The correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.
The correct methods for "thinking out computation" (mental arithmetic) are a, b, and c.
a) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15. This method is correct because it breaks down the calculation into smaller, easier-to-manage parts.
b) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21. This method is also correct because it simplifies the calculation by subtracting 10 first, and then subtracting the remaining 7.
c) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997. This method is correct because it simplifies the calculation by multiplying 1000 by 3 first, and then subtracting 1 three to get the correct answer.
d) 150 ÷ 3 Think: what equals 150 x 3, that's 450. This method is incorrect because it is actually doing the opposite operation (multiplication instead of division) and therefore does not result in the correct answer. The correct method would be to think about how many times 3 can go into 150, which is 50.
In conclusion, the correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.
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The correct methods for "thinking out computation" (mental arithmetic) are:
A) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15
B) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21
C) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997
D) 150 ÷ 3 Think: what equals 150 x 3, that's 450
All four methods of "thinking out computation" provided in the question are correct and valid.
Method (a) is using the "doubles" method, which is a common mental arithmetic technique. By recognizing that 7+7 is 14, it is easy to add 1 more to get 15.
Method (b) is using the "subtracting by tens" method. By recognizing that 38 minus 10 is 28, it is easy to subtract 7 more to get 21.
Method (c) is using the distributive property of multiplication. By recognizing that 999 is very close to 1000, we can multiply 3 by 1000 and then subtract 3 to get 2997.
Method (d) is using the inverse operation of multiplication. By recognizing that 150 is a multiple of 3, we can think of 150 as 3 times some unknown number, and then determine that number by dividing 150 by 3. The answer is 50, which is the same as thinking of what equals 150 times 3 (450).
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Find k so that when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2, the remainder is 0.
The values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.
To find k so that when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2, the remainder is 0, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x-a, the remainder is f(a).
So, if we let f(x) = x^(3)+kx^(2)+k^(2)x+14 and a = -2, we can find the value of k that makes the remainder 0.
f(-2) = (-2)^(3)+k(-2)^(2)+k^(2)(-2)+14 = 0
Simplifying the equation, we get:
-8 + 4k - 2k^(2) + 14 = 0
-2k^(2) + 4k + 6 = 0
Dividing by -2, we get:
k^(2) - 2k - 3 = 0
Factoring the equation, we get:
(k-3)(k+1) = 0
So, k = 3 or k = -1.
Therefore, the values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.
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4. IQ (intelligence) tests are usually specified so that scores are normally distributed with a mean of 100 over the entire population. Suppose that a certain IQ test is designed to have a mean of 100 and standard deviation of 10. (a) What is the probability that a randomly selected individual from the population will score between 90 and 110 on this test? (b) An employer wishes to identify potential "high flyers" and intends to do this using the outcome of the IQ test. If the employer offers these positions to people with IQs in the top 1% of the population, what is the score the employer will use to decide job offers?
The probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826. The score the employer will use to decide job offers is 123.3 to decide job offers for potential "high flyers."
The IQ test is designed to have a mean of 100 and a standard deviation of 10. This means that the test follows a normal distribution with a mean of 100 and a standard deviation of 10.
(a) The probability that a randomly selected individual from the population will score between 90 and 110 on this test can be found using the standard normal distribution table. We need to find the z-scores for 90 and 110 and then use the table to find the corresponding probabilities.
The z-score for 90 is (90 - 100) / 10 = -1
The z-score for 110 is (110 - 100) / 10 = 1
Using the standard normal distribution table, we find that the probability for a z-score of -1 is 0.1587 and the probability for a z-score of 1 is 0.8413.
The probability that a randomly selected individual will score between 90 and 110 is the difference between these two probabilities:
0.8413 - 0.1587 = 0.6826
So the probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826.
(b) The employer wants to identify potential "high flyers" and intends to do this using the outcome of the IQ test. If the employer offers these positions to people with IQs in the top 1% of the population, we need to find the z-score that corresponds to the top 1% of the population.
Using the standard normal distribution table, we find that the z-score that corresponds to the top 1% of the population is 2.33.
