The rectangular form of the polar expression [tex]12(cos\pi+ isin\pi)[/tex] is -12
The given equation is:
[tex]12(cos\pi+ isin\pi)[/tex]
The above equation is in polar form
Note that:
[tex]cos \pi = -1\\\\sin\pi = 0[/tex]
Substituting [tex]cos \pi = -1[/tex] and [tex]sin \pi = 0[/tex] into the expression [tex]12(cos\pi+ isin\pi)[/tex] in order to get the rectangular form of the expression
[tex]12(cos\pi+ isin\pi)[/tex]
= 12(-1 + 1(0))
= 12 ( -1 + 0)
= 12(-1)
= -12
Therefore, the rectangular form of the polar expression [tex]12(cos\pi+ isin\pi)[/tex] is -12
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The slipe of the line passing through the points (7, 5) and (21, 15) is
Answer:
5/7
Step-by-step explanation:
You find a slope by using the equation y2-y1/x2-x1.
In this case: 15-5/21-7
10/14
5/7
Suppose that E and f are two events and that P(E and F)=0.3 and P(E)=0.5. What is P(F/E)?
Answer:
[tex]P(F/E) = 0.6[/tex]
Step-by-step explanation:
If we are given two dependent events [tex]A[/tex] and [tex]B[/tex] such that their chances of occurrence or the probabilities of the events are: [tex]P(A)[/tex] and [tex]P(B)[/tex].
Then the conditional probability that the event [tex]B[/tex] will occur given that [tex]A[/tex] has already occurred is given by the following formula:
[tex]P(B/A) = \dfrac{P(A \cap B)}{P(A)}[/tex]
Here the two events given are [tex]E[/tex] and [tex]F[/tex].
[tex]P(E\ and\ F)\ or\ P(E\cup F) = 0.3[/tex]
and [tex]P(E) = 0.5[/tex]
As per the above formula that we have already discussed, the formula can be written as:
[tex]P(F/E) = \dfrac{P(E \cap F)}{P(E)}\\\Rightarrow P(F/E) = \dfrac{0.3}{0.5}\\\Rightarrow P(F/E) = \dfrac{3}{5}\\\Rightarrow \bold{P(F/E) = 0.6}[/tex]
58 students on a bus how many students were fit on a six buses
Answer:
348
Step-by-step explanation:
In the equation y=kx, which variable is the constant of proportionality?
Answer:the variable k is the constant of proportionality
Step-by-step explanation:
This can be proven when the equation is used to find different values of y. To find these different values, the x variable is substituted for different values while the k value stays the same. hope this helps!!
In the past year, Michael watched 14 movies that he thought were very good. He watched 40 movies over the whole year. Of the movies he watched, what percentage did he think were very good?
Answer:
35%
Step-by-step explanation:
14÷40= 0.35 (35%)
0.35 × 40= 14
What is 3.761 in expanded form
Answer:
3 + 0.7 + 0.06 + 0.001
Answer:3+ 0.7+ 0.06+ 0.001= 3.761
Step-by-step explanation:
At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of D are 2.6 doughnuts and 3.6 (doughnuts)2 , respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of P ? 1.5(3.6) 1.5(3.6) A 1.53.6−−−√ 1.53.6 B 1.5(3.6)−−−−−−√ 1.5(3.6) C 1.5(2.6) 1.5(2.6) D 1.52.6−−−√ 1.52.6 E
Answer: C ( square root of 1.5 x 3.6)
Step-by-step explanation:
The price for the variance is 3.6 times 1.5. Standard deviation is the square root of variance, so the answer is the square root of 1.5 x 3.6.
The standard deviation expression of the distribution P is √(1.50 × 3.6)
Given the Parameters :
Expected value = 2.6Variance = 3.6 Price per doughnut = $1.50The price for the variance of the distribution can be written as :
Price per doughnut × Variance Variance = $1.50 × 3.6The standard deviation of the distribution D is related to the variance by the formular :
Standard deviation = √variance Standard deviation = √(1.50 × 3.6)Therefore, the standard deviation in $ of P will be √(1.50 × 3.6)
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Which statement describes the effect on the parabola f(x)=2x•x-5x+3 when changed to f (x)= 2x•2-5x+1
Answer:
The parabola is translated down 2 units.
Step-by-step explanation:
You have the parabola f(x) = 2x² – 5x + 3
To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:
f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1 Expresion A
The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.
If p> 0 and q> 0, the parabola shifts p units to the right and q units up. If p> 0 and q <0, the parabola shifts p units to the right and q units down. If p <0 and q> 0, the parabola shifts p units to the left and q units up. If p <0 and q <0, the parabola shifts p units to the left and q units down.In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.
This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.
In conclusion, the parabola is translated down 2 units.
Also the explanation:)
Answer:
276 guests were at the wedding.
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{4+5}{12}[/tex] = [tex]\frac{9}{12}[/tex]
1 - [tex]\frac{9}{12}[/tex] = [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{4}[/tex] of the guests are 69 guests ⇒ 69 × 4 = 276 guests were at the wedding.
