We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix
Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.
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The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane
and x represents the number of minutes the plane has been descending:
y=-5x + 100
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening
to the airplane at these time intervals.
Answer:
32x95%?
Step-by-step explanation:
Im so confused with this question statement.
Ticket lines are huge around the Colossal Arena. The Boulders, one of the most popular rock groups ever, are giving a concert on Saturday. When the tickets went on sale Monday, 500 were sold in the first hour, 560 tickets were sold in the second hour, and 640 tickets were sold in the third hour. After the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour. If sales continue at that rate, in what hour will 10,000 tickets be sold for the Boulders concert?Explain your answer in detail
If after the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour, it will take 12 hours to sell 10,000 tickets for the Boulders concert.
To solve this problem, we need to find the number of hours it will take to sell 10,000 tickets for the concert. We are given the number of tickets sold in the first three hours and the rate at which ticket sales increase each hour after the second hour.
Let's denote the number of tickets sold in the fourth hour by "x". Then, the number of tickets sold in the fifth hour will be "x + 20", and the number of tickets sold in the sixth hour will be "x + 40", and so on.
Using this information, we can set up an equation to find "x":
500 + 560 + x + (x + 20) + (x + 40) + ... = 10,000
Simplifying the equation, we get:
3x + 1020 + 20n = 9500
where "n" is the number of hours after the third hour.
Solving for "n", we get:
n = (10,000 - 1020 - 3x) / 20
Now, we need to find the value of "x" that satisfies this equation. We can do this by testing different values of "x" until we find the one that gives an integer value for "n".
Let's start by trying "x = 640 + 20 = 660". Plugging this value into the equation, we get:
n = (10,000 - 1020 - 3(660)) / 20 = 9
We arrived at this solution by using the given information about the rate of increase in ticket sales and setting up an equation to solve for the number of hours it will take to sell 10,000 tickets. We then tested different values of "x" until we found the one that satisfied the equation and gave an integer value for "n".
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if the true population proportion for a sample size of 200 is found to be 0.2, then the standard error will be
The correct option is SE is 0.04. In statistics, a sample proportion is a statistic that represents the proportion of individuals in a sample who have a particular characteristic or belong to a certain category.
The standard error of the sample proportion can be calculated as follows:
SE = sqrt(p * (1 - p) / n)
Where p is the sample proportion and n is the sample size. In this case, the sample proportion is 0.2, and the sample size is 200. So, plugging these values into the formula, we get:
SE = sqrt(0.2 * (1 - 0.2) / 200)
SE = sqrt(0.16 / 200)
SE = 0.04
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how many solutions do 2(x-4)=2x-8 have
The equation 2(x - 4) = 2x - 8 has infinitely many solutions.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is 2(x - 4) = 2x - 8.
Solving this,
Using the distributive property, a (b + c) = ab + ac, 2(x - 4) = (2 × x) - (2 × 4).
Substituting in the original equation,
(2 × x) - (2 × 4) = 2x - 8
2x - 8 = 2x - 8
2x - 2x = -8 + 8
0 = 0
Right hand side and left hand side are equal if we put any value for x.
So it has infinitely many solutions for x.
Hence the given equation has infinitely many solutions.
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hi can i have help with this question please i can’t figure out what c is
Answer: Decagon
Step-by-step explanation:
That would be a decagon because it has 10 sides. It does not matter if the shape looks wonky.
Hope this helps :)
rachel's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs rachel per pound, and type b coffee costs per pound. this month, rachel made pounds of the blend, for a total cost of . how many pounds of type a coffee did she use?
Rachel's Coffee Shop used 33 pounds of type A coffee at a cost of $4.20 per pound, and four times as many pounds of type B coffee at a cost of $5.50 per pound, to create a blend costing a total of $864.60.
Let's use the variable "x" to represent the number of pounds of type A coffee used in the blend.
The amount of type B coffee used in the mix was four times that of type A, therefore we can write:
number of pounds of type B coffee = 4x
The total cost of the blend is given as $864.60, so we can write an equation based on the cost:
[tex]4.2x + 5.5(4x) = 864.60[/tex]
Simplifying and solving for x, we get:
[tex]4.2x + 22x = 864.60[/tex]
[tex]26.2x = 864.60[/tex]
[tex]x = 33[/tex]
As a result, the mix contained 33 pounds of type A coffee.