Now we can use the z-score formula to find the corresponding IQ score:
z = (x - mean) / standard deviation
2.33 = (x - 100) / 10
Solving for x, we get:
x = (2.33 * 10) + 100 = 123.3
So the employer will use a score of 123.3 to decide job offers for potential "high flyers."
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Which of the following proves these triangles as congruent?
Answer:
AAS
Step-by-step explanation:
Answered this question before on Acellus.
HELP PLS PLS PLS PLS
DUE TOMORROW AND WORTH 50 POINTS AND I GIVE THE BRAINLESS!!
PLS STRESSING TIMES
Answer: 1,068 and wil
Step-by-step explanation:
Find an angle in each quadrant with a common reference angle with 12°, from 0°≤θ<360°
Answer: the first quadrant : 12° i the second quadrant : 168° i
the third quadrant : -168° i the forth quadrant : 348°.
Step-by-step explanation:
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A spinner is divided into three equal parts A, B, and C. The repeated experiment of spinning the spinner twice is simulated 125 times. A table of outcomes is shown.
Outcome Frequency
A, A 15
A, B 12
A, C 10
B, A 18
B, B 15
B, C 17
C, A 11
C, B 13
C, C 14
Based on the table, for what probability can you expect the spinner to not land on A?
0.66
0.47
0.33
0.10
The probability of the spinner not landing on A is 0.47.
How to find the probability you can expect the spinner to not land on A?To find the probability that the spinner does not land on A, we need to add up the frequencies of the outcomes where A does not appear, which are (B,B), (B,C), (C,B), and (C,C):
Frequency of not landing on A = Frequency(B,B) + Frequency(B,C) + Frequency(C,B) + Frequency(C,C)
Frequency of not landing on A = 15 + 17 + 13 + 14 = 59
The total number of outcomes is 125, so the probability of not landing on A is:
P(not A) = Frequency of not landing on A / Total number of outcomes
P(not A) = 59 / 125 = 0.47
Therefore, the probability of the spinner not landing on A is 0.47.
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Employees frequently need to work in team projects. We examine the difference in the team efficiency, when employees work in teams through distance working (e.g. with online meetings) in relation to teamwork with physical presence. Data are collected from a sample of 87 employees that have worked in a team project through online meetings and 74 employees that have worked in a team with physical presence. The employees filled a questionnaire, where one question was "The teamwork was efficient", on a scale from 1-5, where 1=strongly disagree and 5=strongly agree. The mean score in this question for the team that had used online meetings was 2.63, with a standard deviation of 0.92, while for the team that had worked with physical presence the mean was 2.35, with a standard deviation of 0.81. Test if teamwork with distance meetings appears to be generally more efficient for employees, in relation to teamwork with physical presence. Use a 1% level of significance.
This hypothesis test indicates that the team efficiency when working through distance working (e.g. with online meetings) is not generally more efficient than when working with physical presence.
The research question being examined is whether teams that work through distance working (e.g. with online meetings) are generally more efficient than those that work with physical presence. To answer this question, a hypothesis test can be used with a 1% level of significance.
The null hypothesis (H0) is that there is no difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence. The alternative hypothesis (H1) is that there is a difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.
To test this hypothesis, a two-tailed independent t-test was used. The mean score for the team that had used online meetings was 2.63 with a standard deviation of 0.92 and for the team that had worked with physical presence the mean was 2.35 with a standard deviation of 0.81. The t-statistic obtained was 1.71 and the corresponding p-value was 0.093.
Since the p-value (0.093) is not less than the level of significance (0.01), the null hypothesis cannot be rejected. Therefore, the data suggests that there is not a significant difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.
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Does this equation have a solution?
10x + 12 = 20x - 2
Answer:
Answer and how to isolate the variablex=1.4
First, subtract 10x on both sides so you get
12=10x-2
Then add 2 odd both sides
14=10x
Then divide both sides by 10
14/10= 10X/10
So you get x=1.4
Find the y intercept and slope of the linear equation x+y=-6 1/2
The slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.
To find the y-intercept and slope of the linear equation x +y=-6 1/2, we
need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y by subtracting x from both sides of the equation:
x + y = -6 1/2
y = -x - 6 1/2
Now we can see that the equation is in slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is -6 1/2.
