Answer:
here
alternate exterior angles--∠1, ∠8 and ∠2, ∠7
alternate interior angles--∠3, ∠6 and ∠4, ∠5
corresponding angles--∠1, ∠5 and ∠2, ∠6
vertical angles--∠2, ∠3 and ∠5, ∠8
Step-by-step explanation:
Answer:
here
alternate exterior angles--∠1, ∠8 and ∠2, ∠7
alternate interior angles--∠3, ∠6 and ∠4, ∠5
corresponding angles--∠1, ∠5 and ∠2, ∠6
vertical angles--∠2, ∠3 and ∠5, ∠8
Step-by-step explanation:
Suppose that a population is known to be normally distributed with £ = 2400 and € = 210. Of a random sample of size n = 8 is selected, calculate the probability that the sample mean will exceed 2,500.
Answer:
0.0885 = 8.85% probability that the sample mean will exceed 2,500.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]\mu = 2400, \sigma = 210, n = 8, s = \frac{210}{\sqrt{8}} = 74.25[/tex]
Calculate the probability that the sample mean will exceed 2,500.
This is 1 subtracted by the pvalue of Z when X = 2500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2500 - 2400}{74.25}[/tex]
[tex]Z = 1.35[/tex]
[tex]Z = 1.35[/tex] has a pvalue of 0.9115
1 - 0.9115 = 0.0885
0.0885 = 8.85% probability that the sample mean will exceed 2,500.
solve p varies directly as the square of s and inversely as r, when s=6,r=3,and p=48 find the value of p when s =10and r=5
Answer:
see explanation
Step-by-step explanation:
Given that p varies directly as s² and inversely as r then the equation relating them is
p = [tex]\frac{ks^2}{r}[/tex] ← k is the constant of variation
To find k use the condition when s = 6, r = 3 and p = 48, that is
48 = [tex]\frac{6^2k}{3}[/tex] ( multiply both sides by 3 to clear the fraction
144 = 36k ( divide both sides by 36 )
4 = k , thus
p = [tex]\frac{4s^2}{r}[/tex] ← equation of variation
When s = 10 and r = 5 , then
p = [tex]\frac{4(10)^2}{5}[/tex] = [tex]\frac{400}{5}[/tex] = 80
Which equation represents the total cost (c) of purchasing cans of vegetables(v) at a price of $1.18 per can? What is the total cost to purchase 98 cans of vegetables? Question 10 options: A) c = 1.18v; $83.05 B) v = 1.18c; $83.05 C) c = 1.18v; $115.64 D) v = 1.18c; $115.64
Answer:
C
Step-by-step explanation:
The equation must be equal to c since that is the total cost.
c = 1.18v
Plug in 98 for v to find the answer.
c = 1.18(98)
c = $115.64
To determine if a particular predictor in a regression analysis is statistically significant, which statistic should one interpret
Answer:
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
Step-by-step explanation:
The general form of a regression equation is:
[tex]y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+...+\beta_{n}x_{n}[/tex]
Here,
α = y-intercept
βi = regression coefficients, (i = 1, 2, ..., n)
A regression analysis is performed to determine whether the predictor variables are statistically significant or not.
The output of the regression analysis consists of two tables.
One is the regression output and the other is the ANOVA table.
The regression output table is used to display which predictor variables are statistically significant and which are not.
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
And the ANOVA table displays overall regression analysis.
The F-test statistic is used to for the overall regression analysis.
Thus, the test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
Ross needs to buy a countertop for a laundry room. He calculated the area to be 12 square feet. The actual area is 11.8 square feet. What is Ross's percentage error? a.1.02% b.1.69% c.20% d.98%
Answer:
b. 1.69
Step-by-step explanation:
So to solve this problem we need to simply find the percentage increase from 11.8 to 12 =>
to solve this we would do 12 - 11.8 = 0.2 --> 0.2 is our "difference in the increase" -->
now we divide this by our amt. which is 11.8 --> 0.2/11.8 = approx. 0.0169
--> finally multiply that by 100 which is simply moving the decimal places 2 places right giving us the final answer of 1.69
Hope this helps!
Answer:
B. 1.69%
Step-by-step explanation:
If Ross calculated the countertop for a laundry room to be 12 square feet but turns out to be actually 11.8 square feet, we need to find out how much percentage error Ross has made!
In order to solve this question,
1) We need to create proportions:
Ross' calculations x
______________ = _________
actual area 100
x represents the percentage error.
100 is the total percentage.
