(a) The trigonometric form of 8 is 8, the trigonometric form of 6i is 6i, and the trigonometric form of cos(-i sin 5) is 1(cos(-i sin 5) + isin(-i sin 5)).
(b) The simplified expression ([tex]\[(1^* - \frac{1+2}{2} + 2) + 3 + 1 = 5\][/tex]) is 4.5, and the simplified expression 2i(i - 1) + (7 + 3i) + (1 + i)(1 + i) is 7 + i.
(a) To write the complex number 8 in trigonometric form, we convert it to the form r(cosθ + isinθ). In this case, r = 8 and θ = 0 since 8 lies on the positive real axis. Therefore, the trigonometric form of 8 is 8(cos0 + isin0), which simplifies to 8.
(b) To write the complex number 6i in trigonometric form, we convert it to the form r(cosθ + isinθ). In this case, r = 6 and θ = π/2 since 6i lies on the positive imaginary axis. Therefore, the trigonometric form of 6i is 6(cos(π/2) + isin(π/2)), which simplifies to 6i.
(c) To write the complex number cos(-i sin 5) in trigonometric form, we convert it to the form r(cosθ + isinθ). In this case, r = 1 and θ = -i sin 5. Therefore, the trigonometric form of cos(-i sin 5) is 1(cos(-i sin 5) + isin(-i sin 5)).
5. Simplify ([tex]\[(1^* - \frac{1+2}{2} + 2) + 3 + 1[/tex]
To simplify this expression, we perform the operations step by step:
([tex]\[(1^* - \frac{1+2}{2} + 2) + 3 + 1\][/tex]
We perform the multiplication and division:
([tex]\[-\frac{3}{2}[/tex] + 2) + 3+1
Finally, we combine like terms:
[tex]\[-\frac{3}{2} + 6\][/tex]
To further simplify, we can convert -3/2 to a decimal:
[tex]\[-\frac{3}{2}[/tex] = -1.5
Therefore, the simplified expression is:
-1.5 + 6 = 4.5
(b) Simplify 2i(i - 1) + (7 + 3i) + (1 + i)(1 + i)
First, let's simplify each term separately:
2i(i - 1) = 2i² - 2i = -2i - 2i = -4i
(1 + i)(1 + i) = 1 + i + i + i² = 1 + 2i - 1 = 2i
Now, let's combine all the terms:
-4i + (7 + 3i) + 2i
Combine the real and imaginary parts separately:
(7 + 0) + (-4i + 3i + 2i) = 7 + i
So the simplified expression is 7 + i.
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Evaluate the triple integral. 4xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = , y = 0, and x = 1
The value of the triple integral ∭E 4xy dV is 2/5. The limits of integration for x are from 0 to 1, and for y, the limits are from 0 to 1 - x, as y is bounded by the line x + y = 1.
To evaluate the triple integral ∭E 4xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = 0, y = 1, and x = 1, we need to set up the integral using appropriate limits of integration.
The region in the xy-plane is a triangle bounded by the lines y = 0, y = 1, and x = 1. Therefore, the limits of integration for x are from 0 to 1, and for y, the limits are from 0 to 1 - x, as y is bounded by the line x + y = 1.
Now, let's determine the limits for z. The plane z = 1 + x + y intersects the xy-plane at z = 1, and as we move up in the positive z-direction, the plane extends infinitely. Thus, the limits for z can be taken from 1 to infinity.
Now, we can set up the triple integral:
∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] ∫[1 to ∞] 4xy dz dy dx
The innermost integral with respect to z evaluates to z times the integrand:
∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] [4xy(1 + x + y)] evaluated from 1 to ∞ dy dx
Simplifying further:
∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] (4xy(1 + x + y) - 4xy(1)) dy dx
∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] 4xy(x + y) dy dx
Now, we can integrate with respect to y:
∭E 4xy dV = ∫[0 to 1] [2xy²(x + y)] evaluated from 0 to 1-x dx
Simplifying further:
∭E 4xy dV = ∫[0 to 1] 2x(1-x)²(x + (1-x)) dx
∭E 4xy dV = ∫[0 to 1] 2x(1-x)² dx
Evaluating the integral:
∭E 4xy dV = 2/5
Therefore, the value of the triple integral ∭E 4xy dV is 2/5.
