The matrix \( A \) is not diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \), because there does not exist a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).
The matrix \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & -1 & 1\end{array}\right] \) is diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \) if and only if there exists a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).
To determine if \( A \) is diagonalizable, we need to find the eigenvalues and eigenvectors of \( A \).
The characteristic polynomial of \( A \) is given by:
\(\det(A-\lambda I)=\left|\begin{array}{ccc}1-\lambda & 0 & 0 \\ 0 & 1-\lambda & 1 \\ 0 & -1 & 1-\lambda\end{array}\right|=(1-\lambda)^{3} \)
The eigenvalues of \( A \) are the roots of the characteristic polynomial, which are \( \lambda=1 \) with multiplicity 3.
To find the eigenvectors of \( A \), we need to solve the equation \( (A-\lambda I)x=0 \) for each eigenvalue.
For \( \lambda=1 \), we have:
\( (A-1I)x=0 \)
\(\left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{array}\right]x=0 \)
The solution to this equation is the eigenspace of \( \lambda=1 \), which is spanned by the eigenvector \( x=\left[\begin{array}{c}1 \\ 0 \\ 0\end{array}\right] \).
Since the eigenspace of \( \lambda=1 \) has dimension 1, there is only one linearly independent eigenvector for this eigenvalue. Therefore, the matrix \( A \) is not diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \), because there does not exist a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).
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Suppose that a distribution is normal, with mean =10 and standard deviation =3. Two samples a and b, each of length N, are independently drawn from this distribution. For which of the following operations on a and b will the resulting distribution also be normal?
If the distribution is normal, state this and provide exact mathematical expressions (integer, fraction, radical, etc.) for the mean, median, and standard deviation of the new distribution (do not use a decimal). If the distribution is not normal, use R to numerically estimate the values and express the result as a decimal (at least 3 significant figures).
Summarize your results in a table similar to the one given below. (Note that some quantities may not be well-defined mathematically. You do not have to check for this, but you can mark possible cases with asterisks.)
Yes, the distribution of a and b is normal, with mean μ=10, median m=10, and standard deviation σ=3.
The resulting distribution of a+b, a-b, a*b, and a/b will also be normal, with the following values:
Operation
Mean
Median
Standard Deviation
a+b
μ=20
m=20
σ=√6
a-b
μ=0
m=0
σ=√6
a*b
μ=100
m=100
σ=30
a/b
μ=3
m=3
σ=1
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What is the value of x in the equation 8+4=2(x-1) brainly 5 11/2
The value of x in the equation 8+4=2(x-1) is 7
To solve for x in the equation 8+4=2(x-1), we can follow these steps:
Simplify the left-hand side of the equation by adding 8 and 4 to get 12:
8 + 4 = 12
Simplify the right-hand side of the equation by distributing the 2 to the expression inside the parentheses:
2(x-1) = 2x - 2
Set the left-hand side and the right-hand side equal to each other:
12 = 2x - 2
Add 2 to both sides of the equation:
12 + 2 = 2x
14 = 2x
Divide both sides of the equation by 2:
14/2 = x
x = 7
Therefore, the value of x in the equation 8+4=2(x-1) is 7.
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Find the image vertices for a dilation with center (0,0) and scale factor of 4.
The real number
t
corresponds to the point
P(− 2
1
, 2
3
)
on the unit circle. Evaluate the six trigonometric functions of
t
. Write your answer as a simplified frection, if necessary, Part 2 of 6
cost=
Part 5 of 6
The real number t corresponds to the point P(-2/1, 2/3) on the unit circle. To evaluate the six trigonometric functions of t, we can use the coordinates of point P.
Part 2 of 6:
cost= x-coordinate of point P = -2/1 = -2
Part 5 of 6:
sect= 1/cost= 1/(-2)= -1/2
The other four trigonometric functions can be evaluated similarly using the coordinates of point P:
sint= y-coordinate of point P = 2/3
cott= x-coordinate/y-coordinate = (-2/1)/(2/3) = -3
csc t= 1/sint= 1/(2/3)= 3/2
tant= y-coordinate/x-coordinate = (2/3)/(-2/1) = -1/3
Therefore, the six trigonometric functions of t are:
sint= 2/3
cost= -2
tant= -1/3
csc t= 3/2
sect= -1/2
cott= -3
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Add Mixed Numbers with unlike denominators!.
5 7/8 +4 1/3 + 7 5/6 ?