2) Now we plug in the numbers:
We plug in 12 for Ross' calculations. We plug in 11.8 for the actual area. So, it will look like this:
12 x
______ = _______
11.8 100
3) Time for cross multiplication:
12 times 100 is 1,200
11.8 times x is 11.8x
So,
1,200 = 11.8x
4) Now we divide:
1,200 divided by 11.8 equals to 101.69 %
5) We are not done! We still have to subtract:
101.69
-100.00
_______
1.69
Finished!!
Our answer is 1.69%, which is B.
Hope this was helpful !!!
Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).
Weekly Usage
(hours) Annual Maintenance
Expense ($100s)
13 17.0
10 22.0
20 30.0
28 37.0
32 47.0
17 30.5
24 32.5
31 39.0
40 51.5
38
40.0
(a) Use the data to develop an estimated regression equation that could be used to predict the annual maintenance expense for a given number of hours of weekly usage. What is the estimated regression model?
Let x represent the number of hours of weekly usage.
If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
(b) Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
(c) How much of the variation in the sample values of annual maintenance cost does the model you estimated in part (b) explain?
If required, round your answer to two decimal places.
(d) If the maintenance contract costs $3000 per year, would you recommend purchasing it? Explain.
Answer:
Step-by-step explanation:
Hello!
The given data corresponds to the variables
Y: Annual Maintenance Expense ($100s)
X: Weekly Usage (hours)
n= 10
∑X= 253; ∑X²= 7347; [tex]\frac{}{X}[/tex]= ∑X/n= 253/10= 25.3 Hours
∑Y= 346.50; ∑Y²= 13010.75; [tex]\frac{}{Y}[/tex]= ∑Y/n= 346.50/10= 34.65 $100s
∑XY= 9668.5
a)
To estimate the slope and y-intercept you have to apply the following formulas:
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{9668.5-\frac{253*346.5}{10} }{7347-\frac{(253)^2}{10} }= 0.95[/tex]
[tex]a= \frac{}{Y} -b\frac{}{X} = 34.65-0.95*25.3= 10.53[/tex]
^Y= a + bX
^Y= 10.53 + 0.95X
b)
H₀: β = 0
H₁: β ≠ 0
α:0.05
[tex]F= \frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg}; Df_{Error}}[/tex]
F= 47.62
p-value: 0.0001
To decide using the p-value you have to compare it against the level of significance:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The decision is to reject the null hypothesis.
At a 5% significance level you can conclude that the average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.
b= 0.95 $100s/hours is the variation of the estimated average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.
a= 10.53 $ 100s is the value of the average annual maintenance expense of the computer wheel alignment and balancing machine when the weekly usage is zero.
c)
The value that determines the % of the variability of the dependent variable that is explained by the response variable is the coefficient of determination. You can calculate it manually using the formula:
[tex]R^2 = \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]} = \frac{0.95^2[7347-\frac{(253)^2}{10} ]}{[13010.75-\frac{(346.50)^2}{10} ]} = 0.86[/tex]
This means that 86% of the variability of the annual maintenance expense of the computer wheel alignment and balancing machine is explained by the weekly usage under the estimated model ^Y= 10.53 + 0.95X
d)
Without usage, you'd expect the annual maintenance expense to be $1053
If used 100 hours weekly the expected maintenance expense will be 10.53+0.95*100= 105.53 $100s⇒ $10553
If used 1000 hours weekly the expected maintenance expense will be $96053
It is recommendable to purchase the contract only if the weekly usage of the computer is greater than 100 hours weekly.
Evauluate 37/100+3/10
Answer:
67/100
Step-by-step explanation:
Find common denominators, note that what you do to the denominator, you must do to the numerator.
The common denominator is 100:
(3/10)(10/10) = (3 * 10)/(10 * 10) = 30/100
Add:
37/100 + 30/100 = 67/100
67/100 is your answer.
~
Answer:
67/100
Step-by-step explanation:
37/100+3/10
Get a common denominator
37/100 + 3/10 *10/10
37/100+30/100
67/100
Robert wants to arrange the books for statistics, calculus, geometry, algebra, and trigonometry on a shelf. In how many arrangements can he keep them on the shelf such that the algebra and trigonometry books are not together?
Answer: 72 arrangements
Step-by-step explanation:
The books are:
Statistics, calculus, geometry, algebra, and trigonometry.
So we have 5 books.
We want that algebra and trigonometry are not together.
Suppose that we have 5 positions:
Now, we can start with algebra in the first position.
Now, we have 3 positions for trigonometry (3rd, 4th and 5th).
Now, once those two books are in position, we have 3 other positions and 3 other books, so for the first selection we have 3 options, for the second position we have 2 options, and for the last option we have 1 option.
