Answer:
B: -6+2i
Step-by-step explanation:
3i + (-6 - i) = ⇒ open parenthesis3i - 6 - i = ⇒ simplify-6 + 2i ⇒ answer in standard form of a+biIf 8 people can pick the apples from trees in 6 days, how long will it take12 people?
Solve 1 over 36 = 6x−3.
Answer:
x = 109/216
Step-by-step explanation:
Solve for x:
1/36 = 6 x - 3
Hint: | Reverse the equality in 1/36 = 6 x - 3 in order to isolate x to the left hand side.
1/36 = 6 x - 3 is equivalent to 6 x - 3 = 1/36:
6 x - 3 = 1/36
Hint: | Isolate terms with x to the left hand side.
Add 3 to both sides:
6 x + (3 - 3) = 3 + 1/36
Hint: | Look for the difference of two identical terms.
3 - 3 = 0:
6 x = 1/36 + 3
Hint: | Put the fractions in 1/36 + 3 over a common denominator.
Put 1/36 + 3 over the common denominator 36. 1/36 + 3 = 1/36 + (36×3)/36:
6 x = 1/36 + (36×3)/36
Hint: | Multiply 36 and 3 together.
36×3 = 108:
6 x = 1/36 + 108/36
Hint: | Add the fractions over a common denominator to a single fraction.
1/36 + 108/36 = (1 + 108)/36:
6 x = (1 + 108)/36
Hint: | Evaluate 1 + 108.
1 + 108 = 109:
6 x = 109/36
Hint: | Solve for x.
Divide both sides by 6:
x = (109/6)/36
Hint: | Multiply 36 and 6 together.
36×6 = 216:
Answer: x = 109/216
Answer:
x = 109/216
Step-by-step explanation:
Add 3, divide by 6.
[tex]\dfrac{1}{36}=6x-3\\\\3+\dfrac{1}{36}=6x\\\\\dfrac{109}{(36)(6)}=\boxed{x=\dfrac{109}{216}}[/tex]
A national survey of 2500 adukt citizens of a nation found that 21 % dreaded Valentine's Day. The margin of error for the survey was 5.4 percentage points with 90% confidence. explain what this means.
which statement below is the best explanation?
a. there is 84.6% to 95.4% confidence that 25% of the adult citizens of the nation dreaded Valentine's Day
b. in 90% of samples of adult citizens of the nation, the proportion that dreaded Valentine's Day is between 0.196 and 0.304.
c. there is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine's Day is between 0.196 and 0.304.
d. there is 90% confidence that 25% of the adult citizens of the nation dreaded Valentines Day.
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 2500[/tex]
The sample proportion is [tex]\r p = 0.21[/tex]
The margin of error is [tex]E = 0.054[/tex]
The 90% confidence interval is mathematically represented
[tex]\r p - E < p < \r p + E[/tex]
=> [tex]0.21 - 0.054 < p < 0.21 + 0.054[/tex]
=> [tex]0.156< p < 0.264[/tex]
last month you had an outstanding check of $87.90 that had not yet been cashed, so it did not show up on your statement. This month, you wrote checks totaling $379.42. You made one deposit of $100, and you withdrew $60 from an ATM. If the check from last month was cashed and recorded on your statement, and if the bank paid $0.23 in interest, then by how much did your account balance change this month?
Answer:
Step-by-step explanation:
Deposit made = + $ 100 . 00
withdrawal made = - $ 60 .00
check of last month encashed = - $ 87 . 90
interest paid by bank = + $ 00 . 23
-----------------------------------------------------------------------
Net effect = - $ 47.67
the account balance reduces by amount = $ 47.67
7-7 im gonna post 7 more please helppp!
Hi there! Hopefully this helps!
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Answer: p = 21~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]p - 18 = 3[/tex]
Add 18 to both sides.
[tex]p = 3 + 18[/tex]
Add 3 and 18 to get, you guessed it, 21!what is onetenth for 19,548
Step-by-step explanation:
one-tenth of 19,548 is 1954.8
Find all values of x for which the series converges. (Enter your answer using interval notation.) [infinity] 9 x − 7 9 n n = 0 For these values of x, write the sum of the series as a function of x.
Answer:
The series converges to [tex]$ \frac{1}{1-9x} $[/tex] for [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]
Step-by-step explanation:
Given the series is [tex]$ \sum_{n=0}^{\infty} 9^n x^n $[/tex]
We have to find the values of x for which the series converges.
We know,
[tex]$ \sum_{n=0}^{\infty} ar^{n-1} $[/tex] converges to (a) / (1-r) if r < 1
Otherwise the series will diverge.