Therefore, the slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.
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A line passes through the points (2, −2) and (3, −9). Write its equation in slope-intercept
form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
An equation in slope-intercept form is y = -7x + 12.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (2, -2), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-2) = (-9 - (-2))/(3 - 2)(x - 2)
y + 2 = (-9 + 2)/(3 - 2)(x - 2)
y = -7x + 14 - 2
y = -7x + 12
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A store manager adjusts the price of an item each week that the item goes unsold. The price of the unsold item, in dollars, after x weeks can be modeled by the exponential function f(x)=320(0.90)^x
: The initial price of the store item before the store manager made any price adjustments were: _________
Can someone help me solve this?
Thanks!
Answer:
The initial price of the store item would be the price before any price adjustments were made, which corresponds to when x=0.
Plugging x=0 into the given function, we get:
f(0) = 320(0.90)^0 = 320(1) = 320
Therefore, the initial price of the store item was $320.
Find the determinant of the triangular matrix.−37−605700−3
Determinant of the given triangular matrix is 105.
What is determinant of a matrix?The determinant of a matrix is a number that represents the volume or area of the matrix. It is calculated by using a formula that involves the entries of the matrix, and is used in solving linear equations and in proving theorems in linear algebra.
The determinant of a triangular matrix can be found by multiplying the elements on the main diagonal. In this case, the main diagonal elements are -3, 5, and -7.
So, the determinant of the triangular matrix is:
-3 * 5 * -7 = 105
Therefore, the determinant of the triangular matrix is 105.
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Suppose that a line passes through the points (5,1) and (-1.5).
Where will it pass through the x-axis?
The line passes through the x-axis at the point (13/2, 0).
To find where the line passes through the x-axis, we need to find the x-intercept of the line. The x-intercept is the point where the line crosses the x-axis, so the y-coordinate of this point will be 0.
We can use the slope-intercept form of a line, y = mx + b, to find the x-intercept. First, we need to find the slope of the line, m. The slope is given by the formula:
m = (y2 - y1)/(x2 - x1)
Plugging in the given points, we get:
m = (5 - 1)/(-1 - 5)
m = -2/3
Now we can plug in one of the points and the slope into the equation to solve for the y-intercept, b:
1 = -2/3(5) + b
b = -13/3
So the equation of the line is:
y = -2/3x + 13/3
To find the x-intercept, we set y to 0 and solve for x:
0 = -2/3x + 13/3
x = 13/2
So the line passes through the x-axis at the point (13/2, 0).
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Adding rational expressions with different Subtract. (5)/(2)-(1)/(2d) Simplify your answer as much as possible.
The simplified rational expression of (5)/(2)-(1)/(2d) is (5d-2)/(2d).
To add rational expressions with different denominators, we first need to find a common denominator. In this case, the common denominator is 2d.
Once we have the common denominator, we can multiply each fraction by a factor that will give us the common denominator. For the first fraction, we need to multiply by d in the numerator and denominator. For the second fraction, we need to multiply by 2 in the numerator and denominator.
After multiplying, we can combine the numerators and keep the common denominator.
So, the steps to simplify (5)/(2)-(1)/(2d) are as follows:
1. Find the common denominator: 2d
2. Multiply the first fraction by d/d: (5d)/(2d)
3. Multiply the second fraction by 2/2: (2)/(2d)
4. Combine the numerators and keep the common denominator: (5d-2)/(2d)
5. Simplify the numerator: (5d-2)/(2d)
Therefore, the simplified rational expression is (5d-2)/(2d).
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Numeric For the following exercises, use the given information to find the unknown value. 24.yvaries directly asx. Whenx=3, theny=12. Findywnehx=20. 25.yvaries directly as the square ofx. Whenx=2, theny=16. Findywhenx=8. 26.yvaries directly as the cube ofx. Whenx=3, theny=5. Findywhenx=4
When x = 4, y = 320/27.
If y varies directly as x, it means that y = kx, where k is a constant. To find k, we can use the given information:
When x = 3, y = 12
12 = k * 3
k = 4
Now that we know k, we can find y when x = 20:
y = k * x
y = 4 * 20
y = 80
Therefore, when x = 20, y = 80.
