Answer: To find the indicated z-score for a shaded area of 0.1949 in the standard normal distribution, we need to use a z-table or a calculator with a built-in normal distribution function.
Using a z-table, we can find the z-score that corresponds to a cumulative area of 0.1949 in the standard normal distribution. The z-table gives us the area to the left of the z-score, so we need to look for the area closest to 0.1949 in the body of the table and then interpolate to find the exact z-score.
Looking at the z-table, we find that the area to the left of the z-score 0.88 is 0.8106, and the area to the left of the z-score 0.89 is 0.8159. Since 0.1949 is closer to 0.8106 than to 0.8159, we can estimate that the z-score corresponding to the area 0.1949 is approximately 0.88.
Therefore, the indicated z-score for a shaded area of 0.1949 in the standard normal distribution is approximately 0.88.
Step-by-step explanation:
16/3 as a decimal correct to 4 decimal places.
Answer:
5.3333
Step-by-step explanation:
We want to divide 16 by 3, and it will be 5.333333....
The 3 is repeating in this question, but to the 4th decimal place it will be 5.3333.
Answer:
5.3333
Step-by-step explanation:
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To convert a fraction to a decimal, you divide the numerator by the denominator. In this case, it is 16 divided by 3.
16 ÷ 3 ≈ 5.3333333333 (The 3 is repeating)To round this number to 4 decimal places, you look at the fifth digit after the decimal point (which is 3). Because this digit is less than 5, you don't need to round the fourth number up, and the final result is 5.3333.
Therefore, 16 divided by 3 is approximately 5.3333 when rounded to 4 decimal places.
1 1/4Cups of sugar to make 20 cookies. How many cups to make 16 cookies
To make 16 cookies it need 1 cup of sugar.
What are problem solving questions?Problem solving questions are questions that require critical thinking and analytical skills to solve a particular issue or challenge, often in a systematic and logical way.
To make 1 cookie, you need 1 1/4 cups of sugar ÷ 20 cookies = 1/16 cups of sugar.
To make 16 cookies, you need 16 cookies x 1/16 cups of sugar per cookie = 1 cup of sugar.
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Rewrite the equation in the form (x−p)2=q 0=x^2-10x+7
Answer:
(x - 5)² = 18
Step-by-step explanation:
x² - 10x + 7 = 0 ( subtract 7 from both sides )
x² - 10x = - 7
using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 5)x + 25 = - 7 + 25
(x - 5)² = 18 ← in the form (x - p)² = q
Simplify by expressing fractional exponents instead of radicals. ab
The simplification by expressing fractional exponents instead of radicals is a^1/2. b^1/2 or (ab)^(1/2)
How can the simplification be done?The expression in radical form was been provided as √ab and this is been expected from use to express it ionform of fractional exponent form.
√ab
note that;
√a = a^1/2
√ab = √a * √b
By utilixzing the properties of square root function, then we can have the expressions as ;
√ab = √a √b
√ab = a^1/2 * b^1/2
√ab =a^1/2. b^1/2
=a^1/2. b^1/2 or (ab)^(1/2)
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Find the zeros of the quadratic function f(x) = 2x^2 – 8x + 6
The answer is 3 and 1
Step-by-step explanation:
Given : 2x ^ 2 - 8x + 6 = 0
To Find: x
Solution:
2x ^ 2 - 8x + 6 = 0
2(x ^ 2 - 4x + 3) = 0
x ^ 2 - 4x + 3 = 0
x ^ 2 - x - 3x + 3 = 0
x(x - 1) - 3(x - 1) = 0
(x - 3)(x - 1) = 0
x - 3 = 0
x = 3
x - 1 = 0
x = 1
Thus the solution are 3 and 1
I need answer to question 4a, b and c
Thank you
Step-by-step explanation:
4a.
as we can see in the table, if we have 1 processor and add a second one, we save 30 minutes (61 - 31 = 30).
4b.
if you solved 3. and filled the table correctly, you see that with 240 processors we need 1 minute + 60/240 = 1 1/4 = 1.25 minutes.
if we add additional 240 processors, we get 480 processors, and we need 1 minute + 60/480 = 1 1/8 = 1.125 minutes.
that means we save 1/8 minute (1 1/4 - 1 1/8 = 1/8) with doubling the amount of processors. that is 7.5 seconds.
