a sector has radius 10 mm and area 40/3 pie mm^2. what is the measure, in degrees, of the central angle of the sector?

The expression for m<3 is 349° - 7x.

To find the measure of angle 3 (m<3), we need to apply the angle sum property, which states that the sum of the angles around a point is 360 degrees.

In the given figure, angles 1, 2, 3, and 4 form a complete revolution around the point. Therefore, we can write:

m<1 + m<2 + m<3 + m<4 = 360°

Substituting the given angle measures, we have:

(x + 6)° + (2x + 9)° + m<3 + (4x - 4)° = 360°

Combining like terms:

7x + 11 + m<3 = 360°

To isolate m<3, we subtract 7x + 11 from both sides:

m<3 = 360° - (7x + 11)

m<3 = 360° - 7x - 11

m<3 = 349° - 7x

Therefore, the expression for m<3 is 349° - 7x.

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The total liabilities and stockholders' equity for Deacon Company as of March 31st is $275,400.

To calculate the total liabilities and stockholders' equity, we need to add the amounts of accounts payable, common stock, and retained earnings. Accounts Payable: The balance sheet provides the information that the accounts payable is $71,100.

Common Stock: The balance sheet states that the common stock is $70,000.

Retained Earnings: The balance sheet shows that the retained earnings are $134,300.

Calculate the total liabilities and stockholders' equity: Add the amounts of accounts payable, common stock, and retained earnings.

Total liabilities and stockholders' equity = Accounts payable + Common stock + Retained earnings

= $71,100 + $70,000 + $134,300

= $275,400

Therefore, the total liabilities and stockholders' equity for Deacon Company as of March 31st is $275,400.

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Answer:

Any equation that has the power of x at 1

Step-by-step explanation:

Since the function f(x) = -2x -3 +8 has an infinite range, so any other equation that only contains x^1 would work

The amount of snow accumulated between 2 am and 5 am is: 1.25 inches

The general formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the given graph attached, we see that the y-axis gives the amount of snow at different specific times.

Meanwhile the x-axis gives the time in hours after midnight

At 2am, the y-axis value is 1.25 inches, and as such at 2am snow accumulation was 1.25 inches.

At 5 am, the y-axis value reads 2.5 inches, and as such at 5am snow accumulation was 2.5 inches.

The difference in both snow accumulations is:  2.5 - 1.25 = 1.25

Hence, 1.25 inches snow accumulated between 2 am and 5 am.

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The vertex for the graph of the equation [tex]v - 3 = - (x+2)^2 is (-2, 3).[/tex]

To find the vertex of the graph of the equation [tex]v - 3 = - (x+2)^2,[/tex] we can rewrite it in the standard vertex form: [tex]v = a(x - h)^2 + k,[/tex]

where (h, k) represents the vertex coordinates.

First, let's rearrange the given equation:

[tex]v - 3 = - (x+2)^2[/tex]

[tex]v = - (x+2)^2 + 3[/tex]

Comparing this with the standard vertex form, we can see that h = -2 and k = 3.

Therefore, the vertex of the graph is (-2, 3).

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The value of the given expression is 1370.

To calculate the given expression, we can group the terms in pairs and simplify them.

We have the following pattern:

1 + 2 - 3 + 4 + 5 - 6 + 7 + 8 - 9 + ... + 97 + 98 - 99

Grouping the terms in pairs, we can see that each pair consists of a positive and a negative term. The positive term increases by 1 each time, and the negative term decreases by 1 each time. Therefore, we can rewrite the expression as:

(1 - 3) + (2 + 4) + (5 - 6) + (7 + 8) + ... + (97 + 98) - 99

The sum of each pair in parentheses simplifies to a single term:

-2 + 6 - 1 + 15 + ... + 195 - 99

Now, we can add up all the terms:

-2 + 6 - 1 + 15 + ... + 195 - 99 = 1370

As a result, the supplied expression has a value of 1370.

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Answer:

0

Step-by-step explanation:

Use the following models to show the equivalence of the fractions 35 and 610 a) Set model

Para representar gráficamente los vectores 2u, -3v y 1/4, necesitamos utilizar los vectores dados A(-1,3), B(-2,4), C(0,-2) y D(8,1).

Vector 2u:

El vector 2u se obtiene al multiplicar el vector u por 2. Si conocemos las coordenadas de u, podríamos multiplicar cada componente por 2. Sin embargo, no se proporciona información sobre las coordenadas de u, por lo que no podemos realizar este cálculo específico.

Vector -3v:

Similar al caso anterior, para obtener el vector -3v, debemos multiplicar el vector v por -3. Sin información sobre las coordenadas de v, no podemos realizar este cálculo específico.