25. If y varies directly as the square of x, it means that y = k * x^2, where k is a constant. To find k, we can use the given information:
When x = 2, y = 16
16 = k * 2^2
k = 4
Now that we know k, we can find y when x = 8:
y = k * x^2
y = 4 * 8^2
y = 4 * 64
y = 256
Therefore, when x = 8, y = 256.
26. If y varies directly as the cube of x, it means that y = k * x^3, where k is a constant. To find k, we can use the given information:
When x = 3, y = 5
5 = k * 3^3
k = 5/27
Now that we know k, we can find y when x = 4:
y = k * x^3
y = 5/27 * 4^3
y = 5/27 * 64
y = 320/27
Therefore, when x = 4, y = 320/27.
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Given the graph of the quadratic function, determine the features.
For the given quadratic function the features are:
Domain: (-∞, ∞): Range :[-1, ∞)Vertex: (-3, -1)Explain about the quadratic function?A parabola, a U-shaped curve, is the shape of a quadratic function's graph.
The graph's vertex, which is an extreme point, is one of its key characteristics. The vertex, or lowest point on the graph or minimal value of a quadratic function, is where the parabola will open up.There are three characteristics that all quadratic functions share:
A quadratic function's graph is always a parabola with an end behaviour that is either upward or downward; its domain will be all real numbers; and its vertex is really the lowest point once the parabola opens upwards.Thus, for the given quadratic function the features are:
Domain: (-∞, ∞): Range :[-1, ∞)Vertex: (-3, -1)Know more about quadratic function
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Mandla, a farmer, wants to buy a new tractor. The tractor costs R160 000 excluding VAT He can pay a deposit of R20 000. He decides to buy the tractor on hire purchase over 60 months at a simple interest rate of 10 % a. What will his instalment be? b. How much interest will he pay? c. How much will he pay in total for the tractor over 60 months?
a) Amount financed is, R164,000
b) Total interest over 60 months is, R98,400
c) The farmer would pay a total of R262,400 after 60 months.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The tractor costs R160 000 excluding VAT
And, He can pay a deposit of R20 000.
Here, He decides to buy the tractor on hire purchase over 60 months at a simple interest rate of 10 %
Hence, We get;
Total price with VAT = R160,000 + 15% of R160,000
= R184,000
Hence, We get;
Amount financed = Total price - Deposit
= R184,000 - R20,000
= R164,000
Thus, Total interest over 60 months = R164,000 x 10% x 5
= R98,400
Here, Total payment = Amount financed + Total interest
= R164,000 + R98,400
= R262,400
Therefore, The farmer would pay a total of R262,400 after 60 months.
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It takes 4 minutes for the wheel to make one complete rotation. Put a star at Bo’s location after riding the wheel for 21 minutes
After 21 minutes the location of BO in the wheel is EO
How to find BO after 21 minutesThe location of BO after 21 minutes is solved using the data:
It takes 4 minutes for the wheel to make one complete rotation
hence in 21 minutes the rotation covered is
= 21 / 4
= 5.25
This is 5 complete rotations and 0.25 (a quarter rotation).
0.25 rotation is
=0.25 * 360
= 90
Each gap in the wheel is
360 / 12 = 30 degrees
hence three steps from B which is EO
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Watch help video Ise synthetic division to find the result when 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2. If there is a remainder, express the result in the form
Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).
To use synthetic division to find the result of the given polynomial division, we need to follow these steps:
1. Write the coefficients of the dividend polynomial in a row: 2 10 8 1 24
2. Write the constant term of the divisor with the opposite sign in front of the row: -2 | 2 10 8 1 24
3. Bring down the first coefficient: -2 | 2 10 8 1 24
-----------
2
4. Multiply the first coefficient by the divisor's constant term and write the result under the second coefficient: -2 | 2 10 8 1 24
-----------
2 -4
5. Add the second coefficient and the result from step 4: -2 | 2 10 8 1 24
-----------
2 6
6. Repeat steps 4 and 5 for the remaining coefficients: -2 | 2 10 8 1 24
-----------
2 6 4 -6
7. The last number in the row is the remainder. If it is 0, the division is exact. If not, we need to express the result in the form: quotient + (remainder)/(divisor)
In this case, the quotient is 2x^(3)+6x^(2)+4x-6 and the remainder is 36. So the result of the division is:
2x^(3)+6x^(2)+4x-6+(36)/(x+2)
Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).
