9 - 3 divided by 1/3 + 1

So the value of X is 15 degree.

Look at the attached picture

Hope it will help you

Good luck on your assignment

AC=180°

\(3x + 8x + 15 = 180 \\ 11x = 165 \\ x = 15\)

Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, and 100

Step-by-step explanation:

Let's pretend that the locker number is represented as a Binary (meaning it's either open or closed).

Looking at this, we can see that each locker is only acted upon if the student number is a factor of it. This is why the 3rd person changes the state of every 3 lockers, the 4th student changes the state of every 4 lockers, etc.

The factors of a number are the numbers that the original number is evenly divisible by. When we divide these, we also receive a factor. With this information, we can conclude that unless one of the factors is the square root of the number, then the "second divided by" factor is itself. For every other number, there will be a "second divided by" factor, so an even number of them. Because an even number + 1 = odd number, then only perfect squares will have an odd number of factors.

Hope this helped!

Answer:

The open lockers are:

1,4,9,16,25,36,49,64,81,100

Step-by-step explanation:

Note that locker 1 is opened by only the first student. So it stays open throughout.

Locker 2 is first opened by student 1, then closed by student 2. Other students don't touch it. So it stays closed.

Locker 3 is first opened by student 1, then closed by student 3. Other students don't touch it. So it stays closed.

Since 4 is a multiple of 1, 2, and 4, it is changed by the 1st, 2nd, and 4th students. Since there is an odd number (3) of changes, locker 4 stays open.

Observe that a locker at position n is opened by students with factors of n.

Every number can be written as the product of a pair of distinct numbers except perfect squares. For example, 6 can be written as 1 × 6 and 2 × 3. Hence, it has 4 factors, which means it is touched an even number of times, making it stay locked.

A number like 9 is written as 1 × 9 and 3 × 3. Hence, it has 3 factors, which is odd, making it stay open.

Since the perfect squares from 1 to 100 are 1,4,9,16,25,36,49,64,81,100, then the open lockers are:

1,4,9,16,25,36,49,64,81,100

Answer: we might have come across different types of lines such as parallel lines, perpendicular lines, intersecting lines, and so on. Apart from that, we have another line called transversal.                                                                                    

This can be observed when a road crosses two or more roads or a railway line crosses several other lines. These give a basic idea of a transversal. Transversals play an important role in establishing whether two or more other lines in the Euclidean plane are parallel.

In this article, you will learn the definition of transversal line, angles made by the transversal with parallel and non-parallel lines with an example.  

SOOO in English its LM is the transversal made by the parallel lines PQ and RS such that:

The pair of corresponding angles that are represented with the same letters are equal.

If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal. Transversal property 2

Answer:

A

Step-by-step explanation:

For a right triangle

\(A=\frac{ab}{2} \\\frac{(10.4)(15.3)}{2} =79.56\)

This is the same as the other triangle because they are the same size because of congruency

Area of the rectangle

\(a^2+b^2=c^2\\\)

\(\sqrt{(10.4^2+15.3^2} =c\)

\(c= 18.5\)

18.5 x 7 = 129.5

Add them all up

129.5+79.56+79.56= 288.62

Answer:

  d, e

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  a^-b = 1/a^b

__

In this case, it means the product is ...

  (6^1)(6^0)(6^-3) = 6^(1+0-3) = 6^-2 = 1/6^2 = 1/36

__

The 6 without an exponent is equivalent to 6^1, an exponent of 1.

The sum of the exponents is -2.

Add the exponents to simplify the expression.

The value of the expression is 1/36.

An equivalent is any expression that results in 6^-2. One such is (6^5)(6^-7).

__

Only the last two choices, d and e, apply.

Answer:

33 * (12-2) = 2 is not correct answer the real answer is 330

Step-by-step explanation:

(12-2) = 10

33 * 10 = 330

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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Answer:

  94.3

Step-by-step explanation:

You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"

The diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.

The solution is found by multiplying both sides by 82:

  (x/82)·82 = (115/100)·82

  x = 94.3

The question can also be written as a statement:

  "what" is 115% of 82

When written as an equation, "is" means "equals", and "of" means "times":

  what = 115% × 82

Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...

  x = 115/100 × 82 = 1.15 × 82

All that remains is to evaluate this expression.

  x = 1.15 × 82 = 94.3

So, the answer to the question is ...

  94.3 is 115% of 82.

Answer:

Step-by-step explanation:

(-4*5 - 1) + (-4)

(-20 - 1) - 4

-21 - 4

-25

Answer:

Step-by-step explanation:480 x o.75=360

and now you add this amount on payed

360 + 480=840 was original price

Answer:

a = -3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

a−2=

3+6a

3

a+−2=2a+1(Distribute)

a−2=2a+1

Step 2: Subtract 2a from both sides.

a−2−2a=2a+1−2a

−a−2=1

Step 3: Add 2 to both sides.

−a−2+2=1+2

−a=3

Listen go to Mathpapa it helps and shows step by step

Answer:

a = -3

Step-by-step explanation:

a - 2 = (3 + 6a)/3

Divide 3 + 6a by 3.

a - 2 = 1 + 2a

Subtract 2a from both sides.

