
Answer:
∠CDF = 48°
Step-by-step explanation:
∠CDE = ∠EDF + ∠CDF
Given that,
∠CDE = 114°
∠EDF = 66°
So, to find the value of ∠CDF, you have to subtract the value of ∠EDF from ∠CDE.
∠CDF = ∠CDE - ∠EDF
∠CDF = 114 - 66
∠CDF = 48°
Hope this helps
Find the slope of the line that passes through (10, 8) and (1, 9)?
Answers
Answer:
The answer is
\( - \frac{1}{9} \)Step-by-step explanation:
The slope of a line given two points can be found by using the formula
\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(10, 8) and (1, 9)
The slope is
\(m = \frac{9 - 8}{1 - 10} = \frac{1}{ - 9} \\ = - \frac{1}{9} \)
We have the final answer as
\( - \frac{1}{9} \\ \)
Hope this helps you
We can use the given points to solve.
Slope formula: y2-y1/x2-x1
9-8/1-10
1/-9
-1/9
Best of Luck!
Compute four-week and five-week moving averages for the time series. If required, round your answers to two decimal places. Week Sales 4 Period Moving Average 5 Period Moving Average 1 17 2 21 3 19 4 23 5 18 fill in the blank 1 6 16 fill in the blank 2 fill in the blank 3 7 20 fill in the blank 4 fill in the blank 5 8 18 fill in the blank 6 fill in the blank 7 9 22 fill in the blank 8 fill in the blank 9 10 20 fill in the blank 10 fill in the blank 11 11 15 fill in the blank 12 fill in the blank 13 12 22 fill in the blank 14 fill in the blank 15
Answers
Answer:
fill in the blank 1 =20
fill in the blank 2 =20.25
fill in the blank 3 = 19.4
fill in the blank 4 = 19.75
fill in the blank 5 =19.6
fill in the blank 6 = 19.25
fill in the blank 7=19.2
fill in the blank 8 = 18
fill in the blank 9= 19
fill in the blank 10 = 76/4=19
fill in the blank 11 = 18.8
Step-by-step explanation:
Week Sales 4 Period Moving Average 5 Period Moving Average
1 17
2 21
3 19
4 23
5 18 fill in the blank 1
=20
6 16 fill in the blank 2 fill in the blank 3
=20.25 19.4
7 20 fill in the blank 4 fill in the blank 5
19.75 19.6
8 18 fill in the blank 6 fill in the blank 7
19.25 19.2
9 22 fill in the blank 8 fill in the blank 9
18 19
10 20 fill in the blank 10 fill in the blank 11
76/4=19 18.8
11 15 fill in the blank 12 fill in the blank 13
20 19.2
12 22 fill in the blank 14 fill in the blank 15
18.75 19
The formula used for moving average is
a1= 1/4 ( W1+W2+W3+W4)
a2= 1/4 ( W2+W3+W4+ W5)
a3= 1/4( W3+W4+ W5+W6)
and so on
Where W1= week 1, W2= week 2 ,W3= week3
a1= 1st average , a2= 2nd average
The similar process is used for five year moving average
a1= 1/5 ( W1+W2+W3+W4)
a2= 1/5 ( W2+W3+W4+ W5)
a3= 1/5( W3+W4+ W5+W6)
Only it is divided by 5 instead of 4
To calculate the four-week and five-week moving averages, we need to sum up the sales for the specified number of weeks and divide by the corresponding period.
Week | Sales | 4-Period Moving Average | 5-Period Moving Average
-----|-------|------------------------|------------------------
1 | 17 | |
2 | 21 | |
3 | 19 | |
4 | 23 | |
5 | 18 | 20.00 |
6 | 16 | 19.25 |
7 | 20 | 19.50 |
8 | 18 | 19.25 |
9 | 22 | 19.00 |
10 | 20 | 19.00 |
11 | 15 | 18.75 | 19.20
12 | 22 | 18.75 | 19.20
13 | 22 | 19.75 | 19.40
14 | | 19.75 | 19.40
15 | | 19.75 | 19.40
The four-week moving average is calculated by summing up the sales of the current week and the previous three weeks, and then dividing by 4. The five-week moving average is calculated similarly, but with a period of five weeks.
Sorry about the messy photo but HELP ASAP!!!