4c.
the answer always depends on the circumstances.
in fast processes 7.5 seconds can be a long time, and it might be worth the effort to save that amount of time (like in real time processing as with industrial robotics, simulating and controlling trains or a space flight).
but for asynchronous calculations of certain numbers it might not matter, if the result is available 7.5 seconds earlier or later, and the extra effort is not worth it.
probably problem for algebra 2 please help as much as u can (4 parts)
The estimated number of unemployed workers in the 16 - 19 age group is 1. 54 million people .
The probability that a person selected at random is in the 25 - 44 age group is 38 %.
The probability that a person selected at random is in the 45 - 64 age group is 25 %.
The probability that a person selected at random is in the 45 or older is 31 %.
How to find the probabilities ?The number of unemployed workers in the 16 - 19 age group is :
= 16 % x 9. 63 million unemployed
= 1. 54 million people
The probability that should an unemployed person be selected at random, they fall into the 25 - 44 age group would be the same percentage as the percentage of people in that group which is 38 %. The same is true for the 45 - 64 age group percentage of 25 %.
The probability that a person would be 45 or older is:
= Percentage of those 45 - 64 + 65 +
= 25 % + 6 %
= 31 %
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when 40 is subtracted from the square of a number, the result is 3 times the number. find the positive solution
Answer: x = 8
Step-by-step explanation: Let 'x' be the number we are looking for.
As per the question, equation will be : x^2 - 40 = 3x
x^2 - 3x - 40 = 0
Factor the equation. Or quadratic equation formula can also be used.
Factoring -
x^2 - 3x - 40 = 0
x^2 - 8x + 5x - 40 = 0
x(x-8) + 5( x-8) = 0
(x+5) ( x-8) = 0
x+5=0 , x-8 =0
x = -5 , x = 8
As we need to find the positive solution, x = 8 is the answer.
VERIFICATION -
= x^2 - 40
= ( 8 )^2 - 40
= 64 - 40
= 24
And 3 times 8 is also 24.
Therefore, if we subtract 40 from the square of 8, the result will be 3 times the number (which is 8).
PLEASE HELP WILL GIVE THE BRAINLISET AND 60 PTS !!!
Answer:C
Step-by-step explanation:
you see x=-3 is match for y=2
Answer:
2
Step-by-step explanation:
Look for where the line crosses x=-3. It crosses at y=2. so the answer is the third, 2
Find the area of the triangle
Answer:
i don’t know sorry
Step-by-step explanation:
nothing
The solution to a system of equations is (5.-19). Choose two equations that might make up the system.
Oy=2x-23
Oy=x-17
Oy=-7x+16
Dy=-21-9
Oy=-3x-6
Answer: The solution to a system of equations in two variables represents the values of the variables that satisfy both equations simultaneously.
To check which equations might make up the system with a solution of (5,-19), we can substitute x = 5 and y = -19 into each equation and see if they are both satisfied.
Substituting x = 5 and y = -19 into the first equation, we get:
y = 2x - 23
-19 = 2(5) - 23
-19 = -13
This is not true, so the first equation is not part of the system.
Substituting x = 5 and y = -19 into the second equation, we get:
y = x - 17
-19 = 5 - 17
-19 = -12
This is not true, so the second equation is not part of the system.
Substituting x = 5 and y = -19 into the third equation, we get:
y = -7x + 16
-19 = -7(5) + 16
-19 = -19
This is true, so the third equation is one of the equations in the system.
Substituting x = 5 and y = -19 into the fourth equation, we get:
y = -21 - 9x
-19 = -21 - 9(5)
-19 = -64
This is not true, so the fourth equation is not part of the system.
Substituting x = 5 and y = -19 into the fifth equation, we get:
y = -3x - 6
-19 = -3(5) - 6
-19 = -21
This is not true, so the fifth equation is not part of the system.
Therefore, one possible system of equations with a solution of (5,-19) is:
y = -7x + 16
We would need another equation to form a complete system with a unique solution.
Step-by-step explanation:
80 newspapers in 5 piles equals newspapers in 1 pile
"To find how many newspapers are in one pile if 80 newspapers are divided into 5 piles, we need to divide the total number of newspapers (80) by the number of piles (5):
80 / 5 = 16
Therefore, there are 16 newspapers in each pile if 80 newspapers are divided into 5 piles." (ChatGPT, 2023)
Consider a student loan of $25,000 at a fixed APR of 12% for 15 years.