Vector 1/4:

El vector 1/4 se obtiene al multiplicar cada componente de los vectores A, B, C y D por 1/4. Podemos calcular las nuevas coordenadas de estos vectores:A' = (-1/4, 3/4)

B' = (-1/2, 1)

C' = (0, -1/2)

D' = (2, 1/4)

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The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.

To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.

The loan amount can be calculated by subtracting the down payment from the property value:

Loan amount = Property value - Down payment

           = $170,000 - $20,000

           = $150,000

Now we can calculate the LTV ratio:

LTV ratio = Loan amount / Property value * 100

         = $150,000 / $170,000 * 100

         = 88.24%

Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.

To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:

PMI payment = (Loan amount * PMI rate) / 12

           = ($150,000 * 0.30%) / 12

           = $450 / 12

           = $37.50

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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.

Use the table to find her monthly PMI payment

Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.

30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%

15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.

A. $51.25

B. $37.50

C. $23.75

D. $42.50

Answer:

a. Let tomorrow's temperature be x

b.

[tex] |93 - x | < 10[/tex]

c.

[tex] - 10 < 93 - x < 10 \\ - 103 < - x < - 83 \\ 103 > x > 83[/tex]

Answer:

perimeter = 75 cm , area ≈ 28.3 in²

Step-by-step explanation:

23 (a)

since the figure is being enlarged by a scale factor of 5

then the perimeter is increased by a factor of 5.

perimeter of larger shape = 5 × 15 = 75 cm

24

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{90}{360}[/tex]

  = π × 6² × [tex]\frac{1}{4}[/tex]

  = 36π × [tex]\frac{1}{4}[/tex]

  = 9π

  ≈ 28.3 in² ( to 1 decimal place )

Answer/Step-by-step explanation:

C., the first proof we would be given if a little box is shown, which indicates a 90 degree angle at the place where to lines touch  in a T kind of manor. So C is the answer.

Answer:

850

Step-by-step explanation:

Our given expression is [tex]8.5*10^{2}[/tex]

To solve, simply use PEMDAS as it applies to the expression.

First, you do the exponent(s): [tex]10^2 = 100[/tex]

Then, you do multiplication: [tex]8.5*100=850[/tex]

So, your answer is 850.

A) The probability that a randomly selected student studies only mathematics would be 20/75.

B) The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.

C) The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.

D) The exact probability that a student studies mathematics and physics cannot be determined without knowing the number of students who study both subjects.

To determine the requested probabilities, we will use the information provided about the group of 75 students.

a) Study only mate:

We know that there are 20 students studying mathematics and physics, so the number of students studying only mathematics would be the total number of students studying mathematics (20) minus the number of students studying both subjects. Since no information is provided on the number of students studying both subjects, we will assume that none of the students study both subjects. Therefore, the number of students studying only mathematics would be 20 - 0 = 20.

The probability that a randomly selected student studies only mathematics would be 20/75.

b) Study math or physics:

To determine this probability, we need to add the number of students who study mathematics and the number of students who study physics, and then subtract the number of students who study both subjects (we again assume that none of the students study both subjects).

Number of students studying mathematics = 20

Number of students studying physics = X (not given)

Number of students studying both subjects = 0 (assumed)

Therefore, the number of students studying mathematics or physics would be 20 + X - 0 = 20 + X.

The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.

c) That he does not study either:

The number of students not studying either subject would be the complement of the number of students studying mathematics or physics. So it would be 75 - (20 + X).

The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.

d) To study math and physics:

Since no information is provided on the number of students studying both subjects, we cannot determine the exact probability that a student will study mathematics and physics.

In summary:

a) The probability that a randomly selected student studies only mathematics would be 20/75.

b) The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.

c) The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.

d) The exact probability that a student studies mathematics and physics cannot be determined without knowing the number of students who study both subjects.

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Answer:

[tex]\textsf{12)} \quad \text{a.}\;\;m \angle 1 = 107^{\circ}, \quad \text{b.}\;\;m \angle 2 = 107^{\circ}, \quad \text{c.}\;\;m \angle 3 = 73^{\circ}[/tex]

[tex]\textsf{13)} \quad EC = 6[/tex]

[tex]\textf{14)}\quad \text{a.}\;\;x = 33, \quad \text{b.}\;\; x = 8[/tex]

Step-by-step explanation:

As the base angles of an isosceles trapezoid are congruent, the measures of angles E and J are the same. Therefore:

[tex]m\angle 3 = 73^{\circ}[/tex]

The opposite angles of an isosceles trapezoid sum to 180°. Therefore:

[tex]\implies m\angle 1 + m\angle 3 = 180^{\circ}[/tex]

[tex]\implies m\angle 1 + 73^{\circ} = 180^{\circ}[/tex]

[tex]\implies m\angle 1 = 107^{\circ}[/tex]

Since the base angles of an isosceles trapezoid are congruent, the measures of angles A and N are the same. Therefore:

[tex]m\angle 2 = 107^{\circ}[/tex]

[tex]\hrulefill[/tex]

The diagonals of isosceles trapezoid ABCD are AC and BD.