The number of combinations is equal to the number of options in each selection:
3*(3*2*1) = 18
Now, if Algebra is in the second place, then for trigonometry we have only 2 possible options (4th and 5th)
and for the other 3 books again we have 3*2*1 combinations:
the total number of combinations is:
2*(3*2*1) = 12
If algebra is in the 3rd position, trigonometry has 2 options (1st and 5th)
For the other 3 books, we have 3*2*1 combinations.
The total number of combinations is:
(3*2*1)*2 = 12
in the fourth position is the same as the second position, so here we have again 12 combinations.
For the fifth position is the same as for the first position, so we have 18 combinations.
The total number of combinations is:
C = 18 + 12 +12 +12 +18 = 72
When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc) estimate Create a t-chart to graph the coordinates Find the 0's of the function Solve for y and use the slope-intercept form
Answer:
creat a t-chart to graph the coordinates.
In a fish tank the number of orange fish is 1 1/4 times the number of blue fish. Drag the blue fish to represent the number of blue fish in the tank dor every 5 orange fish
Answer:
4 blue fish for every 5 orange fish
Step-by-step explanation:
(orange fish) = (1 1/4)·(blue fish) . . . . . the given relation
(orange fish) = (5/4)·(blue fish) . . . . . write as improper fraction
(orange fish)/(blue fish) = 5/4 . . . . . divide by "blue fish"
There are 4 blue fish for every 5 orange fish.
Joel is fertilizing an irregularly shaped garden. the grid has squares with side lengths of 2 m. Estimate the area of the garden. Given that the price of the fertilizer is $2.99 per square meter, find the cost of the fertilizer
Answer:
34.99
Step-by-step explanation:
A copy machine makes 104 copies in 3 minutes and 15 seconds. how many copies does it make per minute
Answer:
32 copiesStep-by-step explanation:
First convert 3 minutes and 15 seconds into minutes by converting 15 sec to min and add it to 3min
60 sec = 1min
15 sec = 15 / 60 × 1 min
= 0.25min
Add it to 3min
3min + 0.25min = 3.25 min
We use ratio and proportion
3.25min = 104 copies
1 min = 104× 1/ 3.25
= 104 / 3.25
= 32
The final answer is 32 copies
Hope this helps you.
Answer:
Step-by-step explanation:
3 min 15 sec = 3*60 + 15 = 180 + 15 = 195 seconds
In 195 seconds 104 copies are made
In one second, the number of copies made = [tex]\frac{104}{195}\\[/tex]
In 60 seconds, the number of copies made = [tex]\frac{104}{195}*60[/tex]
= 32 copies
WHY CAN'T ANYONE HELP ME? Find an equation of the line described. Write the equation in slope-intercept form when possible. Through (-5,-3), perpendicular to the y-axis.
Answer:
y=-3
Step-by-step explanation:
If the line is perpendicular to the y- axis, that means that it must be a horizontal line. Any horizontal line must be in the form y=b. Since the y-value of the point is -3, the equation of the line must be y=-3
Answer:
y = -3
Step-by-step explanation:
A line perpendicular to the y-axis is a horizontal line.
The equation of a horizontal line is of the form
y = k,
where k is the y-coordinate of all points on the line. Since point (-5, -3) is on the line, then the y-coordinate of all points on the line is -3.
Answer: y = -3
What would be the angle of elevation of a tree from the ground, if the height of the
tree and its shadow are equal in length?
Answer:
45°
Step-by-step explanation:
The diagram for this question has been attached to this response. Please check.
The angle of elevation is the angle between a horizontal line from a viewer and the line of sight to an object being viewed which is above the horizontal line.
From the diagram;
θ is the angle of elevation
x = height of the tree
y = length of the shadow of the tree = x
Therefore,
tanθ = [tex]\frac{x}{y}[/tex] [Remember that y = x? Then substitute into the equation]
tanθ = [tex]\frac{x}{x}[/tex]
tanθ = 1
θ = tan⁻¹(1)
θ = 45°
Therefore, the angle of elevation is 45°
A spring has natural length 24 cm. Compare the work W1 done in stretching the spring from 24 cm to 34 cm with the work W2 done in stretching it from 34 to 44 cm. (Use k for the spring constant) So:W1= ? W2:=? These answers must be written in terms of k. How are W2 and W1 related? W2 = ? W1
Answer:
From the analysis W1=W2.
they are directly related
Step-by-step explanation:
the work-done in stretching a spring can be expressed as
[tex]W=\frac{1}{2}kx^2[/tex]
where k= spring constant
x= change on length of spring
Hence for W1
Given data
x= 34-24= 10 cm
solving in terms of k we have
[tex]W=\frac{1}{2}k*10^2\\\W=\frac{1}{2}k*100\\\W=50k[/tex]
Hence for W2
Given data
x= 44-34= 10 cm
solving in terms of k we have
[tex]W=\frac{1}{2}k*10^2\\\ W=\frac{1}{2}k*100\\\ W=50k[/tex]
URGENT!! The diagram shown below represents the height of a blimp flying over a football stadium. Find the height of the blimp if the angle of elevation at the southern end zone, point A, is 70∘, the angle of elevation from the northern end zone, point B, is 62∘, and the distance between the viewing points of the two end zones is 145 yards. Round your answer to the nearest tenth and do not include units.