Answer:
[tex]18\frac{1}{24}[/tex] ≅ 18.0416667
Step-by-step explanation:
5 7/8 + 4 1/3 + 7 5/6 = [tex]\frac{433}{24}[/tex]
1.Conversion a mixed number 5 7/8
to an improper fraction: 5 7/8 = 5 7/8
= 5 · 8 + 7/8
= 40 + 7/8
= 47/8
To find a new numerator:
a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8
b) Add the answer from the previous step 40 to the numerator 7. New numerator is 40 + 7 = 47
c) Write a previous answer (new numerator 47) over the denominator 8.
Five and seven-eighths is forty-seven eighths.
2. Conversion a mixed number 4 1/3
to an improper fraction: 4 1/3 = 4 1/3 = 4 · 3 + 1/3 = 12 + 1/3 = 13/3
To find a new numerator:
a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3
b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 3.
Four and one-third are thirteen-thirds.
3. Add: 47/8
+ 13/3
= 47 · 3/8 · 3
+ 13 · 8/3 · 8
= 141/24
+ 104/24
= 141 + 104/24
= 245/24
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(8, 3) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 3 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - forty-seven eighths plus thirteen-thirds is two hundred forty-five twenty-fourths.
4. Conversion a mixed number 7 5/6
to an improper fraction: 7 5/6 = 7 5/6 = 7 · 6 + 5/6 = 42 + 5/6= 47/6
To find a new numerator:
a) Multiply the whole number 7 by the denominator 6. Whole number 7 equally 7 * 6/6= 42/6
b) Add the answer from the previous step 42 to the numerator 5. New numerator is 42 + 5 = 47
c) Write a previous answer (new numerator 47) over the denominator 6.
Seven and five-sixths are forty-seven-sixths.
5.Add: the result of step No. 3 + 47/6= 245/24 + 47/6 = 245/24 + 47 · 4/6 · 4 = 245/24 + 188/24 = 245 + 188/24 = 433/24
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(24, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 24 × 6 = 144. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - two hundred forty-five twenty-fourths plus forty-seven sixths are four hundred thirty-three twenty-fourths.
Who can help me please
The similarity statements are;
SV/RS = TV/TU
AC/AB = CE/ED
What are similar triangles?Formally, two triangles ABC and DEF are similar if and only if:
Their corresponding angles are congruent, meaning that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F.
The corresponding sides are in proportion to each other, meaning that the ratio of the length of side AB to side DE is equal to the ratio of the length of side BC to side EF, which is also equal to the ratio of the length of side AC to side DF.
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Comparing and Building Functions: Functions That Fit
Answer:
i do not know
Step-by-step explanation:
mmmmdjfhyhbwsdhsiayjbe
Answer:
What i arithmetic property is stated as a multiply by (b+c) =(a multiply by b) +(a multiply by c)use the table that shows air mail letter rates to greenland. weight 5.0, 6.0, 7.0, 80. Rate: 4.20, 5.05, 5.90, 6.75
The set of ordered pairs from the given table is: (5.0, 4.20), (6.0, 5.05), (7.0, 5.90), (8.0, 6.75).
What are ordered pairs?When two items are written inside parantheses and are separated by a comma, they create an ordered pair. For instance, the ordered pair (x, y) indicates an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables or constants, have distinct names depending on the context in which they are used. In an ordered pair, the element order is quite significant. It implies that (x, y) may not always be equivalent to (y, x).
The set of ordered pairs from the given table is:
(5.0, 4.20)
(6.0, 5.05)
(7.0, 5.90)
(8.0, 6.75)
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The complete question is:
HURRY PLEASE
Question 4. A high school sports team is ordering sports drinks online from a company. The price of sports drinks varies, based on the number of drinks purchased. For orders of 50 or fewer sports drinks, the price is $0.80 per drink, plus $10 shipping and handling. When more than 50 sports drinks are ordered, the price is $0.70 per drink, plus $15 shipping and handling. What is the maximum amount of sports drinks you can purchase for $75?
A. 85
B. 81
C. 92
D. 107
The maximum amount that can be purchased is 84.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, a high school sports team is ordering sports drinks online from a company.
Let the amount of drinks be y and number of drinks be x.
