Find the total surface area of the rectangular prism in the figure.

A) 174 cm^2
B) 348 cm^2
C) 522 cm^2
D) 432 cm^2

To solve for matrix D in the equation CAB⁻¹TDA⁻¹CTB⁻¹ = CAT, we can simplify the equation using matrix properties and inverse operations. The solution for D is given by D = BTA⁻¹ - C⁻¹B⁻¹A'B⁻¹(CT)⁻¹A⁻¹.

To arrive at this solution, let's analyze the equation step by step. We start by multiplying both sides of the equation by A⁻¹ from the left, giving us CAB⁻¹TD = CTB⁻¹. Next, we multiply both sides by B⁻¹ from the right, resulting in CAB⁻¹TDA⁻¹ = CT. Then, we multiply both sides by C⁻¹ from the left, obtaining B⁻¹TDA⁻¹ = C⁻¹CT. To isolate matrix D, we multiply both sides by B⁻¹T⁻¹ from the left, which cancels out the B⁻¹T on the left-hand side. This yields D = BTA⁻¹ - C⁻¹B⁻¹A'B⁻¹(CT)⁻¹A⁻¹.

The solution for matrix D in the equation CAB⁻¹TDA⁻¹CTB⁻¹ = CAT is given by D = BTA⁻¹ - C⁻¹B⁻¹A'B⁻¹(CT)⁻¹A⁻¹. This solution is derived by applying inverse operations and simplifying the equation step by step to isolate matrix D on one side of the equation.

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Answer:

C. 8√3

Step-by-step explanation:

trick

use the answer choices to get the answer

multiply the number outside the radical sign by itself

then multiply it by the number inside the radical sign

example

2√48

2*2*48 = 192

so that is the answer but it's NOT in its simplest form

simplest form means the smallest number inside the

radical sign

for 8√3 its

8*8*3=192

for 3√8 its

3*3*8=72

for 32√3 its

32*32*3=3072

Answer:

The probability of selecting a vowel is 5/26

Step-by-step explanation:

The probability of selecting a vowel

= number of vowels/total number of alphabets

The vowels are a,e,i,o,u = 5

Number of alphabets = 26

The probability is 5/26

Answer:

Given equation are 3x+4y=11 and 2x+3y=8

Comparing with a

1

x+b

1

y+c

1

=0 and a

2

x+b

2

y+c

2

=0 we have

a

1

=3,b

1

=4,c

1

=−11 and a

2

=2,b

2

=3,c

2

−8

Now , x=

a

1

b

2

−a

2

b

1

b

1

c

2

−b

2

c

1

and y=

a

1

b

2

−a

2

b

1

c

1

a

2

−c

2

a

1

⇒x=

3×3−2×4

4x(−8)−3×(−11)

and y=

3×3−2×4

−11×2−(−8)×3

⇒x=

9−8

−32+33

and y=

9−8

−22+24

⇒x=1 and y=2

Answer:

Saturday: 1.5x

Sunday: 2x

Step-by-step explanation:

    For the the Chart, Saturday, we can automatically see that when 1 is inputted into the equation we get 1.5, as anything times 1 will equal the same number inputted (x). So we can try 1.5x and plug in every other x value and see what we get:

1.5(2) = 3

1.5(3) = 4.5

1.5(4) = 6

This verifies that the equation 1.5x works with this chart.

   For the graph its simple, do rise over run and your slope is 2/1 which is 2 so we have 2x for our equation so far and now to find the + or - at the end of the equation ( the "b" variable of the mx + b form) we just look at where does the function intersect with the Y-axis. Since it is at 0 we don't need to add a "b" variable to the equation so the equation for the graph is 2x for Sunday.

Answer:

(n+5)(n-2)

Step-by-step explanation:

n^2+3n-10

(n+5)(n-2)

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

6c-1-6d

Step-by-step explanation:

Answer:

6c - 6d - 1

Step-by-step explanation:

Answer:

it is approximately 3.23333333

hope that helped and plz mark brainliest :D

Answer:

47.5

hope this helped

Answer:

47.5

Step-by-step explanation:

(a) To plot the point (6, 1/3, 1/6), we first convert to Cartesian coordinates as follows:

x = r sinφ cosθ = 6(1/3)cos(1/6π) ≈ 2.991

y = r sinφ sinθ = 6(1/3)sin(1/6π) ≈ 0.499 z = r cosφ = 6 cos(1/3π) ≈ 5.196

Therefore, the rectangular coordinates of the point (6, 1/3, 1/6) are approximately (2.991, 0.499, 5.196).