To calculate the monthly payment, we can use the formula for a fixed-payment loan:
P = (Pv * r) / (1 - (1 + r)^(-n))
Where:
Pv = present value of the loan
r = monthly interest rate
n = total number of payments
P = fixed monthly payment
a. To find the monthly payment, we need to first calculate the monthly interest rate and total number of payments:
Monthly interest rate = APR / 12 = 0.12 / 12 = 0.01
Total number of payments = 15 years * 12 months/year = 180
Plugging these values into the formula, we get:
P = (25000 * 0.01) / (1 - (1 + 0.01)^(-180)) = $285.41 per month
Therefore, the monthly payment is $285.41.
b. To determine the total amount paid over the term of the loan, we can simply multiply the monthly payment by the total number of payments:
Total amount paid = monthly payment * total number of payments
Total amount paid = $285.41 * 180 = $51,373.80
Therefore, the total amount paid over the term of the loan is $51,373.80.
c. To find the percentage of the total amount paid that is applied toward the principal and interest, we can use the amortization schedule. An amortization schedule breaks down each payment into its principal and interest components. Using a loan calculator or spreadsheet, we can generate the following schedule: in file attachment
From the table in file attachment, we can see that the total principal paid over the term of the loan is $25,000 (the initial loan amount) plus $281.12, or $25,281.12. To find the percentage of the total amount paid that is applied toward the principal, we can divide the total principal by the total amount paid and multiply by 100:
Percentage of total amount paid applied toward principal = (Total principal / Total amount paid) * 100
Percentage of total amount paid applied toward principal = ($25,281.12 / $51,373.80) * 100 = 49.20%
Therefore, 49.20% of the total amount paid is applied toward the principal, while the remaining 50.80% is paid for interest.
b²-4ac=0 solve for b
The value of b is solved using square root is found to be b = 2√ac.
Explain about the discriminant formula?The section of a quadratic formula following the square root symbol, b²-4ac, is the discriminant. If we have two solutions, single solution, or none at all, the discriminant informs us.
A quadratic equation with a positive discriminant has two unique real number solutions.A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.Both of the answers are not real numbers, according to a negative discriminant.The given equation is:
b²- 4ac = 0
Separating unknown value from the equation:
b² = 4ac
Taking square root both side.
√b² = √4ac
Simplifying
b = 2√ac
Thus, the value of b is solved using square root is found to be b = 2√ac.
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The U.S. population in 1910 was 92 million people. In 1990, the population was 280 million. Create both a linear and an exponential model of the population from 1910 to 1990, with projected data points at least every 20 years, starting with 1910 as year 0. Include both an equation and a graph in your answer.
(Disregard what I wrote - My eraser didn't work well)
The linear model is Population = 92 + 2.35x and the exponential model is Population= 92(1.0187)ˣ.
What distinguishes an exponential model from a linear model?An exponential model implies that the change in y is proportionate to its present value, whereas a linear model assumes that the change in y is constant for each unit change in the explanatory variable (x). To put it another way, an exponential model assumes a varying rate of change, whereas a linear model implies a constant rate of change.
Let us suppose number of years = x.
Given that, the U.S. population in 1910 was 92 million people. In 1990, the population was 280 million.
From 1910 to 1990 is a period of 80 years, the increase in population over this period is 280 million - 92 million = 188 million.
Therefore, the average annual increase in population is 188 million / 80 years = 2.35 million.
Thus, the linear model is:
Population = 92 + 2.35x
The exponential model is:
The population grew from 92 million in 1910 to 280 million in 1990, a factor of 280/92 = 3.0435.
The period of growth is 80 years, so the annual growth rate can be calculated as:
rate = (3.0435)^(1/80) - 1 = 0.0187 or 1.87%
Population= 92(1.0187)ˣ
Hence, the linear model is Population = 92 + 2.35x and the exponential model is Population= 92(1.0187)ˣ.
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A jar contains 7 red marbles, 9 green marbles, and 8 blue marbles. What is the probability that you draw a red marble? = What is the probability that you choose exactly one of each color, if you pick 3 from the jar?= What is the probability that you draw 5 green marbles in a row if you do not replace the marbles after each draw?
