It will take approximately 7.78 years for your salary at job A to exceed your salary at job B.
To solve this problem, we need to set up an equation. Let x represent the number of years that it will take for your salary at job A to exceed your salary at job B. We can use this equation to solve for x:
$46,000(1.05)^x > $55,000(1.02)^x
Now, let's simplify this equation to solve for x:
(1.05)^x > (1.02)^x * (55000/46000)
Taking the natural log of both sides of the equation:
xlog(1.05) > log(1.02) + log(55000/46000)
Solving for x:
x > [log(1.02) + log(55000/46000)]/log(1.05) ~ 7.78
It will take approximately 7.78 years for your salary at job A to exceed your salary at job B.
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You are flipping two coins. The probability of flipping two heads is 1/4. What is one way this can be calculated?
A. 1/2 subtracted from 1/2
B. 1/2 multiplied by 1/2
C. 1/2 divided by 1/2
D. 1/2 added to 1/2
Answer:
B. 1/2 multiplied by 1/2
Step-by-step explanation:
To find the probability, you would multiply. If you did not know this, you could solve each answer choice to find which one equals 1/4 since the problem already said the probability of flipping two heads is 1/4.
A. 1/2 - 1/2 = 0
B. 1/2 x 1/2 = 1/4
C. 1/2 / 1/2 = 1
D. 1/2 +1/2 = 1
The airline industry defines an on-time flight as one that arrives within 15 minutes of its scheduled time. The following table shows the number of on-time and late flights leaving New York and arriving in Miami between November 1 and December 31, 2018, by airlines: Airlines On-Time Late Total United 254 72 326 Delta 292 65 357 American 235 58 683 Total 781 195 a. What is the probability that a randomly selected flight was Delta and was late? b. What is the probability that a randomly selected flight was United or was on-time? c. Given the flight was late, what is the probability that it was from American? d. Given the flight was from Delta, what is the probability that it was late? e. Construct a probability tree for these probabilities.
a) The probability is $\frac{65}{357}$.
b) The probability is $\frac{781}{1000}$.
c) The probability is $\frac{58}{195}$.
d) The probability is $\frac{65}{357}$.
e) We can construct a probability tree for these probabilities. Below is the probability tree:probability tree for airlines. Therefore, the above figure is the probability tree for airlines.
The probability that a randomly selected flight was Delta and was late is $\frac{65}{357}$.Therefore, the probability is $\frac{65}{357}$.
The probability that a randomly selected flight was United or was on-time is $\frac{781}{1000}$.Therefore, the probability is $\frac{781}{1000}$.
Given the flight was late, the probability that it was from American is $\frac{58}{195}$.Therefore, the probability is $\frac{58}{195}$.
Given the flight was from Delta, the probability that it was late is $\frac{65}{357}$.Therefore, the probability is $\frac{65}{357}$.
We can construct a probability tree for these probabilities. Below is the probability tree:probability tree for airlines. Therefore, the above figure is the probability tree for airlines.
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In circle F with
�
∠
�
�
�
=
54
m∠EFG=54 and
�
�
=
19
EF=19 units, find the length of arc EG. Round to the nearest hundredth.
Answer:
forgot how to do this
Step-by-step explanation:
150√374 283727273737272727272
e population of Matteson in t years can be m What is the population of Matteson now?
Cannot be determined
The population of Matteson can be calculated using the given formula: m(t) = 11410 + 220t. However, the current population of Matteson is not given in the question, so it cannot be calculated using the given formula. Therefore, the population of Matteson now cannot be determined based on the given information.
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Rohana wants to find the volume of a sphere that has a radius of 10 feet. Which equation chan she use to solve for this value in cubic feet?
The equation change of volume of a sphere Rohana uses to solve for this value in cubic feet is V = (4/3)π(10)³ which gives the value 4,188.79 cubic feet.
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is a constant value approximately equal to 3.14159.
In this problem, the radius of the sphere is given as 10 feet. So, we can substitute this value into the formula to get the volume of the sphere as:
V = (4/3)π(10)³
Simplifying the right side, we get:
V = (4/3) × π × (1000)
V = (4/3) × 3.14159 × 1000
V = 4.18879 × 1000
V = 4,188.79 cubic feet
Therefore, the volume of the sphere with a radius of 10 feet is 4,188.79 cubic feet.
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match the equation with its graph
[tex]y=-\frac{2}{3} x+1[/tex]
identify the slope and the y-intercept
( i already did the first part i just need help finding the slope also the y intercept )
Answer:
slope is -2/3, and the y intercept is 1.