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Carys calculates the total amount E, in dollars, theat she earns for working h hours using the equation E=10h. How many dollars does she earn per hour?
Answer:
She earns 10 dollars per hour.
Step-by-step explanation:
They substituted h for the amount of hours, since it is unknown. And you can see 10 is multiplied with h. So that is how much she earns an hour.
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Steve gets 4 points for every correct answer and looses 1 point for every wrong answer. If he answered 30 questions and scored 20 points, write a system of equations.
Answer:
Option B.
Step-by-step explanation:
Let r represent right questions and w represent wrong questions
Total number of questions can be written as:
r + w = 30
We can multiply the question type by the number of points and set it to equal to the total points:
4r - 1w = 20
Thus, our two equations match with Option B best.
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.Write an equation for the graph that passes through (0,4) and (5,19).
We can use the two-point form to find the equation of the line passing through the two given points:
y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)
where (x1, y1) = (0, 4) and (x2, y2) = (5, 19).
Substituting the values, we get:
y - 4 = ((19 - 4)/(5 - 0))(x - 0)
Simplifying the equation, we get:
y - 4 = (15/5)x
y - 4 = 3x
Adding 4 to both sides, we get:
y = 3x + 4
Therefore, the equation of the line passing through the points (0, 4) and (5, 19) is y = 3x + 4.
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a) find slope
19-4/5-0 = 15/5 = 3
plug into equation
y = 3x + b
plug in coordinate pair to solve for b
4 = 3(0) + b
4 = 0 + b
b = 4
y = 3x + b
Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below:
x 1 2
p(x) 0.04 0.05
(a) What is P(x = 4)? P(x = 4) = (b) What is P(x4)? P(x4) = (c) What is the probability that the selected student is taking at most five courses? P(at most 5 courses) = (d) What is the probability that the selected student is taking at least five courses? more than five courses? P(at least 5 courses) = P(more than 5 courses) = (e) Calculate P(3x6) and P(3 < x < 6). P(3x6) = P(3 < x < 6) =
a)0
b)0.09
c)0.09
d)0
e)P(3x6) = 0.09 P(3 < x < 6) = 0
A) P(x = 4) = 0
B) P(x4) = 0.09
C) P(at most 5 courses) = 0.09
D) P(at least 5 courses) = 0 P(more than 5 courses) = 0
E) P(3x6) = 0.09 P(3 < x < 6) = 0
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What is the value of x
in the rational equation x5=618
The required, value of x in the rational equation x⁵=618 is approximately 4.951.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
To solve for x in the rational equation x^5 = 618, we need to isolate x on one side of the equation.
Taking the fifth root of both sides, we get:
[tex]x = 618^{1/5}[/tex]
The approximate value of the fifth root of 618 is approximately 4.951.
Therefore, the value of x is approximately 4.951.
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26. G(9, 12), H(−2, −15), J(3, 8) and
G'(9, -2), H'(-2, 25), J'(3, 2)
The transformation between the points is (x, y) = (x, -y + 10)
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
G(9, 12), H(−2, −15), J(3, 8) and
G'(9, -2), H'(-2, 25), J'(3, 2)
We can see that the x coordinates of the image and the preimage are equal
However, the relationship between the y-coordinates is
y' = -y + 10
This means that
(x, y) = (x, -y + 10)
The above rule is a translation transformation
Translation transformation is a transformation that moves each point in a figure or object by a fixed distance in a specified direction.
Hence, the transformation is (x, y) = (x, -y + 10)
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Complete question
26. G(9, 12), H(−2, −15), J(3, 8) and G'(9, -2), H'(-2, 25), J'(3, 2)
Write out the transformation rule from GHJ to G'H'J'
A movie sells only adult tickets and child tickets for one movie the theater sells 126 tickets in all the tape diagram shows the ratio of adult tickets to child tickets the theater sells what does each square of the diagram represent?