-a - 2 = 1

Add 2 to both sides.

-a = 3

Multiply the equation by -1.

a = -3.

Proof:

a - 2 = (3 + 6a)/3

Substitute variable.

-3 - 2 = (3 + 6(-3))/3

Multiply inside parenthesis.

-3 - 2 = (3 + 18)/3

Add inside parenthesis.

-3 - 2 = (-15)/3

Divide.

-3 - 2 = -5

Subtract.

-5 = -5

The ordered triple (p, q, r) that satisfies the given system of linear equations is (7, 2, 2).

To solve the given system of equations:

Start with the first equation: p - 2q = 3.

Multiply this equation by 2 to eliminate the coefficient of q: 2p - 4q = 6.

Next, we'll combine this equation with the second equation: q - 2r = -2.

Add the two equations together: (2p - 4q) + (q - 2r) = 6 + (-2).

Simplifying, we get: 2p - 3q - 2r = 4.

Now, let's consider the third equation: p + r = 9.

Rearrange this equation: p = 9 - r.

We can substitute this value for p in the equation we obtained in step 3:

2(9 - r) - 3q - 2r = 4.

Simplify the equation: 18 - 2r - 3q - 2r = 4.

Combining like terms, we have: -4r - 3q = -14.

We now have a system of two equations with two variables:

-4r - 3q = -14, (Equation 1)

q - 2r = -2. (Equation 2)

To solve this system, we can use various methods such as substitution or elimination. Here, we'll use the substitution method.

From Equation 2, we can solve for q:

q = 2r - 2.Substituting this value for q in Equation 1, we have:

-4r - 3(2r - 2) = -14.

Simplify and solve for r:

-4r - 6r + 6 = -14,

-10r = -20,

r = 2.

Now, substitute the value of r back into Equation 2 to solve for q:

q - 2(2) = -2,

q - 4 = -2,

q = 2.

Finally, substitute the values of q and r into Equation 3 to solve for p:

p + 2 = 9,

p = 7.

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Answer:

42 m

Step-by-step explanation:

First, find <S

<S = 180 - (41+113) [ sum of angles in a triangle)

<S = 180 - 154 = 26°

Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C

Let a = RT = 28m

A = <S = 26°

b = ST

B = <R = 41°

Thus, we have:

28/sin(26°) = b/sin(41°)

Cross multiply

28*sin(41°) = b*sin(26°)

28*0.6561 = b*0.4384

18.3708 = b*0.4384

Divide both sides by 0.4384 to make b the subject of formula

18.3708/0.4384 = b

41.9041971 = b

b ≈ 42m (rounded to nearest meter)

Length of ST to nearest meter = 42 meters

Answer:

Which means that the first number is 251, the second number is 251 + 1 and the third number is 251 + 2. Therefore, three consecutive integers that add up to 756 are 251, 252, and 253. 251 + 252 + 253 = 756 We know our answer is correct because 251 + 252 + 253 equals 756 as displayed above.

Step-by-step explanation:

Due to weaker aggregate demand, the negative demand shock will cause the aggregate demand curve to move to the left.

Result: A lower output and price level.

Part B:

Explanation of part B

Result of negative supply shock , aggregate demand falls cause the lower demand for the money . This will lead towards the left shift in money demand.(MD 1 TO MD 2(R1 TO R2)

Part c:

Interest rate and bond price are related inversely . Due to negative demand shock the interest rate falls down. vice-versa bond price will rise.

Part D:

Due to fall in the interest rate central banks will follow contractionary fiscal policy which will increase interest rate and reduce the money supply.

Part E :

If the central banks need to increase the money supply by $80 billion. Central banks need to buy securities in exchange of cash .This will Raise the money supply.

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The complex expression (i-3) +6i-3(8 - i) when simplified is -27 + 10i

From the question, we have the following parameters that can be used in our computation:

(i-3) +6i-3(8 - i)

Express properly

So, we have

(i - 3) + 6i - 3(8 - i)

When the brackets are opened, we have

(i - 3) + 6i - 3(8 - i) = i - 3 + 6i - 24 + 3i

Collect the like terms

So, we have

(i - 3) + 6i - 3(8 - i) = - 3  - 24 + i + 6i + 3i

Evaluate the like terms

So, we have

(i - 3) + 6i - 3(8 - i) = -27 + 10i

Hence, the complex expression when simplified is -27 + 10i

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Answer:

For the first place, Rachel can put any of the 9 blocks, so we have 9 options. For the second place, there will be 8 blocks left, so 8 options in this case. For the third place there will be 7 options and so on. The number of different arrangements is

N = 9 \times 8 \times 7 \times 6 \times5 \times4 \times 3 \times 2 \times 1 = 362\,880N=9×8×7×6×5×4×3×2×1=362880

Step-by-step explanation:

Answer:

9! = 362 880

Step-by-step explanation:

9! means 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

You multiply all numbers from 9 to 1

So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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A.y-intercept: 4

axis of symmetry: x=2

x-coordinate of the vertex: 2

B.x f(x)

  0   4

  1   1

  2   0

  3     1

  4   4

C. 5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

An intercept refers to the point(s) at which a curve or line intersects an axis. For example, the x-intercept is where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.

