From the given value of z = 3(cos pi/2 + isin pi/2), the exact value of z⁷ is -2187i.
Given z = 3(cos pi/2 + isin pi/2)
which can be represented as 3sin(pi/2) in polar form.
Now, by applying De-Moivre's theorem,
z⁷ = (3cis(pi/2))⁷
= 3⁷cis(7pi/2)
= 3⁷cis(3pi/2) [7pi/2 --- 3pi/2 ]
To write it in complex form,
z⁷ = 3⁷(cos(3pi/2) + isin(3pi/2))
z⁷ = 3⁷(0-i) [cos(3pi/2) = 0 and sin(3pi/2) = -1]
z⁷ = 3⁷(-i)
z⁷ = -2187i
From the above explanation, we can conclude that the value of z⁷ is -2187i.
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A building supply store is selling tiles with an area of 790 cm square Find the length of each side of the tile correct to 3 significant figures.
The length of each side of the tile with an area of 790 cm² correct to 3 significant figures is 28.1 cm.
What are significant figures?Significant figures are the digits in a number that give a reliable accuracy of the quantity of a measurement.
The significant figures do not include the zeros immediately after the decimal place but those that occur between other numbers are regarded as significant.
The area of a square tile = Length x Length
= 790 cm²
The length of each side = √790 = 28.1069
= 28.1 cm
Thus, we can conclude that the length of each side of the square tile is 28.1 cm.
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Two square carpets are used in the reception area of a hotel. The sum of the areas of the carpets is 720 square feet. The difference of the areas of the carpets is 432 square feet. Find the dimensions of each carpet.
Answer:
Let x be the length of one side of the first carpet in feet. Then, the area of the first carpet is x^2 square feet.
Let y be the length of one side of the second carpet in feet. Then, the area of the second carpet is y^2 square feet.
From the problem, we know that the sum of the areas of the two carpets is 720 square feet:
x^2 + y^2 = 720
We also know that the difference of the areas of the two carpets is 432 square feet:
x^2 - y^2 = 432
We can solve this system of equations by using the method of substitution. Solving for x^2 in the second equation, we get:
x^2 = y^2 + 432
Substituting this expression for x^2 into the first equation, we get:
y^2 + 432 + y^2 = 720
Simplifying and solving for y, we get:
2y^2 = 288
y^2 = 144
y = 12
Substituting this value of y into the equation x^2 + y^2 = 720 and solving for x, we get:
x^2 + 144 = 720
x^2 = 576
x = 24
Therefore, the dimensions of the first carpet are 24 feet by 24 feet, and the dimensions of the second carpet are 12 feet by 12 feet.
Step-by-step explanation:
Last week's and this week's low temperatures are shown in the table below.
Low Temperatures for 5 Days This Week and Last Week
Low Temperatures
This Week (°F)
Low Temperatures
Last Week (°F)
4
10
13 9
6
5
9
6
8 5
Which measures of center or variability are greater than 5 degrees? Select three choices.
O the mean of this week's temperatures
O the mean of last week's temperatures
the range of this week's temperatures
the mean absolute deviation of this week's temperatures
the mean absolute deviation of last week's temperatures
The measures of center or variability are greater than 5 degrees
The the mean of this week's temperatures the mean of last week's temperaturesthe range of this week's temperaturesHow to measure for variablilyThis Week's Mean: (4 + 13 + 6 + 9 + 8) / 5 = 40 / 5 = 8
Last Week's Mean: (10 + 9 + 5 + 6 + 5) / 5 = 35 / 5 = 7
Then the ranges
This Week's Range: (13 - 4) = 9
Last Week's Range: (10 - 5) = 5
The MAD for both weeks
|(4 - 8)| + |(13 - 8)| + |(6 - 8)| + |(9 - 8)| + |(8 - 8)|
= 4 + 5 + 2 + 1 + 0 = 12
This Week's MAD: 12 / 5 = 2.4
|(10 - 7)| + |(9 - 7)| + |(5 - 7)| + |(6 - 7)| + |(5 - 7)| = 3 + 2 + 2 + 1 + 2 = 10
Last Week's MAD: 10 / 5 = 2
Hence the measures of center or variability are greater than 5 degrees are:
The the mean of this week's temperatures the mean of last week's temperaturesthe range of this week's temperaturesRead more on measures of center
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One hundred fifty bacteria are put into a petri dish, and the culture triples in size every hour. This is modeled by P(h) = 150(3), where P is the num
of bacteria in the population and h is the number of hours that have passed.