For drink not more than 50.
y=10+0.8x ------(i)
For drinks more than 50
y=15+0.7x ------(ii)
For a purchase of $75, it means that:
y=75
Substitute y=75 in equation (i), we get
y=10+0.8x
75=10+0.8x
0.8x=75-10
0.8x=65
x= 65/0.8
= 81.25
x=81
Substitute y=75 in equation (ii), we get
y=15+0.7x
75=15+0.7x
0.7x=60
x=85.7
x=84
By comparing both values
x=84 and x=81
84>81
Hence, the maximum amount that can be purchased is 84.
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Austin is 6 years older than Roya. In 3 years the sum of their ages will be 54 . How old is Austin now?
Austin is currently 27 years old.
Explanation:
To find out how old Austin is now, we need to use algebra. Let's start by assigning variables to represent their ages. Let A be Austin's current age and R be Roya's current age.
According to the question, we know that:
A = R + 6 (since Austin is 6 years older than Roya)
In 3 years, their ages will be:
A + 3 (for Austin)
R + 3 (for Roya)
And the sum of their ages in 3 years will be 54:
A + 3 + R + 3 = 54
Simplifying the equation gives us:
A + R = 48
Substituting the first equation into the second equation gives us:
R + 6 + R = 48
Combining like terms gives us:
2R = 42
Dividing both sides by 2 gives us:
R = 21
Now that we know Roya's current age, we can use the first equation to find Austin's current age:
A = R + 6
A = 21 + 6
A = 27
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Do segments with lengths 11, 12, and 20 form a triangle? If so, classify the triangle as acute, right, or obtuse?
Answer:
Yes, the segments with lengths 11, 12, and 20 can form a triangle.
To check this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we can check that:
11 + 12 > 20
11 + 20 > 12
12 + 20 > 11
Since all three inequalities are satisfied, the segments can form a triangle.
To classify the triangle, we can use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, for a triangle with sides a, b, and c and angle A opposite side a, we have:
c^2 = a^2 + b^2 - 2ab cos(A)
Using this formula, we can find the cosine of each angle and determine if the triangle is acute, right, or obtuse based on the values obtained.
For the given triangle, we have:
a = 11, b = 12, c = 20
cos(A) = (b^2 + c^2 - a^2) / (2bc) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) ≈ 0.714
Since cos(A) is positive and less than 1, the angle A is acute. Similarly, we can find the cosines of the other angles:
cos(B) = (c^2 + a^2 - b^2) / (2ca) ≈ 0.943
cos(C) = (a^2 + b^2 - c^2) / (2ab) ≈ -0.519
Since cos(B) and cos(C) are both positive and less than 1, angles B and C are also acute.
Therefore, the given triangle is acute.
Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. csc(u) = 3, 0 < u < /2
By answering the supplied question, we may infer that the response is trigonometry Cos(2u) = -7/9, Sin(2u) = 4sqrt(2)/9, and Tan(2u) = 3/4.
what is trigonometry?The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, about in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. Consequently, studying geometry entails learning about the characteristics of all geometric forms.
The values of sin(2u), cos(2u), and tan(2u) in terms of the given value of u may be determined using the double-angle formulae.
The formulae for double angles are as follows:
[tex]2sin = sin(2u) (u)[/tex]
cos(u)
(2u) = cos(2u)
The formula is 2(u) - sin(u) tan(2u) = (2tan(u)) / (1-tan(u)).
We may use the definition of csc(u) to obtain sin(u) given that csc(u) = 3 and 0 u /2:
[tex]sin(u) = 3 sin(u) = 1/3 csc(u) = 1/sin(u)[/tex]
Now we can calculate sin(2u), cos(2u), and tan(2u) using the double-angle formulas:
[tex]2sin = sin(2u) (u)[/tex]
sqrt(1 - sin2(u)) = 2/3 sqrt(8/9) = 4sqrt(2)/9 cos(u) = 2(1/3)
[tex]cos(2u) = sin - cos2(u)[/tex]
2(u) = (1 - sin 2(u)) sqrt
[tex]a^2 - sin^2(u) = 1/9 - 8/9 = -7/9[/tex]
[tex]tan(2u) = (2tan(u)) / (1-tan(2u)) = (2(1/3)) / (1-(1/3)2) = 6/8 = 3/4[/tex]
Cos(2u) = -7/9, Sin(2u) = 4sqrt(2)/9, and Tan(2u) = 3/4.
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If the price of cocoa beans goes up, what will happen to the supply of chocolate?
Producers will produce more chocolate
The supply of chocolate will remain unchanged
Producers will offer less chocolate to the market
The demand for chocolate will immediately increase
Answer:
producers Will grow more chocolate.
