The ordered pairs for the equation is ( 0 , 0.5 ) and ( 1 , 0 )
Given data ,
Let the equation be represented as A
Now , the value of A is
-3x - 6y = -3
To generate two ordered pairs by substituting zero for x and y, we can substitute x = 0 and y = 0 into the given equation -3x - 6y = -3 and solve for y.
For x = 0:
-3(0) - 6y = -3
0 - 6y = -3
-6y = -3
y = -3 / -6
y = 0.5
So the first ordered pair is (0, 0.5)
For y = 0:
-3x - 6(0) = -3
-3x - 0 = -3
-3x = -3
x = -3 / -3
x = 1
So the second ordered pair is (1, 0)
The rate of change is the change in y-coordinate divided by the change in x-coordinate.
In this case, as we move from the first ordered pair (0, 0.5) to the second ordered pair (1, 0), the change in y-coordinate is -0.5 and the change in x-coordinate is 1.
Therefore, the rate of change is -0.5 / 1 = -0.5.
Hence , the ordered pairs are ( 0 , 0.5 ) and ( 1 , 0 )
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why is the domain of sin^-1(x) and cos^-1(x) are different while the domain of sin(x) and cos(x) are the same?
The domain of sin^-1(x) and cos^-1(x) are different while the domain of sin(x) and cos(x) are the same is due to the inverse properties and the range of their respective functions.
The domain of sin(x) and cos(x) are the same because both are trigonometric functions that can accept any real number as input, meaning their domain is all real numbers (-∞, ∞).However, when we consider their inverse functions, sin^-1(x) and cos^-1(x), we need to restrict their domain to ensure that these inverse functions are well-defined and unique. The range of sin(x) is between -1 and 1, so the domain of sin^-1(x) is restricted to the interval [-1, 1]. Similarly, the range of cos(x) is also between -1 and 1, but its behavior is different from sin(x), so the domain of cos^-1(x) is also restricted to the interval [-1, 1].Know more about the domain
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the picture is below I NEED HELP FAST IT'S DUE TOMMOROW
Answer:
I would say -F=0.4
Step-by-step explanation:
if F=-0.4 and -F is the opposite of F then the opposite of -0.4 is 0.4
Linear function K passes through points (-3, 7) and (3, 3). What is the rate of change of function K?
A -3/2
B-2/3
C 3/2
D 2/3
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{3 +3} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}[/tex]
pls help me im rlly bad at math 819 divided by 63
Answer: 13
Step-by-step explanation: take 63 out of 819 and see how many times you can take it that out
Answer: It's 13, hop this helps!!!
If the point representing 64 wins and attendance of 40,786 people per game is removed from the set of data and a new regression analysis is conducted, how would the following be impacted? explain your reasoning. (i) the slope of the least-squares line: (ii) the correlation coefficient:
Removing the point (64, 40,786) from the dataset and conducting a new regression analysis may impact the slope of the least-squares line and the correlation coefficient, depending on whether the point is an outlier or follows the overall trend of the data.
If the point representing 64 wins and attendance of 40,786 people per game is removed from the set of data and a new regression analysis is conducted, the following would be impacted:
(i) The slope of the least-squares line would be impacted. This is because the slope of the line is calculated based on the data points and removing a point from the dataset would change the overall trend of the data. The slope would be recalculated based on the remaining data points, and it would be different from the original slope.
(ii) The correlation coefficient would also be impacted. The correlation coefficient measures the strength and direction of the linear relationship between two variables. Removing a point from the dataset would change the overall pattern of the data, which would in turn affect the correlation coefficient. The new coefficient would reflect the revised relationship between the remaining data points.
Let's consider how the removal of the point representing 64 wins and an attendance of 40,786 people per game would impact the regression analysis.
(i) The slope of the least-squares line:
When you remove a point from a dataset, it may cause the least-squares line to change. If the point is an outlier or significantly different from the other points in the dataset, it may have a substantial impact on the slope. If the point is close to the overall trend of the data, its removal might not affect the slope as much. In this case, if the point (64, 40,786) is an outlier, removing it could cause the slope of the least-squares line to change. If it is not an outlier, the change in slope may be minimal.