Which graph models the function P(h)?
The graph of the population equation is on the image at the end.
Which graph models the function?Here we know that the function p(h) models the population of bacteria as the function of h, the number of hours.
And we can write this as the exponential function:
p(h) = 150*(3)^h
The graph of this will be an exponential that starts at 150 and triples for each increase in the horizontal variable, then the graph of this will be like the one you can see at the end of the answer.
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What is the 3D shape that would form if the following
Answer:
These are all the 3D shapes ;cone, cylinders, cuboid,cubes, sphere, rectangular prism, pyramid
HELP ASAP PLEASE 10 points
A). spinning a spinner that has 5 equal sections marked 1 through 5 and landing on an even number
B). picking a diamond from a standard deck of playing cards which has 13 cards in each of four suits: spades, hearts, diamonds and clubs
(Information for the problem in the photo)
The probability of spinning an even number on the spinner is 40%.
The probability of picking a diamond from a standard deck of playing cards is 25%.
How to calculate the probabilityP(even) = number of even sections / total number of sections
= 2/5
= 0.4
= 40%
Therefore, the probability of spinning an even number on the spinner is 40%.
P(diamond) = number of diamonds / total number of cards
= 13/52
= 1/4
= 0.25
= 25%
Therefore, the probability of picking a diamond from a standard deck of playing cards is 25%.
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The high tide at midnight in Key West was 15.42 feet. A nearing hurricane tripled the tide height. At low tide it went down by 1.2 feet at 7 AM. What was the height of the low tide at 7 AM? 45.06 feet 18.2 feet 2.65 feet 47.4 feet
Answer:45.06
Step-by-step explanation:
no explanation
The height of the low tide at 7 AM was 45.06 feet.
Given that, the high tide at midnight was 15.42 feet.
A nearing hurricane tripled the tide height. At low tide it went down by 1.2 feet at 7 AM.
We need to find the height of the low tide at 7 AM,
So,
When the hurricane is near the height of the tide is triples so the height is 15.42 × 3 = 46.26 feet
Now, at low tide it went down by 1.2 feet at 7 AM.
so, the height will be = 45.26 feet - 1.2 feet = 45.06 feet
Hence, the height of the low tide at 7 AM was 45.06 feet.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
We have,
Equation of circle: x²+ y² – 2x – 8 = 0
The standard equation of a circle is
x² + y² + 2gx + 2fy + C= 0
where Centre is (-g, -f)
and, radius = √g²+f²-C
from given equation the center is
2gx = -2x
x= -1
and, 2fy = 0
f = 0
So, the Centre = (-(-1), 0) = (1, 0)
Now, r = radius = √g²+f²-C
r= √1²+0²-(-8)
r=√9
r = 3 units
Hence, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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3 to the 8th power times 3
Answer:
19683
Step-by-step explanation:
3 to the power of 8 is 6561,
so just put 6561 multiplied by itself 3 times.
(6561 X 6561 X 6561).
Answer:
3⁸ × 3 = 19,683
Joshua and Amahle are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small
boxes of fruit and large boxes of fruit. Joshua sold 15 small boxes of fruit and 15 large boxes of fruit for a
total of $390.00. Amahle sold 20 small boxes of fruit and 25 large boxes of fruit for a total of $592.50. Find the cost of one small box of fruit and the cost of one large box of fruit.
Cost of small box: $
Cost of large box: $
The cost of one small box of fruit and the cost of one large box of fruit is $11.5 and $14.5 respectively.
What is the cost of small and large box?Let
cost of one small box of fruit = x
cost of one large box of fruit = y
15x + 15y = 390
20x + 25y = 592.50
From (1)
x + y = 26
x = 26 - y
Substitute x = 26 - y into (2)
20x + 25y = 592.50
20(26 - y) + 25y = 592.50
520 - 20y + 25y = 592.50
- 20y + 25y = 592.50 - 520
5y = 72.50
divide both sides by 5
y = 72.50/5
y = 14.5
Substitute y = 14.5 into
15x + 15y = 390
15x + 15(14.5) = 390
15x + 217.5 = 390
15x = 390 - 217.5
15x = 172.5
divide both sides by 15
x = 172.5/15
x = 11.5
Therefore, small box cost $11.5 and large box cost $14.5
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Create an equation that has an initial value of 10 and has a rate of change of 4.
