Answer:
The rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].
Step-by-step explanation:
A section of a hiking trail begins at the coordinates (-7, 5). It does mean (x₁, y₁) ⇒ (-7, 5)And follows a straight path that ends at the coordinates (3, 9). It does mean (x₂, y₂) ⇒ (3, 9)In mathematical language, the slope m of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plugging (x₁, y₁) ⇒ (-7, 5) and (x₂, y₂) ⇒ (3, 9) into the slope equation
[tex]m=\frac{9-5}{3-(-7)}[/tex]
[tex]m=\frac{4}{10}[/tex]
[tex]m=\frac{2}{5}[/tex]
So, the rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].
Keywords: rate of change, slope, coordinates
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Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the parking garage. He described his movement with the expression below.
Answer:
7-9
Step-by-step explanation:
Sebastian goes up from 0 by 7 floors. Then, he goes down by 9.
The function C(x) = 25.50x + 50 models the total cost for a cleaning company to clean a house, where x is the number of hours it takes to clean the house. What is the average rate of change of the function between 3 hours and 9 hours? A. $17.00 per hour B. $25.50 per hour C. $31.05 per hour D. $42.15 per hour
Answer:
The average rate of change is $25.5 per hour, option B.
Step-by-step explanation:
Average Rate of Change
When we are explicitly given some function C(x), we sometimes need to know the rate of change of C when x goes from [tex]x=x_1[/tex] to [tex]x=x_2[/tex]. It can be computed as the slope of a line .
[tex]\displaystyle m=\frac{C(x_2)-C(x_1)}{x_2-x_1}[/tex]
The provided function is
[tex]C(x)=25.50x + 50[/tex]
We are required to compute the average rate of change between the points
[tex]x_1=3\ ,\ x_2=9[/tex]
Let's compute
[tex]C(3)=25.50(3) + 50=126.5[/tex]
[tex]C(9)=25.50(9) + 50=279.5[/tex]
[tex]\displaystyle m=\frac{279.5-126.5}{9-3}[/tex]
[tex]\displaystyle m=\frac{153}{6}=25.5[/tex]
The average rate of change is $25.5 per hour, option B.
please help asap please
Answer:
Step-by-step explanation:
The slope of the line needs to be determined first:
[tex]m=\frac{-9+-5}{-12+-8}=\frac{-14}{-20}=\frac{7}{10}[/tex]
Now let's use that and one of the coordinates to write an equation in point-slope form:
[tex]y-5=\frac{7}{10}(x-8)[/tex]
and, simplifying,
[tex]y-5=\frac{7}{10}x-\frac{56}{10}[/tex]
Now let's multiply everything by 10 to get rid of the fractions:
10y - 50 = 7x - 56
and
-7x + 10 y = -6
Apparently, they do not like to lead with negatives, which is not uncommon:
7x - 10y = 6
So his model is not correct.
A bakery wants to determine how many trays of doughnuts it should prepare each day. Demand is normal with a mean of 5 trays and standard deviation of 1 tray. If the owner wants a service level of at least 95%, how many trays should he prepare (rounded to the nearest whole tray)? Assume doughnuts have no salvage value after the day is complete. 6 5 4 7 unable to determine with the above information.
Answer:
4 trays should he prepared, if the owner wants a service level of at least 95%.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 5
Standard Deviation, σ = 1
We are given that the distribution of demand score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(X > x) = 0.95
We have to find the value of x such that the probability is 0.95
P(X > x)
[tex]P( X > x) = P( z > \displaystyle\frac{x - 5}{1})=0.95[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 5}{1})=0.95 [/tex]
[tex]=P( z \leq \displaystyle\frac{x - 5}{1})=0.05 [/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 5}{1} = -1.645\\x = 3.355 \approx 4[/tex]
Hence, 4 trays should he prepared, if the owner wants a service level of at least 95%.
Paul has 2/3 as many postcards as Shawn. The number of postcards Shawn has is 3/5 of the number of postcards Tim has. If the three boys have 280 postcards altogether, how many more postcards does Tim have than Paul
Tim has 84 more postcards than Paul.
