(6 + a) + 8 = 6 + (a + 8)
(Choose one )
Commutative Property
Associative Property
Additive Identity Property
Additive Inverse Property

The correct answer is A. The statement is true. The transpose property states that (A+B)⊤ = A⊤ + B⊤.

The transpose of a matrix is obtained by interchanging its rows with columns. When adding two matrices, the sum is computed by adding the corresponding elements of the matrices.

Let's consider the transpose of (A+B). By definition, the (i, j)-th entry of (A+B)⊤ is equal to the (j, i)-th entry of (A+B). This means that the entry in the i-th row and j-th column of (A+B)⊤ corresponds to the entry in the j-th row and i-th column of (A+B).

Now, let's consider the matrices A⊤ and B⊤. The (i, j)-th entry of A⊤ + B⊤ is obtained by adding the (i, j)-th entries of A⊤ and B⊤. Since A⊤ has its rows and columns interchanged from A, the entry in the i-th row and j-th column of A⊤ corresponds to the entry in the j-th row and i-th column of A. Similarly, the entry in the i-th row and j-th column of B⊤ corresponds to the entry in the j-th row and i-th column of B.

Since the sum of the entries in the i-th row and j-th column of (A+B)⊤ and A⊤ + B⊤ are the same, we can conclude that (A+B)⊤ = A⊤ + B⊤.

Therefore, the statement A⊤ + B⊤ = (A+B)⊤ is true, and the transpose property holds for matrix addition.

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Answer:

32 Fahrenheit

Step-by-step explanation:

Since it is -8, subtract -8.

Now, you have 0 Fahrenheit.

Then, you add 24, since the high was -24 Fahrenheit.

The total number you added and subtracted is 32 Fahrenheit.

Hope this helps!

Answer:

D.

It is the graph of f(x) translated 3 units down.

Step-by-step explanation:

Answer: so your sister sends 14 messages a day

Step-by-step explanation: you send about twelve texts a day and as a total you both send 26 so lets let your sister be x and you are 12

26- 12=x

26-12= 14

I hope this was helpful!

Answer:

10.7a - 6

Step-by-step explanation:

(3 + 16.4a) − (9 + 5.7a)= 3 + 16.4a - 9 - 5.7a

                                   = 10.7a - 6

Answer:

28=-8a+4

Step-by-step explanation:

combine like terms

-6+-2=-8

-3+7=4

Answer: 30 degrees

Step-by-step explanation:

1 hour = 60 min = 360 degree

1 min = 360/60 degree

1 min = 6 degree

and the gap of hour hand and minute hand at 1pm, is of 5 min

therefore acute angle formed is 5 X 6 = 30 degrees.

:-)

Answer:

30 degrees

Step-by-step explanation:

1 hour = 60 min = 360 degree

1 min = 360/60 degree

1 min = 6 degree

and the gap of hour hand and minute hand at 1pm, is of 5 min

therefore acute angle formed is 5 X 6 = 30 degrees.

According to the division property of equality, if both sides of an equation are divided by a common real integer that is not zero, the quotients remain equal.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

The four key terminology used in the division process are dividend, divisor, quotient and remainder. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

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Answer:

34.06=20+0.19m

Step-by-step explanation:

The 20 dollars is a one-time thing so we don't need a variable for that. The 0.19 per mile does because the cost will depend on how many miles you drove (I used the variable 'm' but you could use a different letter). Altogether the bill costs 34.06 so that will go on the opposite side of our equal side.

34.06=20+0.19m

First we need to isolate 0.19m to find the number of miles the customer drove, and we can do that by subtracting 20 on each side.

34.06-20=20-20+0.19m

14.06=0.19m

Now we divide 0.19 because 0.19 is multiplied to m and division is the opposite operation

m=74

This means that the customer drove 74 miles.

The matrix A representing the linear transformation T from R3 to R4 with ker(T)={0} and im(T)=V is:

A = [[1, 1, 0],
    [1, 0, 1],
    [-2, 0, 2],
    [0, 0, 4]]

The subspace V is given by the equation x1 - x2 + 2x3 + 4x4 = 0. To find a linear transformation T with kernel {0} and image V, we need to determine a matrix A that sends each basis vector of R3 to a vector in V. We can find a basis for V by solving the given equation for x1, obtaining x1 = x2 - 2x3 - 4x4.

This implies that a basis for V can be {u1 = (1, 1, 0, 0), u2 = (-2, 0, 1, 0), u3 = (0, 0, 2, 4)}. To define the linear transformation T, we map the standard basis of R3 (e1, e2, e3) to the basis vectors of V: T(e1) = u1, T(e2) = u2, and T(e3) = u3. Combining the basis vectors as columns, we obtain the matrix A above.

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From the given options,√75 and 5π are the irrational numbers with a value greater than 5.

Irrational numbers are real numbers that cannot be represented as simple fractions. It cannot be expressed mathematically.

We need to find an irrational value which is greater than 5 from the options given as follows:

A. √75

B. 5.9

C. 5pi

D. 5

Options B and D are not irrational numbers so both are incorrect options.

For Option A,

\(\sqrt{75}\) = 8.66

For Option C,

5π = 15.70

We can see that both options A and C have irrational value greater than 5.

As a result, from the options given,√75 and 5π are irrational numbers with a value greater than 5.

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Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

4 1/2 servings

Step-by-step explanation:

3 ÷ 2/3 = 3 x 3/2 which is 9/2 or 4 1/2 servings

Complex numbers are represented on a cartesian coordinate system with a horizontal real axis and a vertical imaginary axis.

Any number that can be expressed as a+bi, where i is the imaginary unit and a and b are the real numbers, is a complex number. The number is made up of two parts: real part (a) and imaginary part (b).

