Answer:
f(x) has two imaginary roots and one real root.
Step-by-step explanation:
Complex roots:
I a complex number [tex]a + bi[/tex] is a root of a polynomial, it's conjugate [tex]a - bi[/tex] is also a root.
One root of a third degree polynomial function f(x) is -5 + 2i.
This means that -5 - 2i is another root of the polynomial, and thus, 2 of the roots are complex.
Third degree, so it has three roots, which means that the third root is real(not possible to have a complex root without it's conjugate), and thus, the correct answer is:
f(x) has two imaginary roots and one real root.
Answer:
B!
Step-by-step explanation:
just did it
X and Y are independent random variables. X has mean 100 and standard deviation 12. Y has mean 30 and standard deviation 9. What are the mean and standard deviation of (X–Y)?
Answer:
x is down and up and y is up then down
Step-by-step explanation:
I think
in the pair of triangle, write the similarity statement and identify the postulate of theorem that justifies the similarity.
Answer:
ΔEFG ~ ΔRPQ - Angle Angle Angle Theorem
ΔEFG ~ ΔRFQ - Side Side Side Proportional Theorem
Step-by-step explanation:
First set : using triangle sum theory to find missing angle. Letters should match congruent angles when creating statement.
Second set :
[tex]\frac{EG}{RQ}[/tex] = [tex]\frac{10}{12}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{EF}{RF}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{FG}{FQ}[/tex] = [tex]\frac{20}{24}[/tex] = [tex]\frac{5}{6}[/tex]
sec x tanx( 1- sin^2 x) = __x
Answer:
sin(x)
Step-by-step explanation:
sec x tanx(1 - sin^2 x)
1 - sin^2 x = cos^2 x
sec(x)tan(x)cos^2(x)
[tex]\frac{1}{cos(x)}[/tex] * [tex]\frac{sin(x)}{cos(x)}[/tex] * cos^2(x)
[tex]\frac{sin(x)cos^2(x)}{cos^2(x)}[/tex]
sin(x)
Get brainly if right!! Plsss help
A dozen roses in a gift box cost 21 dollars. Twenty roses in a
gift box cost 32.6 dollars. How much does a gift box cost? How
much does one rose cost?
Answer: [tex]\$1.45[/tex]; [tex]\$3.6[/tex]
Step-by-step explanation:
Given
A dozen roses in a gift box costs $21
Similarly, 20 roses in a gift box costs $32.6
Suppose the price of single rose and gift box is [tex]x[/tex] and [tex]y[/tex]
[tex]\therefore 12x+y=21\quad \ldots(i)\\\Rightarrow 20x+y=32.6\quad \ldots(ii)[/tex]
Solving (i) and (ii) , we get
[tex]x=\$1.45;y=\$3.6[/tex]
Thus, the price of the one rose is [tex]\$1.45[/tex] and the price of gift box is [tex]\$3.6[/tex]
Answer:
1.45 and 3.5
Step-by-step explanation:
Police Chase: A speeder traveling 40 miles per hour (in a 25 mph zone) passes a stopped police car which immediately takes off after the speeder. If the police car speeds up steadily to 55 miles/hour in 10 seconds and then travels at a steady 55 miles/hour, how long and how far before the police car catches the speeder who continued traveling at 40 miles/hour
Answer:
a. 18.34 s b. 327.92 m
Step-by-step explanation:
a. How long before the police car catches the speeder who continued traveling at 40 miles/hour
The acceleration of the car a in 10 s from 0 to 55 mi/h is a = (v - u)/t where u = initial velocity = 0 m/s, v = final velocity = 55 mi/h = 55 × 1609 m/3600 s = 24.58 m/s and t = time = 10 s.
So, a = (v - u)/t = (24.58 m/s - 0 m/s)/10 s = 24.58 m/s ÷ 10 s = 2.458 m/s².
The distance moved by the police car in 10 s is gotten from
s = ut + 1/2at² where u = initial velocity of police car = 0 m/s, a = acceleration = 2.458 m/s² and t = time = 10 s.
s = 0 m/s × 10 s + 1/2 × 2.458 m/s² (10)²
s = 0 m + 1/2 × 2.458 m/s² × 100 s²
s = 122.9 m
The distance moved when the police car is driving at 55 mi/h is s' = 24.58 t where t = driving time after attaining 55 mi/h
The total distance moved by the police car is thus S = s + s' = 122.9 + 24.58t
The total distance moved by the speeder is S' = 40t' mi = (40 × 1609 m/3600 s)t' = 17.88t' m where t' = time taken for police to catch up with speeder.