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a strain of peas has 3 green and one yellow for every four peas. if 12 peas are rendomly selected, what is the probability that exactly 8 peas are green? provide your answer to three decimal places
The probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.
We can use the binomial probability formula to solve this problem.
The formula is given as; $$P(X=k)={n\choose k}p^k(1-p)^{n-k}$$
Where;
n= sample size=12
k= number of green peas=8
p= probability of getting a green pea=3/4
q= probability of getting a yellow pea=1/4
Since we want the probability of exactly 8 green peas out of 12 peas,
we will plug in the values in the formula to get;
$$P(X=8)={12\choose 8}(\frac{3}{4})^8 (1-\frac{3}{4})^{12-8}$$$$
P(X=8)={12\choose 8}(\frac{3}{4})^8(\frac{1}{4})^{4}$$$$P(X=8)=495
(0.3164)(0.0039)$$$$P(X=8)=0.4749$$
Therefore, the probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.
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If you get this question right you’ll get points 100+356-123=?????
Answer:
333 :)
Step-by-step explanation:
The hair color of the players on a tennis team would be considered: a. Ratio data b. Ordinal data c. Nominal data d. Interval data
The hair color of the players on a tennis team would be considered nominal data. Therefore, the most appropriate answer is option (c): Nominal data.
In data classification, there are four main levels of measurement: nominal, ordinal, interval, and ratio. Nominal data is the lowest level of measurement and represents categories or labels that cannot be ranked or ordered. Hair color falls into this category as it represents different categories or labels such as blonde, brunette, red, etc. Nominal data does not have any inherent numerical value or order.
On the other hand, ordinal data represents categories that can be ordered or ranked but do not have a consistent interval between them. Interval and ratio data involve numerical values with a consistent interval and a true zero point, with ratio data having a meaningful zero point.
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Find the volume of each figure. Round the answer
5 min
4 mm
18 nm
8 mm
WHAT WOULD THiS BE! ♀️
no scammers pleaseee!
Answer:
First find the unit rate for julie
3 hours/45 dollars
0.066 hours/1 dollar
Now based off table, find Jacksons
y = 25x
if x = 1, y would be 25
25 - .066 = 24.934 dollars
Step-by-step explanation:
a spinner has three same-sized sectors numbered 1, 3, and 5. the spinner is spun once and a coin is tossed. h represents heads, and t represents tails. what is the sample space of outcomes?
A spinner has three same-sized sectors numbered 1, 3, and 5. The spinner is spun once and a coin is tossed. H represents heads, and T represents tails.
The sample space of outcomes is given below: Sample Space of Outcomes: {1H, 1T, 3H, 3T, 5H, 5T}Explanation: In this given problem, the spinner has three same-sized sectors numbered 1, 3, and 5. It indicates that the probability of each sector is equal. The spinner is spun once and a coin is tossed, where H represents heads, and T represents tails. It means that the spinner will land on one of three sectors, and the coin will land on either heads or tails.Therefore, the sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.
To determine the sample space of outcomes for this situation, we need to consider the possible combinations of the spinner's numbers (1, 3, 5) and the outcomes of the coin toss (H for heads, T for tails).
The spinner has three sectors numbered 1, 3, and 5. Therefore, there are three possible outcomes for the spinner.
The coin toss can result in two outcomes: heads (H) or tails (T).
To find the sample space, we need to consider all possible combinations of the spinner outcomes and the coin toss outcomes.
The sample space of outcomes can be listed as follows:
{1H, 1T, 3H, 3T, 5H, 5T}
Therefore, the sample space of outcomes for this situation consists of the six possible combinations: 1H, 1T, 3H, 3T, 5H, and 5T.