Step-by-step explanation:
Given,
Total number of postcards = 280
Let,
Tim's share of postcards = x
Shawn's share of postcards = [tex]\frac{3}{5}\ of\ Tim's\ share[/tex] = [tex]\frac{3}{5}x[/tex]
Paul's share of postcards = [tex]\frac{2}{3}\ of\ Shawn's=\frac{2}{3}(\frac{3}{5}x)=\frac{2}{5}x[/tex]
According to given statement;
[tex]x+\frac{3}{5}x+\frac{2}{5}x=280[/tex]
Taking LCM
[tex]\frac{5x+3x+2x}{5}=280\\\\\frac{10x}{5}=280\\\\2x=280[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{280}{2}\\x=140[/tex]
Paul's share = [tex]\frac{2}{5}x=\frac{2}{5}(28)=56[/tex]
Difference = Tim's share - Paul's share
Difference = 140 - 56 = 84 cards
Tim has 84 more postcards than Paul.
Keywords: addition, fraction
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On monday,a local hamburger shop sold a total of 330 hamburgers and cheeseburgers.The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on monday?
Answer:
165 Hamburgers
Step-by-step explanation:
330 divided by 2 is 165
Which events are independent?
Select each correct answer.
One ball is drawn from a bag of balls after another ball is drawn without replacement.
A coin is flipped and a spinner is spun.
White marbles are drawn from a bag of marbles without replacing the marbles.
Four number cubes are rolled at the same time.
----
I know I have asked this before but people have given me only one answer, which was C but I think I need to select more than one answer. Thanks so much for any help.
Answer:
Option B) and option D) are independent events. i.e. following events are independent events:
B) A coin is flipped and a spinner is spunD) Four number cubes are rolled at the same time.Step-by-step explanation:
Two events would be termed as Independent events if the occurrence of one event would not affect the occurrence of other event.
Let us first consider the options having independent events.
B) A coin is flipped and a spinner is spunD) Four number cubes are rolled at the same time.Option B) i.e. 'a coin is flipped and a spinner is spun' is treated as neither of the events is affecting the outcome of other event. For example, assuming a coin and spinner are kept isolated, the occurrence of event of a flipping coin is not affecting the outcome of the occurrence of spinner.
The same goes with the option D) i.e. 'four number cubes are rolled at the same time', as neither of the rolling is affecting the rolling of other coin.
Now, let us consider the options having dependent events
A) One ball is drawn from a bag of balls after another ball is drawn without replacement.C) White marbles are drawn from a bag of marbles without replacing the marbles.Let us suppose one ball is drawn from a bag of balls after another ball is drawn without replacement. If there is no replacement, it logically means, after every drawn event, total number of the balls are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event. Hence, the occurrence of every event depends upon the occurrence of other event, meaning the two events will keep affecting the outcome if no replacement is made before the next event.
The same logic goes with when white marbles are drawn from a bag of marbles without replacing the marbles. If there is no replacement, it logically means, after every drawn event, total number of the white marbles and marbles are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event.
So, after all the discussion, we can safely say make a conclusion that option B) and option D) are independent events. i.e. following events are independent events:
B) A coin is flipped and a spinner is spunD) Four number cubes are rolled at the same time.Keywords: dependent events, independent events
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Help!plzzzzzzzzzzzzzzx
He used 86 pounds of type A coffee.
Step-by-step explanation:
Cost of type A coffee = $5.40 per pound
Cost of type B coffee = $4.05 per pound
Total blend made = 138 pounds
Total cost = $675.00
Let,
x represents the pounds of type A coffee
y represents the pounds of type B coffee
According to given statement;
x+y=138 Eqn 1
5.40x+4.05y=675 Eqn 2
Multiplying Eqn 1 by 4.05
[tex]4.05(x+y=138)\\4.05x+4.05y=558.90\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5.40x+4.05y)-(4.05x+4.05y)=675-558.90\\5.40x+4.05y-4.05x-4.05y=116.1\\1.35x=116.1\\[/tex]
Dividing both sides by 1.35
[tex]\frac{1.35x}{1.35}=\frac{116.1}{1.35}\\x=86[/tex]
He used 86 pounds of type A coffee.
Keywords: linear equation, elimination method
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if THE equation of a circle is (x + 5)2 + (y - 7)2 = 36, it’s center point is
Answer:
(-5,7) is the center
Step-by-step explanation:
What is the fiftieth term of the arithmetic sequence 3, 7, 11, 15, ... ?
199
151
53
203
Answer:
53
Step-by-step explanation:
Trey is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 54 feet and its width is 30 feet. Suppose each can of wood stain covers 135 square feet. How many cans will he need to cover the court?