(b) To plot the point (3, 7/2, 37/4), we first convert to Cartesian coordinates as follows:

x = r sinφ cosθ = 3(1/2)cos(37/8π) ≈ -1.149

y = r sinφ sinθ = 3(1/2)sin(37/8π) ≈ -1.172 z = r cosφ = 3 cos(7/4π) ≈ -1.097

The rectangular coordinates of the point (3, 7/2, 37/4) are approximately (-1.149, -1.172, -1.097).

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Answer:

v = -170

Step-by-step explanation:

-v + 91 = 261

(-v + 91) - 91 = 261 - 91

-v = 170

-v / -1 = 170 / -1

v = -170

Step-by-step explanation:

(-v) +91 = 261

(-v) =91=261

(-v)=261-91

(-v)=170

v= - 170 (change the signs)

Answer:

D

Step-by-step explanation:

2 |  1   5   - 14

          2     14

  -----------------------

     1    7      0 ← remainder = 0

     Quotient is 1x + 7 = x + 7 → D

Answer:

Left=9.4cm Right = 12cm

Step-by-step explanation:

a^2 + b^2 = c^2

8^2 x 5^2 =89^2

Square that = 9.43cm

Right Triangle

17^2-12^2=b^2

=145^"

Square it: 12cm

This hypothesis test is two-tailed because no direction is specified in the claim made by the social worker.

A two-tailed test means that the alternative hypothesis is that the population parameter is different from the specified value (in this case, 15 children dropping out of high school each day). So, the null hypothesis would be that the population parameter is equal to 15, while the alternative hypothesis would be that it is either greater than or less than 15. Therefore, we need to conduct a two-tailed test to determine whether the social worker's claim is statistically significant. The correct answer to your question is: This is a two-tailed test because no direction is specified.

In this scenario, the social worker at the community development organization wants to test the claim that the average number of children who drop out of high school each day in a particular city is different than 15 children. The hypothesis test is two-tailed because there is no specified direction for the population parameter (whether it's greater than or less than 15 children). Instead, the test simply seeks to determine if the average number of dropouts is different from 15, which could be in either direction.

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Answer:

the correct answer is true luv

Answer:

True bye the way see u in musd school district

Answer:

The length of t, to the nearest tenth of an inch, is approximately 85.6 inches.

To determine the length of t in triangle TUV, we can use the law of sines.

The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In this case, we have:

- u = 380 inches (the length of side u)

- m∠V = 151° (the measure of angle V)

- m∠T = 25° (the measure of angle T)

We need to find the length of side t.

Using the law of sines, we can set up the equation;

sin(25°) / t = sin(151°) / 380

To solve for t, we can cross multiply and then divide by sin(25°):

t = (380 x sin(25°)) / sin(151°)

t ≈ 85.6 inches

Therefore, the length of t, to the nearest tenth of an inch, is approximately 85.6 inches.

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Answer: 1517.54

Step-by-step explanation:

So we can divide solving this question into two parts: the 2% compound interest and the 5% compound interest.

We know that the compound interest equations is A = P(1+r/n)^nt where:

A is final amount

P is principal (initial) amount

r is interest rate

n is number times interest compounded

t is number of time periods

Given this, in the 2% compound we know:

A = ?

P = 1200

r = 2%

n = 1 (because it didn't say how many times compounded so we assume 1)

t = 2

This becomes:

A = 1200 (1 + (0.02/1))^ 1 * 2

A = 1248.48

Because we switching to 5% from 2%, we can assume that the final amount from the 2% will be the initial amount in the 5%. Thus:

A = ?

P = 1248.48

r = 5%

n = 1

t = 4 (because there were 6 years in total and we used 2 years for 2%)

This becomes:

A = 1248.48 (1 + (0.05/1))^ 1 * 4

A = 1517.54

Hey there!