Which shows two expressions that are equivalent to (-8)(-12)(2)?
The solution is option C.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
(-8)(-12)(2)
=96*2
=192
so. we get,
It would be c because when you multiply 8 and 12 you get 96 and when you multiply 96x2 you get 192 .
so, therefore your answer is c.
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Add the two expressions.
3z−4 and 2z + 5
I need it asap please help!
Answer:
3(1)-4=-1 2(1)+5=7
Answer:
5z+1
Step-by-step explanation:
it was simple
Les had $32.00 when he went to the city Market to buy some fresh fruits and vegetables. When he left, he had $23.05. How much money did he spend on food?
Answer:
$8.95
Step-by-step explanation:
Which of the following data sets has a range of 40?
a. {40, 10, 20, 100}
C. {40, 10, 20, 50}
b. {40, 10, 20, 80}
d. {40, 10, 20, 40}
Please select the best answer from the choices provided
A
B
С
Answer:
The second answer - 40, 10, 20, 50
Step-by-step explanation:
Range is the difference between the largest and smallest number in a data set. The biggest and smallest numbers in the data set are 50 and 10, respectively. 50 - 10 = 40.
Which lines from Natalie Merchant's song "Wonder" most likely inspired R. J. Palacio to give August's mother's great determination in the novel Wonder? O Doctors have come from distant cities just to see me O stand over my bed disbelieving what they're seeing with love, with patience and with faith she'll make her way I'm over your heads how I confound you and astound you
Answer:
C)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The guy above me is correct
Brian is playing a carnival game. He is blindfolded while he throws a dart at a board of 12 balloons, as shown below. Each balloon is labeled "S" for small, "M" for medium, "L" for large, or "XL" for extra-large. The board has 3 small balloons, 5 medium balloons, 2 large balloons, and 2 extra-large balloons. He hits one of the balloons at random and wins a stuffed animal of that size.
what’s the value of x?
Answer:
x = -11
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+50 + 72+ x+80 = 180
Combine like terms
2x + 202 = 180
Subtract 202 from each side
2x+202-202 = 180-202
2x =-22
Divide each side by 2
2x/2 = -22/2
x = -11
A recent study has shown that 10% of computer science concentrators suffer from symptoms of Carpal Tunnel Syndrome. Researchers have developed a diagnostic test for this condition and in a recent trial, the test gave a positive result in 96% of the patients who were known to truly have Carpal Tunnel Syndrome.
a) For an initial version of the diagnostic test, the false positive rate (the percentage of people without Carpal Tunnel who incorrectly test positive) was 44%. If a student received a positive result from this test, what would be the posterior probability that they truly have Carpal Tunnel Syndrome?
b) The researchers believe their test will be practically useful if a positive result implies the student has Carpal Tunnel with at least 75% probability. What is the largest possible false positive rate that would achieve this accuracy target?
Answer:
1. 0.1951
2. 3.56%
Step-by-step explanation:
Probability of disease = 0.10
Probability of disease and positive = 0.96
1.
Probability of no disease and positive = 0.44
Probability of disease and positive result = 0.10x0.96/0.10x0.96+0.90x0.44
= 0.096/0.096+0.396
= 0.096/0.492
= 0.1951
2.
Probability of disease false positive result
P(disease|positive result)
= (0.10x0.96/0.10x0.96+0.90xP) >= 0.75
= 0.096/0.096+0.90p >= 0.75
We cross multiply
0.096 >= 0.75(0.096+0.90p)
0.096 >= 0.072 + 0.675p
0.096-0.072 >= 0.675p
0.024 >= 0.675p
P <= 0.03555
Therefore the largest possible false positive rate = 0.0356
= 3.56%
Use the given x and y values to write a direct variation
equation.
x = 5, y = 25
Answer:
k= 1/5
Step-by-step explanation:
x is proportional to y
x = ky (k is const.)
k = x/y
k= 5/25
k = 1/5
Answer:
Equation of direct variation is : [tex]\mathbf{y=5x}[/tex]
Step-by-step explanation:
We are given: x= 5 and y=25
We need to write equation of direct variation.
The formula for direct variation is: [tex]\mathbf{y=kx}[/tex]
So, if y=25 and x=5, k will be:
[tex]y=kx\\25=k(5)\\k=\frac{25}{5}\\k=5[/tex]
So, equation of direct variation is : [tex]\mathbf{y=5x}[/tex]
true or false , the best way to represent all the solutions to a linear inequality is to graph a single line through the x intercept and y intercept where neither side of the line is shaded
Ruth got to the library at 1030 am.
She stayed at the library for 50 minutes.
Then she walked home.
Ruth took 1 1/4 hours to walk home.
(b) At what time did Ruth get home?
Answer:
She got home at 12:35 P.M.
Step-by-step explanation:
She got to the library at 10:30 am.
She spent 50 minutes there
10:30 + 50 mins can be seperated to 30 mins and 20 mins
So, 30 mins goes to 11 and 20 mins more equals 11:20.