Answer:
The number of cans that he will need to cover the court is 12 cans
Step-by-step explanation:
The court is in the shape of a rectangle. Its length is 54 feet and its width is 30 feet. The formula for the area of a rectangle is expressed as length × width. Therefore, the area of the wooden floor is
54×30 = 1620 square foot
Suppose each can of wood stain covers 135 square feet, the number of cans that would cover the rectangular floor of the court would be
1620/135 = 12
Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term bonds pay 4%, the intermediate-term bonds pay 5%, and the long-term bonds pay 6% simple interest per year. Mark wishes to realize a total annual income of 5.25%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond?
Answer:
Short-Term investment: 5000$
Intermediate-Term investment: 65000$
Long-Term investment: 30000$
Step-by-step explanation:
To construct our first equation lets define sort-term bond investment as x, long-term investment as y.
So the equation is:
[tex]x*0,04+(100000-x-y)*0,05+y*0,06=5250[/tex]
From the equation it is found that:
[tex]y=25000+x[/tex]
Instead of y, if we put 25000+x the equation will be as following:
[tex]x*0,04+75000*0,05+(25000+x)*0,06=5250[/tex]
From the equation it is found that:
[tex]x=5000[/tex]
Short-Term investment is 5000$
[tex]x+25000=y[/tex]
Long-Term investment is 30000$
Rest of the money is Intermediate-Term investment 65000$
Find f(2) if f(x) = 2x + 1.
A) 3
B) 5
C) 7
D) 9
Answer:
The answer to your question is letter B
Step-by-step explanation:
Process
1.- Write the equation
f(x) = 2x + 1
find f(2)
2.- Substitute x for 2
f(2) = 2(2) + 1
3.- Simplify
f(2) = 4 + 1
f(2) = 5
Answer:
5
Step-by-step explanation:
2(2) + 1 = 5
an agent of a broker-dealer wishes to create a website to solicit securities business from customers. based on each customer's reponses to questions asked, appropriate investment recommendations will be made. which statement are true?
Answer:
The following statements are true:
The broker-dealer must review and approve the content of the website The broker-dealer must be registered in each State where a customer responds to the website The agent must be registered in each State where a customer responds to the websiteStep-by-step explanation:
An agent of a broker-dealer wishes to create a website to solicit securities business from customers based on each customer's response to questions asked, appropriate investment recommendation will be made. The statement which is not true under the given conditions is: "The Administrator must review and approve the content of the website." because the broker-dealer has to approve the content of the website.These recommendations which are discussed above are for the benefit and will ensure the safety and prevent the damage.The perimeter of a rectangular lot is 74 feet. The cost of fencing along the two lengths is $1 per foot, and the cost of fencing along the two widths is $3.50 per foot. Find the dimensions of the lot if the total cost of the fencing is $159.
Answer:
340 ft²
Step-by-step explanation:
perimeter of rectangle = 2 x (L+W) = 2L + 2W = 74 .....(1)
cost of two length : $1 x 2L
cost of two width: $3.50 x 2W
($1 x 2L) + ($3.50 x 2W) = $159
2L + 7W = 159 ....... (2)
(2) - (1) ... 5W = 85
W = 17
L = (74 - 2 x 17) / 2 = 20
dimension = 17 x 20 = 340 ft²
The dimensions of the rectangular lot are 162.67 feet by 325.34 feet. The perimeter equation is 2L + 2W = 74. The cost equation is L + 3.50W = 159.
Explanation:Let's say the length of the rectangular lot is L feet and the width is W feet.
The perimeter of a rectangle can be defined as: 2L + 2W.
According to the question, the perimeter is 74 feet, so we can write the equation as: 2L + 2W = 74.
The cost of fencing along the two lengths is $1 per foot, so the cost for the length fencing is 1 * L dollars.
The cost of fencing along the two widths is $3.50 per foot, so the cost for the width fencing is 3.50 * W dollars.
The total cost of fencing is $159, so we can write the equation as: 1 * L + 3.50 * W = 159.
Now we have two equations:
2L + 2W = 74
L + 3.50W = 159
To solve these equations, we can use substitution or elimination method.
Let's use the elimination method:
Multiply the second equation by 2 to eliminate L: 2L + 3.50W = 318Subtract the first equation from the second: (2L + 3.50W) - (2L + 2W) = 318 - 74This simplifies to: 1.50W = 244.
