Answers
Answer:
78.5 square meters
Explanation:
• Given:, A circle with a radius of 5 meters.
,• To find:, Area of the circle
The area of a circle is calculated using the formula:
[tex]A=\pi r^2[/tex]Substitute 5 for r and 3.14 for π:
[tex]\begin{gathered} A\approx3.14\times5^2 \\ =78.5\text{ square meters} \end{gathered}[/tex]The area of the circle is approximately 78.5 square meters.
Related Questions
Find the distance between the points (-16, 20) and (-16, -14).2007(-16, 20)161284-20-16-12-8-4048121620-4-812(-16, -14)-16-20units
Answers
Point A
(-16, 20)
Point B
(-16, -14)
The Distance Formula itself is actually derived from the Pythagorean Theorem which is a
[tex]\begin{gathered} d=\sqrt[]{(y2-y1)^2+(x2-x1)^2} \\ d=\sqrt[]{(-14-20)^2+(-16-(-16}))^2 \\ d=\sqrt[]{(-34)^2} \\ d=34 \end{gathered}[/tex]The distance would be 34 units
Please help.
Answer choices:
ASA
SSS
AAS
HL
Answers
Answer:
sss
Step-by-step explanation:
a+b=0
What does b equal
Answers
Answer: D) -a
Step-by-step explanation:
a+b=0 , add -a for both side
- a + a + b = 0 - a
we cancel (- a + a) and we get
b = 0 - a => b = -a
Answer:
option d -a
if you take a to the opposite side of the equal mark it's sign is going to change since it's positive it's going to be negative on the other side 0 -a = -a
baam answer
I have two cans of paint. Can a has 9 parts of blue paint to one part of yellow paint. Can b is 20 percent blue paint and the rest is yellow paint. How much paint should i use from each can to obtain 9 liters of paint which is half blue and half yellow.
Answers
The amount of paint that must be used from can A and can B is 3.86 liters and 5.14 liters respectively to obtain 9 liters of paint which is half blue and half yellow.
Can A has 9 parts of blue paint and 1 part of yellow paint, this can be expressed in percentage as;
Can A = 90% blue, 10% yellow
Similarly,
Can B = 20% blue, 80% yellow
Now consider an algebraic expression as follows;
A + B = 9 liters
90% A + 20% B = 50% [Blue]
10% A + 80% B = 50% [Yellow]
Resolving;
90% A + 20% B = 10% A + 80% B
80% A = 60% B
Solving the equation, A + B = 9, for one variable;
A + B = 9
B = 9 - A
80% A = 60% (9 - A)
80% A = 540% - 60% A
140% A = 540%
A = 3.86 Liters
Now solving for B;
B = 9 - A
B = 9 - 3.85
B = 5.14 Liters
Therefore 3.86 liters should be used from can A and 5.14 liters should be used from can B.
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Select whether the pair of lines is parallel, perpendicular, or neither.
y = 5, y = −3
Answers
The given pair of lines are parallel lines.
What are parallel lines?Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a fixed minimum distance between them and no contact or intersection are said to be parallel. A line with the same slope is said to be parallel. To put it another way, these lines won't ever cross. At the interception, perpendicular lines always intersect and form right angles.So, graph the lines on the given equation:
y = 5y = -3(Refer to the graph attached below)
We can easily look at the graph and tell that the given lines of the equations are parallel to each other.
Therefore, the given pair of lines are parallel lines.
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I'm not good with graphs so I really need help solving and understanding this
Answers
4x + 3y = -24 (option D)
Explanation:To determine the orrect option, we would find the equation of the line.
Equation of line: y = mx + c
m = slope, c = y-intercept
Using the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]We would use any two points on the graph.
Using points: (-6, 0) and (0, -8)
[tex]\begin{gathered} x_1=-6,y_1=0,x_2=0,y_2\text{ = -}8 \\ m\text{ = }\frac{-8-0}{0-(-6)} \\ m\text{ =}\frac{-8}{0+6}=\frac{-8}{6}=-\frac{4}{3} \end{gathered}[/tex]The y intercept is the point where the line crosses the y axis and the value of x is zero. It crosses the line at y = -8
The equation of line becomes:
y = -4/3 x + (-8)
y = -4/3x - 8
Multiply both sides by 3:
3(y) = 3(-4/3 x) - 3(8)
3y = -4x - 24
3y + 4x = -24
4x + 3y = -24 (option D)
Use the figure to find measures of the numbered angles.