1. The prοbability that yοu draw a red marble 7/24
2. The prοbability οf chοοsing exactly οne οf each cοlοr is 63/253
3. The prοbability that yοu draw 5 green marbles in a rοw is 0.0057
What is prοbability?Prοbability is a branch οf mathematics in which the chances οf experiments οccurring are calculated. It is by means οf a prοbability, fοr example, that we can knοw frοm the chance οf getting heads οr tails in the launch οf a cοin tο the chance οf errοr in research.
1. The prοbability οf drawing a red marble is given by the number οf red marbles divided by the tοtal number οf marbles in the jar:
P(red) = 7/(7+9+8) = 7/24
2. The prοbability οf chοοsing exactly οne οf each cοlοr, if yοu pick 3 marbles frοm the jar, can be fοund using the hypergeοmetric distributiοn. The tοtal number οf ways tο chοοse 3 marbles frοm 24 is:
C(24,3) = 2024
The number οf ways tο chοοse οne οf each cοlοr is:
C(7,1) * C(9,1) * C(8,1) = 798 = 504
Therefοre, the prοbability οf chοοsing exactly οne οf each cοlοr is:
P(1 οf each cοlοr) = 504/2024 = 63/253
3. The prοbability οf drawing 5 green marbles in a rοw withοut replacement can be fοund as fοllοws. Therefοre, the prοbability can be calculated as:
P(5 green in a rοw) = (9/24) * (8/23) * (7/22) * (6/21) * (5/20) = 0.0057 (rοunded tο fοur decimal places)
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Here is the graph of y= 5-x for values of x from 0 to 5.
a) On the same grid, draw the graph of y=x+1
b) Use the graphs to solve the simultaneous equations y=5-x and y=x+1
Answer:
Step-by-step explanation:
I can provide you with the steps to solve the simultaneous equations y=5-x and y=x+1 using the given graphs.
a) To draw the graph of y=x+1 on the same grid, we can plot the points where x=0 and x=5, and connect them with a straight line. When x=0, y=1 and when x=5, y=6, so the line passes through (0,1) and (5,6).
b) To solve the simultaneous equations y=5-x and y=x+1, we can look for the point where the two graphs intersect on the same grid. This point represents the values of x and y that satisfy both equations simultaneously.
From the first equation, we know that when x=0, y=5, and when x=5, y=0. From the second equation, we know that when x=0, y=1, and when x=5, y=6.
By looking at the graphs, we can see that the two lines intersect at the point where x=4 and y=1. Therefore, the simultaneous solution of the equations is x=4 and y=1.
May any kind soul teach me on how to do this primary six math question .
The unknown length in the rectangle is ? = 8cm
How to find the unknown length?We we want to find the unknown length.
First, if we look just at the pink and yellow rectangles we can see that these have a combined area of:
A = 12cm² + 18cm²
A = 30cm²
And we know that one side measures 6cm, then the length of AD is:
AD*6cm = 30cm²
AD = 30cm²/6cm
AD = 5cm
Now, the yellow and purple rectangles have a combined area of:
A = 18cm² + 22cm² = 40cm²
Then we can write:
?*AD = 40cm²
?*5cm = 40cm²
? = 40cm²/5cm
? = 8cm
That is the unknown lenght.
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Lush Gardens Co. bought a new truck for $54,000. It paid $5,940 of this amount as a down payment and financed the balance at 4.46% compounded semi-annually. If the company makes payments of $1,600 at the end of every month, how long will it take to settle the loan?
0
years
0
months?
Express the answer in years and months, rounded to the next payment period
It will take Lush Gardens Co. 3 years and 3 months to settle the loan if it makes payments of $1,600 at the end of every month.
To find how long will it take to settle the loan?First, we need to find the amount of the loan.
Amount of loan = Total cost of the truck - Down payment
Amount of loan = $54,000 - $5,940 = $48,060
Next, we need to find the monthly interest rate. Since the interest is compounded semi-annually, we first need to find the semi-annual interest rate:
Semi-annual interest rate = 4.46% / 2 = 2.23%
Then, we can find the monthly interest rate using the formula:
(1 + Monthly interest rate)^12 = 1 + Semi-annual interest rate(1 + Monthly interest rate) = (1 + Semi-annual interest rate)^(1/12)Monthly interest rate = (1 + Semi-annual interest rate)^(1/12) - 1Plugging in the numbers:
Monthly interest rate = (1 + 0.0223)^(1/12) - 1 = 0.001845
Now we can use the formula for the loan payment:
Loan payment = Monthly interest rate * Loan amount / (1 - (1 + Monthly interest rate)^(-n))
Where n is the number of months.