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Given information is that, a spinner has three same-sized sectors numbered 1, 3, and 5. The spinner is spun once and a coin is tossed. h represents heads, and t represents tails. We need to find the sample space of outcomes.
The required sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.
We can use the formula for the sample space,
Sample space = Set of all possible outcomes.
The possible outcomes of the spinner are 1, 3, and 5. The possible outcomes of the coin are H and T. Therefore,
Sample space of outcomes = {1H, 1T, 3H, 3T, 5H, 5T}.
Hence, the required sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.
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An object completes one round of circle of radius 7m in 20 sec. find the distance travelled after 10sec.
Answer: 7pi
Step-by-step explanation: If it completes the circumference distance (14pi) of the circle in 20 seconds, in 10 seconds it will complete half of that. or 7pi. Hope this helped!
:.the distance travelled after 10sec. =7πm
Answer:
in 20 sec distance travelled =2πr=2π×7=14πm
in 10 sec distance travelled=14πm×10/20=7πm
Factor this expression completely and then placed the factors in the proper location on the grid. Note: please factors alphabetically in the grid!
ab + 4 + a + 4b
PLEASE ANSWER, WILL MARK BRAINLYEST!
Answer:
(a + 4)(b + 1)
Step-by-step explanation:
ab + 4 + a + 4b
Rearrange the expression to find the GCF.
ab + a + 4b + 4
Now find the GCF.
a (b + 1) + 4 (b + 1)
Divide the whole thing by b+1
(a + 4)(b + 1)
GIVING BRAINLIEST!!!!!!
Answer:
y+x = -4
Step-by-step explanation:
-4 indicates where the line intercept the y axis
if we put y=0 we can find where line intercepts the x axis.
it results x = -4
the two values are negative
A rectangle has a perimeter of 150 cm. The length is 3 cm more than twice the width. Find the length and width of the rectangle.
Answer:
Length of rectangle = 51 cm
Width of rectangle = 24 cm
Step-by-step explanation:
Given:
Perimeter of rectangle = 150 cm
Find:
Length and width of the rectangle
Computation:
Assume;
Width of rectangle = a cm
Length of rectangle = 2a + 3 cm
Perimeter of rectangle = 2[l + b]
150 = 2[(2a + 3) + a]
2[3a + 3] = 150
6a + 6 = 150
6a = 144
a = 24
Width of rectangle = 24 cm
Length of rectangle = 2a + 3 cm
Length of rectangle = 2(24) + 3 cm
Length of rectangle = 51 cm
Which of the following sets of points would create a rectangle when connected?
A.
(1,2) , (2,3) , (3,5) , (5,1)
B.
(2,1) , (3,2) , (5,3) , (1,5)
C.
(1,2) , (3,1) , (3,2) , (1,5)
D.
(1,2) , (3,2) , (3,5) , (1,5)
Express the function G in the form f o g. (There is more than one correct answer. The function is of the form y = f(g(x)). Use non-identity functions for f(x) and g(x).)
G(x) = 1/x+8
(f(x), g(x) = ([_________])
To express the function [tex]\(G\)[/tex] in the form [tex]\(f \circ g\)[/tex] , where [tex]\(y = f(g(x))\)[/tex] , we need to find suitable non-identity functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x)\)[/tex].
Let's choose [tex]\(g(x) = \frac{1}{x}\)[/tex] and [tex]\(f(x) = x + 8\)[/tex].
Now, we can express [tex]\(G\)[/tex] as [tex]\(G(x) = f(g(x))\)[/tex] , which becomes:
[tex]\[G(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \frac{1}{x} + 8\][/tex]
Therefore, the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x) = \frac{1}{x} + 8\) are \(f(x) = x + 8\)[/tex] and [tex]\(g(x) = \frac{1}{x}\)[/tex].
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What is the greatest common factor of the numbers
15,30 , and 75 ?