Answers
The measure of the numbered angles formed by the common transversal to the two parallel lines are;
[tex] \angle 1 = 113^{ \circ} [/tex]
[tex] \angle 2 = 67^{ \circ} [/tex]
[tex] \angle 3 = 67^{ \circ}[/tex]
[tex]\angle 4 = 113^{ \circ} [/tex]
What are the relationships between the angles formed by the common transversal to two parallel lines?The relationships between the angles are;
Corresponding angles are congruentVertical angles are congruentSame side exterior angles are supplementarySame side interior angles are supplementaryAlternate interior angles are congruentAlternate exterior angles are congruentThe given angle is 113°
According to corresponding angles theorem, we have;
[tex] \angle 1 = 113^{ \circ} [/tex]
[tex]\angle 1 \: and \: \angle 4 [/tex] are vertical angles
According to vertical angles theorem, we have;
[tex]\angle 1 = \angle 4 = 113^{ \circ} [/tex]
[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are same side exterior angles.
According to same side exterior angles theorem, we have;
[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are supplementary angles. Which gives;
[tex] \angle 3 + 113^{ \circ} = 180^{ \circ} [/tex]
[tex] \angle 3 = 180^{ \circ} - 113^{ \circ} = 67^{ \circ}[/tex]
[tex] \angle 2 \: and \: \angle 3 [/tex] are vertical angles, which gives;
[tex] \angle 2 = \angle 3 [/tex] = 67°
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Is the ordered pair a solution of the equation?
y = x + 16; (-1,-17)
a. yes
b. no
Answers
Answer:
b.
Step-by-step explanation:
No, because -1 is x and -17 is y. if You plug it in, it will look like this:
-17=-1+16
-1+16=15
15 is not equal to -17, so the answer is no, b.
Hope this helps!
Answer:
a.)yes. у=х+16
Answer:
(-1)
the repair time for air conditioning units is believed to have a normal distribution with a mean of 38 minutes and a standard deviation of 12 minutes. find the probability that the repair time for an air conditioning unit will be between 29 and 44 minutes.
Answers
The probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648
We are given:
u= 38,s = 12
We have to find P(29 < x< 44)
Using the z-score formula, we have:
P(29 <x <44) = P(-0.75 < z <0.5)
Using the standard normal table, we have:
P(29 <x<44) = P(-0.75 < z < 0.5) = 0.4648
Therefore, the probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648
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An item has a listed price of $90. If the sales tax rate is 3%, how much is the sales tax (in dollars)?
Answers
$2.70
reasoning:
90*0.03 = 2.7
2.7 —> $2.70
In a state's lottery, you can bet $3 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect $500. Complete parts (a) through (e).
Answers
Using the Fundamental Counting Theorem, it is found that:
a) 1000 combinations are possible.
b) The probability of winning is of 0.001.
c) If you win, the net profit is of $497.
d) The expected value of a $3 bet is of -$2.5.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In the context of this problem, three digits that can be repeated are chosen, hence the parameters are:
[tex]n_1 = n_2 = n_3 = 10[/tex]
Hence the number of combinations is:
N = 10³ = 10 x 10 x 10 = 1000.
The order also has to be correct, hence the there is only one winning outcome and the probability is:
p = 1/1000 = 0.001.
You bet $3, and if you win you collect $500, hence the net profit is of:
500 - 3 = $497.
Then the distribution of earnings are as follows:
P(X = -3) = 0.999 -> losing.P(X = 497) = 0.001. -> winning.Hence the expected value is:
E(X) = -3 x 0.999 + 497 x 0.001 = -$2.5.
Missing informationThe problem is given by the image at the end of the answer.
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suppose that a tall child with arm span 120 cm and height 118 cm was added to the sample used in this study. what effect will this addition have on the correlation and the slope of the least-squares regression line?
Answers
A tall child with an arm span of 120 cm and height of 118 cm was added to the sample used in this study then the correlation will increase whereas the slope stays the same.
Correlation is a relation between two variables, by shifting one independent variable, how the dependent variable will shift, that's the degree of correlation since Correlation can be fitted in any shape or condition. It can be fitted nonlinear, straight or curvy straight, etc whereas slope is related to a straight variety of two variables, it is characterized as the rate of altering of the dependent variable in order with the independent variable. By and large you'll discover equation incline =( y2-y1)/(x2-x1).