(ii) The correlation coefficient:
The correlation coefficient measures the strength and direction of the relationship between two variables. If the removed point is an outlier, its removal can impact the correlation coefficient. If the point is closely following the overall trend of the data, removing it might not have a significant effect on the correlation coefficient. In this case, if the point (64, 40,786) is an outlier, removing it could cause the correlation coefficient to increase or decrease in magnitude, depending on how it deviates from the trend. If it is not an outlier, the change in the correlation coefficient may be minimal.
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How many solutions are possible?
y = 5x + 3
2y = 10x + 6
O one
O two
O No
O infinite
Answer:
infinite number of solutions
Step-by-step explanation:
y = 5x + 3 → (1)
2y = 10x + 6 → (2)
substitute y = 5x + 3 into (2)
2(5x + 3) = 10x + 6
10x + 6 = 10x + 6
since both sides are the same then any value of x will make the equation true.
This means there are an infinite number of solutions to the system
Answer:
Step-by-step explanation: there are infinite solutions
Piper cut the corner off a piece of wood to use for a project. What is the area, in square feet, of the piece of wood that is left? 5 ft 8 ft 2.5 ft 2.5 ft .
Answer:
5(8) - (.5)(2.5)(2.5) = 40 - 3.125
= 36.875 square feet
PART 1
John is saving money to buy a car. He takes $8,000 to the bank and opens an annual CD upon which the bank agrees to pay him 2% interest.
Principal = 8000
Term = 1 year
APR = 2% = 0.02
8000 x 0.02 = $160
8000 + 160 = $8,160
Beginning Balance
2% Interest
Ending Balance
$8,000.00
$160
$8,160
After one year, Michael earned $160 in interest on his initial deposit of $8,000, so his balance is now $8,160.
Calculate the Annual interest below (first image):
PART B:
Now, let’s say John leaves his money in the bank for four years. The term of the annual CD is four years, so he will be earning 2% interest per year for four years. Since this is an annual CD, interest will be added to the principal at the end of every year. This is called annual compounding. Complete the following table (2nd Image), filling in the cells for years 5 through 10.
John will earn an annual interest of $500 on a beginning balance of $10,000 at a rate of 5% per year. After one year, the ending balance will be $10,500. John earned $160 in interest after leaving his initial deposit of $8,000 in the bank for first year with annual compounding at a 2% interest rate. His ending balance was $8,160. The table shows his ending balance for years 5-10.
We can use the formula for simple interest to calculate the annual interest earned by John on a balance of $10,000 at a rate of 5% per year
Annual interest = (Principal x Rate x Time) / 100
where Principal is the beginning balance, Rate is the interest rate, and Time is the duration of investment in years.
Substituting the given values, we get
Annual interest = (10000 x 5 x 1) / 100 = $500
Therefore, the annual interest earned by John on a balance of $10,000 at a rate of 5% per year is $500.
Ending balance after one year = Beginning balance + Annual interest = $10,000 + $500 = $10,500.
since the term of the annual CD is four years, and John will leave his money in the bank for four years, we can calculate the ending balance at the end of each year using the formula above.
For year 5
P = $8,160
r = 0.02
n = 1
t = 1
A = $8,160 (1 + 0.02/1)^(1x1) = $8,324.80
For year 6
P = $8,324.80
r = 0.02
n = 1
t = 1
A = $8,324.80 (1 + 0.02/1)^(1x1) = $8,492.78
For year 7
P = $8,492.78
r = 0.02
n = 1
t = 1
A = $8,492.78 (1 + 0.02/1)^(1x1) = $8,664.28
For year 8
P = $8,664.28
r = 0.02
n = 1
t = 1
A = $8,664.28 (1 + 0.02/1)^(1x1) = $8,839.44
For year 9
P = $8,839.44
r = 0.02
n = 1
t = 1
A = $8,839.44 (1 + 0.02/1)^(1x1) = $9,018.34
For year 10
P = $9,018.34
r = 0.02
n = 1
t = 1
A = $9,018.34 (1 + 0.02/1)^(1x1) = $9,201.05
Therefore, the table for years 5 through 10 would look like
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2.5 kg of onions and 2 kg of carrots cost a total of £2.36
3 kg of carrots cost £1.74
Stuart has £2
He wants to buy 4kg of onions.
