Answer:
0.004
Step-by-step explanation:
The probability of rolling any number is 1/6 so that times 3 is 1/216 that as a decimal i 0.004
Find z1z2 if z1 = 3(cos37° + isin37°) and z2 = 2/3(cos53° + isin53°).
Answer:
[tex]z_{1}\cdot z_{2} = 2\cdot (\cos 90^{\circ} + i \cdot \sin 90^{\circ})[/tex]
Step-by-step explanation:
Both variable can be rewritten into polar form:
[tex]z_{1} = 3\cdot e^{i\cdot 0.205\pi}[/tex] and [tex]z_{2} = \frac{2}{3}\cdot e^{i\cdot 0.294\pi}[/tex]
The complex product is equal to:
[tex]z_{1}\cdot z_{2} = (3)\cdot \left(\frac{2}{3}) \cdot e^{i\cdot (0.205\pi+0.294\pi)}[/tex]
[tex]z_{1}\cdot z_{2} = 2 \cdot e^{i\cdot 0.499\pi}}[/tex]
The resultant expression in rectangular form is:
[tex]z_{1}\cdot z_{2} = 2\cdot (\cos 90^{\circ} + i \cdot \sin 90^{\circ})[/tex]
Answer:
The correct question is:
Find [tex]z_{1}.z_{2}[/tex] if [tex]z_{1}= 3(cos37 + isin37)[/tex] and [tex]z_{2}= \frac{2}{3} (cos53 + isin53)[/tex].
(Note: the angles mentioned in the equations above are in degrees)
The answer is [tex]z_{1}.z_{2}= 2i[/tex]
Step-by-step explanation:
[tex]z_{1}.z_{2}= 3(cos37 + isin37)* \frac{2}{3} (cos53 + isin53)[/tex]
[tex]z_{1}.z_{2}= (3cos37 + 3isin37)* (\frac{2}{3} cos53 + \frac{2}{3}isin53)[/tex]
[tex]z_{1}.z_{2}= 3cos37*\frac{2}{3} cos53 + 3cos37*\frac{2}{3}isin53+3isin37*\frac{2}{3} cos53+3isin37*\frac{2}{3}isin53[/tex]
[tex]z_{1}.z_{2}= 0.961+1.275i+0.724i-0.961[/tex] (Because [tex]i*i=i^{2}=-1[/tex] & [tex]i=\sqrt{-1}[/tex])
[tex]z_{1}.z_{2}= 0.961+1.275i+0.724i-0.961[/tex]
[tex]z_{1}.z_{2}= 2i[/tex]
Which expression represents a factorization of 32m + 56mp ?
Answer:
8m(4 + 7p)
Step-by-step explanation:
Take out the greatest common factor:
8m(4 + 7p)
What is the area of a rectangle with sides length of 5/12 feet and 2/3 feet
Answer:
The answer is 10/36 or if you want to simplify, 5/18
Step-by-step explanation:
To solve the area of a rectangle, you need to multiply the sides with each other, so 5/12 x 2/3 is 10/36 (unsimplified) . You multiply the numerators and then the denominators and simplify.
g(t) = 6t - 1
g ( ) = -7
Answer:
g(-1) = -7
Step-by-step explanation:
Put the given value for g(t) into the first equation and solve for t.
-7 = 6t -1
-6 = 6t . . . . . . add 1
-1 = t . . . . . . . . divide by 6
g(-1) = -7
Answer: -1
Step-by-step explanation:
(13 – 6)^2 (5 + 2)^2÷(5 – 2)^3
Answer:
88 25/27
Step-by-step explanation:
(13 – 6)^2 (5 + 2)^2÷(5 – 2)^3
PEMDAS
Parentheses first
(7)^2 (7)^2÷(3)^3
Then exponents
49*49 ÷27
Then multiply and divide from left to right
2401÷27
2401/27
88 25/27
88.92592593
Answer:
Step-by-step explanation:
(7)^2(7)^2 / (3)^3
49*49 / 27
2401/27
88 25/27
Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
Answer:
93.25% probability that they have taken this steroid
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test
Event B: Taking the steroid.
Suppose the probability of an athlete taking a certain illegal steroid is 10%.
This means that [tex]P(B) = 0.1[/tex]
Given that the athlete has taken this steroid, the probability of a positive test result is 0.995.
This means that [tex]P(A|B) = 0.995[/tex]
Positive test:
99.5% of 10%(If the athlete has taken).