A company makes wax candles in the shape of a cylinder. Each candle has a radius of 3 inches and a height of 4 inches. How much wax will the company need to make 140 candles?
Use 3.14 for \pi , and do not round your answer.
Answer:
15825.6 [tex]in^3[/tex]
Step-by-step explanation:
using 3.14 for pi you follow the formula for volume of a cylinder which is [tex]\pi r^2 h[/tex] when we plug in it comes to [tex]3.14\cdot3^{2}\cdot4[/tex] and then you solve that to get 113.04, but since you need 140 candles, we multiply the volume of one candle by 140 to get 15825.6 [tex]in^3[/tex]
Calculate the present value to purchase a watch of land if 18,000 is put down and 2000 is paid per quarter for five years assume that there a 6% interest is compounded quarterly  if the cash price for the land is 25,000 is it better to pay cash or finance the purchase according to the present value of an annual tea table at 1.5% interest for five years the factor is 17.16864.
The present value of the land is $52,337.28
What is Present Value?The worth of an anticipated revenue stream assessed as of the valuation date is known as a present value in the fields of economics and finance.
There are different kinds of PV models including:
net present value (NPV),internal rate of return (IRR),maximum (minimum) bid (sell),annuity equivalent (AE),loan formula,optimal term,replacement,incremental,How to solve:
We use the formula:
Present value of land = put down payment = PV of annuityPresent value of land= $18,000 + (Quarterly payment + Annuity factor)Present value of land= $18,000 + (2,000 * 17.1684)= $52,337.28
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then simplify. ything you can FIRST, 10. (4a^(2)b^(2))/(15ab^(3))*(5a^(3)b^(6))/(12a^(4)b^(7))
The simplified expression is 1/(9a²b⁵).
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
To simplify the given expression, we need to cancel out any common terms in the numerator and denominator. We can do this by dividing both the numerator and denominator by the highest power of a and b that they have in common. Here are the steps:
1. (4a²b₂²)/(15ab³)*(5a³b⁶)/(12a⁴b⁷)
2. Cancel out the common terms in the numerator and denominator:
= (4/15)*(5/12)*(a²/a⁴)*(b²/b⁷)*(a³/a⁴)*(b⁶/b⁷)
3. Simplify the terms:
= (1/9)*(1/a²))*(1/b⁵)
4. Multiply the terms together:
= 1/9a²b⁵
So the simplified expression is1/(9a²b⁵)
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The Class 2022 had 202 students who took the Statistics course. Their mean score in the Final Test was 80.
a) Suppose a friend of yours concluded 50% of students had a test score higher than 80 with an estimation error of 0.07. Are you skeptical of your friend’s claim? Explain why.
b) For the Class 2023, suppose the mean score of the Final Test is 70. The friend of yours now concludes that Class 2022 did better than Class 2023 in the Final Test. Are you skeptical of your friend’s claim? Explain why.
a) Yes, I am skeptical of my friend's claim. The mean score of the class is 80, which means that the average score of all the students is 80.
b) I am also skeptical of my friend's claim that Class 2022 did better than Class 2023 in the Final Test. While the mean score of Class 2022 is higher than the mean score of Class 2023, this does not necessarily mean that Class 2022 did better.
If 50% of the students had a score higher than 80, then the other 50% of the students would have to have a score lower than 80 in order for the mean to be 80. However, my friend's estimation error of 0.07 means that there is a possibility that the true percentage of students with a score higher than 80 is actually between 43% and 57%. Therefore, it is not certain that 50% of the students had a score higher than 80.
It is possible that the distribution of scores for Class 2022 is more spread out, with some students scoring very high and some students scoring very low, while the distribution of scores for Class 2023 is more consistent. Without knowing the standard deviation or the range of the scores for each class, it is not possible to accurately compare the performance of the two classes.
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La importancia de los vectores en la vida diaria
Answer: I speak a little spanish but hopefully this helps:)
Los vectores son muy utilizados en muchos ámbitos de la vida cotidiana porque permiten conocer magnitudes y representarlas a partir de su módulo, sentido y dirección. Suelen usarse para: Marcar recorridos.
Step-by-step explanation:
I really need the answers to this math equation
Length of the side of square is x = 5.7 unit
What is Pythagoras theorem?The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base and the hypotenuse. Here, the hypotenuse is on the opposite side of the 90° angle, so it is the longest side.