Does Stuart have enough money to buy 4kg of onions?
You must show how you get your answer.
The cost of 4 kilograms is £1.10, so Stuart has enough to buy it.
Does Stuart have enough money to buy 4kg of onions?We can define the variables:
x = cost of a kg of onions.
y = cost of a kg of carrots.
We can write the system of equations.
2.5x + 2y = 2.36
3y = 1.74
Solving the second one we get:
y = 1.74/3 = 0.58
We can replace that in the other equation to get:
2.5x + 2*0.58 = 2.36
2.5x = 2.36 - 2*0.58
x = 0.6844/2.5 =0.274
Then the cost of 4 kg of onions is:
C = £0.274*4 = £1.10
And Stuart has 2 pounds, so he has enough.
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A date in the month of October and a letter of the alphabet are chosen at random. How many outcomes are possible?
Could someone help with this question??
Answer:
(i) [tex]B^c =[/tex] {1, 4, 6, 8}
(ii) A - (B - C) = {4, 6, 8}
(iii) A ∩ (B ∪ C) = {2, 3, 5, 7}
Step-by-step explanation:
We have the following sets
Universal set U = {x ∈ N, x ≤ 8}
This would all the numbers from 1 to 8 inclusive
U = {1, 2, 3, 4, 5, 6, 7, 8}
Set A = {x : 1 < x² < 65}
This would be all the numbers from U such that the square of those numbers lies between 1 and 65
Thus
A = {2, 3, 4, 5, 6, 7 ,8}
We exclude 1 because 1² = 1 is not included in the set definition
Highest is 8 because 8² = 64 < 65 and also 8 is the highest element in the set U
B = (x ∈ N: x is a prime number less than 10}
B = {2, 3, 5, 7 } these being the prime numbers less than 10
C = {x: x³ + 1 = 0, x ∈N}
if x³ + 1 = 0 ==> x³ = -1 and there is only one value of x that satisfies this relationship and that is x = -1 since (-1)³ = -1 and (-1)³ + 1 = 0
Now that we have enumerated the elements of all 4 sets we can solve the questions
(i) [tex]B^c[/tex] is the complement of set B = set of all elements not in set B
This would be the set of all numbers from 1 through 8 that are not prime
[tex]B^c[/tex] ={x: x is not a prime number and ≤ 8}
= {1, 4, 6, 8}
(ii) A - (B - C)
B - C is the set difference between B and C
It is the set of all elements in B that are not in C
Since B = {2, 3, 5, 7} and C = {-1} no element of B appears in C so
B - C = B = {2, 3, 5, 7}
A - (B - C) = A - B
{2, 3, 4, 5, 6, 7 ,8} - {2, 3, 5, 7} = {4, 6, 8}
(iii) A ∩ ( B ∪ C)
B ∪ C = {2, 3, 5, 7} ∪ {-1} = {-1, 2, 3, 5, 7}
A ∩ (B ∪ C) = {2, 3, 4, 5, 6, 7 ,8} ∩ {-1, 2, 3, 5, 7}
= {2, 3, 5, 7}
= B
I hope I got it right :)
A 26-volume encyclopedia is placed on a bookshelf in numerical order. Each volume is 3 inches thick, including the front and back covers. Each cover is 1 4 inch thick. The volumes are placed on the shelf so that the front cover is on the right side of each volume and the back cover is on the left side of each volume. A bookworm eats straight through the encyclopedia, beginning inside the front cover of the first volume and ending after eating through the back cover of the last volume. How many inches of book did the bookworm eat?
Answer:
The encyclopedia has 26 volumes, each 3 inches thick. Since each volume has a front and back cover that is 1/4 inch thick, the actual pages in each volume are 3 - 1/4 - 1/4 = 2 1/2 inches thick.