Step-by-step explanation:
Using y=Mx+b (slope intercept form), where M=slope, and B = Y intercept , you can find which valurs are which.
what is 4% of 1 million people?
Answer:
40000
Step-by-step explanation:
To find 4 percent of a number, multiply the number by 0.04. In this instance, 0.04 x 1000000 = 40000. Therefore, 4 percent of 1000000 is equal to 40000.
What is the volume of a spherical boulder is 10 ft in diameter and weighs almost 6 tons?
The volume of the spherical boulder is approximately 71.21 cubic feet.
To find the volume of a spherical boulder, we can use the formula for the volume of a sphere:
V = (4/3)πr³
where V is the volume and r is the radius of the sphere.
We are given that the diameter of the boulder is 10 feet, so the radius is half of that, or:
r = 10/2 = 5 feet
We are also given that the boulder weighs almost 6 tons. To convert this weight to pounds, we can multiply by 2000 (since 1 ton is equal to 2000 pounds):
6 tons * 2000 pounds/ton = 12,000 pounds
The weight of the boulder is related to its volume through its density. The density of a boulder will depend on its composition, but we can make an estimate based on common rock types. For example, granite has a density of about 2.7 grams per cubic centimeter, or 2.7 metric tons per cubic meter (since 1 metric ton is equal to 1000 kilograms). A boulder made of granite would therefore weigh about 2.7 times its volume in cubic meters.
Assuming the boulder is made of granite, we can find its volume by setting its weight equal to its volume times its density:
12,000 pounds = V * 2.7 metric tons/m³
To convert pounds to metric tons, we can divide by 2204.62 (since 1 metric ton is equal to 2204.62 pounds):
12,000 pounds / 2204.62 pounds/metric ton = 5.44 metric tons
Substituting this into the equation above, we get:
5.44 metric tons = V * 2.7 metric tons/m³
Dividing both sides by 2.7, we get:
V = 5.44 metric tons / 2.7 metric tons/m³ = 2.0148 m³
To convert this volume to cubic feet, we can use the conversion factor 1 cubic meter = 35.3147 cubic feet:
V = 2.0148 m³ * 35.3147 ft³/m³ = 71.21 ft³
Therefore, the volume of the spherical boulder is approximately 71.21 cubic feet.
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he j and k in the jk-ff (and jk-latch) are very much like the s and r in the sr-ff (and sr-latch), respectively. the j acts like the s and the k acts like the r. the only difference for these devices in 3701 is which of the following? group of answer choices j
The only difference for these devices in 3701 is that the jk-FF (or jk-latch) has an additional control input, which is the clock (CK). The CK input is used to enable and disable the device so that the inputs, j and k, do not always affect the output (Q) of the device.
The SR-FF (or SR-latch) has two inputs, S and R, which directly affect the output, Q. When S=1, the output is set to 1, and when R=1, the output is reset to 0.
On the other hand, the jk-FF (or jk-latch) has three inputs, J, K and CK. When CK is 0, the device is disabled and the outputs remain the same. When CK is 1, the J and K inputs can be used to either set (J=1, K=0) or reset (J=0, K=1) the output, Q.
In summary, the j and k in the jk-FF (or jk-latch) are similar to the s and r in the SR-FF (or SR-latch).
So, the only difference is the addition of a clock (CK) input in the jk-FF (or jk-latch). This clock (CK) input enables and disables the device, which allows the inputs, j and k, to affect the output (Q) of the device.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answer:
Please Mark as Brainliest
Step-by-step explanation:
Based on the information provided, the three true statements about Josiah's solution are:
"300 = x." - This statement is true because Josiah predicted that there were 300 rock songs on his MP3 player.
"He did not multiply the numerator and denominator by the correct number to equal 1,500." - This statement is true because in his proportion, Josiah multiplied the numerator and denominator by 30, which is not a multiple of 1,500.
"He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500." - This statement is true because to set up a proportion with 1,500 as the denominator, Josiah should have multiplied the numerator and denominator by a multiple of 1,500. In this case, 75 is a multiple of 1,500, so multiplying by 75 would have been the correct approach.
The original price of a laptop was £200.
The price of the laptop was reduced by 10% in sale.
A) work out 10% of the original price of the laptop.
B)work out the sale price of the laptop.
Answer:
A) £20
B) £180
Step-by-step explanation:
The original price is £200. The price was reduced by 10% so the sale price is 90% of the original price.
A) Price Reduction = 200 * 0.1 = £20
B) Sale Price = Original Price - Price Reduction = 200 - 20 = £180
Original Price * Percent Paid = 200 * 0.9 = £180
three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. demetria got a score of 85.1 ; this version has a mean of 61.1 and a standard deviation of 12 . vincent got a score of 299.2 ; this version has a mean of 264 and a standard deviation of 22 . tobias got a score of 7.26 ; this version has a mean of 7.1 and a standard deviation of 0.4 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
The best applicant to fill the only position available based on the test score is Vincent as he scored highest. The method for determining which applicant performed the best on the aptitude test is to use z-scores, which are measurements of how far from the mean a test score falls in standard deviation units.
Since the test is not on the same scale, it is impossible to compare raw test scores. What are Z-scores?A z-score, also known as a standard score, is a score that indicates the number of standard deviations from the mean a raw score is. In other words, a z-score tells you how far from the mean the score is in terms of standard deviations.
In other words, we can use the following formula to calculate the z-score for each person's test result.$$Z = \frac {x - \mu}{\sigma}$$where x is the test score, μ is the test mean, and σ is the standard deviation.The Z-scores for each of the candidates based on their test results are as follows: Demetria:$$Z = \frac {85.1 - 61.1}{12} = 2.00$$,Vincent:$$Z = \frac {299.2 - 264}{22} = 1.6$$,Tobias:$$Z = \frac {7.26 - 7.1}{0.4} = 0.4$$. From the calculations, Vincent has the highest z-score, indicating that he outperformed the other candidates. The candidate with the highest z-score is the best performer, thus Vincent is the best candidate for the job.
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A hose for a sprinkler system lies along one diagonal of a square garden. the exact length of the hose is25\sqrt{2} feet. what is the perimeter of the garden?
The perimeter of the square garden is 100 feet.
To find the perimeter of the square garden, first we need to determine the length of one side of the square. The given
information states that the hose, which lies along one diagonal of the garden, has a length of 25√2 feet.
Recall that the diagonal of a square divides it into two congruent right triangles, with the diagonal being the
hypotenuse.
Use the Pythagorean theorem to find the side length of the square. Let 'a' represent the side length of the square.
Then, we have:
a² + a² = (25√2)²
Simplify the equation:
2a² = 625 × 2
Divide both sides by 2:
a² = 625
Find the square root of both sides:
a = 25
Now that we know the side length of the square garden is 25 feet, we can calculate the perimeter.
The perimeter of a square is given by the formula:
Perimeter = 4 × side length
Substitute the side length:
Perimeter = 4 × 25
Calculate the perimeter:
Perimeter = 100
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The table below represents the number of NFL teams that won or lost their first game of the season. What is the probability that a team selected won their first game, given the team is from the AFC?
The prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.
What is Prοbability?Prοbability is a measure οf the likelihοοd οf an event οccurring, expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, and a prοbability οf 1 means the event is certain.
Out οf the tοtal number οf teams that wοn their first game, 12 are frοm the AFC and 6 are frοm the NFC. Out οf the tοtal number οf teams that lοst their first game, 4 are frοm the AFC and 10 are frοm the NFC.
Therefοre, the tοtal number οf AFC teams is 12 + 4 = 16, and the tοtal number οf NFC teams is 6 + 10 = 16.
If we randοmly select a team that wοn their first game, the prοbability that the team is frοm the AFC is:
P(AFC) = number οf AFC teams / tοtal number οf teams
= 16 / (16 + 16)
= 1/2
The prοbability that the team selected wοn their first game and is frοm the AFC is:
P(wοn first game AND AFC) = number οf AFC teams that wοn first game / tοtal number οf teams that wοn first game
= 12 / (12 + 6)
= 12/18
= 2/3
Therefοre, the prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.
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Assessment Practice 18. Data were collected from a random sample of 50 eighth-grade students. It was found that 15 eighth-grade students spent 2 hours each night on homework. If there are 280 eighth graders in the school, how many can you estimate spend 2 hours each night on homework?
We can estimate that 84 eighth graders in the school spend 2 hours each night on homework.We can use the proportion of students in the sample who spend 2 hours each night on homework to estimate the number of students in the school who spend the same amount of time on homework.
We are given that a random sample of 50 eighth-grade students was taken, and 15 of them spent 2 hours each night on homework. Therefore, the proportion of students in the sample who spend 2 hours each night on homework is:
15/50 = 0.3
We can use this proportion to estimate the number of eighth graders in the school who spend 2 hours each night on homework. If we assume that the sample is representative of the larger population, we can multiply the proportion by the total number of eighth graders in the school:
0.3 x 280 = 84
Therefore, we can estimate that 84 eighth graders in the school spend 2 hours each night on homework. It's important to note that this is just an estimate and the actual number may differ due to sampling variability.
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Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. f(x) = 6x3 + 7x2 + x + 5 The number of variations in sign in f(x) is 3 x. Therefore, the number of positive real zeros of f is either 3 or 0x. The number of variations in sign in f(-x) is 3 . Therefore, the number of negative real zeros of f is either 3 or 0x Need Help? Read It Watch It Talk to a Tutor Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. f(x) = 7x3 - 8x2 - 5x - 4 The number of variations in sign in f(x) is 1 Therefore, the number of positive real zeros of f is 0 The number of variations in sign in f(-x) is 2 . Therefore, the number of negative real zeros of f is either 2 or 0 Need Help? Read It Watch It Talk to a Tutor
The number of negative real zeros of f is either 3 or 0.
Using Descartes's Rule of Signs, the possible numbers of positive and negative zeros of the function f(x) = 6x3 + 7x2 + x + 5 can be determined. The number of variations in sign in f(x) is 3. This means that the number of positive real zeros of f is either 3 or 0. The number of variations in sign in f(-x) is 3. This means that the number of negative real zeros of f is either 3 or 0.
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Brian wants to exchange south African Rand for British pound. If R1 is worth 0. 075199 pound, how many pounds will he get for R2100 if he must pay an agent commission of 1. 5%
After deducting a commission of 1.5%, Brian will receive 155.71 pounds in exchange for R2100.
To find out how many pounds Brian will get, we first need to calculate the amount of commission he will pay. The commission is 1.5% of R2100, which is equal to 0.015 x R2100 = R31.50.
The amount of money he will actually receive in pounds is the remaining R2100 minus the commission, which is R2068.50. To convert this to pounds, we multiply by the exchange rate of R1 = 0.075199 pound:
2068.50 x 0.075199 = 155.706675 pounds
Therefore, Brian will get 155.71 pounds for R2100 after paying the agent commission.
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(Please answer quickly!!!)Simplify negative 4 and 1 over 4 minus 6 and 2 over 5.
negative 213 over 20
negative 43 over 20
negative 10 and one third
10 and 13 over 20
Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:
-17/4 * 5/5 = -85/20, 32/5 * 4/4 = 128/20, -85/20 - 128/20 = -213/20
what are fractions?A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers. The depiction of fractions appears easier than when decimal values are used.
A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To simplify:
-4 and 1/4 - 6 and 2/5
For the two mixed integers, we must identify a common denominator. The least frequent multiple of 4 and 5 is 20 since their prime components are 2 and 5. Both mixed numbers can be transformed into improper fractions with a denominator of 20 as follows:
-4 and 1/4 = -17/4
6 and 2/5 = 32/5
Now we can subtract these fractions:
-17/4 - 32/5
We must locate a common denominator in order to subtract fractions. Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:
-17/4 * 5/5 = -85/20
32/5 * 4/4 = 128/20
We can now take the two fractions apart:
-85/20 - 128/20 = -213/20
Therefore, -4 and 1/4 - 6 and 2/5 simplify to -213/20.
So, the answer is negative 213 over 20.
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Select the correct statement about the function represented by the table.
X
1
2
3
4
5
y
6
24
96
384
1536
A. It is an exponential function because the y-values increase by an
equal factor over equal intervals of x-values.
B. It is a linear function because the y-values increase by an equal
difference over equal intervals of x-values.
C. It is a linear function because the difference between each and
y value is constant.
D. It is an exponential function because the factor between each x- and y-value is constant
The true statement about the function is (a) It is an exponential function because the y-values increase by an equal factor over equal intervals of x-values
How to determine the true statement about the functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
In this table, each y-value is obtained by multiplying the previous y-value by 4.
This means that the function has a constant ratio or factor between each x- and y-value.
Such a pattern is typical of exponential functions, where equal intervals of x-values produce increasing or decreasing ratios of y-values.
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Find the volume of a right circular cone that has a height of 3. 5 ft and a base with a diameter of 11. 9 ft. Round your answer to the nearest tenth of a cubic foot
By dividing the diameter by 2, one may get the radius of the cone's base:[tex]r = d/2 = 11.9/2 = 5.95 ft[/tex] The volume of a cone is calculated as follows: V = (1/3)πr^2h Inputting the values provided yields.
[tex]V = (1/3)π(5.95^2)(35) (3.5) V equals 138.2 cubic feet[/tex]. Using tenths of a cubic foot increments, we obtain: V ≈ 138.2 ft^3 Hence, the right circular cone has a volume of around 138.2 cubic feet. some further data on the volume of the cone. The formula: can also be used to express a cone's volume in terms of its height and slant height. V is equal to (1/3)r2h plus (1/3)r2(h2 + r2). where the square root symbol is represented by. Since we already know the height and radius, we can use the Pythagorean theorem to get the slant height.
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Solve for vertex algebraically 3x^2+6x+7
Suppose demand d for a company's product at cost x is predicted by the function d(x) = 0. 36x2 + 810, and that the price p that the company can charge for the product is given by p(x) = x + 14. Find the company's revenue function
The revenue for a company's product is the amount of money the company earns from selling the product. R(x) = 0.36x^3 + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.
R(x) = 0.36x^3 + 824x
The revenue for a company's product is the amount of money the company earns from selling the product. To find the revenue function for a company, we can use the demand and price functions given. The demand function tells us how much of the product customers are willing to buy at a certain cost, while the price function tells us how much the company can charge for the product. R(x) = 0.36x^3 + 824x + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.
At x = 10,
R(10) = 0.36(10^3) + 824(10) + 824
R(10) = 3600 + 8240 + 824
R(10) = 17,664
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AB=A, B, equals
Round your answer to the nearest hundredth. A right triangle A B C. Angle A C B is a right angle. Angle B A C is forty degrees. Side A C is five. Side A B is unknown
The length of side AB in the right triangle ABC is approximately 3.21 units.
To find the length of side AB in the right triangle ABC, we can use trigonometric ratios.
Given:
Angle BAC = 40 degrees
Side AC = 5 units
Let's use the trigonometric ratio for the sine of angle BAC:
sin(BAC) = opposite/hypotenuse
sin(40°) = AB/AC
Rearranging the equation to solve for AB, we have:
AB = AC * sin(BAC)
Substituting the given values, we get:
AB = 5 * sin(40°)
Using a calculator to evaluate sin(40°), we find:
AB = 5 * 0.6428
≈ 3.21
Therefore, the length of side AB in the right triangle ABC is approximately 3.21 units.
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Mrs. Williams and her husband went to dinner in NYC last night. The total bill was $265 for the two of them. There was a 7% sales tax added to the bill. They decided to tip the waiter 15% on the bill after tax. How much tip did she leave?
The value of the tip she left is $42.53.
How much tip did she leave?Sales tax is a compulsory amount levied by the government on the sales price of a good or service. Sales price increase the cost of a good or service.
The first step is to determine the total bill after the sales tax has been included.
Total bill after sales tax = (1 + percent sales tax/100) x total bill
(1 + 7/100) x $265
(1 + 0.07) x $265
1.07 x $265
= $283.55
Now, multiply the total bill after sales tax by the percentage value of the tip.
Value of the tip = 15% x $283.55
0.15 x $283.55 = $42.53
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Find the distance between the two points rounding to the nearest tenth (if necessary). (-6 and -1) and (-9 and -6)
Step-by-step explanation:
Use the distance formula ( a modified Pyhtagorean theorem)
d^2 = (x1-x2)^2 + ( y1-y2)^2
d^2 = ( -6 - -9)^2 + ( -1 - -6)^2
d^2 = ( 3^2) + ( 5^2)
d^2 = 34
d = sqrt (34 ) =~ 5.8 units
Consider the equation z^16=(−1−i). Find the value of z which satisfies this equation and which has the second smallest positive argument θ, 0<θ<2π. Express your answer as z=re^iθ where r=______and theta=_________.
Consider the equation z^13=(−1+sqrt3i). Find the value of z which satisfies this equation and which has the second smallest positive argument θ,0<θ<2π. Express your answer as z=re^iθ where r=_________ and theta=__________
I have found the r values of both, I just need help finding theta. Show work so I can practice, please!
After considering and calculating, the modulus of z is r = [tex]2^{1/32}[/tex] and the argument of z is θ = 5π/32.
To solve this equation, we can first express −1−i in polar form as:
−1−i = √2cis(3π/4)
where cis(θ) = cos(θ) + i sin(θ) is the polar form of a complex number.
Now, we can express z in polar form as:
z = r cis(θ)
where r is the modulus of z and θ is its argument. Substituting this into the equation z¹⁶ = √2cis(3π/4), we get:
r¹⁶ cis(16θ) = √2cis(3π/4)
Taking the modulus of both sides, we get:
r¹⁶ = √2
Taking the argument of both sides, we get:
16θ = 3π/4 + 2kπ or 16θ = -3π/4 + 2kπ
where k is an integer. Solving for θ in the range 0 < θ < 2π, we find that the second smallest positive solution is:
θ = (3π/4 + 2π)/16 = 5π/32
Therefore, the value of z is:
z = r cis(θ) = [tex]\sqrt{2}^{1/16}[/tex] cis(5π/32)
We can simplify this as:
z = [tex]2^{1/32}[/tex]cis(5π/32)
So, the modulus of z is:
r = [tex]2^{1/32}[/tex]
And the argument of z is:
θ = 5π/32
Therefore, the answer is:
z = [tex]2^{1/32}[/tex] cis(5π/32)
So, the modulus of z is r = [tex]2^{1/32}[/tex] and the argument of z is θ = 5π/32.
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express in the form n:1
Answer:3/2
Step-by-step explanation:
[tex]\frac{9}{6} = \frac{\frac{9}{3} }{\frac{6}{3} }=\frac{3}{2}[/tex]
Pls help me answer this too <3
A race official needs to know how long it takes an average contestant to run an obstacle course. There are a total of 200 contestants. How can he find a reasonable estimate for the amount of time it takes to run the obstacle course?
time any contestant on the course and use that time
time himself on the course and use that time
time 2 contestants and average their times
time 20 contestants and average their times
Time 20 contestants and average their times is the best option to find a reasonable estimate for the amount of time it takes to run the obstacle course. Thus, option D is the correct answer.
A good estimate is an approximation amount of value that is based on analytical reasoning and data available. That estimation must be within a valid margin of error. It is not expected to be accurate, but it is expected to deliver a fair view of the value being estimated.
The official time for 20 contestants is a large sample size which is enough to provide a reasonable estimate of the meantime for all 200 contestants. The actual can average the times for the 20 contestants to calculate the average time for the whole group.
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Click the icon to view the table. a. Find the probability of getting exactly 1 girl in 8 births. _________ (Type an integer or a decimal. Do not round.) b. Find the probability of getting 1 or fewer girls in 8 births. _________ (Type an integer or a decimal. Do not round.) c. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part (a) or part (b)? A. Since getting 0 girls is an even lower number of girls than getting 1 girl, the result from part (b) is the relevant probability. B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability. C. Since the probability of getting 1 girl is the result from part (a), this is the relevant probability. D. Since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (a) is the relevant probability. d. Is 1 a significantly low number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event. A. Yes, since the appropriate probability is greater than 0.05, it is a significantly low number. B. No, since the appropriate probability is greater than 0.05, it is not a significantly low number. C. No, since the appropriate probability is less than 0.05, it is not a significantly low number. D. Yes, since the appropriate probability is less than 0.05, it is a significantly low number.
a. The probability of getting exactly 1 girl in 8 births is given as follows: 0.0313 = 3.13%.
b. The probability of getting 1 or fewer girls in 8 births is given as follows: 0.0352 = 3.52%.
c. The relevant probability for significantly low is given as follows: B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.
d. The correct option regarding whether the probability is significantly low is: D. Yes, since the appropriate probability is less than 0.05, it is a significantly low number.
What is the binomial distribution formula?The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The mass probability formula is given as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single independent trial of the experiment.The relevant probabilities for this problem are given as follows:
P(X = 0) = 0.5^8 = 0.0039.P(X = 1) = 8 x 0.5^8 = 0.0313.Hence the probability of 1 or fewer, used to verify if the event is significantly low, is:
P(X <= 1) = P(X = 0) + P(X = 1)
P(X <= 1) = 0.0352.
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What is the perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6)?
The perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6) is given as follows:
31.04 units.
How to calculate the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The vertices of the polygon in this problem are given as follows:
D(-4, 5), E(-4, -6) and F(3, -6).
Hence the side lengths are given as follows:
DE = 11 units -> x constant, subtract y.DF = sqrt((-4 - 3)² + (5 - (-6))²) = 13.04 units.EF = 7 units, y constant, subtract x.Hence the perimeter of the polygon is given as follows:
11 + 13.04 + 7 = 31.04 units.
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