To check our answer, we can substitute x = 33 into the equation we used to solve for it and verify that the total cost is indeed $864.60.
[tex]4.2(33) + 5.5(4*33)[/tex]
= [tex]138.6 + 726.0[/tex]
= [tex]864.6[/tex]
The total cost matches, so our answer is correct.
Therefore, Rachel's Coffee Shop used 33 pounds of type A coffee in the blend.
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The complete question is:
A blend made by Rachel's Coffee Shop combines two different kinds of coffee. Rachel pays $4.20 per pound for type A coffee and $5.50 for type B coffee. This month's blend cost $864.60 and included four pounds more of type B coffee than type A. How many pounds of coffee of type A were consumed?
The number b is irrational. Which statement about
41+b is true?
An irrational number is created by adding two rational numbers, according to the answer to the given question. If the oppositely irrational numbers a and b.
What is rational numbers?Rational numbers are those that may be written as a ratio (or fraction) of two integers. A fraction with a non-zero denominator is said to be rational.
A few instances of rational numbers are 1/2, 1/5, and 3/4. A rational number, “0,” can also be stated in a number of different ways, such as 0/1, 0/2, and 0/3. But 1/0, 2/0, 3/0, and so forth.
The number seven makes sense. A rational number is produced when two integers are split. To get the rational number 7, divide the whole number 7 by the whole number 1. Since 7 can be obtained by dividing two integers, it is referred to as a rational number.
Two rational integers added together yield an irrational number. Ab is irrational if and only if a and b are mutually exclusive irrational numbers.
Therefore, a = 2 and b = ab = 2 is an irrational number.
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Louise is planning to renovate her house. She intends to spend no more than $30 000. She has
$20 000 to invest in an account that pay 4.28% compounded monthly. How long will it take
Louise to meet her goal? Show your work. Round your answer to the nearest tenth of a year.
Answer: To solve this problem, we can use the formula for calculating the future value of an investment:
FV = PV * (1 + r/n)^(nt)
where:
FV is the future value of the investment
PV is the present value of the investment (the initial amount Louise has to invest)
r is the annual interest rate (4.28%)
n is the number of times the interest is compounded in a year
t is the number of years the investment is made
Since the interest is compounded monthly, we need to convert the annual interest rate to a monthly rate:
r/12 = 4.28% / 12 = 0.3566666666666667%
Now, we can use the formula to calculate the future value of Louise's investment:
FV = $20,000 * (1 + 0.3566666666666667%)^(12t)
We can use trial and error or iterative methods to find the value of t that satisfies the condition: FV = $30,000.
A quick approximation is to use the formula for simple interest:
FV = PV * (1 + r * t) = $20,000 * (1 + 0.0428 * t)
t = ($30,000 - $20,000) / ($20,000 * 0.0428) = 2.857142857142857 years, or approximately 2.9 years.
This is an approximation, but it should be close to the actual answer. To get a more accurate answer, we can use an iterative method, such as Newton-Raphson or bisection, to solve for t in the formula above.
Step-by-step explanation:
1. An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50' with the wall.
The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation
of the Sun is more than 65'. See the figure. Find the length of L of the awning. Round to the nearest
Inch.
At MeDonald's four cheeseburgers and three medium fries have a total of 2290 calories.Six cheeseburgers and two medium fries have 2560 calories. How many calories does each
Item contain?
Answer:
350 calories
Step-by-step explanation:
see the attachment.
Calories in one cheeseburgers = 135
And, Calories in one medium fries = 583
We have to given that,
At McDonald's four cheeseburgers and three medium fries have a total of 2290 calories.
And, Six cheeseburgers and two medium fries have 2560 calories.