Point E is the point of intersection of the diagonals. Therefore:

[tex]BE + ED = BD[/tex]

[tex]AE + EC = AC[/tex]

As the diagonals of an isosceles trapezoid are the same length, BD = AC. Therefore:

[tex]AE + EC = BD[/tex]

Given BD = 20 and AE = 14:

[tex]\implies AE + EC = BD[/tex]

[tex]\implies 14 + EC = 20[/tex]

[tex]\implies 14 + EC - 14 = 20 - 14[/tex]

[tex]\implies EC = 6[/tex]

[tex]\hrulefill[/tex]

The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides (legs) of the trapezoid.

The formula for the midsegment of a trapezoid is:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Midsegment of a trapezoid}\\\\$M=\dfrac{1}{2}(a+b)$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the midsegment.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides.\\\end{minipage}}[/tex]

a)  From inspection of the given trapezoid:

Substitute these values into the midsegment formula and solve for x:

[tex]x=\dfrac{1}{2}(18+48)[/tex]

[tex]x=\dfrac{1}{2}(66)[/tex]

[tex]x=33[/tex]

Therefore, the value of x is 33.

b)  From inspection of the given trapezoid:

Substitute these values into the midsegment formula and solve for x:

[tex]15=\dfrac{1}{2}(22+x)[/tex]

[tex]30=22+x[/tex]

[tex]x=8[/tex]

Therefore, the value of x is 8.

Answer:

To find the length of AB using the segment addition postulate , we need to add the lengths of segments AC and CB.

AC + CB = AB

Substituting the given lengths:

2x-3 + 24 = 5x+6

Simplifying and solving for x:

21 = 3x

x = 7

Now that we know x, we can substitute it back into the expression for AB:

AB = 2x-3 + 24 = 2(7)-3 + 24 = 14-3+24 = 35

Therefore, the length of AB is 35.

Step-by-step explanation:

Answer: D: The cost of one hand towel is $8 and the cost of one bath towel is $5.

Step-by-step explanation:

Let's assume the cost of one hand towel is 'x' dollars and the cost of one bath towel is 'y' dollars.

For the first hotel, Mr. Miller ordered 27 hand towels and 48 bath towels, resulting in a bill of $540. This can be expressed as the equation:

27x + 48y = 540 ...(equation 1)

For the second hotel, Mr. Miller ordered 50 hand towels and 24 bath towels, resulting in a bill of $416. This can be expressed as the equation:

50x + 24y = 416 ...(equation 2)

To solve this system of equations, we can use any suitable method such as substitution or elimination. Let's use the elimination method:

Multiplying equation 1 by 2 and equation 2 by 3, we get:

54x + 96y = 1080 ...(equation 3)

150x + 72y = 1248 ...(equation 4)

Now, subtracting equation 4 from equation 3, we have:

(54x + 96y) - (150x + 72y) = 1080 - 1248

-96x + 24y = -168

Dividing both sides of the equation by -24, we get:

4x - y = 7 ...(equation 5)

Now, we have a system of equations:

4x - y = 7 ...(equation 5)

50x + 24y = 416 ...(equation 2)

Solving this system of equations, we find that x = 8 and y = 5.

Therefore, the cost of one hand towel is $8 and the cost of one bath towel is $5.

So, the correct answer is option D: The cost of one hand towel is $8 and the cost of one bath towel is $5.

Answer:

Step-by-step explanation:

Total cost of hand towels for first hotel = 27 * $5 = $135

Total cost of bath towels for first hotel = 48 * $8 = $384

Total cost of hand towels for second hotel = 50 * $5 = $250

Total cost of bath towels for second hotel = 24 * $8 = $192

Total cost of all hand towels = $135 + $250 = $385

Total cost of all bath towels = $384 + $192 = $576

Total number of hand towels = 27 + 50 = 77

Total number of bath towels = 48 + 24 = 72

Average cost of one hand towel = $385 / 77 = $5

Average cost of one bath towel = $576 / 72 = $8

The correct answer is option (b): Square root of 4x^2.

The standard deviation of a random variable Y is the square root of its variance. In this case, the variance of Y is given as 4x^2. Taking the square root of 4x^2, we get the standard deviation of Y as 2x.

Therefore, the correct answer is the square root of 4x^2, which is the standard deviation of Y.

Answer:

Only one scalene triangle with side lengths of 12 in, 15 in, and 18 in exists. Therefore, exactly one unique triangle exists with the given side lengths.