To find the total thickness of all the pages in the encyclopedia, we can multiply the thickness of one volume by the number of volumes:
Total thickness of pages = 2 1/2 inches/volume x 26 volumes = 65 inches
Since the bookworm ate through the front cover of the first volume and the back cover of the last volume, it did not eat through 2 1/2 inches of pages for those volumes. Therefore, the bookworm ate through:
65 inches - 2 1/2 inches - 2 1/2 inches = 60 inches
So the bookworm ate through 60 inches of book.
at a bus station buses begin their routes at 7:30 am the schedule of the buses is based on time intervals listed below.what is the next time bus a and bus b will leave the bus station at the same time
Answer:
To determine when Bus A and Bus B will leave the station at the same time, we need to find the least common multiple (LCM) of their time intervals.
The time intervals for Bus A and Bus B are:
Bus A leaves every 45 minutes (i.e. intervals of 45 minutes)
Bus B leaves every 60 minutes (i.e. intervals of 60 minutes)
To find the LCM of 45 and 60, we can first factor each number into its prime factors:
45 = 3 x 3 x 5
60 = 2 x 2 x 3 x 5
The LCM is the product of the highest power of each prime factor, so:
LCM(45, 60) = 2 x 2 x 3 x 3 x 5 = 180
Therefore, Bus A and Bus B will leave the station at the same time every 180 minutes, or every 3 hours.
Since the buses begin their routes at 7:30 am, we can add multiples of 3 hours to this time to find when Bus A and Bus B will leave together.
The first time after 7:30 am when Bus A and Bus B leave together is:
7:30 am + 3 hours = 10:30 am
So Bus A and Bus B will leave the station together at 10:30 am, and then every 3 hours after that.
What is the total volume of Mountain Dew in this six pack? Each can is 5 inches tall and has a diameter of 3 inches.
The total volume of Mountain Dew in this six-pack is approximately 212.058 cubic inches.
Assuming that each can in the six-pack of Mountain Dew is cylindrical in shape, we can use the formula for the volume of a cylinder to calculate the volume of each can, and then multiply that by the total number of cans in the pack.
The formula for the volume of a cylinder will be;
V = πr²h
where V is volume, r is radius (half the diameter), and h is height.
The radius of each can is 1.5 inches (half of 3 inches), and the height is 5 inches. So the volume of each can is;
V = π(1.5)²(5) = 35.343 cubic inches
To find the total volume of the six-pack, we need to multiply this by the number of cans;
Total volume = 35.343 cubic inches/can × 6 cans
= 212.058 cubic inches
Therefore, the total volume is 212.058 cubic inches.
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What is the slope of the linear relationship shown on the graph?
Answer:
Step-by-step explanation:
Li is a professional nature photographer. She takes a photograph of a spider web and prints a copy. The original dimensions of her copy are 6 inches by 4 inches. Li decides to advertise her business by printing smaller copies of the spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of the original printed photograph?
A.1.5 inches by 1 inch
B.2 inches by 1 inch
C.1 inch by 0.5 inches
D. 12 inches by 8 inches
Let R(s, t) = F(u(s, t), v(s, t)), and assume the following are true.
u(1, 0) = 2
us(1, 0) = −2
ut(1, 0) = 6
v(1, 0) = 3
vs(1, 0) = 5
vt(1, 0) = 4
Fu(2, 3) = −1
Fv(2, 3) = 10
Find the values below.
Rs(1, 0) =
Rt(1, 0) =
Answer:
To find Rs(1,0) and Rt(1,0), we need to use the chain rule of partial differentiation.
Rs(1,0) can be found by computing the partial derivative of R with respect to s, while holding t constant and then evaluating the result at (1,0). Similarly, Rt(1,0) can be found by computing the partial derivative of R with respect to t, while holding s constant and then evaluating the result at (1,0).
Using the chain rule, we have:
Rs = Fu * us + Fv * vs
Rt = Fu * ut + Fv * vt
We are given the values of u, v, us, ut, vs, vt, Fu, and Fv at the point (1,0) and the values of u and v at the point (2,3). We can use these values to compute Rs(1,0) and Rt(1,0) as follows:
Rs(1,0) = Fu(2,3) * us(1,0) + Fv(2,3) * vs(1,0)
= (-1) * (-2) + (10) * (5)
= 52
Rt(1,0) = Fu(2,3) * ut(1,0) + Fv(2,3) * vt(1,0)
= (-1) * (6) + (10) * (4)
= 34
Therefore, Rs(1,0) = 52 and Rt(1,0) = 34
The area of a rectangular field is 4235 m2. If the width of the field is 55m, what is the length?