The equation that has an initial value of 10 and has a rate of change of 4 is y= 4x+ 10.
We have,
Initial value= 10
Rate pf change= 4
We know from slope intercept form
y= mx+ b
where is m is slope or rate of change and b is y intercept or initial value.
So, we can take m = 4 and b= 10
Then, the required equation is
y= 4x +10.
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K
In 2019, 2 out of every 5 members of an army reserve were female. There were 188,667 army reserve personnel that year. Estimate the number of
female members of the army reserve in 2019.
The approximate number of female members of the army reserve in 2019 was.
(Do not round until the final answer. Then round to the nearest whole number as needed.)
ew an example Get more help.
Clear all
Skill builder
Check answer
The approximate number of female members of the army reserve in 2019 was 75,467.
What is the number of female members in 2019?If 2 out of every 5 members of the army reserve were female, then the proportion of female army reserve personnel can be represented as:
= 2/5
= 0.4.
Now, we can multiply the proportion to total number of army reserve to get the number of female members which is:
= 0.4 x 188,667
= 75,466.80
= 75,467
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Suppose we have data about a three-stock financial market that satisfies the single-index model as below: (the standard deviation of the market-index portfolio is 18%)
Capitalization Beta Excess Return Std Dev
A $3,000 0.15 10% 40%
B $2,000 0.95 2% 30%
C $1,500 1.7 17% 50%
What is the mean excess return of the value-weighted index portfolio?
Express your answer in percent and round it to 2 decimal places. For example, if your answer is 0.25456, then please write down 25.46 (without the percent sign).
The mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.
To calculate the mean excess return of the value-weighted index portfolio, we need to first calculate the total market capitalization of the three stocks:
Total Market Cap = $3,000 + $2,000 + $1,500 = $6,500
Next, we can calculate the weight of each stock in the index portfolio as follows:
Weight of Stock A = $3,000 / $6,500 = 0.4615
Weight of Stock B = $2,000 / $6,500 = 0.3077
Weight of Stock C = $1,500 / $6,500 = 0.2308
The capitalization-weighted beta of the portfolio can then be calculated as the sum of the product of each stock's weight and its beta:
Beta of Index Portfolio = (0.4615 x 0.15) + (0.3077 x 0.95) + (0.2308 x 1.7) = 1.081
The mean excess return of the index portfolio can be calculated using the single-index model as:
Mean Excess Return = Beta of Index Portfolio x Standard Deviation of Market-Index Portfolio
= 1.081 x 18%
= 19.458%
Finally, we need to adjust for the risk-free rate to obtain the actual mean return of the index portfolio. If the risk-free rate is 2%, then the mean return of the index portfolio would be:
Mean Return = Mean Excess Return + Risk-Free Rate
= 19.458% + 2%
= 21.458%
Therefore, the mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.
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Which of the following choices is a linear function?
Answer: f(x)=x-2
Step-by-step explanation:
Linear function means a straight line, so graph each one to find which is a straight line
How many
1/4-foot cubes would fill the inside of the prism?
Write the answer in the box.
There are 4 cubes of size 1/4 foot would fill the inside of the prism.
We have to given that;
Height of cuboid = 3 feet
Length of cuboid = 3/4 feet
Width of cuboid = 1/2 feet
We know that;
Volume of cuboid = Length x width x height
Hence,
V = 3/4 x 3 x 1/2
V = 9/8
Thus, Number of 1/4-foot cubes which would fill the inside of the prism is,
= (9/8) ÷ (1/4)
= (9/8) x 4
= 9/2
= 4.5
Thus, There are 4 cubes of size 1/4 foot would fill the inside of the prism.
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not sure why I cant get the right answer
The composite figure has an area of 142 square yards
The composite figure has one square, right triangle, two rectangles
Area of square = side × side
=8×8
=64 yards
Area of triangle =1/2×8×6
=24 square yards
Area of 1st rectangle = 3×6
=18 square yards
Area of 2 nd rectangle = 9×4
=36 square yards
Total area is sum of square, rectangles and triangle
total area = 64+24+18+36
=142 square yards
Hence, the composite figure has an area of 142 square yards
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Which shapes have teo pairs of parallel side choose all that apply
Answer:
A parallelogram is a quadrilateral with 2 pairs of parallel sides.
Step-by-step explanation:
Mark brainliest, pls
Find the volume of this sphere.