Divide both sides by 1.50: W = 244 / 1.50 = 162.67 feet.
Plug this value back into the first equation to find L: 2L + 2(162.67) = 74.
Simplify: 2L + 325.34 = 74.
Subtract 325.34 from both sides: 2L = -251.34.
Divide both sides by 2: L = -251.34 / 2 = -125.67 feet.
Since the dimensions of the lot cannot be negative, we discard the negative value.
Therefore, the dimensions of the lot are 162.67 feet by 325.34 feet.
One apple and two plums cost $1.11. Two apples and 2 plum cost $1.38. How much does 1 apple and 1 plum cost?
answer: 0.69
answer explanation:
to start take 1.38 and 1.11 and subtract to find a price of a plum which is 0.27 since 1.38 have a extra plum then take 1.11 and take away 0.27 from 1.11 and get 0.84 then divide by 2 and get 0.42 so a apple cost 0.42 and a plum cost 0.27 together cost 0.69 which is nice
To find the cost of 1 apple and 1 plum, set up and solve a system of equations based on the given costs of different fruit combinations.
To solve this problem, we need to set up a system of equations:
Let x be the cost of one apple and y be the cost of one plum.From the given information, we have the equations: x + 2y = 1.11 and 2x + 2y = 1.38.Solve the system of equations to find the cost of 1 apple and 1 plum, which is $0.47.
Raina is putting 13 colored light bulbs into a string of lights. There are 5 white light bulbs, 6 orange light bulbs, and 2 blue light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
Answer: The number of ways would be 36,036.
Step-by-step explanation:
Since we have given that
Number of white light bulbs = 5
Number of orange light bulbs = 6
Number of blue light bulbs = 2
Total number of light bulbs = 13
So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.
[tex]N=\dfrac{n!}{r!}\\\\N=\dfrac{13!}{5!\times 6!\times 2!}\\\\N=36036[/tex]
Hence, the number of ways would be 36,036.
The number of different orders in which Raina can put the colored light bulbs into a string is 1,324, calculated using the formula of permutations with indistinguishable items.
Explanation:The question is about the number of different possible arrangements, or combinations, of the colored light bulbs. Since all light bulbs of the same color are identical, this is a problem of permutations with indistinguishable items. The formula to calculate this is n!/(r1!*r2!*...*rn!), where n is the total number of items, and r1, r2,...,rn are the number of each type of identical items.
So in this case, there are 13 colored light bulbs in total (n=13), with 5 white light bulbs (r1=5), 6 orange light bulbs (r2=6), and 2 blue light bulbs (r3=2).
The total different orders of light bulbs can be found by calculating 13!/(5!*6!*2!) = 1,324 possibilities.
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If the lengths of two sides of a certain triangle are 5 and 10, what is the length of the third side of the triangle?
Answer:
Step-by-step explanation:
let x be the length of third side.
10-5<x<10+5
or 5<x<15
so third side is between 5 and 15 .
Answer: The length of the third side is greater than 5 and less than 15 units.
Step-by-step explanation: Given that the lengths of two sides of a certain triangle are 5 and 10 units.
We are to find the length of the third side of the triangle.
Let x represents the length of the third side of the given triangle.
We know that the sum of the lengths of two sides of a triangle is always greater than the length of the third side, so we must have
[tex]5+10>x\\\\\Rightarrow x<15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
[tex]5+x>10\\\\\Rightarrow x>5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
and
[tex]x+10>5\\\\\Rightarrow x>-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From inequalities (i), (ii) and (iii), we get
[tex]5<x<15.[/tex]
Thus, the length of the third side is greater than 5 and less than 15 units.
Sammy is making a bacon wrapped pizza for dinner. She is wrapping 47.1 inches of bacon around the outside edge of the pizza. What is the area of the pizza?
Answer:
Approx. 1.8 in.²
Step-by-step explanation:
Circumference of a circle (the pizza) = 2πr
Area of a circle = πr²
Set 2πr = 4.71 (because that's the length of bacon around the pizza) and solve for the radius "r". Then plug that "r" into the area equation πr² to find the area. You should get 1.8 square inches if I plugged them in correctly.
The residents of a city voted on whether to raise property taxes. The ratio of yes votes was 5 and no votes was 7.
If there were 3710 yes votes, what was the total number of votes?