Plugging in the numbers:
$1,600 = 0.001845 * $48,060 / (1 - (1 + 0.001845)^(-n))
Solving for n using a financial calculator :
n = 38.98 months
Rounding up to the next payment period (which is 39 months), we get:
n = 3 years, 3 months
Therefore, it will take Lush Gardens Co. 3 years and 3 months to settle the loan if it makes payments of $1,600 at the end of every month.
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The tallest tower built before the era of television masts was the Eiffel Tower which was completed on March 31, 1889. If you stand at a distance of 80 ft from a point directly beneath the center of the tower, you will find the angle of elevation to the top of the tower to be a staggering 85°. How tall is the Eiffel Tower? Round the answer to the nearest tenth.
Answer:
We can use trigonometry to solve the problem. Let's call the height of the tower "h". Then we can use the tangent function to find "h":
tan(85°) = h/80
Multiplying both sides by 80, we get:
h = 80 tan(85°) ≈ 884.2 ft
Rounding to the nearest tenth, the height of the Eiffel Tower is approximately 884.2 ft.
Step-by-step explanation:
Solve to find the value of ‘a’ 10a-2=4a-1a
Therefore, the value of 'a' that satisfies the equation is a = 2/7.
What is the meaning of a mathematical equation?A relationship between two expressions in mathematics is known as an equation, and it is written as an equality on both sides of the equal to sign. An equation is, for instance, 3y = 16.
To solve for 'a' in the equation 10a-2=4a-1a, we need to simplify and isolate the variable on one side of the equation.
10a - 2 = 4a - 1a
First, we can simplify the right side of the equation by combining the like terms:
10a - 2 = 3a
Next, we can isolate the variable 'a' on one side of the equation by subtracting 3a from both sides:
10a - 2 - 3a = 0
Simplifying the left side of the equation:
7a - 2 = 0
7a = 2
a = 2/7
Therefore, the value of 'a' that satisfies the equation is a = 2/7.
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Convert the following to logarithmic form:
a^3 = y
Choose one:
a. 0 = loga y
b. 3 = loga y
c. a = log3 y
d. - 3 = loga y
The logarithmic form of the equation a^3 = y is log_a(y) = 3
What is a logarithmic equationA logarithmic equation is an equation that involves the logarithm of one or more variables.
How to convert the expression to a logarithmic formFrom the question, we have the following parameters that can be used in our computation:
a^3 = y
Take the logarithm of both sides of the equation
So, we have
3log(a) = log(y)
Divide both side by log(a)
So, we have
3 = log_a(y)
Rewrte as
log_a(y) = 3
Hence, the equation is (b) 3 = log_a(y)
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y = −3x2, y = −5x2, y = −1x2
Answer:
Step-by-step explanation:
y=-6
y=-10
y=-2
Use Venn Diagrams in the error detection process to find when a “word” has been
transmitted incorrectly.
In the Venn Diagram, it is verified that 11-bit word 10011011100 has the 15-bit Hamming code 100110111001010.
What is a Venn Diagram?
In order to solve problems based on the sets, we can use a Venn diagram to depict the logical relationship between sets and their components. Although other closed figures like squares may be used, a Venn diagram commonly uses intersecting and non-intersecting circles to indicate the relationship between sets.
To verify that the 11-bit word 10011011100 has the 15-bit Hamming code 100110111001010 for the Venn Diagram given, we need to check that the parity bits in the Hamming code are calculated correctly.
The Hamming code has three parity bits, calculated based on the positions of the 1's in the code word.
Using the rules for calculating the parity bits, we get -
Parity bit 1: covers all bit positions that have an odd index (i.e., 1, 3, 5, 7, 9, 11, 13, 15).
Calculated as the XOR of these bit positions: 1 XOR 0 XOR 0 XOR 1 XOR 1 XOR 0 XOR 0 XOR 1 = 0.