Answer:
The length of the rectangular field is 77 meters.
Step-by-step explanation:
We can use the formula for the area of a rectangle to solve this problem:
Area = length x width
We are given that the area is 4235 m² and the width is 55 m. We can substitute these values into the formula and solve for the length:
4235 = length x 55
To isolate the variable "length" on one side of the equation, we can divide both sides by 55:
4235/55 = length
Simplifying the right side gives:
77 = length
I NEED HELP!! what is going on with this problem???? A point in the figure below is chosen at random. Find the probability that the point lies in the region. Give answer as a percent.
The probability that the point lies in the region is 21.5%
How to determine the probabilityNote that percentage is the ratio of a number and 100.
From the information given, we have that;
The total area of the figure = 22(22 ×2)
expand the bracket
Total area = 22(44)
Total area = 968 units square
Area of the shaded area is expressed as;
= Total area - 2area of a circle
substitute the values
= 968 - 2πr/2²
=968 - 2(3.14 × 11²)
find the square
= 968 - 759. 88
= 208. 12 units square
The probability is;
Area of shaded are/total area × 100/1
208. 12/968 × 100/1
21. 5%
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each digit shown below to create a 5-digit number with the greatest value and a
5-digit number with the least value. Each digit can only be used once in each number. Ther
write a number sentence using >,<, or = to compare the two numbers you created.
2, 9, 1, 3, 8
Answer:
6 ft 9.5 ft 6 ft 8.5 ft Which measurement is closest to the area of the desk in square feet?
The measurement that is closest to the area of the given desk would be = 103.26ft²
How to calculate the area of the desk?To calculate the area of the desk is to determine both the area of a trapezium and a quarter circle and add up the areas derived.
The formula of the area of trapezium = ½(a+b)h
where;
a = 9.5ft
b = 9.5+6 = 15.5
h = 6ft
area =½(9.5+15.5 )×6
= 25/2×6
= 75ft²
The area of quarter circle = πr²/4
r = 6ft
area = 3.14×36/4
= 3.14× 9
= 28.26ft²
Therefore the area of the shape;
= 75+28.26 = 103.26ft²
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Harry goes to Hogwarts School of Witchcraft and Wizardry. He can travel to school and back in
3
33 different ways: by the Hogwarts Express, a flying car, or the Knight Bus. He's decided to choose his methods of transportation to and from Hogwarts at random this year.
Which of these tables lists all the different ways Harry can get to Hogwarts and back? (Each row represents one outcome.)
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Table A
A
Table A
(Choice B) Table B
B
Table B
Table A:
To Hogwarts From Hogwarts
Knight Bus Knight Bus
Knight Bus Flying Car
Knight Bus Hogwarts Express
Flying Car Knight Bus
Flying Car Flying Car
Flying Car Hogwarts Express
Hogwarts Express Knight Bus
Hogwarts Express Flying Car
Hogwarts Express Hogwarts Express
Table B:
To Hogwarts From Hogwarts
Knight Bus Hogwarts Express
Flying Car Flying Car
Hogwarts Express Knight Bus
Knight Bus Knight Bus
Flying Car Hogwarts Express
Hogwarts Express Flying Car
Knight Bus Flying Car
Flying Car Knight Bus
Hogwarts Express Hogwarts Express
Table B lists all the different ways Harry can get to Hogwarts and back. See the attached tables.
What explanation justifies the above?One mus tnote that both tables detail all of the alternative routes Harry can take to and from Hogwarts, however Table B is the only one that lists all of the different modes of transportation.
Table B includes all of the potential scenarios in which Harry can use the Knight Bus, Flying Car, or Hogwarts Express to and from Hogwarts, including situations in which he uses the same form of transportation both times. Table A, on the other hand, simply covers transit combinations, not all conceivable outcomes. So it is correct to state that as a result, Table B is the right solution.
See attached tables.