Answer:
Step-by-step explanation:
Set this up as a proportion. The idea is that if we can find out the number of "no" votes based on the ratio of 5:7, then we can add the "no" votes to the number of "yes" votes to get the total number of votes.
[tex]\frac{yes}{no}:\frac{5}{7}=\frac{3710}{x}[/tex]
Cross multiply to get
5x = 25790 so
x = 5194 "no" votes.
5194 + 3710 = 8904 total votes
The scoring of modern IQ tests is such that IQs have a Normal distribution with mean
100 and standard deviation 15. What is the approximate IQ of someone with a z-score of 0.93?
Answer:
114
Step-by-step explanation:
z = (x − μ) / σ
0.93 = (x − 100) / 15
x ≈ 114
Keys went to the grocery store on Monday and bought 5 apples and 2 oranges for a total of 3.45. On Thursday she bought 3 oranges and 7 apples for a total of $4.90
Answer:
Keys would have to spend $6.60 on apples for both days.
Step-by-step explanation:
Keys went to buy 5 apples and 2 oranges for $3.45 and 7 apples and 3 oranges for $4.90 .
We have to find how much money she spends on apples on both the days.
Let price of apples be x and oranges be y.
We have to make equations and solve them to find the price of oranges and apples.
5x + 2y = 3.45
7x + 3y = 4.90
Solve both these equations to find x and y.
We get x= $0.55 and y = $0.35
Key has bought 12 apples and it would cost = 12 [tex]\times[/tex] 0.55
= $6.60
What is the length of the midsegment of the trapezoid
Answer:
The length of the mid-segment of the trapezoid = 7
==================================================
Step-by-step explanation:
The mid-segment of a trapezoid is the segment that connecting the midpoints of the two non-parallel sides.
As shown in the figure the two non-parallel sides are AB and CD
∴ The mid-segment of the trapezoid = [tex]\frac{BC +AD}{2}[/tex]
From the figure: BC = 8 and AD = 6
∴ The mid-segment of the trapezoid = [tex]\frac{8+6}{2} = 7[/tex]
In the parallelogram below, y = ?
Answer:
y = 33°
Step-by-step explanation:
The left side and the right side are parallel, so the angles marked y and 33° are alternate interior angles, hence congruent.
y = 33°
3(5j+2)=2(3j-6)(if there is no solution,type in ''no solution'')j= Answer
Answer:
j = -2
Step-by-step explanation:
It usually works well to start by eliminating parentheses.
15j +6 = 6j -12
Now you can subtract 6j from both sides to get the variable term on one side of the equation only:
9j +6 = -12
And you can subtract 6 from both sides to get the variable term by itself:
9j = -18
Now, dividing by the coefficient of the variable gives you the solution:
j = -2
The solution is j = -2.
Answer:
j = -2
Step-by-step explanation:
3 (5j + 2) = 2 (3j - 6)
15j + 6 = 6j - 12
15j - 6j = - 12 - 6
9j = - 18
j = - 18/9
j = - 2
answer plzzz 30 pointss for eachh
Answer:
D. [tex]y<\frac{2}{3}x-4\ and\ y\geq-2x+2[/tex]
Step-by-step explanation:
Given:
Let us find the equations of the lines from the graph.
First let us determine the equation of the broken line.
The slope of the broken line is positive as 'y' values increases with increase in 'x'. The slope is the ratio of the absolute value of y-intercept to that of the x-intercept.
x-intercept = 6, |y-intercept| = |-4| = 4
So, [tex]m=\frac{4}{6}=\frac{2}{3}[/tex]
Now, equation of a line with slope 'm' and y -intercept 'b' is given as:
[tex]y=mx+b[/tex]
Here, [tex]m=\frac{2}{3},b=-4[/tex].So, equation of the broken line is:
[tex]y=\frac{2}{3}x-4[/tex]
Now, from the graph, the solution is below the broken line. So, the equality sign is replaced by the less than inequality sign. So,
[tex]y<\frac{2}{3}x-4[/tex]
Now, let us determine the equation of the other line.
y-intercept, [tex]b = 2[/tex], x-intercept = 1
Slope is negative as 'y' decreases with increase in 'x'. So,
Slope, [tex]m=-\frac{2}{1}=-2[/tex]
Now, equation is given as:
[tex]y=-2x+2[/tex]
From the graph, the solution region is to the left of the line. So, the 'equal to' sign is replaced by the 'greater than or equal to' sign' as the line is also included in the solution region. So, the inequality becomes:
[tex]y\geq-2x+2[/tex]
Therefore, the last option is correct.