Answer:
15
Step-by-step explanation:
Prime Numbers Check
15: 5 * 3
30: 2 * 3 * 5
75: 3 * 5 * 5
Both 3 and 5 are prime numbers present in all 3 greater numbers, then you multiply them
3*5 = 15
GCF is 15
Use the CVP Formulas to solve the following. JBL Speakers has annual fixed costs of $2,450,000, and variable costs of $25 per unit. The selling price per unit is $90. A) What annual revenue is required to break even? BER B) What annual unit sales are required to make a $1,000,000 profit?
Using the CVP Formulas to solve the following. JBL Speakers has annual fixed costs of $2,450,000, and variable costs of $25 per unit. The selling price per unit is $90.
A) 37,692 units
B) 53,077 units
A) To calculate the annual revenue required to break even, we need to find the point where total revenue equals total costs.
Total cost (TC) = Fixed costs (FC) + Variable costs per unit (VC) * Quantity (Q)
Total revenue (TR) = Selling price per unit (SP) * Quantity (Q)
At the break-even point, total revenue equals total cost:
TR = TC
SP * Q = FC + VC * Q
Substituting the given values:
$90 * Q = $2,450,000 + $25 * Q
$90Q - $25Q = $2,450,000
$65Q = $2,450,000
Q = $2,450,000 / $65
Q ≈ 37,692.31
Therefore, approximately 37,692 units need to be sold to break even.
B) To calculate the annual unit sales required to make a $1,000,000 profit, we can use the following formula:
Profit (P) = (SP * Q) - (FC + VC * Q)
Substituting the given values and the desired profit:
$1,000,000 = ($90 * Q) - ($2,450,000 + $25 * Q)
$90Q - $25Q = $1,000,000 + $2,450,000
$65Q = $3,450,000
Q = $3,450,000 / $65
Q ≈ 53,076.92
Therefore, approximately 53,077 units need to be sold to make a $1,000,000 profit.
In conclusion, to break even, JBL Speakers needs to generate an annual revenue of approximately $2,450,000, and to make a $1,000,000 profit, they need to sell approximately 53,077 units annually.
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I need help plzzz
-6p + 19 > 7
Answer:
p < 2
Step-by-step explanation:
hope this is right and have a good day
139°
(17x + 3)
answer
Answer:
x= 8
Step-by-step explanation:
17x + 3 = 139
17x = 136
x = 8
at time t = 0 the capacitor in the circuit below is fully charged with qmax, and the current through the circuit is 0.
At time t = 0, the capacitor in the circuit is charged to its maximum charge, qmax, and the circuit has zero current.
At t = 0, the capacitor in the circuit is fully charged, which means it has accumulated its maximum charge, qmax. The capacitor acts as a temporary energy storage device in the circuit. When the capacitor is fully charged, it contains potential energy. The charge on the capacitor creates an electric field, which opposes the flow of current through the circuit.
Since the capacitor is fully charged at t = 0, it resists any change in the current. Therefore, the circuit has zero current flowing through it. As time progresses, the capacitor will start to discharge, releasing the stored energy and allowing the current to flow. The discharge process is governed by the relationship between the voltage across the capacitor, the capacitance of the capacitor, and the resistance in the circuit.
Finally, at t = 0, the capacitor in the circuit is charged to its maximum capacity, qmax, and the circuit has zero current flowing through it.
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Dean wants to buy a scooter. He has a coupon for 20% off his purchase, and has already saved $50. If the scooter is $79, how much more money does Dean need to be able to purchase it?
Give an example to show that when two prime numbers are added, the result
may be an odd number.
Answer:
2+3=5
Step-by-step explanation:
prime numbers =2 and 3
sum =5 which is odd
4) A spinner has 8 congruent sections as shown in the diagram. If the
spinner is spun twice, what is the probability that the first spin will land on
a whistle and the second spin will land on a yo-yo?"
a. 1/2
b. 1/8
c. 2/8
d. 1/32
HELP MATH ASAP! I GIVE BRAINLIEST
In the expression 8k + 5. which best describes what 8 represents?
Answer:
it represents a variable
Step-by-step explanation:
The number 8 is the coefficient of the variable k.
What is a coefficient?A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.
Given that the expression is 8k + 5. In the given expression the number 8 is the coefficient of the given expression.