Let us assume that,
Calories in one cheeseburgers = x
And, Calories in one medium fries = y
Hence, We get;
4x + 3y = 2290 . (i)
6x + 3y = 2560 .. (ii)
From (i);
3y = 2290 - 4x
Substitute above value in (ii);
6x + (2290 - 4x) = 2560
6x - 4x + 2290 = 2560
2x = 2560 - 2290
2x = 270
x = 270 / 2
x = 135
From (ii);
6 x 135 + 3y = 2560
810 + 3y = 2560
3y = 2560 - 810
3y = 1750
y = 1750/3
y = 583
Therefore, Calories in one cheeseburgers = 135
And, Calories in one medium fries = 583
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1589
Calculator
120°
126
What is the value of x?
125
139
Enter your answer in the box
121°
Answer:aaaa
Step-by-step explanation:because
what's the geometric mean between 3√5 and 6√5
Answer:
3√10
Step-by-step explanation:
[tex]GM=\sqrt{(3\sqrt{5})(6\sqrt{5})}=\sqrt{18*5}=\sqrt{90}=3\sqrt{10}[/tex]
Answer: [tex]3\sqrt{10}[/tex]
Work Shown:
Part 1
[tex]g = \text{geometric mean of x and y}\\\\g = \sqrt{\text{x}\text{y}}\\\\g = \sqrt{3\sqrt{5}*6\sqrt{5}}\\\\g = \sqrt{(3*6)*(\sqrt{5}*\sqrt{5})}\\\\g = \sqrt{18\sqrt{5*5}}\\\\g = \sqrt{18\sqrt{5^2}}\\\\g = \sqrt{18*5}\\\\g = \sqrt{90}\\\\[/tex]
Part 2
[tex]g = \sqrt{90}\\\\g = \sqrt{9*10}\\\\g = \sqrt{9}*\sqrt{10}\\\\g = 3\sqrt{10}\\\\[/tex]
Need answers stat trigonometry
The required measure of x is given in each triangle are given as,
2. x = 74.01 3. 25.09 4. x = 23.78
5. x = 26.64 6. x = 21.03° 7. x = 39.55°
If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
2.
For the given triangle
Apply the trigonometric ratios,
Tan 62 = x/25
x = 25 tan62
x = 74.01
Similarly,
3. x = 11/sin26 = 25.09
4. x = 32sin48 = 23.78
5. x = 29/cos12 = 29.64
6. cosx = 14/15 = 21.03°
7. tanx = 19/23 = 39.55°
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8x^{2}-8x8x
2
−8x from -6x^{2}-10x+4−6x
2
−10x+4.
The value of the equation 8x² - 8x + 2 -( 6x² - 10x + 4) is 2x² + 2x - 2.
How to illustrate the equationIt should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that
two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
The equation can be illustrated thus:
8x² - 8x + 2 -( 6x² - 10x + 4)
8x² - 8x + 2 - 6x² + 10x - 4
= 2x² + 2x - 2
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What is 42−6×4(12) to the third power?
Answer:
Step-by-step explanation:
First, we need to evaluate the expression inside the parenthesis: 4(12) = 4 * 12 = 48.
Next, we can simplify the expression: 42 - 6 * 48 = 42 - 288 = -246.
Finally, we raise the result to the third power: (-246)^3 = (-246) * (-246) * (-246) = -158,048.
So, the result is -158,048.
120 pens and pencils triple the number of pens than pencils how many pens
If number of pencils are triple the number of pens, then the number of pens is 30
Total number of pens and pencils = 120
Number of pencil is triple the number of pens
Consider the number of pens as x
Number of pencils = 3x
Sum of the pens and pencils = 120
Then the equation will be
Number of pens + Number of pencils = Sum of number of pens and pencils
Substitute the values in the equation
x + 3x = 120
Add the like terms
(1 + 3)x = 120
4x = 120
Move 4 to the right hand side of the equation
x = 120 / 4
x = 30
Therefore, the number of pens is 30
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Answer please! 50 Points!
A stereo that regularly sells for $330 is on sale at 15% off. How much will a customer save on the stereo during the sale?