A vertex is a point where two or more lines or curves meet. In the context of a parabolic curve, the vertex is the point at which the curve changes direction.

According to the given information:

A. The y-intercept occurs when x=0. Therefore, f(0) = 0² - 4(0) + 4 = 4. So the y-intercept is (0, 4).

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients of x² and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Therefore, the equation of the axis of symmetry is x = 2.

To find the vertex, we use the fact that the vertex occurs at the axis of symmetry. So when x=2, f(x) = 2² - 4(2) + 4 = -4. Therefore, the vertex is at (2, -4).

B. We can use the vertex to make a table of values:

x f(x)

0 4

1 1

2 0

3 1

4 4

C. We can use the table of values to plot the points and sketch the graph of the function. The graph of the function is a parabola that opens upward, since the coefficient of x² is positive.

  5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

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Answer:

E. 1/3

Step-by-step explanation:

In this sequence, the numbers are descending and are 1/3 of the previous number.

243 / 3 = 81

81 / 3 = 27

9 / 3 = 3

3 / 3 = 1

1 / 3 = 1 / 3 (the next term)

Answer:

(x, y) → (x – 3, y + 5)

Step-by-step explanation:

If you move up or down, it affects the y coordinate and going up is positive so 5 units up is y +  5  and if moving left or right affects the x coordinate and moving left is negative so x - 3

"5 units up" would be "5 added to the current y-value".

"3 units to the left" would be "3 subtracted from the current x-value".

So, the translation rule is: (x, y) → (x – 3, y + 5)

~Lenvy~

The value of the constant π is located between 3 and 4 on a number line

The value is given as

Value = π

As a general rule, the value of π is

π = 22/7

So, we have

Value = 22/7

Evaluate the quotient of 22/7

So, we have

Value = 3.143

The number 3.143 is greater than 3 but less than 4

This means that, 3.143 is between 3 and 4

In other words, the value of the constant π is located between 3 and 4 on a number line

Hence, the value of the constant π is located between 3 and 4 on a number line

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Answer:

\(x=11\)

Step-by-step explanation:

It is a linear pair

\(7x + 12 + 8x + 3 = 180\)

\(15x + 15 = 180-15\\15x = 165\)

\(x=11\)

Every point in the interval [2, 6] has an equal probability of occurring, 1/(6 - 2) = 1/4. So the PDF of X is

\(f_X(x) = \begin{cases} \frac14 & \text{if } 2 \le x \le 6 \\ 0 & \text{otherwise} \end{cases}\)

Compute the CDF by integrating the PDF.

• If \(x<2\), we have

\(\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^x 0 \, dt = 0\)

• If \(2\le x< 6\), we have

\(\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^2 f_X(t) \, dt + \int_2^x f_X(t) \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \int_{-\infty}^2 0 \, dt + \int_2^x \frac{dt}4 \\\\ ~~~~~~~~~~~~~~~~~ = 0 + \frac14 \int_2^x \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \frac{x-2}4\)

• If \(x\ge6\), we have

\(\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^2 f_X(t) \, dt + \int_2^6 f_X(t) \, dt + \int_6^x f_X(t) \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \int_{-\infty}^2 0 \, dt + \int_2^6 \frac{dt}4 + \int_6^x 0 \, dt \\\\ ~~~~~~~~~~~~~~~~~ = 0 + 1 + 0 \\\\ ~~~~~~~~~~~~~~~~~ = 1\)

Putting the pieces together, we find the CDF to be

\(\boxed{F_X(x) = \begin{cases} 0 & \text{if } x < 2 \\\\ \dfrac{x-2}4 & \text{if } 2\le x < 6 \\\\ 1 & \text{if } x\ge6 \end{cases}}\)

Compute the expectation of X.

\(\Bbb E[X] = \displaystyle \int_{-\infty}^\infty x\,f_X(x)\,dx \\\\ ~~~~~~~ = \int_{-\infty}^2 0 \, dx + \int_2^6 \frac x4 \, dx + \int_6^\infty 0 \, dx \\\\ ~~~~~~~ = 0 + \frac{6^2 - 2^2}8 + 0 \\\\ ~~~~~~~ = \boxed{4}\)

Answer:

Step-by-step explanation:

Answer:

..................................................................................

Step-by-step explanation:

hahaahahah

The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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Answer:

No

Step-by-step explanation:

10 is not less than 6, so 10 < r when r=6 is not true.

The area of the object is 104 square inches.

To find the area of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.

In this case, the object is made up of triangle and a rectangle.

Where:

length of rectangle is z and width of rectangle is w.

Height of of triangle is h and base of triangle is z.

Thus,

Area of object = area of rectangle + area of triangle

Area of object = (w * z) + (1/2 * z * h)

Area of object = (3 * 16) + (1/2 * 16 * 7)

Area of object = 48 + 56

Area of object = 104 square inches

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