Parity bit 2: covers all bit positions that have a "2" bit in their binary representation (i.e., 2, 3, 6, 7, 10, 11, 14, 15).
Calculated as the XOR of these bit positions: 0 XOR 0 XOR 1 XOR 1 XOR 1 XOR 0 XOR 1 XOR 0 = 0.
Parity bit 3: covers all bit positions that have a "4" bit in their binary representation (i.e., 4, 5, 6, 7, 12, 13, 14, 15).
Calculated as the XOR of these bit positions: 1 XOR 1 XOR 1 XOR 1 XOR 0 XOR 1 XOR 0 XOR 0 = 1.
Therefore, the 15-bit Hamming code for the 11-bit word 10011011100 is:
100110111001010
which matches the given code.
Thus, we have verified that the 11-bit word 10011011100 has the 15-bit Hamming code 100110111001010.
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On January 1, 20x1, Entity A acquires 25% interest in Entity B for
₱800,000. Entity B reports profit of ₱1,000,000 and declares dividends of ₱100,000 in 20x1. How much is the carrying amount of the investment in associate on December 31, 20x1?
The number of nations participating in the Winter Games competition has been increasing over the
years, as shown in the table Use linear regression to find a linear function that can be used to predict the
number of nations participating x years after 1988. Then predict those years in which more than 100
nations will participate in the games
What is the linear function that can be used for prediction?
Year
1988
1992
1995
1998
2002
2006
Number of Nations
51
58
61
66
71
74
Answer:
Step-by-step explanation:
o find a linear function that can be used to predict the number of nations participating x years after 1988, we can use linear regression analysis. Using a spreadsheet program or calculator with linear regression capabilities, we obtain:
y = 1.9632x + 51.3276
where y is the predicted number of nations participating and x is the number of years after 1988.
To predict those years in which more than 100 nations will participate, we can substitute y = 100 into the linear function and solve for x:
100 = 1.9632x + 51.3276
48.6724 = 1.9632x
x ≈ 24.8
Therefore, more than 100 nations will participate in the Winter Games approximately 24.8 years after 1988, or in the year 2013.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The center of the circle lies on the x-axis.
The radius of the circle is 3 units.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The standard equation of a circle is expressed as: Centre is (-g, -f)radius = √g²+f²-CGiven a circle whose equation is Get the centre of the circle2gx = -2x2g = -2g = -1Similarly, 2fy = 0f = 0Centre = (-(-1), 0) = (1, 0)This shows that the center of the circle lies on the x-axisr = radius = √g²+f²-Cradius = √1²+0²-(-8)radius =√9 = 3 unitsThe radius of the circle is 3 units.
For the circle x² + y² = 9, the radius is expressed as:r² = 9r = 3 units Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Need help with problem 3
Answer:
The reduced echelon form of the given matrix B is [ 1 0 0 -5 | 0 ], [ 0 1 0 3 | 0 ], and [ 0 0 1 0 | 0 ]. The parametric description of the set of solutions for the given system of linear equations is { [5x4, -3x4, 0, x4] | x4 ∈ R }.
Step-by-step explanation:
Using row operations to reduce the matrix B to reduced row echelon form, we have:
[ 1 3 -5 4 | 0 ]
[ 1 4 -8 7 | 0 ]
[-3 -7 9 -6 | 0 ]
R2 - R1 -> R2
R3 + 3R1 -> R3
[ 1 3 -5 4 | 0 ]
[ 0 1 -3 3 | 0 ]
[ 0 2 4 6 | 0 ]
R1 - 3R2 -> R1
R3 - 2R2 -> R3
[ 1 0 4 -5 | 0 ]
[ 0 1 -3 3 | 0 ]
[ 0 0 10 0 | 0 ]
R3/10 -> R3
[ 1 0 4 -5 | 0 ]
[ 0 1 -3 3 | 0 ]
[ 0 0 1 0 | 0 ]
R2 + 3R3 -> R2
R1 - 4R3 -> R1
R2 + 3R3 -> R3
[ 1 0 0 -5 | 0 ]
[ 0 1 0 3 | 0 ]
[ 0 0 1 0 | 0 ]
Therefore, the reduced echelon form of the matrix B is:
[ 1 0 0 -5 | 0 ]
[ 0 1 0 3 | 0 ]
[ 0 0 1 0 | 0 ]
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can you make it step by step easy to understand
Certainly! Here are the steps to find the reduced row echelon form of the matrix B = [1, 3, -5, 4, 1, 4, -8, 7, -3, -7, 9, -6]:
Write the matrix in augmented form, with a vertical line separating the coefficients from the constant terms.