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Use inverse trigonometric functions to solve the following equations. If there is more than one solution, enter all solutions as a comma-separated list (like "1, 3"). If an equation has no solutions, enter "DNE".Solve tan(θ)=1 for θ (where 0≤θ<2π).θ=Solve 7tan(θ)=−15 for θ (where 0≤θ<2π).θ=
Answers
Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]PLS HELP ASAP (100 POINTS) The line of best fit for the following data is represented by y = 0.81x + 6.9.
x y
3 9
6 9
5 13
7 13
8 16
8 11
What is the sum of the residuals? What does this tell us about the line of best fit?
A. 0.37; This indicates that the line of best fit is not very accurate and is a good model for prediction.
B. −0.37; This indicates that the line of best fit is accurate and is an overall a good model for prediction.
C. 0; This indicates that the line of best fit is very accurate and a good model for prediction.
D. 0; This indicates that the line of best fit is not very accurate and is not a good model for prediction.
Answers
Answer:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.Step-by-step explanation:
y = 0.81x + 6.9
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
x y y1 residual (y-y1)
3 9 9.33 -0.33
6 9 11.76 -2.76
5 13 10.95 2.05
7 13 12.57 0.43
8 16 13.38 2.62
8 11 13.38 - 2.38
Sum of residuals:
sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)
sum of residuals = -0.37ANSWER:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.
(Though not very accurate as it should have been if the sum of residuals was equal to 0).
A total discrepancy of -0.37 is not too bad.
Answer:Answer:
B. −0.37;
This indicates that the line of best fit is accurate and is an overall good model for prediction.
Step-by-step explanation:
y = 0.81x + 6.9
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
x y y1 residual (y-y1)
3 9 9.33 -0.33
6 9 11.76 -2.76
5 13 10.95 2.05
7 13 12.57 0.43
8 16 13.38 2.62
8 11 13.38 - 2.38
Sum of residuals:
sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)
sum of residuals = -0.37
ANSWER:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.
(Though not very accurate as it should have been if the sum of residuals was equal to 0).
A total discrepancy of -0.37 is not too bad.
Dilate this figure by a scale factor of 1.5. Is the image a stretch or compression?
Answers
Answer:
compression
Step-by-step explanation:
If b>1 then the graph will compress
(6-6)x 6=0
(6 + 6):6=2
6? 6?6 = 4
Answers
Answer:
I don't know if you can use permutations but
(6P2-6)/6=4 ????
How many times can 3x go into -14x^2
Answers
[tex]-14x^2 \div 3x\implies \cfrac{-14x^2}{3x}\implies -\cfrac{14}{3}\cdot \cfrac{x^2}{x}\implies -\cfrac{14}{3}x[/tex]
Analyze each situation. Identify a reasonable
domain and range. Is the domain continuous of discrete? A car has a 15-gallon gas tank and gets a
maximum average mileage of 24 miles per gallon
Answers
The reasonable domain and range are 0 ≤ x ≤ 15 and 0 ≤ y ≤ 360 and the domain is continuous
How to determine the domain?From the question, we have
Gallon gas tank = 15 gallons
This means that the domain is from 0 to 15
This can be represented as 0 ≤ x ≤ 15
For the range, we have
0 * 24 ≤ y ≤ 15 * 24
Evaluate
0 ≤ y ≤ 360
This means that
Range: 0 ≤ y ≤ 360
Lastly, the domain of the situation is continuous
This is so because the gas in the tank can take decimal values
Take for instance, the gas tank can be 13.79 gallons full
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What is 541,000 rounded to the nearest 10,000
Answers
Answer:
540,000
Step-by-step explanation:
Since you are rounding to the 10,000s place you must look at the 1,000s place to decide what to round to. Since in the 1,000s place is a 1, you will round the number down (1 < 5).
IMAGE ATTACHED,please help me with this one please.
Answers
Answer:
Step-by-step explanation:
$17.64 for 147 text messages
Therefore 1 text message will cost $17.64 ÷ 147 Text messages = $0.12 per text message
discuss the advantages and disadvantages of using sampling to reduce the number of data objects. would simple random sampling (without replacement) be a good approach to sampling? why or why not? what kind of sampling method that you would like to use? g
Answers
The advantage and disadvantages are sampling.
We have to find the advantages and disadvantages of sampling.
The advantage is:
It provides an opportunity to do data analysis with a lower likelihood of carrying an error.
Researchers can analyze the data that is collected with a smaller margin of error thanks to random sampling. This is permitted since the sampling procedure is governed by predetermined boundaries. The fact that the entire procedure is random ensures that the random sample accurately represents the complete population, which enables the data to offer precise insights into particular topic matters.