Answer:
So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.
Step-by-step explanation:
Assuming that the tape diagram shows the ratio of adult tickets to child tickets as 3:2, we can represent this as follows:
AAA
AAA
AAA
CCC
CCC
In this diagram, each square represents a certain number of tickets. To determine how many tickets each square represents, we need to know the total number of squares in the diagram.
There are a total of 3 + 3 + 3 + 2 + 2 = 13 squares in the diagram. Since the theater sold 126 tickets in total, we can divide 126 by 13 to find out how many tickets each square represents:
126 ÷ 13 ≈ 9.69
So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.
For f(x)=6x+8 and g(x)= 5x, find the following composite functions and state the domain of each (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = _____ (Simplify your answer.)
The composite functions and their domains are:
(a) (fog)(x) = 30x + 8, domain: all real numbers
(b) (gof)(x) = 30x + 40, domain: all real numbers
(c) (fof)(x) = 36x + 56, domain: all real numbers
(d) (gog)(x) = 25x, domain: all real numbers
The composite functions are formed by substituting one function into another. We can find the composite functions for f(x)=6x+8 and g(x)=5x by following these steps:
(a) (fog)(x) = f(g(x)) = f(5x) = 6(5x) + 8 = 30x + 8
The domain of (fog)(x) is the set of all real numbers, since there are no restrictions on the values of x.
(b) (gof)(x) = g(f(x)) = g(6x+8) = 5(6x+8) = 30x + 40
The domain of (gof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
(c) (fof)(x) = f(f(x)) = f(6x+8) = 6(6x+8) + 8 = 36x + 56
The domain of (fof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
(d) (gog)(x) = g(g(x)) = g(5x) = 5(5x) = 25x
The domain of (gog)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
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What is the volume of the composite solid?
The volume of the composite solid is 5104 cubic ft.
What is triangular prism?A triangular prism's volume is the area that it takes up in all three dimensions. A prism is a solid object that has the same cross-section throughout its entire length, equal bases, and flat, rectangular side faces. Prisms can be divided into many categories and given different names depending on the form of their bases. A triangular prism has three rectangular lateral sides and two identical triangular bases.
The area of a triangular prism is given as:
V = 1/2(bhl)
Here, h = 22 - 12 = 10 ft.
Substituting the values we have:
V = 1/2(13)(10)(32)
V = 2080 cubic ft.
The volume of the rectangular prism is given as:
V = lwh
V = (28)(9)(12)
V = 3024 cubic ft.
The volume of the composite solid is:
V = V1 + V2
V = 2080 + 3024
V = 5104 cubic ft.
Hence, the volume of the composite solid is 5104 cubic ft.
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Jimmy is paying for a meal with group of friends. They received great service, so he is giving a 20% tip. The meal came to 166.60 before sales tax. How much will he leave as a tip?
Tip=$
Jimmy will leave a $33.32 tip for the great service.
What is the total of the cost?
Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.
To calculate the tip, we need to first find 20% of the total cost of the meal (before sales tax):
20% of 166.60 = 0.20 x 166.60 = 33.32
Therefore, Jimmy will leave a $33.32 tip for the great service.
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Compare the similarities and differences between Binomial and Normal distributions.
.What types of data does each use?
.What kinds of statistical formula and techniques are used with each?
.What similar characteristics do they share in their distributions?
Binomial and Normal distributions are two different types of probability distributions that are commonly used in statistics. Both distributions involve a set of possible outcomes, and the probability associated with each outcome.
The Binomial Distribution is used for discrete data such as coin flips, the number of defective items in a production run, and the number of wins and losses in a series of games. It is used with the formula P(x;n,p) and the techniques of probability, permutations, and combinations.
The Normal Distribution is used for continuous data such as height, weight, IQ scores, and test scores. It is used with the formula P(x;μ,σ) and the techniques of statistics, standardization, and z-scores.
Both distributions have the same basic shape and the same basic idea of a probability of a certain outcome. The main difference between them is that the Binomial Distribution is discrete and the Normal Distribution is continuous.
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