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Twenty students volunteered to take a fitness test. We want to know if there is a convincing evidence of a positive linear relationship between speed (mph) and jump height. What is the p value of this test
Twenty students volunteered to take a fitness test. If there is a convincing evidence of a positive linear relationship between speed (mph) and jump height.
To find the p-value for this test, we need to perform a hypothesis test. Let's assume that the null hypothesis is that there is no relationship between speed and jump height (i.e., the slope of the regression line is zero), and the alternative hypothesis is that there is a positive linear relationship between speed and jump height (i.e., the slope of the regression line is positive).
We can use a simple linear regression model to test this hypothesis. Let x be the speed (in mph) and y be the jump height (in inches). We can fit a linear regression model to the data and obtain the estimated slope and intercept of the regression line, denoted by b1 and b0, respectively. We can also compute the standard error of the slope, denoted by SE(b1), and the t-statistic for testing the null hypothesis, given by
t = b1 / SE(b1)
Under the null hypothesis, this t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size (in this case, n=20).
To find the p-value for this test, we need to calculate the probability of observing a t-statistic as extreme as the one we computed, assuming that the null hypothesis is true. We can use a t-distribution table or a statistical software package to obtain this probability.
Assuming that the null hypothesis is true, if the p-value is less than the significance level (e.g., 0.05), we reject the null hypothesis and conclude that there is convincing evidence of a positive linear relationship between speed and jump height.
Hence, we cannot provide an exact p-value without knowing the specific data values and the results of the regression analysis.
The given question is incomplete.
The complete question is "Twenty students volunteered to take a fitness test. The computer output below is a regression analysis of the relationship between x = how fast they can ran a mile (in mph) and y = how high they can jump (in inches).
(1) We want to know if there is convincing evidence of a positive linear relationship between speed (mph) and jump height (in) for students like these. What is the P-value of this test?"
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pls help due soon if your right ill mark you brainliest asap
Answer:
D
Step-by-step explanation:
pls aswerrr
worth 30 pointsss
Answer:
divide d by 1
6.7÷1 so it will be the answer
a 41 gram sample of a substance that's used to detect explosives has a k value of 0.1392 find the substance's half life in days round your answer to the nearest tenth
If, 41 gram sample of a substance that's used to detect explosives has a k value of 0.1392 then, the substance's half-life is approximately 4.98 days.
Half-life is the time it takes for half of the atoms in a radioactive substance to decay. It is a characteristic property of a specific radioactive substance and is independent of its amount or condition.
The half-life formula is given by;
[tex]t_{1/2}[/tex] = (ln 2) / k
where k is the decay constant.
Given k = 0.1392, we can find the half-life as follows;
[tex]t_{1/2}[/tex] = (ln 2) / k
[tex]t_{1/2}[/tex] = (0.693) / 0.1392
[tex]t_{1/2}[/tex] = 4.978 days
Therefore, the half-life of the substance's will be 4.98 days.
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a) Express √√√3+ √12 in the form a√3 where a is an integer. √3 b) (i) Express 1 (5) in the form b√3 where b is an integer. 1 (ii) Express (5) 3 in the form 3 C where c is an integer. √√3 √3
Answer & Step-by-step explanation:
a)
√√√3 + √12
= √√(3)^(1/2) + √(4 x 3)
= √√(√3)^2 + √(4 x √3)^2
= √(√3 + 2√3)
= √3(1 + 2)
= 3√3
Therefore, √√√3 + √12 can be expressed in the form of a√3, where a = 3.
b)
(i)
1 + √(3)
To rationalize the denominator, we multiply the numerator and denominator by √3:
= 1 + √(3) * √(3) / √(3)
= 1 + √(9) / √(3)
= 1 + 3√(3) / 3
= (3 + √(3)) / 3
Therefore, 1 + √(3) can be expressed in the form of b√3, where b = (3 + √3) / 3.
(ii)
(5)^(1/3)
To rationalize the denominator, we multiply the numerator and denominator by √(3):
= (5)^(1/3) * √(3) / √(3)
= (5√(3)) / √(27)
= (5√3) / (3√3)
= (5/3)√3
Therefore, (5)^(1/3) can be expressed in the form of c√3, where c = 5/3.
The circle graph describes the distribution of preferred transportation methods from a sample of 300 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Bus is the preferred transportation for 25 residents.