Since both distances are the same,
S' = S
17.88t' = 122.9 + 24.58t
Also, the time taken for the police car to catch up with the speeder, t' = time taken for car to accelerate to 55 mi/h + rest of time taken for police car to catch up with speed, t
t' = 10 + t
So, substituting t' into the equation, we have
17.88t' = 122.9 + 24.58t
17.88(10 + t) = 122.9 + 24.58t
178.8 + 17.88t = 122.9 + 24.58t
17.88t - 24.58t = 122.9 - 178.8
-6.7t = -55.9
t = -55.9/-6.7
t = 8.34 s
So, t' = 10 + t
t' = 10 + 8.34
t' = 18.34 s
So, it will take 18.34 s before the police car catches the speeder who continued traveling at 40 miles/hour
b. how far before the police car catches the speeder who continued traveling at 40 miles/hour
Since the distance moved by the police car also equals the distance moved by the speeder, how far the police car will move before he catches the speeder is given by S' = 17.88t' = 17.88 × 18.34 s = 327.92 m
what is the correct answer to my question ?
Answer:
13/17
Step-by-step explanation:
When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B) the same as P(B|M)?
Answer:
See explanation
Step-by-step explanation:
Given
[tex]M \to[/tex] randomly selecting a male
[tex]B \to[/tex] randomly selecting someone with blue eyes
Solving (a): Interpret P(M|B)
The above implies conditional probability
The interpretation is: the probability of selecting a male provided that a person with blue eyes has been selected
Solving (b): is (a) the same as P(B|M)
No, they are not the same.
The interpretation of P(B|M) is: the probability of selecting a person with blue eyes provided that a male has been selected
PLEASE HELP ME
If f(x) = -3 and g(x) = 4x2 + x = 4, find (f+ g)(x).
ОА
A. 4x2 + x - 1
O B. 6x2 - 7
O 4x
C. 43+ + 2x-1
O D. 4x+3x-7
Answer:
D. 4x² + 3x/2 - 7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x/2 - 3
g(x) = 4x² + x - 4
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in functions: (f + g)(x) = x/2 - 3 + 4x² + x - 4Combine like terms: (f + g)(x) = 4x² + 3x/2 - 7Answer:
The answer is C.
Step-by-step explanation:
(f+g)(x)= f(x)+g(x).
So that would be x/2-3 + 4x^2+x-4.
If you combine like terms that would be:
4x^2+x/2+x-4-3=
4x^2+3/2x-7
Mackenzie earns 4% commission as a salesperson. She sold a digital camera that cost $767. How much commission did Mackenzie earn?
Answer:
like about $500 and because of the ca!erlsn
A test taker gets 70 on 1st exam, 80 on 2nd exam, 2/3 of 4/5 of his 2nd exam on his 3rd test. If the professor gives 5 points extra credit on his 4th exam and his average score is 80, what was his score on the 4th exam
=================================================
Explanation:
The phrasing "2/3 of 4/5 of his 2nd exam on his 3rd test" is a bit clunky in my opinion. It seems more complicated than it has to be.
The student got 80 on the second exam. 4/5 of this is (4/5)*80 = 0.8*80 = 64. Then we take 2/3 of this to get (2/3)*64 = 42.667 approximately. If we assume only whole number scores are given, then this would round to 43.
Let x be the score on the fourth exam. Since 5 points of extra credit are given, the student actually got x+5 points on this exam.
So we have these scores
first exam = 70second exam = 80third exam = 43fourth exam = x+5Adding up these scores and dividing by 4 will get us the average
(sum of scores)/(number of scores) = average
(70+80+43+x+5)/4 = 80
(x+198)/4 = 80
x+198 = 4*80
x+198 = 320
x = 320 - 198
x = 122
So the student got a score of x+5 = 122+5 = 127 on the fourth exam.
The slope of diagonal OA is ? and its equation is ?