[ 1 3 -5 4 | 0 ]
[ 1 4 -8 7 | 0 ]
[-3 -7 9 -6 | 0 ]
Use row operations to transform the matrix into row echelon form. The goal is to create zeros below the leading entries (the first nonzero element) in each row. Here are the steps:
a. Subtract the first row from the second row, and subtract 3 times the first row from the third row:
[ 1 3 -5 4 | 0 ]
[ 0 1 -3 3 | 0 ]
[ 0 2 4 6 | 0 ]
b. Subtract 3 times the second row from the first row, and subtract 2 times the second row from the third row:
[ 1 0 4 -5 | 0 ]
[ 0 1 -3 3 | 0 ]
[ 0 0 10 0 | 0 ]
c. Divide the third row by 10 to create a leading 1 in the third row:
[ 1 0 4 -5 | 0 ]
[ 0 1 -3 3 | 0 ]
[ 0 0 1 0 | 0 ]
Use row operations to transform the matrix into reduced row echelon form. The goal is to create leading 1's in each row, and zeros above and below the leading 1's. Here are the steps:
a. Subtract 4 times the third row from the first row, and subtract 3 times the third row from the second row:
[ 1 0 0 -5 | 0 ]
[ 0 1 0 3 | 0 ]
[ 0 0 1 0 | 0 ]
The matrix is now in reduced row echelon form. The leftmost nonzero entry in each nonzero row is 1, and each leading 1 is the only nonzero entry in its column. The rows are arranged so that all rows with all zeros are at the bottom of the matrix.
Therefore, the reduced row echelon form of the matrix B is:
[ 1 0 0 -5 | 0 ]
[ 0 1 0 3 | 0 ]
[ 0 0 1 0 | 0 ]
For (b):
From the reduced echelon form obtained in part (a), we can write the system of equations as:
x1 + 0x2 + 4x3 = -5
0x1 + x2 - 3x3 = 3
0x1 + 0x2 + x3 = 0
We can solve for the basic variables (x1, x2, x3) in terms of the free variable(s):
x1 = -5 - 4x3
x2 = 3 + 3x3
x3 = free
Therefore, the general solution to the system of equations is:
x = [-5 - 4x3, 3 + 3x3, x3]
where x3 is any real number, since it is the free variable. This is the parametric description of the set of solutions. We can also write this solution set in set-builder notation as:
{ [-5 - 4x3, 3 + 3x3, x3] | x3 ∈ R }
This means that any vector in the solution set can be obtained by choosing a value for the free variable x3 and plugging it into the expressions for x1, x2, and x3. For example, if we choose x3 = 0, we get the solution (x1, x2, x3) = (-5, 3, 0). If we choose x3 = 1, we get the solution (x1, x2, x3) = (-9, 6, 1), and so on.
Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]
Given that f(x) = 3x – 5 g(x) = 2x – 6 and h(x) = x + 4 4 2x
Therefore , the solution of the given problem of function comes out to be f[g(x)] = 3x² - 2 is the formula for the function f[g(x)].
Explain function.The mathematics programme covers a wide range of topics, including mathematics, numbers, but also their subsets, along with building, construction, and the both real and fictional geographic locations. A work covers the connections between different variable elements that all work together to produce the same result. A utility is made up of several distinctive components that, when combined, produce specific results for each input.
Here,
We must first assess g(x) in order to determine f[g(x)], and then we can use the outcome to determine f[g(x)].
=> g(x) = x² + 1
When we substitute g(x) for f(x), we obtain:
=> f[g(x)] = f(x² + 1)
=> 3(x² + 1) - 5 = 3x² + 3 - 5
=> 3x² - 2
Therefore, f[g(x)] = 3x² - 2 is the formula for the function f[g(x)].
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slope = y2 − y1 x2 − x1 A line has points (5, 12) and (7, 16). slope =
Answer:
m = 2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (5, 12) (7, 16)
We see the y increase by 4 and the x increase by 2, so the slope is
m = 4/2 = 2
So, the slope is 2