Bicycle is the preferred transportation for 48 residents.
Together, Streetcar and Cable Car are the preferred transportation for 42 residents.
Together, Walk and Streetcar are the preferred transportation for 165 residents.
The correct conclusion we can draw from the circle graph is an option (D) "Together, Walk and Streetcar are the preferred transportation for 165 residents."
As per the information provided, it is given that:
Bicycle is the preferred transportation for 8% of 300 residents, which is 0.08 x 300 = 24 residents.
Therefore, option (B) "Bicycle is the preferred transportation for 48 residents" is not correct, as it represents twice the actual number.
Option (A) "Bus is the preferred transportation for 25 residents" is not supported by the information in the graph, as the bus section represents 10% of the graph, but we don't know the actual number of residents who prefer the bus.
Option (C) "Together, Streetcar and Cable Car are the preferred transportation for 42 residents" is not correct, as the cable car section alone represents 27% of the graph, which is more than 42 residents.
Option (D) "Together, Walk and Streetcar are the preferred transportation for 165 residents" is supported by the information in the graph, as the walk section represents 40% of the graph, which is 0.4 x 300 = 120 residents, and the streetcar section represents 15% of the graph, which is 0.15 x 300 = 45 residents.
Therefore, the total number of residents who prefer walking or streetcar is 120 + 45 = 165.
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Lena bought a total of 20 postcards. She bought 6 more large postcards than small. Write a system of equations that represents the postcards Lena purchased. Solve the system by substitution. Interpret the solution.
The solution to the system is (x, y) = (7, 13), which means Lena bought 7 small postcards and 13 large postcards.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
Let x be the number of small postcards that Lena bought, and let y be the number of large postcards she bought.
From the problem statement, we know that:
Lena bought a total of 20 postcards, so x + y = 20.
Lena bought 6 more large postcards than small, so y = x + 6.
Now we can substitute the second equation into the first one to eliminate y:
x + (x + 6) = 20
Simplifying the equation, we get:
2x + 6 = 20
2x = 14
x = 7
So Lena bought 7 small postcards and y = x + 6 = 13 large postcards.
The solution to the system is (x, y) = (7, 13), which means Lena bought 7 small postcards and 13 large postcards.
Interpretation: Lena bought more large postcards than small postcards, and the difference between the two is 6. Out of the 20 total postcards, 13 were large and 7 were small.
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to estimate the population parameter, will you construct a confidence interval to estimate a population proportion or a confidence interval to estimate a population mean? select the best answer option below.group of answer choiceswe will use a confidence interval to estimate a population mean becasue iat-score is quantitative variable.we will use a confidence interval to estimate a population mean becasue iat-score is categorical variable.we will use a confidence interval to estimate a population proportion becasue iat-score is quantitative variable.we will use a confidence interval to estimate a population proportion becasue iat-score is categorical variable. flag question: question 2question 25 ptsassuming conditions are met, which model should you use, a z-model or a t-model? select the best answer option below.group of answer choicesuse a t-model because the population standard deviation, , is known.a z-model because population standard deviation, , is known.a t-model because population standard deviation, , is not known.a z-model because the population standard deviation, , is not known.
The t-model is used to estimate the population means when the sample size is small or when the population standard deviation is unknown. It takes into account the variability in the sample and provides a more accurate estimate of the population mean.
To estimate a population parameter, we need to use a confidence interval. But the question is whether we should use a confidence interval to estimate a population proportion or a population mean. In this case, we need to consider the nature of the variable being measured. If the variable is quantitative, such as the IAT score, we should use a confidence interval to estimate a population means.
On the other hand, if the variable is categorical, such as gender or race, we should use a confidence interval to estimate a population proportion. Therefore, the correct answer is "We will use a confidence interval to estimate a population means because the IAT score is a quantitative variable."
Now, assuming that the conditions are met, we need to determine which model to use – a z-model or a t-model. This decision depends on whether we know the population standard deviation or not. If we know the population standard deviation, we should use a z-model. However, in most cases, we do not know the population standard deviation, so we need to use a t-model. Therefore, the correct answer is "a t-model because population standard deviation, sigma, is not known."
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