Answer:
Hello There!
~~~~~~~~~~~~~~~~~~~`
The height of the blimp over the football stadium = 161.9 yards
Hope this helepd you. Brainliest would be nice!
6x - 2y = 18
3x + 4y= -6
Which of the following ordered pairs (x, y) is the
solution to the system of equations shown above?
A. (-3,2)
B. (-2,3)
C. (2, -3)
D. (3,-2)
Answer:
C. (2, -3)
Step-by-step explanation:
Easiest and fastest way to get the solution set is to graph the systems of equations and analyze where the graphs intersect.
Please help me. Please....
Answer:
20
Step-by-step explanation:
1/2(a+b)=180
1/2(6+12)=18
1/2(18)=180
9/9=180/9
=20
which of the following describes an irrational number?
A. a repeating and non-terminating decimal.
B. a fraction
C. a terminating decimal
D. a non-terminating and non-repeating decimal
Answer:
A.
Step-by-step explanation:
B is wrong because irrational numbers can include pie.
C and D are wrong because irrational numbers don't get a whole number, and instead gives a decimal numbers.
Members of a gymnastics team are traveling to a tournament. They must pay $250 for a bus plus $40 per athlete to register for the tournament. What is the average total cost per athlete if 20 gymnasts attend? Do not include the dollar sign ($) in your answer.
Answer:
1050 in total, 52.50 for each athlete
Step-by-step explanation:
We can start by writing an equation with x as the number of athletes
250+40x= Total cost
Now we can substitute 20 for x
250+40(20)
250+800
1050
The total cost is 1050
If you need the amount that each athlete is paying individually, just divide it by 20
1050/20=52.50
52.50 for each athlete
What is the simple interest earned on
$300 over 6 years at 4% interest?
Answer:
$72
Step-by-step explanation:
I = Prt
I = ($300)(0.04)(6)
I = $72
An item has a listed price of $30 if the sales tax rate is 7% how much is the sales tax in dollars
Answer:
The sales tax is 2.10
Step-by-step explanation:
Take the price of the item and multiply by the sales tax rate to determine the tax
30 * 7%
30 * .07
2.10
The sales tax is 2.10
Licence plates in Costa Rica are made up of 6 one-digit number. How many license plates can be made if the numbers can be repeated? (Probability unit grade 12 data management)
Answer:
There are 10 digits and 6 numbers so the answer is 10 * 10 * 10 * 10 * 10 * 10 = 10⁶ = 1,000,000.
3. A strip of wood 78 inches long is to be cut into pieces 3 3la inches long. How many pieces can be cut?
A. 21
B. 12
C. 26
D.20
Answer:
Option D (20) is the right answer.
Step-by-step explanation:
The given values are:
Length of wood,
= 78 inches
Wood pieces,
= [tex]3\frac{3}{4} \ inches[/tex]
On converting this in proper fraction, we get
= [tex]3\frac{3}{4}[/tex]
= [tex]\frac{15}{4}[/tex]
= [tex]3.75 \ inches[/tex]
Now,
On dividing "78" from "3.78", we get
= [tex]\frac{78}{3.75}[/tex]
= [tex]20.8 \ pieces[/tex]
So we got "20 pieces".
Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly because individuals who deviate too much from the mean have lower fitness. If this is the case, does variance in a trait rise after it becomes less functionally important? Billet et al. (2012) investigated this question with the semicircular canals (SC) of the three-toed sloth (Bradypus variegatus). The authors proposed that since sloths don't move their heads much, the functional importance of SC is reduced, and may vary more than it does in more active animals. They obtained the following measurements of the ratio of the length to width of the anterior SC in 7 sloths. Assume this represents a random sample. In other, more active animals, the standard deviation of this ratio is 0.09.
Sloth CW Ratios
1.5
1.09
0.98
1.42
1.49
1.25
1.18
Fill in the blank for a with the estimate of the standard deviation of this measurement in three-toed sloths to two decimals, and include the leading zero
The 95% confidence interval for the standard deviation of this data is < σ < (two decimals - include the leading zero)
Does this interval include the value obtained from other species? (answer yes or no in blank d)
Answer:
Step-by-step explanation:
Hello!