100-99.2 = 0.8% of 100-10 = 90%(Athlete has not taken)
Then
[tex]P(B) = 0.995*0.1 + 0.008*0.9 = 0.1067[/tex]
Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.1*0.995}{0.1067} = 0.9325[/tex]
93.25% probability that they have taken this steroid
We conduct a study to determine whether the majority of community college students plan to vote in the next presidential election. We choose a significance level of 0.05. We survey 650 randomly selected community college students and find that 54% of them plan to vote. The P-value is 0.02. H0: 50% of community college students plan to vote in the next presidential election. Ha: More than 50% of community college students plan to vote in the next presidential election. What can we conclude
Answer:
we can conclude that more than 50% of community college students plan to vote in the next presidential election
Step-by-step explanation:
Decision Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Null hypothesis H0: 50% of community college students plan to vote in the next presidential election
H0: p = 0.50
Ha: More than 50% of community college students plan to vote in the next presidential election
Ha: p > 0.50
P-value = 0.02
From the decision rule;
Since the p-value for this study is less than the significance level.
0.02 < 0.05
So, we reject the null hypothesis, there is enough evidence to reject the null hypothesis. We thereby accept the alternative hypothesis.
Therefore, we can conclude that more than 50% of community college students plan to vote in the next presidential election
Just the 46×23 to the fourth power times 1000
Answer:1.2872686 x 10^10
Step-by-step explanation:
46 x 23^4 x 1000
46 x 23 x 23 x 23 x 23 x 1000
1.2872686 x 10^10
A sphere is inscribed in a cube. Explain the relationship between the surface areas of the two solid figures
Answer:
No one knows. Jk just go look at the other brainly links. the question has already been asked and answered so you can go see them there.
Step-by-step explanation:
:)
what is this phrase in numerical expression
triple the sum of seventeen and ten
pls help
Answer: so you would do 17 plus ten which is 27 so triple 3 so your answer is 27^3
Step-by-step explanation:
sum so your adding plus you need the exponent which is times 3
a rectangular rug measures 8 feet long and 12 feet wide . what is the area of the rug
Answer:
96 square feet
Step-by-step explanation:
Area= length x width
So for the rug it would be 12x8
12x8=96
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
D. Vertx: (3,-16); Intercepts: x = -1, 7
Step-by-step explanation:
I graphed the equation on the graph below.
A bag contains 10 Yellow, 4 Green and 7 Blue marbles. Find the following probabilies.
P(blue)
Answer:
1/3
Step-by-step explanation:
The total number of marbles
10+4+7 = 21
P(blue) = blue marbles / total marbles
= 7 / 21
= 1/3
Tate is paid $17.35 per hour with time and a half overtime. What will his gross pay period in which he worked 35 hours one week and 44 hours next week for a total 79 hours?
Answer:
The new rule has a higher salary level for exemption from overtime, at $684 a week. This means that lower-pay exempt employees may qualify for overtime.
Step-by-step explanation: this is your answer plz rate e the most brainlest
What is the median of the following numbers?
1, 2, 10, 6, 4, 4, 6, 3, 1,4
Answer:
4
Step-by-step explanation:
The median is the middle number after ordered into numberical order. If there's two and the numbers are different, you add them and divide the total by 2.
Answer: 4
Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.
So let's write our data set from least to greatest.
So we have 1, 1, 2, 3, 4, 4, 4, 6, 6, 10.
Now, notice that there are two numbers that appear in the middle.
I have underlined them above.
When two numbers appear in the middle that are the same number (4 and 4), the median will be the same number too.
So the median of the given data set is 4.
If you flipped a fair coin 18 times about how many times would you expect heads to appear?
Answer:
9 times
Step-by-step explanation:
hope this helps
Answer:
9
Step-by-step explanation:
Mathematically, 9, although reality wise, you could flip the coin and get heads every time, or the opposite.
I think you mean mathematically though, so yes, it would be 9.
j+ 12 =25 find the solution to equation algebtaically
Answer:
j= 13
just subtract 12 from 25
Start by isolating the j.
Subtract 12 from both sides.
On the left, the 12 and -12 cancel.
On the right, 25 - 12 is 13.
So we have j = 13.
A spinner is divided into 8 equal sections numbered 1 to 8. About how many times would you expect the pointer to land on a number less than 6 if the pointer is spun 30 times.
Answer:
The answer is
6.25×30= 18.75
I'm not sure but this is what I think
Consider the graph of the exponential function, y =3(2)^x. The x- intercept of the graph is
Answer:
the x intercept is 2
Step-by-step explanation:
I just went over this unit
Answer:
2
Step-by-step explanation:
How do I type in exponents
Answer:
on what
Step-by-step explanation: normaly you have a button that you can have certain characters
which is equivalent to sin^-1 ( sqrt 3/2 )? Give your answer
Give your answer in radians.
Answer: pi/3
Step-by-step explanation:
correct on edge 2020
The equivalent value of trigonometric relation sin⁻¹ ( √3/2 ) = π/3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
sin⁻¹ ( √3/2 ) = θ
Now , the value of θ is calculated by
In a triangle , sin θ = opposite / hypotenuse
So , sin θ = √3/2
The value of θ = 60°
So , the measure of 60° in radians is θ = π/3
Hence , the value of θ from the trigonometric relation is π/3
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
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What is the slope for the linear function y=3x-4
Answer:
3
Step-by-step explanation:
This is written in the form
y= mx+b
where m is the slope and b is the y intercept
3 is the slope and -4 is the y intercept
Find the area of the regular polygon.