Answer: 49.5 dollars
Step-by-step explanation: the original price is 330, but the sale takes 15 percent off
so we turn 15% into a decimal so we can multiply 330 and 15%
we get 0.15 × 330 = 49.5
what is the problem from y=x+1
Answer: Change x to a number, and that number + 1 will be y
Step-by-step explanation: the reason for this is simple, change the independent variable, which is always in the problem, and you can figure out the dependent variable.
Answer:
X +1
Step-by-step explanation:
the graph is x +1.....
Alexa is saving up to buy a new jacket. She already has $45 and can save an
additional $7 per week using money from her after school job. How much total
money would Alexa have after 8 weeks of saving? Also, write an expression that
represents the amount of money Alexa would have saved in w weeks.
Answer:
Step-by-step explanation:
Answer: 101because if you multipled 7 times 8 you will get 56 and if you add it with 45 you will get 101
i hope this help
After 8 weeks of saving, Alexa will have a total of $101. The expression to show the money Alexa saves in 'w' weeks is 45 + 7w.
Explanation:The subject of this question is
Mathematics
and it is geared towards
Middle School
grades. To solve this problem, we need to use
algebraic expressions
. Based on the problem given, Alexa has $45 initially and saves $7 per week additionally from her after school job. So if she saves for 8 weeks, Alexa would have accumulated an additional $7 times 8 = $56. Therefore, the total amount of money Alexa would have after 8 weeks is her initial amount of $45 plus the additional $56, which equals $101. To represent this in terms of an expression, where 'w' stands for weeks, you can write 45 + 7w. This expression lets us calculate the total savings for any number of weeks 'w'.
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the product 2√3 and 3√12 in simplified form is
The product of 2√3 and 3√12 in simplified form is 6√36. To simplify this expression, we can first multiply 2 and 3 to get 6. Then, we can simplify the square root of 3 and the square root of 12 by finding their prime factorizations:
√3 = √(3 * 1) = √3
√12 = √(12 * 1) = √(2^2 * 3) = 2√3
So, 2√3 = 2 * √3 = 2 * √3
And, 3√12 = 3 * 2√3 = 6√3
Finally, the product of 2√3 and 3√12 is 6 * 6√3 = 6√36.
11) Dalton calls a local moving company to determine how much it will cost him to move. If he hires 2 movers and rents a truck for an hour it costs $65. It costs $80 to hire 3 movers and rent a truck for an hour. What is the hourly rate to hire a mover? What is the hourly rate to rent the truck?
Answer: $35.
Step-by-step explanation: Let A = 2 movers and one truck for hour = $65
B = 3 movers and one truck for hour = $80
So, 1 mover = B - A
= $80 - $65
= $15
Hence, 2 movers cost = 2 × $15
= $30
SO, rent of the truck hourly = A - cost of 2 movers
= $65 - $30
= $35
Therefore cost of renting the truck for an hour = $35
a= 340 rounded to the nearest 10
b= 49.8 rounded to 1 DP
Find the minimum of a × b
Answer: First, we'll round the values of A and b:
A = 340 rounded to the nearest 10 = 340
b = 49.8 rounded to 1 decimal place = 49.8
Next, we'll find the product of A and b:
A × b = 340 × 49.8 = 16872
Finally, we'll find the minimum of A × b:
Minimum of A × b = 16872
So, the minimum value of A × b is 16872.
Step-by-step explanation:
At hannah’s school 3/5 of the school playground is covered with grass and 5/8 of the grassy area is a baseball field. How much of the school playground is taken up by the baseball field
The baseball field takes up 3/8 or 37.5% of Hannah’s school playground. This means that the remaining 62.5% of the playground is taken up by other materials and the grassy area not occupied by the baseball field.
Hannah’s school playground is divided into two parts, with the majority of it being covered in grass. Specifically, 3/5 of the playground is grassy and the remaining 2/5 is taken up by other materials such as pavement or gravel. Of the grassy area, 5/8 is taken up by the baseball field. This means that the baseball field occupies a total of 15/40 or 3/8 of the entire playground.