The disadvantage is:
No extra information is taken into account.
Although unconscious bias is eliminated by random sampling, deliberate bias remains in the process. Researchers can select areas for random sampling in which they think particular outcomes can be attained to confirm their own bias. The random sampling does not take into account any other information, however sometimes the data collector's supplementary information is retained.
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Use the following function rule to find g(r + 2). Simplify your answer.
g(k)= k-4
g(r + 2) =
Answers
Using the function rule, the value of g(r +2) is r-2
How can we evaluate and simply g(r + 2) using the function rule?Given the function rule g(k) = k-4.
Then g(r + 2) can be found by replacing k with r+2 in the function g(k):
g(r+2) = r + 2 - 4
= r - 2
Therefore, g(r+2) gives r - 2 when evaluated using the function rule.
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The equation y =1/2x represents a proportional relationship. What is the constant of proportionality? A. 1/2B.XC. 0D. 2
Answers
You have the following equation:
y = 1/2 x
In order to determine what is the constant of proportionality, consider the general fom of proportional relatioship, given by:
y = kx
by comparing the previous equation with y=1/2x, you can notice that k=1/2. Then, the constant of proportionality is k = 1/2
A. 1/2
State if the three side lengths form an acute obtuse or a right triangle
Answers
Given three side lengths form an acute obtuse or a right triangle 17, 21, & 28
Check Right triangle
[tex]\begin{gathered} Hyp^2=opp^2+adj^2 \\ 28^2=17^2+21^2 \\ 28^2\text{ = 289 +441} \\ 784\text{ }\ne\text{ 730} \end{gathered}[/tex]Not a Right triangle
An obtuse triangle is a triangle with one obtuse angle and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry.
Not an Obtuse triangle
[tex]\begin{gathered} \sin \text{ A= }\frac{opp}{hyp} \\ \sin \text{ A = }\frac{17}{28} \\ A=sin^{-1}\text{ }\frac{17}{28} \\ A=37.4^0\text{ (less than 90)} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ B = }\frac{adj}{hyp} \\ \cos \text{ B = }\frac{21}{28} \\ B=cos^{-1}\frac{21}{28} \\ B=41.4^0\text{ (less than 90)} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ C = }\frac{opp}{adj} \\ \tan \text{ C = }\frac{17}{21} \\ C=tan^{-1\text{ }}\frac{17}{21}\text{ } \\ C=38.9^0\text{ (less than 90) } \end{gathered}[/tex]Hence it is acute angle because all angles are less than 90°
The table shows the number of cars and trucks that used a certain toll road on a particular day. The number of cars and trucks that used, and did not use, an electronic toll pass on that same day was also recorded.Toll PassCars Trucks TotalUsed537330867Did not use9046491553Total14419792420a) If one of these vehicles is selected at random, determine the probability that the vehicle is a car.b) If one of these vehicles is selected at random, determine the probability that the vehicle is a car, given that it used the toll passa) The probability that the vehicle was a car is(Round to four decimal places as needed.)
Answers
We are given a two-way probability table
Part a)
If one of the vehicles is selected at random, determine the probability that the vehicle is a car.
From the table, we see that the total number of cars are 1441
Also, the total number of vehicles is 2420
Then the probability of selecting a car is
[tex]P(car)=\frac{1441}{2420}=0.5955[/tex]Therefore, the probability that the vehicle was a car is found to be 0.5955
Part b)
If one of the vehicles is selected at random, determine the probability that it used the electronic toll pass, given that it was a car.
This is a conditional probability problem.
The conditional probability is given by
[tex]P(used\: |\: car)=\frac{n(used\: and\: car)}{n(car)}[/tex]From the table, we see that,
[tex]\begin{gathered} n(car\: and\: used)=537 \\ n(car)=1441 \end{gathered}[/tex]So, the probability is
[tex]\begin{gathered} P(used\: |\: car)=\frac{n(used\: and\: car)}{n(car)} \\ P(used\: |\: car)=\frac{537}{1441} \\ P(used\: |\: car)=0.3727 \end{gathered}[/tex]Therefore, the probability that it used the electronic toll pass, given that it was a car is found to be 0.3727
The probability that the randomly chosen vehicle is a car is 59.54 %.
The probability that the randomly chosen vehicle is a car given that it used the toll pass is 61.94%.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
The probability that the randomly chosen vehicle is a car is the total no of cars divided by the total no. of vehicles which is,
= 1441/2420.
= (1441/2420)×100%.
= 59.54 %.