Step-by-step explanation:

Answer:

Angle C must measure 40 degrees.

Step-by-step explanation:

All angles in a triangle add up to 180 degrees

(90-50)=40 degrees

We can check our answer by adding all the angles up

90+50+40=180

Angle C must be 40 degrees

Answer:

18.84 in

Step-by-step explanation:

The circumference of a circle = pi * diameter = 6*3.14 = 18.84 in.

Answer:

211%

Step-by-step explanation:

percent = part/whole × 100%

percent = 19/9 × 100%

percent = 211%

The surface area of the given triangle is approximately 33.74 square centimeters.

To calculate the surface area of a triangle, we need the lengths of two sides and the included angle between them. However, in this case, you provided the lengths of all three sides (6 cm, 7 cm, and 12 cm).

To determine the surface area, we can use Heron's formula, which is applicable to triangles with all three side lengths known.

Heron's formula states that the surface area (A) of a triangle with side lengths a, b, and c is given by:

[tex]A = \sqrt(s \times (s - a) \times (s - b) \times (s - c))[/tex]

where s is the semi perimeter of the triangle, calculated as:

s = (a + b + c) / 2

Plugging in the given side lengths, we have:

s = (6 cm + 7 cm + 12 cm) / 2 = 25 / 2 = 12.5 cm

Now we can substitute the values into Heron's formula:

[tex]A = \sqrt(12.5 cm \times (12.5 cm - 6 cm) \times (12.5 cm - 7 cm) \times (12.5 cm - 12 cm))[/tex]

[tex]= \sqrt(12.5 cm \times 6.5 cm \times 5.5 cm \times 0.5 cm)[/tex]

= √(1137.5 cm^4)

≈ 33.74 cm^2

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Answer:

The range of this graph is (-4, 6], or

-4 < y < 6.

The range of the graph is [-4, 6].

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.

Based on the information provided in this scenario, the domain and range of the graph of this equation can be determined are as follows:

Domain = [1, 10] or 1 ≤ x < 10

Range = [-4, 6], or -4 < y ≤ 6.

Therefore, the range can be rewritten as [-4, 6].

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Using the given operations and nine 9s, you can make 1001.

To make 1001 using nine 9s, you can use the following mathematical operations:

1. (9 + 9 + 9) * 9 * 9 - 9 - 9 - 9 = 1001

- Adding three 9s together: (9 + 9 + 9) = 27

- Multiplying the sum by two 9s: (27 * 9 * 9) = 2187

- Subtracting three 9s: (2187 - 9 - 9 - 9) = 2160

- Adding one 9: (2160 + 9) = 2169

- Adding 832 (which is (9 * 9 * 9 + 9 * 9 + 9)) to 2169: (2169 + 832) = 3001

- Subtracting two 9s: (3001 - 9 - 9) = 2983

- Adding nine 9s: (2983 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9) = 1001

Therefore, using the given operations and nine 9s, you can make 1001.

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Answer: C

b = 6; JG = 34; HF = 29

Answer:

[tex] \frac{a}{2x - 3} + \frac{b}{3x +4} = \frac{x + 7}{ 6{x}^{2} - x - 12} [/tex]

[tex](3x + 4)a + (2x - 3)b = x + 7[/tex]

3a + 2b = 1---->9a + 6b = 3

4a - 3b = 7---->8a - 6b = 14

--------------- ----------------

17a = 17

a = 1, b = -1

Using Gauss-Jordan method, the value of x, y and z are 0, -2 and 1

To solve the system of equations using the Gauss-Jordan method, we'll perform row operations to transform the augmented matrix into row-echelon form and then further transform it into reduced row-echelon form. Here are the steps:

1. Write the augmented matrix for the system of equations:

  [1  -2   4  |  20]

  [1   1  13  | -31]

  [-2   6  -1 | -69]

2. Perform row operations to transform the matrix into row-echelon form:

  R2 = R2 - R1

  R3 = R3 + 2R1

  [1  -2   4  |  20]

  [0   3   9  | -51]

  [0   2   7  | -29]

3. Perform row operations to further transform the matrix into reduced row-echelon form:

  R2 = R2 / 3

  R3 = R3 - 2R2

  [1  -2   4  |  20]

  [0   1   3  | -17]

  [0   0   1  |   1]

4. Perform row operations to obtain a diagonal of 1s from left to right:

  R1 = R1 + 2R2 - 4R3

  R2 = R2 - 3R3

  [1  0  0  |   0]

  [0  1  0  |  -2]

  [0  0  1  |   1]

The resulting matrix corresponds to the system of equations:

x = 0

y = -2

z = 1

Therefore, the solution to the given system of equations is x = 0, y = -2, and z = 1.

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