Answer:
Slope = [tex]\frac{4}{3}[/tex]
Equation of the line → [tex]y=\frac{4}{3}x[/tex]
Step-by-step explanation:
Let the equation of diagonal OA is,
y = mx + b
Here, m = Slope of the line OA
b = y-intercept
Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through O(0, 0) and A(3, 4) will be,
m = [tex]\frac{4-0}{3-0}[/tex]
m = [tex]\frac{4}{3}[/tex]
Since, line OA is passing through the origin, y-intercept will be 0.
Therefore, equation of OA will be,
[tex]y=\frac{4}{3}x[/tex]
Robert paid $4.5 for 3 apples. Find the cost per apple.
Answer:
$1.50
Step-by-step explanation:
so its
4.5 ÷ 3
which
1.5
i need helpp pleaseee
X+ y = 18
X = 2y
What is the solution of the system of equations?
i need the answer asap lol!!!!
Answer:
( 12 , 6 ) or x=12,y=6
Step-by-step explanation:
Answer:
Step-by-step explanation:
if x = 2y then
2y+y=18
3y=18
=6
A Line passes through the .4 -6 and has a slope of -3 and four which is the equation of the line
Answer:
(in the image)
Step-by-step explanation:
I'm not sure I understood your question completely but I hope this helps.
A shopkeeper supplies 42 kg of vegetables to a school canteen in the morning and 58 kg of vegetables in the evening if cost of 1kg vegetable is 16 rupees how much money is due to the canteen per day?
William invested $12,000 in a bank account that pays 9 percent simple interest. His friend invested the same amount at another bank that pays 8 percent interest compounded quarterly. These two functions, where t is time in years, represent the value of the investments: f(t) = 12(1.02)4t g(t) = 12(1.09)t The functions are graphed, and the point of intersection lies between 0.5 and 1.2. Based on the table, approximately how long will it be until both investments have the same value? Value of t f(t) = 12(1.02)4t g(t) = 12(1.09)t 0.5 12.48 6.54 0.6 12.58 7.84 0.7 12.68 9.16 0.8 12.79 10.46 0.9 12.89 11.87 1.0 12.99 13.08 1.1 13.09 14.39 1.2 13.20 15.70 A. 0.9 year B. 1.0 year C. 1.1 years D. 1.2 years
===========================================================
Explanation:
We have these two functions
f(t) = 12(1.02)^(4t)g(t) = 12(1.09)twhich represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.
The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1
The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.
I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0
So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0
It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.
It takes about a year for the two accounts to have the same approximate amount of money.
Answer:
B
Step-by-step explanation:
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 82 months with a standard deviation of 7 months. If the claim is true, what is the probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Answer:
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean life of 82 months with a standard deviation of 7 months.
This means that [tex]\mu = 82, \sigma = 7[/tex]
Sample of 71
This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]
What is the probability that the mean monitor life would be greater than 83.8 months?
1 subtracted by the p-value of Z when X = 83.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]
[tex]Z = 2.17[/tex]
[tex]Z = 2.17[/tex] has a p-value of 0.985.
1 - 0.985 = 0.015
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
How can you use transformations to graph this function?
Answer:
What function?
Step-by-step explanation:
QUICKKKKKKKKKKKKKKKKKKKKKKK
Answer:
Step-by-step explanation:
It’s G
1. What is the area of the figure below? (1 point)
5 in.
3 in.
12 in
O 18 in.2
O 30 in.2
O 36 in.2
O 60 in.2
Answer: 36in2
Step-by-step explanation:
A= base *height
=12*3
=36
The Area of the figure is 36 in².
What is Area of parallelogram?The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm2, m2, in2, etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.
two equal, opposite sides,two intersecting and non-equal diagonals, andopposite angles that are equalThe area of a parallelogram can be calculated by multiplying its base with the altitude. The base and altitude of a parallelogram are perpendicular to each other. The formula to calculate the area of a parallelogram can thus be given as,
Area of parallelogram = b × h square units
where,
b is the length of the base
h is the height or altitude
Given:
base= 12 in
height= 3 in
Area of parallelogram,
= base * height
=12* 3
= 36 in²
Learn more about Area of parallelogram here:
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Two positive integers are 3 units apart on a number line. Their product is 108.