Use 3 for T
8 in
V ≈ [?]in³
V = πr3
The volume of this sphere is 1607. 68 in³
How to determine the volumeIt is important to note that the formula that is used to calculate the volume of a sphere is expressed as;
V = 4/3 πr3
Given that the parameters are;
V is the volume of the sphereπ takes the constant value of 3.14r is the radius of the sphereFrom the information given,
Substitute the values, we have;
Volume = 4/3 × 3.14 ×8³
Find the cube values, we get;
Volume = 4/3 × 3.14 × 512
Multiply the values
Volume = 2143. 57 in³
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In a standard deck of cards (NOT including jokers), there are:
4 suits (diamonds, hearts, clubs, spades)
13 number and face cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King)
2 colors (red, black)
Face cards are Jack, Queen, King
a) What is the probability of drawing a red or black card?
b) What is the probability of drawing a 7 of spades?
c) What is the probability of NOT drawing a Diamond?
d) What is the probability of drawing a black 2?
hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((
A right triangle has side lengths 6 centimeters and 8 centimeters. Is it possible for there to be more than one right triangle with whole-number side lengths that includes the given side lengths? Explain.
The given side lengths, 6 cm and 8 cm, satisfy the Pythagorean theorem because $6^2 + 8^2 = 100 = 10^2$, which means that the triangle is a right triangle.
To determine if there is more than one right triangle with whole-number side lengths that includes these given side lengths, we need to check if there exist other pairs of whole numbers that satisfy the Pythagorean theorem and include 6 cm and 8 cm as two of their sides.
Let's call the third side of the right triangle x. Then we have:
62+82=x26^2 + 8^2 = x^262+82=x2
which simplifies to:
36+64=x236 + 64 = x^236+64=x2
100=x2100 = x^2100=x2
x=100=10x = \sqrt{100} = 10x=100
=10
So the only other possible triangle with whole-number side lengths that includes the given side lengths has side lengths of 6 cm, 8 cm, and 10 cm.
Therefore, there is only one other right triangle with whole-number side lengths that includes the given side lengths, and it is unique.
an aquarium tank can hold 6000 liters of water. there are two pipes that can be used to fill the tank. the first pipe alone can fill the tank in 50min. the second pipe can fill the tank in 75min by itself. when both pipes are working together how long does it take them to fill the tank?
10 points!!
Please help! Show explanation.
Answer: D
Step-by-step explanation:
Point of tangency is where the line on the left touches the circle. Have you ever heard the term "She's going off on a tangent"- it means they only touch the topic(tangent point and go off (tangent line) and talk way off away from where you need to be(circle)
So you can see from the graph the point of tangency (where line touches circle is (-5,0)
the equation for the line is going to be a constant. The line only touches the x-axis never the y-axis at all points it is x=-5
so the equation of the line x= -5
the diagram shows a right angled triangle, find value of h
The value of the side length h is 19.1 cm.
What is the value of side h?The figure in the image is a right triangle:
Angle θ = 47 degrees
Opposite to angle θ = 14cm
Hypotenuse = h
To solve for side length h, we use trigonometric ratio.
Note that: sine = opposite / hypotenuse
Plug in the values and solve for h.
sin( 47° ) = 14 / h
h = 14 / sin( 47° )
h = 19.1 cm
Therefore, the value of h is 19.1 cm.
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The Cruiser Bicycle Company makes two styles of bicycles: the Traveler (x), which sells for $300, and the Tourister (y), which sells $600. Each bicycle has the same frame and tires, but the assembly and painting time required for the Traveler is only 1 hour, while it is 3 hours for the Tourister. There are 300 frames and 360 hours of labor available for production.
Write an inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products).
An inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products is:
x + y ≤ 300
x1 + y3 ≤ 360
What is an inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.
Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
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Find the Independent and Dependent variables in the below Research Question.
Is there a difference in time finding a parking spot at SDSU than across other San Diego universities?
The independent variable in the research question is the location of the universities, with SDSU being the specific location of interest. The dependent variable is the time it takes to find a parking spot.
The research question is seeking to compare the time it takes to find a parking spot at SDSU to the time it takes at other San Diego universities, with the location being the independent variable that may affect the dependent variable, which is the time taken to find a parking spot.
By identifying the independent and dependent variables in the research question, researchers can design a study that will collect data on these variables, analyze the data, and
draw conclusions about whether there is a significant difference in the time it takes to find a parking spot at SDSU compared to other universities in San Diego.
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Given the following equation, x^4 -4x^2+10x+13 use synthetic division and show if they are root or not.