Here, [tex]$ \sum_{n=0}^{\infty} 9^n x^n = \sum_{n=0}^{\infty} (9x)^{n} $[/tex] is a geometric series with |r| = | 9x |
And it converges for |9x| < 1
Hence, the given series gets converge for [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]
And geometric series converges to [tex]$ \frac{a}{1-r} $[/tex]
Here, a = 1 and r = 9x
Therefore, [tex]$ \frac{a}{1-r} = \frac{1}{1-9x} $[/tex]
Hence, the given series converges to [tex]$ \frac{1}{1-9x} $[/tex] for [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]
HELP ASAP
8^2 – 10x - 3
NEED ALL STEPS PLZZZZ
Answer:
hope this attachment will help you
A teacher records the amount of time it took a random sample of students to finish a test and their scores on that test. Let x be the score and y be the amount of time. Conduct a hypothesis test of the claim that there is a linear correlation between the variables, using a 0.10 level of significance. Find the PERCENTAGE OF THE VARIANCE IN THE Y-VALUES THAT CAN BE EXPLAINED BY THEIR LINEAR RELATIONSHIP WITH THE X-VALUES.
Answer:
The question is incomplete. The complete table is:
Score in percent (X): 80, 75, 70, 90, 95, 100, 75, 60, 75, 95
Time in minute (Y) : 45, 48, 40, 50, 40, 30, 30, 39, 38, 55
The answer is 0.55 %
Step-by-step explanation:
ΣX = 815
ΣY = 425
ΣX x Y = 34565
Σ = 67925
Σ[tex]$Y^2$[/tex] = 18699
So, correlation coefficient, b
[tex]$b= \frac{n \Sigma XY- \Sigma X \Sigma Y}{\sqrt{n \Sigma X^2-( \Sigma X)^2} \times \sqrt{(n \Sigma Y^2 -(\Sigma Y)^2}}$[/tex]
[tex]$b = \frac{(10 \times 34565)-(815 \times 425)}{\sqrt{(10 \times 67925)-(815)^2} \times \sqrt{(10 \times 10699)-(425)^2}}$[/tex]
[tex]$b= -\frac{725}{9779 \times 2702}$[/tex]
b = -0.0741
Correlation Determination:
[tex]$B^2 = (-0.0741)^2$[/tex]
= = 0.0055 = 0.55%
Therefore, 0.55 percentage of the variation in y can be explained by x variable.
An bus station has determined that the relationship between the number of passengers on a bus and the total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation y=118+14x. Predict the weight of luggage for a flight with 142 passengers.
Answer:
The weight of luggage for a flight with 142 passengers is 2,106
Step-by-step explanation:
The total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation:
y=118+14*x
where y is the total weight of luggage stored in the luggage compartment and x is the number of passengers on a bus.
If you want to predict the weight of luggage for a flight with 142 passengers, this means that x must have a value of 142. So, replacing in the expression:
y=118+14*142
you get:
y=118+1,988
y=2,106
The weight of luggage for a flight with 142 passengers is 2,106
40% of the cost was tax. if the taxes paid were $15,000, what was the total cost of the car?
Answer:
$37500
Step-by-step explanation:
For this we can simply create a proportion of the percentages.
.4 / 1 == 15000 / x
Now we solve for x:
x = 15000/.4
x = 37500
Thus, the cost of the car was $37,500.
Cheers.
If 15 oranges cost Rs. 70,how much do 39 oranges cost ?
Answer:
firstly divide 70 by 15 and when the product came multiply it with 39Step-by-step explanation:
70 ÷ 15 = 4.66
4.66 × 39 = 181.974
What is the probability of getting a 10 or a jack from a deck of poker cards (52 cards)?
Answer:
15.38%
Step-by-step explanation:
there are four 10 cards and four jack cards.
4+4=8
you want to get one from 52 cards, so it's 8 out of 52. 8/52
to calculate the percentage, you multiply 8 by 100, then divide by 52.
8*100/52=15.38 (rounded answer)
In a certain year, 23% of all teenagers in the United States had checking accounts. Your bank, TeenChex Inc., is interested in targeting teenagers who do not already have a checking account. (a) If TeenChex selects a random sample of 1,000 teenagers, what number of teenagers without checking accounts can it expect to find? teenagers What is the standard deviation σ of this number? (Round the standard deviation to one decimal place.)