Which equation can be used to solve for m, the greater integer?
m(m – 3) = 108
m(m + 3) = 108
(m + 3)(m – 3) = 108
(m – 12)(m – 9) = 108
Answer:
m(m – 3) = 108
The correct equation can be used to solve for m, the greater integer is,
⇒ m (m - 3) = 108
We have to given that,
Two positive integers are 3 units apart on a number line.
And, Their product is 108.
Let us assume that,
In a number line, first point is m
Then, Second point is, m - 3
So, We get;
The correct equation can be used to solve for m, the greater integer is,
⇒ m (m - 3) = 108
Learn more about the equation visit:
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I WILL MARK BRAINLIEST:))
Please translate this expression into a verbal expression 4(5j+2+j). (5 points)
How many students rank themselves as introverts? Demonstrate your work.
Answer:
36 introverts
Step-by-step explanation:
Total number of adults in the survey = 120
Ratio of introverts to extroverts = 3:7
Number of introverts = ratio number of introverts / ratio total × 120
Ratio number of introverts = 3
Ratio total = 3 + 7 = 10
Number of introverts = 3/10 × 120
= 36
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 volt, and the manufacturer wishes to test volts against volts, using units. In your intermediate calculations, use z-scores rounded to two decimal places (e.g. 98.76).
(a) The acceptance region is_____. Find the value of a.
(b) Find the power of the test for detecting a true mean output voltage of 5.1 volts.
Answer: hello your question was poorly written but i was able to the get missing parts online which enabled me resolve your question
answer:
a) a = 0.1096
b) 1.89 watts
Step-by-step explanation:
Std of output voltage = 0.25 volt
H0 : μ = 5 volts
Ha : μ ≠ 5 volts
n = 16
a) Acceptance region = 4.9 ≤ X ≤ 5.1
Determine the value of a
value of a = 0.0548 + 0.0548
= 0.1096
attached below is the reaming solution
note : a is a type 1 error
b) power of test
True mean output voltage = 5.1 volts
P = - 1.89 watts
power cant be negative hence the power of the test = 1.89 watts
what is the quotient?
Answer:
the result gaven by dividing one number by another
Assigned Media
Use integers to represent the values in the following statement.
Jon Applebee deposited $619 in his savings account. He later withdrew $230.
The integer that represents the amount Jon Applebee deposited is
Answer:
Jon Applebe withdrew 37.15% of the amount he initially deposited.
Step-by-step explanation:
Given that Jon Applebee deposited $ 619 in his savings account, and I have later withdrew $ 230, to determine the integer that represents the amount Jon Applebee deposited the following calculation must be performed:
619 = 100
230 = X
230 x 100/619 = X
23,000 / 619 = X
37.15 = X
Therefore, Jon Applebe withdrew 37.15% of the amount he initially deposited.
Given the functions below, find f(x)+g(x)
CHECK MY ANSWERS PLEASE
The answer is (a)..........
if A={1,2,3,4,5},B={4,5,6,7} and C={2,3,4}find (A-B)-C
Answer:
(A - B) - C = { 1 , 4 , 6 , 7 }
Step-by-step explanation:
A = { 1 , 2 , 3 , 4 , 5 }
B = { 4 , 5 , 6 , 7 }
A - B = { 1 , 2, 3 ,6 , 7 }
C = { 2 , 3 , 4 }
(A - B) - C = { 1 , 4 , 6 , 7 }
A rectangular garden is 5 ft longer than it is wide. Its area is 1800ft^2. What are its dimensions?
Answer:
The dimensions are 45 feet by 40 feet.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A=w\ell[/tex]
Where w is the width and l is the length.
The length is five feet longer than the width. Thus, we can write that:
[tex]\ell = w+5[/tex]
The total area is 1800 square feet. Substitute:
[tex]1800=w(w+5)[/tex]
Solve for w. Distribute:
[tex]w^2+5w=1800[/tex]
Subtract 1800 from both sides:
[tex]w^2+5w-1800=0[/tex]
Factor. We can use 45 and -40. Hence:
[tex]\displaystyle (w+45)(w-40)=0[/tex]
Zero Product Property:
[tex]w+45=0\text{ or } w-40=0[/tex]
Solve for each case:
[tex]\displaystyle w=-45\text{ or } w=40[/tex]
Since the width cannot be negative, we can ignore the first solution.
So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.
The dimensions are 45 feet by 40 feet.