She took 1 1/4 hours to get home
1 hour more means 12:20, and since 1/4 of an hour is 15 mins,
12:20 + 15 = 12:35 P.M
hope this helped!
helppppp please I will give brainliest
Answer:
y=1/3x-2
Step-by-step explanation:
Plz Help. Euler Equations are hard!
Find the general solution to the following differential equation.
An
2 pie/3
Step-by-step explanation:
helppppp pleaseee!!
Evaluate the function
Answer:
10
Step-by-step explanation:
go to mathaway.com and type in the equation and when x=-6. Press show graph and it says 10. The graph is my proof.
explain why the oppisite of a positive number will always be a negitive number
Answer:
because a positive is over zero and a negative is below zero so from that you can tell that the opposite of any positive will be a negative.
Step-by-step explanation:
The opposite of positive numbers are negative. There are numbers on the right and left side on the number line of zero.
I typed in a detailed "essay" of this but it didn't save. I even put in an example...
The polynomial p is a function of x. The graph of p has four zeros at -4, -2/3, 0, and 9
Select all the expression that could represent p.
A
-3x(x + 4)(3x + 2)(x - 9)
B
3x(x – 4) (x + 3)(x +9)
с
3x(x + 4)(2x - 3)(x -9)
D
- x(x + 4) (x + })(x – 9)
E
-3x(x + 4)(3x + 2)(x - 9)2
The only expression of that can represent polynomial p as a function on a graph having four zeros at -4, -2/3, 0, and 9 is: A. [tex]\mathbf{-3x(x + 4)(3x + 2)(x - 9)}[/tex]
Given the four zeros of the graph of p are at:
-4, -2/3, 0, and 9From the options given, the expression in option A will represent a function of a polynomial p with zeros at -4, -2/3, 0, and 9.
Here's why:
[tex]-3x(x + 4)(3x + 2)(x - 9)[/tex] (option A)
Therefore are four factors in the polynomial above which are:
[tex]3x\\\\(x + 4)\\\\(2x - 3), $ and\\\\(x -9)[/tex]
The zeros of polynomial p will be the following:
[tex]3x = 0\\\\x = \frac{0}{3} \\\\\mathbf{x = 0}[/tex]
[tex](x + 4) = 0\\\\\mathbf{x = -4}[/tex]
[tex](3x + 2) = 0\\\\3x = -2\\\\\mathbf{x =-\frac{2}{3}}[/tex]
[tex](x -9) = 0\\\\\mathbf{x = 9}[/tex]
Therefore, the only expression of that can represent polynomial p as a function on a graph having four zeros at -4, -2/3, 0, and 9 is: A. [tex]\mathbf{-3x(x + 4)(3x + 2)(x - 9)}[/tex]
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g The average work week in Los Angeles was 40.1 hours in the first quarter of 2019. It is believed that the pandemic has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are
Answer:
b. Hо : μ ≥ 40.1; Ha : μ > 40.1
Step-by-step explanation:
Note: The complete options to the question is attached as picture below
The alternative hypothesis is focusing on "the recession has led to a reduction in the average work week".
So, it will be less than the past average. i.e, 40.1.. so, we will use a less than (<) sign to write the alternative hypothesis.
The hypotheses are as below:
Hо : μ ≥ 40.1 (Null hypothesis)
Ha : μ > 40.1 (Alternative hypothesis)
What is the inequality of y-2x<=-3
Of the 30 girls who tried out for the lacrosse team at Euclid middle school 12 were selected . Of the 40 boys who tried out, 16 were selected. Are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls?how do you know?
Answer:
Yes they are the same i know this because for every 10 girls or boys there are 4 who try out for the team. so for every 10 Boys or Girls there are 4 that will try out for the team. For those wondering the ratio is 4:10
Step-by-step explanation:
Answer:
Yes, when simpilfied or written as a fraction they are equal
Step-by-step explanation:
12:30 = [tex]\frac{12}{30\\ \left \\\}[/tex] = [tex]\frac{4}{10\\}[/tex]
16:40 = [tex]\frac{16}{40}[/tex] = [tex]\frac{4}{10}[/tex]
A package of 4 pairs of insulated socks costs $26.36. What is the unit price of the pairs of socks?
The unit price is $
per pair of socks
Answer: The unit price is $6.59 per pair of socks
Step-by-step explanation: 26.36. divided by 4 = 6.59
Jessica has an account with a credit union. Her account earns 2.6% simple interest yearly. Exactly a year and a half ago, she opened her account with $900.
How much interest has she earned so far?
Answer:
$35.1
Step-by-step explanation:
2.6% of 900 = 23.4
Since it's a year and a half you might want to divide by two.
2.6/2 = 1.3
1.3% of 900 = 11.7
add them up,
23.4 + 11.7 = 35.1
It's asking for how much she EARNED not HAS in her bank account in 1.5 years. So include what she earned with interest, do not include the 900 dollars because she didn't earn it with interest, she already had that.