The probability that the randomly chosen vehicle is a car given that it used the toll pass is the total no. of cars that used the toll pass divided by the no. of vehicles that used the toll pass which is,
= (537/867)×100%.
= 61.94%.
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In a class of 25 students, 15 of them have a cat, 16 of them have a dog and 3 of them have neither. Find the probabillity that a student chosen at random has both
Answers
9/25
Step-by-step explanation:
students who have either cat or dog =25-3=22
students who have both= 15+16-22= 9
probabillity that a student chosen at random has both= 9/25
Number 6. For questions 5-7, (a) use synthetic division to show that x is a zero.(b) find the remaining factors of f(x).(c) use your results to find the complete factorization of f(x).(d) list all zeros of f(x).(e) graph the function.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given polynomials
[tex]f(x)=x^3+6x^2-15x-100[/tex]One of the zeroes is:
[tex]\begin{gathered} x=-5 \\ \text{this implies that:} \\ (x+5)=0 \end{gathered}[/tex]STEP 2: Use synthetic division to divide the polynomials
[tex]\frac{x^3+6x^2-15x-100}{x+5}[/tex]Write the coefficients of the numerator
[tex]1\:\:6\:\:-15\:\:-100[/tex][tex]\begin{gathered} \mathrm{Write\:the\:problem\:in\:synthetic\:division\:format} \\ \begin{matrix}\texttt{\:\:\:\:-5¦\:\:\:\:\:1\:\:\:\:\:6\:\:\:-15\:\:-100}\\ \texttt{\:\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix} \\ Carry\:down\:the\:leading\:coefficient,\:unchanged,\:to\:below\:the\:division\: \\ \begin{matrix}\texttt{\:\:\:\:-5¦\:\:\:\:\:1\:\:\:\:\:6\:\:\:-15\:\:-100}\\ \texttt{\:\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix} \\ \end{gathered}[/tex][tex]\begin{gathered} Multiply\:the\:carry-down\:value\:by\:the\:zero\:of\:the\:denominator,\:and\:carry\:the\:result\:up\:into\:the\:next\:column \\ 1\left(-5\right)=-5 \\ \begin{matrix}\texttt{\:\:\:\:-5¦\:\:\:\:\:1\:\:\:\:\:6\:\:\:-15\:\:-100}\\ \texttt{\:\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:\:\:-5\:\:\:\:\:\:\:\:\:\:\:\:}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix} \end{gathered}[/tex][tex]\begin{gathered} \mathrm{Add\:down\:the\:column:} \\ 6-5=1 \\ \begin{matrix}\texttt{\:\:\:\:-5¦\:\:\:\:\:1\:\:\:\:\:6\:\:\:-15\:\:-100}\\ \texttt{\:\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:\:\:-5\:\:\:\:\:\:\:\:\:\:\:\:}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:1\:\:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix} \end{gathered}[/tex][tex]\begin{gathered} Multiply\:the\:carry-down\:value\:by\:the\:zero\:of\:the\:denominator,\:and\:carry\:the\:result\:up\:into\:the\:next\:column: \\ 1\left(-5\right)=-5 \\ \begin{matrix}\texttt{\:\:\:\:-5¦\:\:\:\:\:1\:\:\:\:\:6\:\:\:-15\:\:-100}\\ \texttt{\:\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:\:\:-5\:\:\:\:-5\:\:\:\:\:\:}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:1\:\:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix} \end{gathered}[/tex][tex]\begin{gathered} \mathrm{Add\:down\:the\:column:} \\ -15-5=-20 \\ \begin{matrix}\texttt{\:\:\:\:-5¦\:\:\:\:\:1\:\:\:\:\:6\:\:\:-15\:\:-100}\\ \texttt{\:\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:\:\:-5\:\:\:\:-5\:\:\:\:\:\:}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:1\:\:\:\:\:1\:\:\:-20\:\:\:\:\:\:}\end{matrix} \end{gathered}[/tex][tex]\begin{gathered} Multiply\:the\:carry-down\:value\:by\:the\:zero\:of\:the\:denominator,\:and\:carry\:the\:result\:up\:into\:the\:next\:column: \\ \left(-20\right)\left(-5\right)=100 \\ \begin{matrix}\texttt{\:\:\:\:-5¦\:\:\:\:\:1\:\:\:\:\:6\:\:\:-15\:\:-100}\\ \texttt{\:\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:\:\:-5\:\:\:\:-5\:\:\:100}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:1\:\:\:\:\:1\:\:\:-20\:\:\:\:\:\:}\end{matrix} \end{gathered}[/tex][tex]\begin{gathered} \mathrm{Add\:down\:the\:column:} \\ -100+100=0 \\ \begin{matrix}\texttt{\:\:\:\:-5¦\:\:\:\:\:1\:\:\:\:\:6\:\:\:-15\:\:-100}\\ \texttt{\:\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:\:\:-5\:\:\:\:-5\:\:\:100}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:1\:\:\:\:\:1\:\:\:-20\:\:\:\:\:0}\end{matrix} \end{gathered}[/tex][tex]\begin{gathered} \mathrm{The\:last\:carry-down\:value\:is\:the\:remainder} \\ 0 \end{gathered}[/tex]The last carry-down value is the remainder and it is 0 (zero)