Please show steps.
The remainder of the synthetic division of x^4 - 4x^2 + 10x + 13 is 33 which is a non-zero number, x - 2 is not a root of the polynomial.
What is the remainder of the synthetic division?The remainder of the synthetic division of x^4 - 4x^2 + 10x + 13 is obtained as follows:
Using the method of synthetic division x^4 - 4x^2 + 10x + 13 to divide by x - 2 using synthetic division:
2 | 1 0 -4 10 13
| 2 4 0 20
|--------------
| 1 2 0 10 33
The final remainder is 33.
Therefore, by synthetic division:
x^4 - 4x^2 + 10x + 13 = (x - 2)(x^3 + 2x^2 + 10) + 33
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Find the slope of a line perpendicular to the line whose equation is x + 6y = -24.
Fully simplify your answer.
Answer:
[tex]m_{perpendicular}[/tex] = 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x + 6y = - 24 ( subtract x from both sides )
6y = - x - 24 ( divide through by 6 )
y = - [tex]\frac{1}{6}[/tex] x - 4 ← in slope- intercept form
with slope m = - [tex]\frac{1}{6}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{6} }[/tex] = 6
Find two numbers with a sum of 3 and product of -40.
Answer:
8 and -5
Step-by-step explanation:
8 - 5 = 3
(-5) (8)=-40
Answer:
-8,+5
Step-by-step explanation:
-8+5 = 3
-8×+5 = -40
A quiz consists of 20 multiple-choice questions, each with 4 possible answers. for someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 60 %.
The probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.
To pass the quiz with a minimum passing grade of 60%, a person needs to answer at least 12 questions correctly out of the 20 total questions.
If a person is making random guesses for all of the answers, the probability of guessing one question correctly is 1/4, since there are 4 possible answers for each question. The probability of guessing one question incorrectly is 3/4.
Using the binomial probability formula, we can find the probability of passing the quiz by correctly guessing at least 12 questions:
P(X >= 12) = 1 - P(X < 12)
where X is the number of questions answered correctly.
P(X < 12) = sum of the probabilities of getting 0, 1, 2, ..., or 11 questions correct:
P(X < 12) = C(20,0)(1/4)⁰(3/4)²⁰ + C(20,1)(1/4)¹(3/4)¹⁹ + ... + C(20,11)(1/4)¹¹(3/4)⁹
where C(20,0), C(20,1), ..., C(20,11) are the binomial coefficients.
We can use a calculator or a computer to evaluate this sum of probabilities, or we can use a normal approximation to the binomial distribution if we assume that np = 20(1/4) = 5 and n x (1-p) = 20 x (3/4) = 15 are both greater than 10.
Using the normal approximation, we can find the mean and standard deviation of the binomial distribution:
mean = np = 20(1/4) = 5
Standard deviation = √(np(1-p)) = √(20*(1/4) x (3/4)) = √(15/2) = 1.94 (rounded to 2 decimal places)
Then, we can standardize the distribution by subtracting the mean and dividing by the standard deviation:
z = (12 - 5) / 1.94 = 3.61 (rounded to 2 decimal places)
Using a standard normal distribution table or a calculator, we can find the probability of getting a z-score greater than 3.61:
P(Z > 3.61) = 0.0002 (rounded to 4 decimal places)
Therefore, the probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.
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i-Ready
Dilations and Similarity-Quiz-Level H
Rays are shown from point D, the center of dilation, through the vertices of AABC.
Dilate ABC by a scale factor of 3.
A
1
C
D
B
1
Based on the information provided dilate triangle ABC by a scale factor of 3, with point D as the center of dilation.
To perform a dilation, each point in the original figure is transformed by multiplying its coordinates by the scale factor and then translating the figure according to the center of dilation. In this case, each point in triangle ABC will be multiplied by a scale factor of 3, with point D as the center of dilation.
To dilate the triangle by a scale factor of 3, you can follow these steps
Draw rays from point D to the vertices of triangle ABC.Measure the distance between each vertex and point D. This distance will be the radius of the dilation.Multiply the x-coordinate and y-coordinate of each vertex by 3, since the scale factor is 3.Use the measured distances as a guide to draw the dilated triangle, with each vertex located at the end of a ray from point D.Hence, if the scale factor is greater than 1, the dilated figure will be larger than the original. If the scale factor is between 0 and 1, the dilated figure will be smaller than the original. If the scale factor is negative, the figure will be reflected across the center of dilation.
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