Answer:
1. 770
2. 13.31
Step-by-step explanation:
n = 1000
P (probability of those with account) = 23% = 0.23
q(probability of those without account) = 1-p = 0.77
a. We are expected to find the expected number of those without checking account
= n * q
= 1000 * 0.77
= 770
b. Standard deviation
= √n*p*t
= √1000x0.77x0.23
= √177.1
= 13.31
I do not understand this, can anyone help me out?
Answer:
the Answer what have to be the fist bc c is the only on that is not with a ,g or b
Step-by-step explanation:
a car takes 8 hours to reach to its destination with a speed of 75km/hr. how much time will it take if the speed is 60km/hr?
Answer:
10 hours
Step-by-step explanation:
speed = distance/time
s = d/t
d = st
d = 75 km/h * 8 h = 600 km
t = d/s
t = 600 km/(60 km/h) = 10 h
Answer: 10 hours
I don’t know the answer to this question
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).
Answer: [tex]\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV[/tex] = 1087.5
Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right][/tex][tex]\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
[tex]a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0[/tex]
Then, replacing with point P and normal vector n:
[tex]36(x-5) + 20(y-0) + 45(z-0) = 0[/tex]
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
[tex]z = \frac{180-36x-20y}{45}[/tex]
When z = 0:
[tex]y = 9 + \frac{-9x}{5}[/tex]
When z=0 and y=0:
x = 5
Then, triple integral is:
[tex]\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx[/tex]
Calculating:
[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex]
[tex]\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx[/tex]
[tex]\frac{1}{45} [30375-60750+118462.5-39150][/tex]
[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex] = 1087.5
The volume of the tetrahedon is 1087.5 cubic units.
The tripple integration will be [tex]\int\limits^a_E \int\limits^a_E \int\limits^a_E {xy} \, dV[/tex] = 1087.5
What is triple integration?The triple integration is used to identify the volumes of the objects or for analyzing three dimension of the object.
To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedron is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&-0\\0&9&-4\end{array}\right] \left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
[tex]a(x-x_o)+b(y-y_o)+c(z-z_o)=0[/tex]
Then, replacing with point P and normal vector n:
[tex]36(x-5)+20(y-0)+45(z-0)=0[/tex]
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
[tex]z=\dfrac{180-36x-20y}{45}[/tex]
When z = 0:
[tex]y=9+\dfrac{-9x}{5}[/tex]
When z=0 and y=0:
x = 5
Then, triple integral is:
[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]
Calculating:
[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]
[tex]\int\limits^5_0 \int\int xy\ (\dfrac{180-36x-20y}{45}-0)dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 180xy-36x^2y-20xy^2dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 90xy^2-18x^2y^2-\dfrac{20}{3}xy^3dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 2430x-1458x^2+\dfrac{94770}{125}x^3-\dfrac{23490}{375}x^4dx[/tex]
[tex]\dfrac{1}{45} [30375-60750+118462.5-39150][/tex]
[tex]\int\limits^5_0 \int\int xy\ dzdydx=1087.5[/tex]
The volume of the tetrahedron is 1087.5 cubic units.
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A rectangular cake has a length of 25in, a width of 18in, and a height of 4in. Each container of frosting can cover 200 square inches.
Answer:
9 containers of frosting
Step-by-step explanation:
25 x 18 x 4, gives you 1800 square inches, divide 1800 by 200 and you get 9
Which fraction below is NOT equivalent to 1/3 2/6 3/9 4/12 5/13
Answer:
5/13 (irreducible)
Step-by-step explanation:
1/3=2/6=3/9=4/12 are all thirds of the total.
Find the equation of the line that contains the points (3,5) and (7, 7). Write the equation in the form y = mx + b and identify m and b.
m=
b=
Step-by-step explanation:
Using Point - Slope formula :
[tex](y - y_1) = \frac{(y_2 - y_1)}{(x_2 - x_1)} (x - x_1)[/tex]
[tex](y - 5) = \frac{2}{4} (x - 3)[/tex]
2y - 10 = x - 3
[tex]y = \frac{1}{2} x + \frac{7}{2} [/tex]
m = 1 / 2
b = 7 / 2
10) The perimeter of a rectangular yard is 60 meters. What is its length if its width
is twice its length?
*
A 10 meters
B 18 meters
C 20 meters
D 24 meters
Answer:
Length = 20 metres
Width = 10 mteres
Step-by-step explanation:
Let the width be x metres
Let the length be 2x metres
Perimeter = 60 metres
therefore, by the problem ,
2(length+breadth)= perimeter
=>2(2x+x)=60
=>2 *3x=60
=>6x=60
=>x=10
length = 20 metres
width = 10 mteres
13 The diagram shows nine identical squares inside a rectangle.
The length of the rectangle is 12 cm.