Given,
Figure of a rectangle and a right triangle share its hypotenuse with length of rectangle
diagonal of rectangle = 8
length of both sides of right triangle other than hypotenuse = 4
Let length of rectangle be l
By Pythagoras theorem
l² = 4² + 4²
l² = 32
l = 4√2
Now, In the rectangle
8² = l² + x²
64 = 32 + x²
x² = 32
x = 4√2
x = 5.7
rectangle is an square.
Hence value of x, length of the side of square is 5.7 unit.
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I need help! ty !!!! I gatta pass math class
The answer should be D.
let ABC be a triangle. Determine the exact values of
the three angles A, B, C. if we know that A = 5x, B = 6x, and C =
7x
For the given triangle ABC, the exact values of the three angles are: A = 50°, B = 60°, and C = 70°.
Let ABC be a triangle. The angles A, B, and C can be determined using the fact that the sum of the angles in any triangle is 180°.
We know that
A = 5x, B = 6x, and C = 7x, so:
A + B + C = 5x + 6x + 7x = 18x
Since the sum of the angles in a triangle is 180°, we can set
18x = 180°
and solve for x:
18x = 180°, x = 10°
Therefore, A = 50°, B = 60°, and C = 70°.
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Factor the following complex matrices into unitary times upper triangular:
(i) i 1 , (ii) 1+i 2-1 , (iii) i 1 0 , -1 2i 1-i -1 1 i 1
0 1 i
(iv) 1 1 -i
1-i 0 1+i
-1 2+3i 1
The answer is calculated by elementary row operations
To factor the given complex matrices into unitary times upper triangular, you will need to use elementary row operations. Specifically, you can use scaling, addition, subtraction, and multiplication of rows.
(i) i 1:
Row 1: Scale by i
Result: i2 1 = -1 1
(ii) 1+i 2-1:
Row 1: Subtract Row 2
Result: 1 0 -1
Row 2: Scale by i
Result: i 1 -i
(iii) i 1 0 , -1 2i 1-i -1 1 i 1
Row 1: Subtract i times Row 2
Result: 0 1 0 , -1 2i 0 -i -1 0 i
Row 2: Scale by i
Result: 0 1 0 , i 0 -1 -i -1 0 1
Row 3: Subtract Row 1
Result: 0 0 0 , i 0 -1 -i -1 0 1
(iv) 1 1 -i
Row 1: Subtract Row 2
Result: 1 0 -i
Row 2: Scale by i
Result: i 0 1+i
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer: x=-6
Step-by-step explanation:
8x+14=4x-10
-4x -4x
4x+14=-10
-14 -14
4x=-24
/4 /4
x=-6
Given:-
[tex] \tt \: 8x + 14 = 4x - 10[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 8x + 14 = 4x - 10[/tex][tex] \: [/tex]
[tex] \tt \: 8x - 4x = -10 - 14[/tex][tex] \: [/tex]
[tex] \tt \: 4x = -24[/tex][tex] \: [/tex]
[tex] \tt \: x = \cancel\frac{ - 24}{4} [/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \purple{ \: x = -6 \: }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
The sum of two numbers is 54 and the difference is 2. What are the numbers?
Answer:
25, 27
Step-by-step explanation:
maybe ,,,,,,,,,hhy2u2u
Answer: Sum: 28 + 26 = 54
Difference: 28 - 26 = 2
Step-by-step explanation:
x + y = 54
x + 26 = 54
X = 28
Use the compound interest formula \( A=P e^{\lambda t} \) to solve. Round to two decimal places. Find the accumulated value of an investment of \( \$ 5,000 \) at \( 9 \% \) compounded continuously for
The accumulated value is $A = 5000 \times e^{(0.09 \times 4)} = 7,311.12$.
The accumulated value of an investment of $\$ 5,000$ at 9% compounded continuously for 4 years is $7,311.12.
This can be calculated using the compound interest formula
\(A=P e^{\lambda t}\).
In this equation, A is the accumulated value of the investment, P is the principal investment amount (which is $\$ 5,000$), $\lambda$ is the interest rate per compounding period (which is 0.09) and t is the number of compounding periods (which is 4 years).
Therefore, the accumulated value is $A = 5000 \times e^{(0.09 \times 4)} = 7,311.12$.
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Which number is NOT in the solution set of x + 8 > 15
A. 10
B. 12
C. 8
D. 6
Answer:
6
hope this helps! :)
the number that is not in the solution set of x + 8 > 15 is 6
Eight people are to be seated in a row of 8 chairs. In how many ways can these people be seated if two of them insist on sitting next to one another?