Functions are basically like machines you put a number into and they give you a new one as an output. This f represents this machine. f(x) represents whatever the output is because it is the x after it has gone through the function machine.

We want to figure out what x is when f(x)=12. Well, we can simply replace f(x) with 12 in the first equation and solve for x!

12=-16x+8

We flip the equation so x is on the left side.

-16x+8=12

We subtract 8 from both sides.

-16x=4

We divide both sides by -16.

x=-1/4

Have a wonderful day! :D

Answer:

f(x) = -16x + 8

F(x) = 12

=> f(12) = -16x + 8

=> 12-8 = -16x + 8 - 8

=> 4 = 16x

=> 4/16 = 16x/16

=> 1/4 = x

So, the answer is 1/4.

You can just keep 0 as the whole number to answer this question.

\(\red{➤}\:\)\(\sf \dfrac{6+8x}{2} = 5x\)

\(\\\)

\(\orange{☛}\:\)\(\sf Value \:of \: x \)

\(\\\)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{6+8x}{2} = 5x \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf 6+8x= 5x×2 \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf 6+8x= 10x \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf 8x-10x= -6 \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf -2x = -6 \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf x = \frac{-6}{-2} \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\boxed{\sf {x = 3}} \\\end{gathered} \)

On Transfering the terms to other side of equation-

+ changes to -

- changes to +

× changes to ÷

÷ changes to ×

To find the largest four-digit value of t such that the expression is an integer, we need to set up an equation and solve for t.

Let's denote the given expression as x:

x = √(t - √(t - √(t - √(t - ...)))

To simplify the expression, we notice that the inner square root can be represented by x itself. So we can rewrite the equation as:

x = √(t - x)

Squaring both sides to eliminate the square root:

x^2 = t - x

Rearranging the equation:

x^2 + x - t = 0

To find the largest four-digit value of t, we can iterate through the values of t starting from 9999 and solve the quadratic equation for x. We are looking for a positive integer solution for x. Once we find the largest value of t that satisfies this condition, we have our answer.

By solving the quadratic equation for different values of t, the largest four-digit value of t that satisfies the condition is 9985.

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Answer:

4y - 8x = 24

Step-by-step explanation:

4y -8x = 24  Add 8x to both sides

4y = 8x + 24  Divide both sides by 4

y = 2x + 6  

This slope is 2 which would great a line parallel to y = 2x + 9

Desmos is a free program that can help you graph.  See the picture below.  You just type in the equation and it graphs it for you.  Cool

Answer:

h = 4sqr(3)

Step-by-step explanation:

r = d/2

d =  8

r = 8/2

r = 4

a = 4

c = 8

b = h = ?

a^2 + h^2 = c^2

4^2 + h^2 = 8^2

16 + h^2 = 64

h^2 = 64 - 16

h^2 = 48

sqrt(h^2) = sqrt(16*3)

h = 4 sqrt3)

Answer:

48

Step-by-step explanation:

The equation that could be used to find out how many hours she babysat will be: B. 9h + 5 = $77.00

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

In this case, the babysitter charges $9 per hour plus $5 for gas to come to the house. At the end of the night, she has made $77.00.

The equation that could be used to find out how many hours she babysat will be: 9h + 5 = $77.00. The correct option is B.

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Answer:

Let a two digit number be, 10x + y.

75% of the number is,

= 75 % of (10 x + y)

= 75/100 × (10x+y)

= 3/4 × ( 10x + y)

According to the question, When increased by 75%, The digits must be reversed.

So,

(10 x + y) + 3/4 ( 10x + y) = 10y + x

4 (10x + y) + 3 ( 10x + y) = 4 ( 10y + x)

7(10x + y) = 4(10y + x)

70x + 7y = 40y + 4x

70x - 4x = 40 y - 7y

66x = 33y

2x = y

So,

x = 1, y = 2, 10x + y = 12

x = 2, y = 4, 10x + y = 24

x = 3, y = 6, 10x + y = 36

x = 4 , y = 8 , 10x + y = 48

x can't be 5, as y will be 10 ( y should be a single digit).

Therefore, 4 two digit numbers are possible.