[tex]y<\frac{2}{3}x-4\ and\ y\geq-2x+2[/tex]
The family size bottle of sunscreen holds 12 fluid ounces (fl oz)left parenthesis, start text, f, l, space, o, z, end text, right parenthesis of sunscreen. The regular bottle holds 75%, percent less. How many fewer fluid ounces does the regular bottle of sunscreen hold?
Twenty different video games showing alcohol use were observed. The duration times of alcohol use (in seconds) were recorded.
1. When using this sample for a t-test of the claim that the population mean is greater than 89 sec, what does df denote?
A. The sample standard deviation
B. The number of degrees of freedom
C. The sample size
D. The test statistic
2. What is its value?
Answer:
Degree of freedom = 19
Step-by-step explanation:
We are given the following information in the question:
Sample size, n = 20
For a t-test hypothesis it was claimed that the population mean is greater than 89 second.
1) df
Df denotes the degree of freedom.
The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary.2) Degree of freedom = n - 1
where n is the sample size
Degree of freedom = 20 - 1 = 19
Use synthetic division with the factor x + 1 to completely factor LaTeX: x^3+2x^2-5x-6x 3 + 2 x 2 − 5 x − 6.
Answer:
[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex].
Step-by-step explanation:
To find [tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}[/tex] using synthetic division you must:
Write the problem in a division-like format. To do this:
Take the constant term of the divisor with the opposite sign and write it to the left.
Write the coefficients of the dividend to the right.
[tex]\begin{array}{c|cccc}&x^{3}&x^{2}&x^{1}&x^{0}\\-1&1&2&-5&-6\\&&\\\hline&\end{array}[/tex]
Step 1: Write down the first coefficient without changes:
[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\\\hline&\1\end{array}[/tex]
Step 2:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\left(-1\right) \cdot 1=-1\\\hline&{1}&{2}+\left({-1}\right)={1}\end{array}[/tex]
Step 3:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}{-1}&1&2&{-5}&-6\\&&-1&\left({-1}\right) \cdot {1}={-1}\\\hline&1&{1}&\left({-5}\right)+\left({-1}\right)={-6}\end{array}[/tex]
Step 4:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}{-1}&1&2&-5&{-6}\\&&-1&-1&\left({-1}\right) \cdot \left({-6}\right)={6}\\\hline&1&1&{-6}&\left({-6}\right)+{6}={0}\end{array}[/tex]
We have completed the table and have obtained the following resulting coefficients: 1, 1, −6, 0.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is [tex]x^{2}+x-6[/tex], and the remainder is 0.
[tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}=x^{2} + x - 6+\frac{0}{x + 1}=x^{2} + x - 6[/tex]
Now, we factor [tex]x^{2}+x-6[/tex]
[tex]\left(x^2-2x\right)+\left(3x-6\right)\\x\left(x-2\right)+3\left(x-2\right)\\\left(x-2\right)\left(x+3\right)[/tex]
Therefore,
[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex]
The American Veterinary Association claims that the annual cost of medical care for dogs averages $100, with a standard deviation of $30, and for cats averages $120, with a standard deviation of $35.
a) What's the expected difference in the cost of medical care for dogs and cats?
b) What's the standard deviation of that difference?
c) If the costs can be described by Normal models, what's the probability that medical expenses are higher for someone's dog than for her cat?
d) What concerns do you have?
Answer:
a)20$
b)46,1$
c)0,3336
d)No concerns
Step-by-step explanation:
A) To find expected difference of cost of medical care for dogs and cats we can simply subtract average costs of cats and dogs.
[tex]120-100=20[/tex]
Expected difference will be 20$.
B) To find the standard deviation of that difference, we need to square deviations and add them and square root it again.
[tex]\sqrt{(30^2+35^2)} =46,1[/tex]
Expected difference will be 46,1$.
C)We need to find the Z value to find the probability of more expensive dogs than cats in a Vet vise.[tex]Z=(0-20)/46,1=-0,434[/tex]
Z value of the function is -0,434
From the Z table that you can find at the attachment. The probability is %33,36 or 0,3336
D) This is a subjective part. I don't have any concerns