The final answer is 8*2=16 ways
Eight people are to be seated in a row of 8 chairs. In how many ways can these people be seated if two of them insist on sitting next to one another?
There are a couple of steps to solving this problem.
Step 1: Consider the two people who insist on sitting next to one another as one unit. This means that there are now 7 units to be seated in the 8 chairs.
Step 2: Calculate the number of ways that the 7 units can be seated in the 8 chairs. This is done using the formula n!/(n-r)!, where n is the number of chairs and r is the number of units. In this case, n=8 and r=7, so the formula is 8!/(8-7)!, or 8!/1!, which simplifies to 8.
Step 3: Calculate the number of ways that the two people who insist on sitting next to one another can be seated within their unit. There are 2! or 2 ways that they can be seated.
Step 4: Multiply the number of ways that the 7 units can be seated in the 8 chairs by the number of ways that the two people can be seated within their unit. This gives us the total number of ways that the 8 people can be seated if two of them insist on sitting next to one another.
So the final answer is 8*2=16 ways.
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help me what is it i need urgent help
Answer:
#1 is equivalent
#2 is not equivalent
#3 is not equivalent
#4 is not equivalent
#5 is not equivalent
Hope this helps!
Which of the following shows a set of equivalent rational numbers?
A. 2/5 0.4 25%
B. 2/3 0.6 66%
C. 3/10 0.3 30%
D. 73/100 0.73 730%
Answer:
D is not equivalent because 730% is not a rational number.
PLEASE HELP!!! I don’t have to show any work btw! <33
1) Which of the following are the coordinates of point B’ , the image of point B after a translation of (x-4, y-3)
A- B’(-1,2)
B- B’(-4,-3)
C- B’(1,5)
D- B’(1,-2)
2) The two figures are congruent. Describe the isometry that maps the original figure onto the new figure.
A- Translation (x-3,y-1)
B- Reflection over the line x = 1
C- 90 Degree Rotation
D- 270 Degree Rotation
3) The smaller figure is a dilation of the original figure. Which two statements below are true?
A- The dilation is an enlargement.
B- The dilation is a reduction.
C- The dilation has a scale factor of 1/2
D- The dilation had a scale factor of 2
E- The dilation has a scale factor of 1/4
4) Complete a glide translation (x-2,y) and then reflect over x axis. What would be the new ordered pairs for P’ and S’?
A- P’(1,-2) S’(2,5)
B- P’(5,-2) S’(6,-5)
C- P’(1,2) S’(2,5)
D- P’(3,2) S’(4,5)
5) Complete a dilation with scale factor of 1/2 around the origin and then reflect over the y-axis. What are the new ordered pair of A’?
A- A’(-4,-10)
B- A’(-1,-2.5)
C- A’(2,5)
D- A’(1,2.5)
Tysm
The coordinates of B' after the translation represented by (x - 4, y - 3) is (1, -2). See other solutions below
The coordinates of B' after the translationB is located at the point (5, 1) in the figure.
If we translate the point by (x - 4, y - 3), the new location of B, denoted by B', can be found by subtracting 4 from the x-coordinate and 3 from the y-coordinate.
Therefore, B' is located at (1, -2).
The isometry transformationThe given information provides us with a set of matching points, which are:
Preimage = (2, 1)
Image = (-1, 2)
These points can be represented by the equation:
(x, y) = (-y, x)
This equation indicates that the points have undergone a (d) clockwise rotation of 270 degrees.
The statements of the dilationHere, the smaller shape is created by scaling down a larger shape, the transformation is a dilation that results in a reduction.
The scale factor for this transformation could be either 1/2 or 1/4.
The glide transformatonGiven the points P = (3, -2) and S = (4, -5), we apply two transformations.
The first transformation (x - 2, y) is defined as shifting the x-coordinate of each point left by 2 units, while keeping the y-coordinate the same.
This results in new points P' = (1, -2) and S' = (2, -5).
The second transformation involves reflecting the new points across the x-axis, which changes the sign of their y-coordinates.
The resulting points are P'' = (1, 2) and S'' = (2, 5).
The new ordered pair of point AIn this context, we are given the coordinates of point A as (-2, -5).
This implies that if we scale down the original coordinates by a factor of 1/2, we get the new coordinates of point A, which become (-1, -2.5).
Therefore, the coordinates of point A' are (-1, -2.5).
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