Since the remainder is a zero, hence, x=-5 is a zero
Step 3: Answer question b
To get the factors, the remainder of the division in step 2 is given as:
The remaining factors of f(x) is:
[tex]x^2+x-20[/tex]STEP 4: Answer Question c
[tex]\begin{gathered} roots=(x+5)(x^2+x-20) \\ Factorize\text{ the other root to have:} \\ Using\text{ factorization methods:} \\ (x^2+x-20)=(x^2+5x-4x-20) \\ x(x+5)-4(x+5)=0 \\ (x-4)(x+5)=0 \end{gathered}[/tex]The complete factorization will give:
[tex](x+5)(x-4)(x+5)[/tex]STEP 5: Answer question d
The zeroes of f(x) will be:
[tex]\begin{gathered} zeroes\text{ of f\lparen x\rparen=?, we equate the roots to 0} \\ zeroes\Rightarrow x=-5,4,-5 \end{gathered}[/tex]zeroes are: -5,4,-5
STEP 6: Plot the graph
Which is another way to represent
five hundred six and ninety-two
thousandths?
Select all that apply.
(5 x 100) + (6 × 1)
+ X
(9 × 10) + (2x 100)
(5 x 100) + (6 × 1)
+(9 × 100) + (2.× 1,000)
506.092
506.902
506.92
Answers
suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.5 and a mean diameter of 205 inches. if 79 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.3 inches? round your answer to four decimal places.
Answers
The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.
How to estimate population mean?Let X the random variable that represent the diameters of interest for this case, and for this case we know the following info
Where [tex]$\mu=205$[/tex] and [tex]$\sigma=1.5$[/tex]
Let the probability be
[tex]$P(205-0.3=204.7 < \bar{X} < 205+0.3=205.3)$$[/tex]
For this case they select a sample of n = 79 > 30, so then we have enough evidence to utilize the central limit theorem and the distribution for the sample mean can be approximated with:
[tex]$\bar{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$$[/tex]
To simplify this problem is utilizing the normal standard distribution and the z score given by:
[tex]$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]
To find the z scores for each limit and we got:
[tex]$z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778$$[/tex]
[tex]$z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778$$[/tex]
To find this probability:
P(-1.778 < Z < 1.778) = P(Z < 1.778) - P(Z < -1.778)
simplifying the above equation, we get
= 0.962 - 0.0377
= 0.9243
The interest exists the probability that the mean diameter of the sample shafts would vary from the population mean by more than 0.3 inches utilizing the complement rule we got:
P = 1 - 0.9243 = 0.0757
The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.
To learn more about probability refer to:
brainly.com/question/13604758
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Solve each system of the new equations by adding or subtracting
Answers
Given the equations
x + y = 5----------------------(1)
x - 3y = 3-----------------------(2)
Subtract equation (2) from (1)
x - x -3y - y = 3 - 5
-4y = -2
Divide both -4
[tex]\begin{gathered} \frac{-4y}{-4}\text{ = }\frac{-2}{-4} \\ y\text{ = }\frac{1}{2}\text{ = 0.5} \\ \end{gathered}[/tex]Substitute y = 1/2 into equation (1)
x + y = 5
[tex]\begin{gathered} x\text{ + }\frac{1}{2}\text{ =5} \\ x\text{ = 5 -}\frac{1}{2} \\ x\text{ = }\frac{10-1}{2} \\ x=\frac{9}{2}\text{ = 4.5} \\ \end{gathered}[/tex]Hence, the solution to the equations is
[tex]\begin{gathered} x\text{ = }4.5,\text{ y = 0.5} \\ Or\text{ in coordinate form, (4.5, 0.5)} \end{gathered}[/tex]