Given the variable
X: Ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloth.
The researcher's claim is that the ratio of the SC of the sloths is more variable than in other animal species that are more active.
For more active species the standard deviation of the ratio is σ= 0.09
1)
To calculate the sample standard deviation you have to calculate the sample variance first:
[tex]S^2= \frac{1}{n-1} [sumX^2-\frac{(sumX)^2}{n} ][/tex]
n=7; ∑X= 8.91; ∑X²= 11.8599
[tex]S^2= \frac{1}{6} [11.5899-\frac{(8.91)^2}{7} ]= 0.0287= 0.029[/tex]
S= √S²= √0.029= 0.169≅ 0.17
The sample standard deviation of the ratio is 0.17
2)
The parameter of interest is the population standard deviation. To calculate a confidence interval for the standard deviation of a population you have to estimate the population variance first. Then calculate the square root of both limits of the interval for the variance to obtain the interval for the standard deviation.
The statistic to use is the Chi-Square and the formula for the interval is:
[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{6; 0.025}= 1.2373[/tex]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{6; 0.975}= 14.449[/tex]
[tex][\frac{6*0.029}{14.449} ;\frac{6*0.029}{1.2373} ]\\[/tex]
[0.0120; 0.1406]
Using a 95% confidence level you'd expect the interval [0.0120; 0.1406] to include the true value of the population variance of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.
Now you have to calculate the square root of each limit:
[√0.0120; √0.1406]
[0.1097; 0.3750]
Using a 95% confidence level you'd expect the interval [0.1097; 0.3750] to include the true value of the population standard deviation of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.
3)
As you can see the calculated interval doesn't include the value obtained for the other species.
I hope this helps!
Rafael is saving money to buy a game. So far he has saved $30, which is five-sixths of the total cost of the game. How much does the game cost?
Answer:
$36
Step-by-step explanation:
30 is 5/6 of the game, so we can think that 1/6 is equal to 6, since 5(6) is 30.
If we add another sixth, we get 36, which will be the total cost of the game.
Triangle ABC is a right triangle. The sides measure AB = 3 and BC = 4. Use the Pythagorean theorem to find CA. A. CA = 25 B. CA = 2.5 C. CA = 20 D. CA = 5
Answer:
CA = 5
Step-by-step explanation:
Since the sides are 3 and 4, we recognize this as a 3:4:5 right triangle, with CA = 5. Using the Pythagorean theorem confirms this:
CA² = AB² +BC²
CA² = 3² +4² = 9 +16 = 25
CA = √25
CA = 5
Answer:
D. CA = 5
Step-by-step explanation:
The Pythagorean Theorem states that given a right triangle with legs a and b and hypotenuse (longest side) c:
a² + b² = c²
Here, the legs are 3 and 4, so a = 3 and b = 4. Plug these in to find c:
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
c = √25 = 5
The answer is thus D.
~ an aesthetics lover
P(x)⋅Q(x)=R(x); if P(x)=x+2 and R(x)=x3−2x2−6x+4, what is Q(x)?
Answer: Q(x) = x² - 4x + 2
Step-by-step explanation:
P(x) · Q(x) = R(x) ⇒ Q(x) = R(x)/P(x)
R(x) = x³ - 2x² - 6x + 4 ÷ P(x) = x + 2
I will use synthetic division (but you can also use long division).
-2 | 1 -2 -6 4
| ↓ -2 8 -4
1 -4 2 0 ← remainder
The reduced polynomial is: x² - 4x + 2
How many triangles exist with the given side lengths? 3 cm, 5 cm, 9 cm A. Exactly one unique triangle exists with the given side lengths. B. More than one unique triangle exists with the given side lengths. C. No triangle exists with the given side lengths.
Answer:c is the correct ans
Step-by-step explanation:
Feel pleasure to help u
Answer:
B-. More than one unique triangle exists with the given side lengths.
Step-by-step explanation:
according to to tringle inequality theorem he sum of the length of two sides of a triangle should be greater than the third side”. In order to verify the mentioned theorem, some cal. are preforemed below
12+15>18
15+18>12
select the option for "?" that continues the pattern in each question
3,-6, 12, 4, 20
13
14
6
16
Answer:
The next number in the sequence is: 13
Step-by-step explanation:
So we start with 3, then the pattern is:
subtract 9, add 18, subtract 8, add 16, subtract 7, add 14...
If we apply this to the pattern we can see that it works. You should be able to continue the pattern if needed.