Work out the width of the rectangle
Answer:
5...is the width of the rectangle .
On the graph of the equation 3x+ 2y=18, what is the value of the y-intercept?
A) -9
B) -6
C) 6
D) 9
Answer:
D) 9Step-by-step explanation:
[tex]3x+ 2y=18\\\\Let \:x\:equal\:to\:0\\\\3(0)+2y=18\\\\0+2y=18\\\\2y=18\\\\Divide \:both\:sides\:of\:the\:equation\:by \:2\\\frac{2y}{2} =\frac{18}{2} \\\\y =9\\(0,9)[/tex]
Answer:
y = 9
Step-by-step explanation:
3x + 2y = 18
required:
find the y-intercept
we have to eliminate x to get the y intercept value
3(0) + 2y = 18
2y = 18
y = 18/2
y = 9
so the x & y intercept would be (0, 9)
Shown below is the solution to the linear program for finding Player A's optimal mixed strategy in a two-person, zero-sum game.
VARIABLE VALUE REDUCED COSTS
PA1 0.050 0.000
PA2 0.600 0.000
PA3 0.350 0.000
GAINA 3.500 0.000
CONSTRAINT SLACK/SURPLUS DUAL PRICES
1 0.000 -0.500
2 0.000 -0.500
3 0.000 0.000
4 0.000 3.500
a.
What is Player A's optimal mixed strategy?
b.
What is Player B's optimal mixed strategy?
c.
What is Player A's expected gain?
d.
What is Player B's expected loss?
use this area to narratively respond to all four parts of the question
Answer:
Following are the answer to this question:
Step-by-step explanation:
For Option a:
Its optimal mixed approach for Player A's to Player A
A1 with a chance of .05 utilizing technique
Using the .60 chance strategy for A2
Use the .35 possibility strategy for A3
For Option b:
Optimal level mixed approach for team B:
Use the strategy for B1 with a probability of 50
Using the chance strategy for B2 at .50
no use strategy for B3
For Option c:
The estimated gain of Player A will be= 3.500
For Option d:
The estimated loss of Player B will be 3.500
Use a t-test to test the claim about the population mean µ at the given level of significance using the given sample statistics. Assume the population is normally distributed.
Claim: μ ≥8300, α=0.10
Sample statistics: ¯x=8000, s=440, n=24
Required:
a. What are the null and alternative hypotheses?
b. What is the value of the standardized test statistic? (Round to 2 decimal places as needed.)
c. What is the p-value? (Round to three decimal places as needed.)
d. Decide whether to reject or fail to reject the null hypothesis.
Answer:
uoooooohuuuuuuuuuuuihouu
How can you create a cone and a cylinder using this tool? Describe the shapes and the specific axes of rotation that produce a cone and a cylinder. If there is more than one polygon that can generate the same cone or cylinder, state each shape in the table.
Answer:
The answer is in the image.
Step-by-step explanation:
Answer:
Cone- 1 isosceles triangle revolved 180° about its height
2 isosceles triangle revolved 180° about its height
cylinder 1 rectangle revolved 180° about either axis of symmetry
2 revolved 360° about any side
Step-by-step explanation: plato edmentum
Convert 2 centimeters into feet. Round your answer to the nearest hundredth.
.066
1 Centimeter = 0.03280839895 Feet
The conversion of 2 centimeters into feet would be 0.066 feet.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
We have to determine the conversion of 2 centimeters into feet.
Since one centimeter = 0.03280839895 feet
Therefore two centimeters = 2×0.03280839895 feet
⇒ two centimeters = 0.0656167
Round the answer to the nearest hundredth.
⇒ two centimeters = 0.066
Therefore, the conversion of 2 centimeters into feet would be 0.066 feet.
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The equivalent resistance of R1 = 1000 ohms and R2 = 1500 ohms connected in parallel is _____ ohms.
Answer:
600 Ω see attachement
Step-by-step explanation:
A researcher examines the records of all registered voters in one city and finds that 43% are registered democrats. Is the evaluated group a population or a sample?
Answer: Population
Step-by-step explanation: Population is refers to the whole or entire members or of a given set. This is different from a sample which is used to refer to members of a subset (a subset is a certain portion or fraction of an entire set). In the scenario above, since the evaluation was based on the entire number of registered voters in the country, this means we are referring to a population. The inference about the percentage of democratic voters was drawn from a pool of all the entire number of registered voters available in the country and not from a certain subset or portion of registered voters. Hence, the evaluated group is a population.