Answers
____________________________
1.) Convert each number into a decimal:\(0.3=0.3\)\(\frac{1}{3}=0.333\)\(1.25=1.25\)\(\frac{2}{5}=0.4\)\(12.5\)% \(=0.125\)2.) Order from Smallest to Largest: \(12.5\)% \((0.125)\)\(0.3\)\(\frac{1}{3}~(0.333)\)\(\frac{2}{5}~(0.4)\)\(1.25\)
So your answer would be \(\bold{12.5}\)%, \(\bold{0.3}\), \(\bold{\frac{1}{3}}\), \(\bold{\frac{2}{5}}\), \(\bold{1.25}\).
____________________________
Home Liquidators marks up its merchandise 35% on cost. What is the company’s equivalent markup on selling price?
Answers
Based on the fact that Home Liquidators marked up their merchandise by 35% on cost, the company equivalent markup on selling price is 26%.
How to find the equivalent markup?The equivalent markup by Home Liquidators on the selling price can be found by the formula:
= Percentage markup / Percentage selling price x 100%
The percentage markup = 35%
Percentage selling price = (100% + 35%) = 135%
The equivalent markup by Home Liquidators is therefore:
= 35% / 135% x 100%
= 26%
In conclusion, the Home Liquidators has an equivalent markup of 26% on selling price.
Find out more on equivalent markup at https://brainly.com/question/11999225
#SPJ1
what are the solutions to ^log6(x^2+8)=1+log6(x)
Answers
Answer:
x=2
x=4
Step-by-step explanation:
the range is x>0
Move the expression to the left side and change it's sign to get
log6(x^2+8)-log6(x)=1
using loga(x)-loga(y) = loga (x/y) to simplify log6(x^2+8/x)=1
convert it to exponential form to get x^2+8/x=6
multiply both sides of the equation by x to get x^2+8=6x
move variable to the left
x^2-6x+8
factor out x from the expression
x (x-2) -4 (x-2) =0
factor out x-2
(x-2) x (x-4) = 0
set both equal to 0 and get x=2 x=4
Solve the system of equations:
x-y=4
4x-7z=24
4y+z=8
Answers
Answer:
Solve for x, y, and z. 1st Equation: 2x + 2y + 4z = 48. 2nd Equation: 2x + 9y + 7z = 105. 3rd Equation: x + 4y + z = 37. Subtract the 2nd Equation from the 1st Equation. This will eliminate the variable “x”.
Step-by-step explanation:
Question 6(Multiple Choice Worth 5 points)
(Reflections MC)
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Please Fast only have 10 minutes.
Answers
The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).
What is the image coordinates?To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2 from the y-coordinates of each vertex:
N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)
M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)
O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)
Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)
So the reflected vertices are:
The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have a y-coordinate of -6.
The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so one need to move down 3 units to have a y-coordinate of -5.
The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so one need to move down 5 units to have a y-coordinate of -7.
So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)
Learn more about image coordinates from
https://brainly.com/question/31020448
#SPJ1
Answer:
D) N′(−5, −6), M′(−2, −5), O′(−3, −7)---------------------
Given triangle MNO with vertices:
N = (-5, 2), M = (-2, 1) and O = (-3, 3)It is reflected in line y = - 2.
This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.
Since y = - 2 is the line of symmetry, it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.
Using midpoint equation, find the y-coordinates.
Point N'(2 + y)/2 = - 2 ⇒ 2 + y = - 4 ⇒ y = - 6Point M'(1 + y)/2 = - 2 ⇒ 1 + y = - 4 ⇒ y = - 5Point O'(3 + y)/2 = - 2 ⇒ 3 + y = - 4 ⇒ y = - 7So the coordinates of the image are:
N′(−5, −6), M′(−2, −5), O′(−3, −7)This is matching the option D.
See attached for visual representation of the problem.
What must be multiplied by (2 − 6) to get −10 + 30
Answers
Let x be multiply with ( 2-6 ) to get ( -10+30 )
Therefore, x ( 2 - 6 ) = (-10 + 30 )
or, x = (- 10 + 30 ) / ( 2 - 6 )
or, x = 20 / -4
or, x = -5
Therefore, -5 must be multiplied by (2 − 6) to get −10 + 30 .
Multiplying positive integers always bring about a positive integer. Multiplying negative integers constantly result in a negative integer. Multiplying a positive or negative integer usually result in a negative integer.
Multiplication and division of Integers. RULE 1: The product of a positive integer and a negative integer is negative. RULE 2: The product of positive integers is positive. RULE 3: The product of two negative integers is positive.
Learn more about multiplication of integers here https://brainly.com/question/11453536
#SPJ1
what is 0.05 x 300 please step by step explanation asap
Answers
0.05 x 300 in a calculator which would equal 15.
0.05x300=15
Help help math math
Answers
Answer:
Step-by-step explanation:
