Answer:
To solve the problem, we need to first determine the value of the quarters Anna has. Since there are 5 quarters, we have:
5 quarters = 5 x $0.25 = $1.25
Thus, Anna has $2.00 - $1.25 = $0.75 left. We can find the maximum number of dimes she can have by dividing this amount by the value of a dime, which is $0.10. Therefore:
$0.75 ÷ $0.10 = 7.5
Since Anna cannot have a fraction of a dime, we round down to the nearest whole number to get a maximum of 7 dimes. Therefore, the answer is option B, 5.
Clark and bruce went to taco hut for lunch. Clark bought 4 burriots and 5 tacos. Which cost him $13. Bruce bought 5 burritos and 3 tacos, which cost him $13. Determine how much a burriot cost at taco hut
A burrito costs $2 at Taco Hut. Let's use "b" to represent the cost of a burrito and "t" to represent the cost of a taco.
From the problem, we know that:
4b + 5t = 13 (for Clark)
5b + 3t = 13 (for Bruce)
We want to determine the cost of a burrito, so we can solve for "b" using the second equation:
[tex]5b + 3t = 13\\5b = 13 - 3\\b = (13 - 3t)/5[/tex]
Now we can substitute this expression for "b" into the first equation:
[tex]4b + 5t = 13\\4[(13 - 3t)/5] + 5t = 13\\52/5 - 12t/5 + 5t = 13\\52 - 12t + 25t = 65\\13t = 13\\t = 1[/tex]
So we know that a taco costs $1. Now we can substitute this value into either of the original equations to solve for "b":
[tex]5b + 3t = 13\\5b + 3(1) = 13\\5b = 10\\b = 2[/tex]
Therefore, a burrito costs $2 at Taco Hut.
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5) The graph of the equation y = −3x - 5 is shown below. What would happen to the graph if the slope was changed to 1?
Answer:
The equation y = -3x - 5 represents a linear function with a slope of -3 and a y-intercept of -5.
To understand what would happen to the graph if the slope was changed to 1, we need to compare the graphs of y = -3x - 5 and y = x - b, where b is some constant.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. So, when we change the slope of the equation y = -3x - 5 to 1, we get:
y = x - b
To find the value of b, we can substitute the coordinates of any point on the line. Let's use the y-intercept, which is -5:
-5 = 1(0) - b
b = -(-5)
b = 5
Therefore, the equation y = x - 5 represents the line with a slope of 1 and a y-intercept of 5.
To compare the graphs of y = -3x - 5 and y = x - 5, we can graph both equations on the same coordinate plane. Here's what the two graphs look like:
Graph of y = -3x - 5 (slope = -3, y-intercept = -5):
|
-5| x
| x
| x
| x
| x
| x
x---------------
-3 -2 -1 0 1 2 3
Graph of y = x - 5 (slope = 1, y-intercept = 5):
|
5| x
| x
| x
| x
| x
| x
x---------------
-5 -4 -3 -2 -1 0 1 2 3
As we can see, changing the slope of the equation from -3 to 1 rotates the line counterclockwise and makes it steeper. The y-intercept remains the same at -5.
a newsletter publisher believes that under 69% 69 % of their readers own a rolls royce. is there sufficient evidence at the 0.10 0.10 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69
A newsletter publisher believes that under 69% of their readers own a Rolls Royce.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.
Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.
Null Hypothesis (H0): p ≤ 0.69
Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.
Alternative Hypothesis (H1): p > 0.69
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Juan spent 10 minutes on his history homework and 3 minutes per question on his math homework. Which graph shows the total homework time, t, related to the number of math questions, q?
Discrete graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 5 to 40, on the vertical axis. Solid circles appear at points (0, 10), (1, 13), (2, 15), (3, 19), (4, 22), (5, 25), (6, 29), (7, 32), (8, 34).
Continuous graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 5 to 40, on the vertical axis. Solid circles appear at points (0, 10), (1, 13), (2, 15), (3, 19), (4, 22), (5, 25), (6, 29), (7, 32), (8, 34).
Discrete graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 3 to 24, on the vertical axis. Solid circles appear at points (0, 0), (1, 3), (2, 6), (3, 9), (4, 12), (5, 15), (6, 18), (7, 21), (8, 24).
Answer:Graph attached below. : Given : Juan spent 10 minutes on his history homework and 3 minutes per question on his math homeworkWe have to plot the graph that shows the total homework time, t, related to the number of math questions, q.Since, t denotes the total homework time taken by Juanand q denotes the number of math questions done by JuanThen we can represent the situation using a linear equation.Since he spent 10 minutes on his history homework and 3 minutes per question on his math homework.Then q questions take 3q timeand 10 minutes are fixed so, Total time is given by equation t = 10 + 3qAnd graph for the equation is attached below.
Step-by-step explanation:
Answer: Its A (the one all the way to the left)
explanation: Just guessed
Write a phrase in words for each algebraic
expression.
22. m+83_
23.42s
24. 9/d
25. t - 29
26. 2+g
27. 11x
28. h/12
29. 5- k
t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .
what is expression ?An expression in mathematics is a group of digits, variables, and operations that illustrates a mathematical connection or concept. Symbols, words, or a combination of both can be used to write expressions in a variety of ways. Expressions that are examples include: 3x + 4, 2y - 7z , (a + b) ,x2 + y2 = 2 5sin(x) + 3cos(x). Equations, inequalities, functions, formulae, and many other mathematical ideas can all be represented as expressions. Additionally, they can be altered or simplified using algebraic methods like factoring, combining like terms, and solving for a variable.
given
The sum of m and 83.
Forty-two times s.
Nine divided by d.
t decreased by 29.
Two more than g.
Eleven times x.
h divided by twelve.
Five minus k
t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .
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Which of the contexts below represents exponential growth?
A town's population shrinks at a rate of 8.1% every year.
A taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile.
A town's population grows at a rate of 4% every year.
A radioactive compound decays at a rate of 5% per hour.
The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The context that represents exponential growth is "A town's population grows at a rate of 4% every year."
Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.
As the population grows, the growth rate also increases, resulting in an exponential increase over time.
Let P(t) be the population of the town after t years, where t is a positive integer.
The exponential function that models the population growth is -
[tex]P(t) = P0 \times (1 + r)^t[/tex]
where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.
In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.
Therefore, the exponential function for the town's population growth is -
[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]
Simplifying the expression, we get -
[tex]P(t) = P0 \times 1.04^t[/tex]
This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.
In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).
Therefore, the exponential growth is displayed by town's population growing 4% every year.
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The table shows the ratios of black and white keys on pianos of various size
The ratio of black and white keys of piano give correct values of A, B, C as 9, 52, 130.
The ratio of black to white keys of Piano of different sizes are as follow,
Black A 36 63 90
White 13 B 91 C
From the table of black and white keys relation of proportionality is equal to,
( A / 13 ) = ( 36 / B ) = ( 63 / 91 ) = ( 90 / C )
This implies ,
( A / 13 ) = ( 63 / 91 )
⇒ A = ( 63 / 91 ) × 13
⇒ A = ( 9 / 13 ) × 13
⇒ A = 9
Similarly,
( 36 / B ) = ( 63 / 91 )
⇒ B = 36 × ( 91 / 63 )
⇒ B = 36 × ( 13 / 9 )
⇒ B = 52
And
( 63 / 91 ) = ( 90 / C )
⇒ C = 90 × ( 91 / 63 )
⇒ B = 90 × ( 13 / 9 )
⇒ B = 130
Therefore, the correct values of A , B, C using the ratio of black and white keys of the piano is equal to 9, 52, 130.
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The above question is incomplete, the complete question is:
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
The following shows a graph of y = x^2+ 5
Can we use this graph to find the solutions of 0 = c^2 + 5? Why or why not?
we can, now if we look at 0 = x² + 5, that's when the parabola y-value is 0, that is, what's "x" when y = 0? well, if we look at the graph, the graph never touches the x-axis, so that means the graph never has any "real roots", only complex ones or imaginary ones. We can tell because the graph never touches the x-axis.
Pls help answer with good detailed explanation
assume that 50 million households in the u.s. watched a particular show at 9:00 pm, and 90 million households had their television sets turned on at 9:00 p.m. calculate the share of audience.
The share of audience for the particular show at 9:00 pm is 55.56% for 50 million households.
We need to know the number of households that watched the programme and the total number of households with televisions on at 9:00 p.m. in order to determine the proportion of audience for that programme.
In this instance, it is stated that 90 million homes had their televisions on at 9:00 p.m. in addition to 50 million households watching the programme. Consequently, the following formula can be used to determine the show's viewership share:
Share of audience is calculated as follows: (Number of households that watched the programme / Total number of households with TVs on) x 100%
= 100% x (50 million / 90 million)
= 55.56%
As a result, 55.56% of the audience watched the specific show at 9:00 p.m. This indicates that the programme was viewed by more than half of the homes with on-air televisions at the time.
The share of audience is a crucial measurement in television ratings since it aids networks and advertisers in understanding how popular a show is and how far it might be able to reach the intended audience.
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Choose the statements that describe characteristics of a probability distribution? Select all that apply.
A. Half of the possible outcomes have associated probabilities grater than 0. 5.
B. The probability of an outcome is between 0 and 1.
C. The sum of the probabilities of all possible outcomes is 1.
D. The distribution is symmetrical.
E. The outcomes are mutually exclusive
B. The probability of an outcome is between 0 and 1. C. The sum of the probabilities of all possible outcomes is 1.
Option B is correct because probability values must be between 0 and 1.
Option C is correct because the sum of the probabilities of all possible outcomes must equal 1.
Option A is incorrect because it is not necessary for half of the possible outcomes to have probabilities greater than 0.5.
Option D is incorrect because the distribution does not have to be symmetrical.
Option E is incorrect because the outcomes can have common events and can be dependent.
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i need help on this math problem
Answer:
no the didn't hear the question
Answer:
I am pretty sure the answer is that the question can't be heard
Step-by-step explanation:
where is the water table in a swamp? group of answer choices well below the surface. at the surface. well above the surface. generally, 2 miles below the surface.
Generally, the water table in a swamp is located 2 miles below the surface.
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9. There are 8 black socks, 6 blue socks, and 14 white socks in a drawer. If one sock is randomly chosen from the
drawer, then what is the probability that the sock will not be blue?
The probability that the socks will not be blue would be =11/14.
How to calculate the probability of socks that are not blue in colour?Probability can be defined as the expression that shows the possibility of the occurrence of an event.
The formula that is used to calculate probability = the chosen events/total number of outcomes.
The total number of black socks = 8
The total number of blue socks = 6
The total number of white socks = 14
The total number of socks (outcomes) = 8+6+14 = 28
The socks that are not blue = 8+14 = 2
Therefore the probability that they socks won't be blue = 22/28 = 11/14.
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Of the following, which is NOT an immediate goal of treatment for individuals with anorexia nervosa?
helping them recover from malnourishment
helping them eat normally again
helping to make family changes within the dysfunctional system
helping them regain their lost weight
The answer is: "helping to make family changes within the dysfunctional system."
Step-by-step explanation:
While family-based therapies can be effective for treating anorexia nervosa, helping to make family changes within the dysfunctional system is not an immediate goal of treatment for individuals with anorexia nervosa.
The immediate goal of treatment for individuals with anorexia nervosa is to restore their physical health, which includes helping them recover from malnourishment, helping them eat normally again, and helping them regain their lost weight.
Once their physical health is stabilized, additional therapies may be recommended to address the psychological, emotional, and social factors that contribute to their eating disorder, which may include family-based therapies.
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Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one eighth to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(3.5, −5.25), B′(1.75, −1.75), C′(−3.5, 1.75), D′(−3.5, −3.5)
A′(3.2, −4.8), B′(1.6, −1.6), C′(−3.2, 1.6), D′(3.2, 3.2)
A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5)
A′(−12, 14), B′(−10, 10), C′(12, −14), D′(12, 12)
The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).
What is Dilation:In geometry, dilation is a transformation that changes the size of a figure but not its shape. It is a type of similarity transformation.
When a figure is dilated, each point of the figure moves away or towards the center of dilation by a certain scale factor.
Here we have
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one-eighth to create polygon A′B′C′D′.
To dilate polygon ABCD using a scale factor of one-eighth i.e 1/8 multiply the coordinates of each vertex by the scale factor of 1/8.
The coordinates of A are (-4, 6), multiply each coordinate by 1/8
A' = (-4/8, 6/8) = (-1/2, 3/4) = (-0.5, 0.75)
The coordinates of B are (-2, 2), multiplying each coordinate by 1/8
B' = (-2/8, 2/8) = (-1/4, 1/4) = (-0.25, 0.25)
The coordinates of C are (4, -2), multiplying each coordinate by 1/8
C' = (4/8, -2/8) = (1/2, -1/4) = (0.5, - 0.25)
The coordinates of D are (4, 4). Multiplying each coordinate by 1/8
D' = (4/8, 4/8) = (1/2, 1/2) = (0.5, 0.5)
Therefore,
The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).
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John's parents deposited $1000 into a savings account as a collage fund when he was born. How much will john have in this account after 18 years at a yearly simple interest rate of 3. 25%?
John's parents deposited 1000 into a savings account as a college fund when he was born. We need to find out how much John will have in this account after 18 years at a yearly simple interest rate of 3.25%.
We can use the formula for simple interest to solve this problem.
The formula for simple interest is:
I = PRT
Where,I = interest
P = principal (the initial amount of money)
R = rate of interest (as a decimal)
T = time (in years)
We are given that John's parents deposited 1000 when he was born. So, P = 1000. The interest rate is 3.25% per year, which is 0.0325 as a decimal. And we are given that the time is 18 years, so T = 18 years.Using the formula for simple interest, we can find the amount of interest earned:
I = PRTI = (1000)(0.0325)(18)I = 585
We can then add the interest earned to the principal to find the total amount of money in the account after 18 years:
A = P + IA = 1000 + 585A = 1585
Therefore, John will have 1585 in this account after 18 years at a yearly simple interest rate of 3.25%.
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which answer refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time? group of answer choices
The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.
Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.
Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.
Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.
Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.
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PLEASE HELP ME
A pizza shop surveyed a random group of customers to determine their favorite pizza topping. Out of 400 people, how many would you expect to say their favorite topping is sausage?
The percent that reported mushroom as their favorite from the pizza shop survey would be 10 %.
The percent that instead reported cheese or pepperoni as their favorite is 62.5 %.
Out of 400 people, the number that would say their favorite was sausage is 50 people .
How to find the number of people in the survey ?The percent that prefer mushroom would be:
= Number of those who chose mushroom / Number surveyed
= 8 ( 35 + 8 + 15 + 12 + 10 )
= 8 / 80
= 10 %
The percentage that instead chose cheese or pepperoni:
= ( 15 + 35 ) / ( 35 + 8 + 15 + 12 + 10 )
= 50 / 80
= 62.5 %
The number out of 400 that would be expected to choose sausage :
= 10 / ( 35 + 8 + 15 + 12 + 10 ) x 400
= 50 people
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How to elimination 18x-6y=-20 -9x+3y=15
The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10, which is a contradiction. This means that there is no solution to the system of equations.
What is an elimination?
To eliminate one of the variables, we need to manipulate one or both of the equations so that when we add them together, one of the variables is eliminated.
Let's start with the given equations:
18x - 6y = -20
-9x + 3y = 15
We can see that the coefficients of y in both equations are opposite, which means we can eliminate y by adding the two equations together. However, we need to make sure the coefficients of y have the same absolute value, so we'll multiply the second equation by 2:
18x - 6y = -20
-18x + 6y = 30
Now we can add the two equations together:
0x + 0y = 10
This equation simplifies to 0 = 10, which is a contradiction. This means that there is no solution to the system of equations. In other words, the two equations represent two parallel lines that never intersect.
Alternatively, we can recognize that the two equations represent the same line when simplified, since the second equation is simply half of the first equation. In this case, there are infinitely many solutions, since any point on the line satisfies both equations.
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Complete question is: The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10.
24÷4=6
24
÷
4
=
6
can be thought of as 24
24
broken into 4
4
groups of 6
6
each
The equation 24÷4=6 can be thought of as 24 broken into 4 groups of 6 each. This can be shown mathematically as follows: 24/4 = 6.
The division 24 ÷ 4 = 6 can be represented as 24 divided into 4 groups of 6 each. Therefore, each group contains 6 elements.
Another way to represent this division is by using a division box. In this case, 24 is the dividend, 4 is the divisor, and 6 is the quotient. Here's how to write it in the division box format:``` 6|24----4```The divisor is outside the division box, while the dividend is inside the division box. Then, we divide 24 by 4 to obtain 6. Therefore, 24 ÷ 4 = 6.
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how many ways are there to distribute five balls into three boxes if (c) the balls are unlabeled, but the boxes are labeled?
There are 243 ways to distribute five unlabeled balls into three labeled boxes.
Since the balls are unlabeled, we only need to consider the number of balls in each box, rather than which specific ball goes where.
We can use a combination approach to solve this problem. Let's think about distributing the balls one at a time. For the first ball, there are three boxes to choose from. For the second ball, there are also three boxes to choose from. We can continue this process until all five balls have been distributed.
So, for each ball, there are three choices of which box to put it in. Therefore, the total number of ways to distribute the five balls into the three labeled boxes is
3 x 3 x 3 x 3 x 3 = 3^5 = 243
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two positive whole numbers greater than 1 multiply to 576 and have no common factors other than 1. what is the sum of those two numbers?
Thus, the two positive whole numbers that are greater than one multiply to 576 and share only the number one in common is 5.
Explain about the positive whole numbers?One of the categories that mathematicians have created for numbers is titled whole numbers, and it contains all of the numbers from 0 to infinity.
The specific class or collection of numbers known as whole numbers includes:
Are all positive numbers with no fractional or decimal parts, including zero.Positive numbers with no decimal or fractional portions are referred to as whole numbers, including zero. They are numerical representations of whole, unbroken things. The set of whole numbers is mathematically represented by the numbers 0 through 9.Two positive whole numbers greater than 1 are 2 and 3.
2 and 3 does not have any common factor except 1.
sum of 2 and 3 = 5
Thus, the two positive whole integers that are greater than one multiply to 576 and share only the number one in common is 5.
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the angle below has a measure of 5.8 radians. determine the exact coordinates of the terminal point ( x , y ) .
Exact coordinates of the terminal point (x, y) are (-3.40, 4.71).
Let's dive deeper into the details below.
The angle below has a measure of 5.8 radians. The exact coordinates of the terminal point (x, y) can be determined by using trigonometry.
First, we must remember that the formula for the x-coordinate is x = r cos θ, where r is the length of the radius and θ is the measure of the angle. Therefore, we can calculate the x-coordinate by plugging in the radius (which is given) and the measure of the angle (5.8 radians) into the formula:
x = 5.8 cos (5.8) = 5.8 × -0.5806 = -3.40
Now, we must use the formula for the y-coordinate which is y = r sin θ. Plugging in the radius and the measure of the angle, we can calculate the y-coordinate:
y = 5.8 sin (5.8) = 5.8 × 0.8139 = 4.
Therefore, the exact coordinates of the terminal point (x, y) are (-3.40, 4.71).
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what is the probability of obtaining at least one tail when a coin is flipped six times? (enter the probability as a fraction.)
The radius of a circle is 3 miles. What is the circle's area?
Answer:
A≈28.27mi²
Step-by-step explanation:
[tex]A=\pi r^2[/tex]
[tex]\pi \times 3^2[/tex]
≈ 28.27433mi²
A≈28.27mi²
F(x)=l3xl+3
g(x)=-x+8x-5
Represent the interval where both functions are increasing on the number line provided
the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:
To find the interval where both functions F(x) and g(x) are increasing, we need to determine where the derivative of each function is positive. A function is increasing when its derivative is positive, which means that the function is becoming larger as x increases.
The derivative of F(x) can be found by applying the derivative rules for absolute value and addition, which gives us:
F'(x) = 3x/|x|
Now, we need to determine where F'(x) is positive. This occurs when either 3x is positive and |x| is positive, or when 3x is negative and |x| is negative. Therefore, F'(x) is positive for x > 0 and x < 0.
Next, we need to find the derivative of g(x) by applying the derivative rules for subtraction and multiplication, which gives us:
g'(x) = -1 + 8
Simplifying the expression, we get:
g'(x) = 7
Since g'(x) is a constant, it is always positive, which means that g(x) is increasing for all values of x.
To find the interval where both F(x) and g(x) are increasing, we need to identify where both F'(x) and g'(x) are positive. This occurs when x < 0, as this satisfies the condition for F'(x) being positive, and g'(x) is always positive.
Therefore, the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:
<=====o------------------------>
x<0 x>0
In this interval, both functions are increasing as x becomes more negative.
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the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm is:
The probability that the number of calls between 2:00 pm and 2:10 pm is exactly 200 is 0.000002204.
This can be calculated using the Poisson distribution. The Poisson distribution is used to model the probability of a given number of events occurring in a given time interval.
The Poisson equation is P(x) = (λ^x e^-λ)/x!
where λ is the expected number of occurrences per interval.
For this question, λ = 3/min, since the rate of calls to the computer software help desk is 3 per minute.
Plugging λ = 3/min into the Poisson equation, we get
P(x) = ((3/min)^200 e^-(3/min))/200!.
This simplifies to
P(x) = 0.000002204.
The probability of having exactly 200 phone calls to a computer software help desk in the 10-minute period from 2:00 pm to 2:10 pm is 0.000002204.
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PLS I HAVE TO TURN ALL OF THIS IN BY LIKE TONIGHT
Answer:
1. irrational
2. irrational
3. rational
4. rational
5. irrational
6. rational
Step-by-step explanation:
A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction.
1.) pi is a never ending number which means that, according to the definition above, it must be IRRATIONAL
2.) the line above the 46 means that it is repeating, making it IRRATIONAL
3.) the square root of 100 is 10, making it RATIONAL
4.) -16 is an integer (a whole number that can be positive, negative, or zero), making it RATIONAL
5.) the square root of 21 results in a long decimal that cannot be converted into a fraction, by the definition above, it is IRRATIONAL
6.) 10 is a whole number, making it RATIONAL
I have a square piece of card. I cut a triangle from each corner so that the remaining card is in the shape of a regular octagon. The perimeter of the regular octagon is 32cm. Work out length y
The required length of y representing the length of the cut piece from each corner of triangle to form regular octagon is equal to 2√2cm.
Let us consider the length of the side of the square card be x
Cut the corners of the triangle of length y cm.
Then as triangles at the corner are right angled triangle.
Using Pythagoras theorem we have,
Each side of the regular octagon is same as hypotenuse .
Hypotenuse = √y² + y²
⇒Hypotenuse = y√2
Length of each of regular octagon = y√2
Perimeter of the octagon = 8y√2
⇒8y√2 = 32
⇒ y = 4/√2
⇒ y = 2√2cm.
Therefore, the length of y with the given perimeter of the regular octagon is equal to 2√2cm.
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