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Your friend Sam wants to paint her room. She wants to paint the ceiling
white and the four walls purple.
You are helping Sam determine the cost and the amount of time needed to
paint her room.
The room is shaped like a rectangular prism with a height of 8 feet, length of
12 feet, and width of 10 feet as shown.
one hundred and twenty approximately
How does the graph of the
function g(x) = 2* + 6 differ from
the graph of f(x) = 2*?
Answer:
YUH
Step-by-step explanation:
Answer:
you'll see...
Step-by-step explanation:
Given that the transformed graph is of function f(x) = (x + 2)^4 + 6 and the parent function g(x) = x^4
The transformed graph function g(x) was shifted two (2) units to the left and was translated six (6) units upward.
When the function is shifted to the right, the factor of x will be negative and when it's shifted to the left, the factor of x will be positive.
Therefore, function g(x) = x^4 is shifted 2 units to the left and translated 6 units upward to form f(x) = ( x + 2 )^4 + 6.
Perform a hypothesis test for the following sample, the significance level alpha is 5%. Sample: 3.4,2.5,4.8, 2.9,3.6,2.8, 3.3, 5.5, 3.7, 2.8,4.4,4,5.2,3,4.8 Standard deviation is sd-1.05. Test if mean is greater than 3.16 Assume normality of the data. 1 Formulate the hypothesis by entering the corresponding signs
Based on the given sample, there is sufficient evidence to conclude that the mean is greater than 3.16 at a significance level of 5%.
To perform a hypothesis test, we need to state the null hypothesis and alternative hypothesis.
We want to test if the mean is greater than 3.16.
Null hypothesis (H0): μ ≤ 3.16 (Mean is less than or equal to 3.16)
Alternative hypothesis (Ha): μ > 3.16 (Mean is greater than 3.16)
Now, we can proceed with the hypothesis test.
We'll use a one-sample t-test since we don't know the population standard deviation and our sample size is relatively small.
The sample mean (X) and sample size (n) from the given data.
X= (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.5 + 3.7 + 2.8 + 4.4 + 4 + 5.2 + 3 + 4.8) / 15 = 3.66
n = 15
Now calculate the test statistic (t-value).
t = (X - μ) / (sd / √n)
= (3.66 - 3.16) / (1.05 / √15)
≈ 2.26
Since our alternative hypothesis is one-tailed (μ > 3.16), we need to find the critical value for a significance level of 5% in the right tail of the t-distribution.
Using a t-table, the critical value for a one-tailed test with α = 0.05 and degrees of freedom (df) = n - 1 = 15 - 1 = 14 is 1.761.
If the test statistic is greater than the critical value, we reject the null hypothesis.
t-value (2.26) > critical value (1.761)
Since the test statistic is greater than the critical value, we reject the null hypothesis.
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6. The table shows the number of manatee deaths caused by watercraft in Florida each year
beginning in 1980. The years are coded that 1980 is 1, 1981 is 2, and so on. Use the table to
find the best model and the R2 value.
Year
1
2
3
4
5
6
7
8
9
10
Deaths
16
24
20
15
34
33
33
39
43
50
(1 point)
linear model, 0.845
exponential model, 0.779
power model, 0.682
quadratic model, 0.866
Answer: quadratic model, 0.866
Step-by-step explanation:
HELP ME PLS
how do you graph a function??????
Answer:
It depends on the type of function, but essentially the process is the same
Step-by-step explanation:
You gather up all of the y values and x values and plot them onto a coordinate grid. If you are using a calculator, go to the "y=" button and input the function and then hit "graph"
The count of bacteria in a certain experiment was increasing at a rate of 2.5% per hour. if the experiment started with 1600. find the count of the bacteria at the end of 22 hours.
DONT ADD ANY LINK PLEASE I WILL REPORT AND PLEASE ANSWER CORRECTLY AND FAST I WILL MARK BRAINLIEST
Solve the inequality for d
df+9h>2
Answer:
d=2_f - 9h_f
Step-by-step explanation:
es la segunda opción