Round your answer to the
nearest tenth if necessary.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as the dimension of the polygon is not given.
However, I'll give a general explanation of how to calculate the area of a regular polygon.
If you follow these simple steps, you'll arrive at your answer.
The area of a polygon is calculated as thus;
A = ½(nbh)
Where A represent the area
n represents the number of sides
b represents the length of the base
h represent the height of the polygon
Take for instance, the polygon is a regular pentagon.
This means n = 5.
Also assume that the base and the height are 5cm and 7cm respectively.
This means that
Area = ½ * (5 * 5 * 7)
Area = ½ * 175
Area = 87.5cm²
Hence, the area of the polygon is 87.5cm²
In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. (a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03? Use a 95% confidence level. (Round your answer up to the nearest whole number.)
Answer:
A sample size of 657 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent.
This means that [tex]\pi = 0.19[/tex]
(a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03?
A sample size of n is needed.
n is found when [tex]M = 0.03[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.19*0.81}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.19*0.81}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.19*0.81}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.19*0.81}}{0.03})^{2}[/tex]
[tex]n = 656.91[/tex]
Rounding up to the nearest whole number.
A sample size of 657 is needed.
What is the quotient?
(6 * 108) = (1.5 x 10-4)
4 x 1012
4 x 104
4 x 10-32
4 * 10-2
Answer:
The first choice.
Step-by-step explanation:
6 * 10^8 / 1.5 * 10^-4
= (6/1.5) * (10^(8 - (-4))
= 4 * 10^12.
Answer:
4 x 1012
Step-by-step explanation:
Andre hit 46 balls at practice. He hit no fewer than 20 less than double the number of hits Jason had. Which inequality represents the situation if j represents the number of hits Jason had?
46 minus 20 less-than 2 j
2 j minus 20 less-than-or-equal-to 46
46 minus 20 less-than-or-equal-to 2 j
2 j minus 20 greater-than-or-equal-to 46
Answer:
2j -20 ≤ 46
Step-by-step explanation:
"20 less than double the number Jason [hit]" can be represented by 2j-20.
We are told that 46 is no fewer than this value, so it is greater than or equal to this value:
46 ≥ 2j -20
2j -20 ≤ 46 . . . . . swapping sides to match answer choices
Answer:
2j -20 ≤ 46
Step-by-step explanation:
Simplify (-2x^3)2•y•y^9
Simplify (-2x^3)^2 •y•y^9 Answer 4x^6y^10
If you flip a coin 10 times, what is the best prediction possible for the number of times it will land on tails?
Answer:
5
Step-by-step explanation:
The probability of tails is 1/2, so the expected value is (1/2) (10) = 5.
Answer:
5
Step-by-step explanation:
Probability of land a tail when the coin is tossed once is 1/2 because a coin has two sides and contains one head
Then when it is tossed 10 times, the no of time a tail appears is. 1/2 * 10 =5
Shira packs 170 lemon bars in boxes for the bake sale. Each box holds 8 lemon bars. She takes home the lemon bars tha are leg over after she has filled as many boxes as possible. Ahora use partial quotients to find how many boxes of lemon bars she can fill to sell at the bake sale. She finds only two partial quotients when she divides. Use the numbers in the box to answer the questions
1 2 7 8 20 21 23 27 29
Question:
1. How many full boxes of lemon bars can Shira fill?
2. How many delicious lemon bars will she be taking home?
Answer:
1. Number of filled box = 21
2. Number of take home = 2
Step-by-step explanation:
Given
Number of lemon bars = 170
Each bar contains 8 lemon bars
Required
(1) & (2)
To calculate the number of boxes Shira can fill, we simply divide the total number of bars by constituents of each bar .
i.e.
Number of filled box = 170/8
Number of filled box = 21.25
But here, we only need the quotient of the division because it represents the filled boxed.
So,
Number of filled box = 21
Calculating the number of take home.
We'll follow the same steps as (1) above but here, we only need the remainder of the division.
When 170 is divided by 8, the remainder is 2.
So, number of boxes she'll take home is 2.
See calculation below
Number of take home = 170 % 8
Number of take home = 2
568,924,126 each digit stands for what
Answer:
500,000,00060,000,0008,000,000900,00020,0004,000100206Step-by-step explanation:
To find what a digit stands for, make all the other digits zero.
This is substantially what we do when we write the number in "expanded form."
568,924,126
= 500,000,000 +60,000,000 +8,000,000 +900,000 +20,000 +4,000 ...
... +100 +20 +6
The list of numbers in the sum is the list of numbers the digits stand for.