Just like we can use the number line to visualize a set of real numbers, we can use the complex plane to visualize a set of complex numbers. The complex plane consists of two number lines intersecting at a right angle at the point (0,0)(0,0)left parenthesis, 0, comma, 0, right parenthesis.

The horizontal number line (what we know as the xxx-axis on a Cartesian plane) is the real axis. The imaginary axis is the vertical number line (the yyy-axis on a Cartesian plane).A point in the complex plane can represent every complex number.

For example, consider the number 3-5i3−5i3, minus 5, i. This number, also expressed as 3+(-5)i, has a real part of 3 and imaginary part of -5. The location of this number on the complex plane is the point that corresponds to 3 on the real axis and -5 on the imaginary axis.

So the number 3+(-5) corresponds with the point (3,-5). In the general complex number, a+bi corresponds to the complex plane's point(a,b).

Hence, complex numbers are represented on a cartesian coordinate system with a real horizontal axis and an imaginary vertical axis.

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Answer:

Step-by-step explanation:

Use distributive property, then combine like terms. Don't forget if you divide by a negative number you have to reverse the symbol. Very important! See image.

Given a cylinder of radius = r = 6 ft, and a height = h = 10 ft

A conic portion removed from the cylinder

So, the volume of the remaining portion =

the volume of the cylinder - the volume of the cone

The volume of the cylinder =

The volume of the cone =

so, the answer will be =

So, the answer is option 3) 240pi

The number of salespeople that should be sampled is approximately 133.

To determine the number of salespeople that should be sampled to estimate the mean number of travel days per year with a 0.90 degree of confidence and an estimated population mean within two days, we can use the formula for sample size calculation.

The formula for sample size calculation is:

n = (Z * σ / E)^2

Where:

n = Sample size

Z = Z-score corresponding to the desired confidence level (0.90 in this case)

σ = Standard deviation of the population (14 days in this case)

E = Margin of error (2 days in this case)

Plugging in the values, we have:

n = (Z * σ / E)^2

n = (1.645 * 14 / 2)^2

n ≈ 133

Therefore, the number of salespeople that should be sampled is approximately 133.

To estimate the mean number of travel days per year with a desired degree of confidence and an estimated population mean within a certain margin of error, we need to calculate the appropriate sample size. In this case, the sample size is calculated using the formula that takes into account the desired confidence level, the standard deviation of the population, and the margin of error.

The Z-score is used to determine the critical value corresponding to the desired confidence level. In this case, the Z-score for a 0.90 confidence level is 1.645. The standard deviation of the population is given as 14 days, and the desired margin of error is 2 days.

By plugging in these values into the sample size formula, we can calculate the required sample size. In this case, the calculated sample size is approximately 133 salespeople. This means that if a sample of 133 salespeople is selected and their travel days per year are measured, we can estimate the mean number of travel days for the population with a 0.90 degree of confidence and an estimated population mean within two days.

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Answer:

25j=800 i may be wrong

Step-by-step explanation:

Answer:

Domain: x > -4

Range: y > -1

Step-by-step explanation:

Domain is the points on the x axis that could be vaild for that line.

Range is the points on the y axis that could be valid for that line.

Answer:

86 calories per serving

Step-by-step explanation:

430/5 =86

Answer:

-33x+2 I hope this is the answer

Answer:

15,000

Step-by-step explanation:

15×1000

Answer:

Look at the solution I gave properly. Not only the answer.

Answer:

X4

Step-by-step explanation:

Answer:

C. $42.00

Step-by-step explanation:

You use the equation:  amount earned × hours worked

So you will do $8.50 × 5 and you should get $42.00

So therefore, Katie's total earnings for the day is C. $42.00

The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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Answer:

.5 and .5, .75 and .25, ect

Answer:

0.5

Explanation:

Take one, divide that by two. You get a decimal number, which is .5.

(Not the only two numbers which go into one, but eh, it'll do)

Answer:

\( \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}\)

Step-by-step explanation:

Slope-intercept is in form of y = mx + b where m is slope and b is y-intercept. We simply solve for y in term of x and then we will obtain the slope-intercept form.

Given the linear equation:

\( \displaystyle{3x + 2y = 2}\)

First, subtract both sides by 3x:

\( \displaystyle{3x + 2y - 3x= - 3x + 2} \\ \\ \displaystyle{2y = - 3x + 2}\)

Then divide both sides by 2:

\( \displaystyle{ \dfrac{2y}{2} = \dfrac{ - 3x + 2}{2}} \\ \\ \displaystyle{ y = \dfrac{ - 3x + 2}{2}}\)

Separate fractions (Simplify):

\( \displaystyle{ y= \dfrac{ - 3x}{2} + \dfrac{2}{2}} \\ \\ \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}\)

And we have finally converted the equation to slope-intercept form.

If the diagonal of a rhombus id x-4d and x+ 4d then the area of rhombus is (x² - 16d²) / 4 unit²

In a rhombus, the diagonals are perpendicular bisectors of each other, and they divide the rhombus into four congruent right triangles. Let's call the length of one half of the diagonal "a" and the length of the other half of the diagonal "b". So we have:

a = (x - 4d) / 2

b = (x + 4d) / 2

The area of a rhombus can be calculated as half the product of its diagonals, or as half the product of its side lengths:

Area = (1/2) × a × b × 2

Area = a × b

Substituting the expressions for "a" and "b" from above, we get:

Area = [(x - 4d) / 2] × [(x + 4d) / 2]

Area = (x² - 16d²) / 4

Therefore, the area of the rhombus is (x² - 16d²) / 4 square units.

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Answer:

Solution is in the attached photo.

Step-by-step explanation:

Take note for this question we can use the Sine rule to straightaway find the unknown value.