In terms of proportions, if we consider the entire playground to be 100%, then the amount of the playground taken up by the baseball field is 3/8, or 37.5%. This means that 62.5% of the playground is taken up by the other materials and the remaining grassy area not occupied by the baseball field.In terms of area, the total size of the playground can be determined by multiplying the length of the playground by its width. If we assume that the length and width are equal, then the area of the playground can be calculated as the length squared. The area of the baseball field can then be calculated by multiplying 3/8 by the total area of the playground. This will give us the total area of the baseball field.
Overall, the baseball field takes up 3/8 or 37.5% of Hannah’s school playground. This means that the remaining 62.5% of the playground is taken up by other materials and the grassy area not occupied by the baseball field.
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Lena estimate is there a bottle contains 500 mm of water but actually contains 473 mm of water what is the percent error and Lena's estimate rounded to the nearest 10th of a percent HURRY FAST PLS!!!
5.4% is the percent error .
What is the formula for errors?
The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error.
The relative error is multiplied by 100 to calculate the % error, in other words. The absolute value of the difference between the measured value and the actual value is divided by the actual value, then multiplied by 100 to get the percent error.
= 500 - 473/500 * 100
= 27/500 * 100
= 5.4%
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The proportion of twins born in a town is p = 0.12. Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the mean of the sampling distribution of p hat ?
Mu Subscript p hat = p = 0.12
Mu Subscript p hat = n p = 100 (0.12) = 12
Mu Subscript p hat = 1 minus p = 1 minus 0.12 = 0.88
Mu Subscript p hat = n (1 minus p) = 100 (1 minus 0.12) = 88
The sampling distribution of p hat follows a normal distribution thus, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
The most typical form of distribution assumed in technical stock market analysis and other statistical investigations is the normal distribution. The mean and the standard deviation are the two variables that make up the standard normal distribution.
The sampling distribution of p hat follows a normal distribution thus,
Mu Subscript p hat = p
Here, the value of p = 0.12
Hence, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.
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Answer:
A. Mu Subscript p hat = p = 0.12
Step-by-step explanation:
Now look at the exponential expression you found to be equivalent to 100,000 • 1/100,000 can you use addition or multiplication on the powers of this exponential expression to simplify it if not which operation works and which one doesn’t
The expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1.
The exponential expression that is equivalent to 100,000 • 1/100,000 is:
[tex](10^5) * (10^-5)[/tex]
To simplify this expression using addition or multiplication on the powers, we can use the property of exponents that states:
[tex]a^m *a^n = a^{(m+n)[/tex]
This means that when we multiply two numbers with the same base, we can add their exponents to simplify the expression. However, this property does not work for division, as we need to subtract the exponents instead.
Using this property, we can simplify the expression as follows:
[tex](10^5) * (10^-5) = 10^{(5-5)} = 10^0 = 1[/tex]
Therefore, the expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1. We can see that in this case, addition and multiplication do not help us simplify the expression, but we can use the exponent property to do so.
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Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.
Enter the correct answer in the box by replacing the values of m and b.
The slope-intercept equation of this linear function is y = -3x + 5.
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.Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (5, 2).At point (0, 5), a linear equation of this line can be calculated in slope-intercept form as follows:
y - 5 = (2 - 5)/(1 - 0)(x - 0)
y - 5 = -3(x - 0)
y = -3x + 5
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A hotel swimming pool measures 20 m by 8m.The hotel manager wants to put a 2 m wide deck around the pool. Caluculate the area of the deck.
Help please Hurry
What conclusion can be drawn about the number of trials and the probability of the coin landing on heads or tails? (1 point)
O a
О b
• c
O d
The experimental probability is closer to the theoretical probability for group Y than group X.
The experimental probability and the theoretical probability for group X is the same.
The experimental probability and the theoretical probability for group Y is the same.
The experimental probability is closer to the theoretical probability for group X than group Y.
The conclusion that can be drawn about the number of trials and the probability is A. The experimental probability is closer to the theoretical probability for group Y than X.
How to find the probability ?The theoretical probability for picking a heads or tails is 50 % as there are only two outcomes of heads and tails.
The experimental probability for heads is 53 % in Group Y and 47 % for tails. This is close enough to the 50 % theoretical probability.
For group X, the experimental probability for heads for Group x is :
= 33 / 50
= 66 %
This is too far from the theoretical probability.
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