Find angle ABD please help fast i will mark brainiest

Therefore, it takes the flare 2 seconds to hit the water.

In mathematics, a factor refers to a number or an algebraic expression that divides another number or expression without leaving any remainder. For example, the factors of 6 are 1, 2, 3, and 6, since these numbers divide 6 evenly with no remainder. Similarly, the factors of x^2 - 4 are (x-2) and (x+2), since when multiplied together, they produce x^2 - 4.

Factors are important in many areas of mathematics, including algebra, number theory, and geometry. They are used to simplify and solve equations, factorize polynomials, and find common factors and multiples. Factors are also used in prime factorization, where a number is expressed as a product of its prime factors.

To find the time it takes the flare to hit the water, we need to solve the equation -16t² + 140t + 56 = 0 for t. We can start by factoring out a common factor of -4:

[tex]-16t^{2} + 140t + 56 = 0[/tex]

[tex]-4(4t^{2} - 35t - 14) = 0[/tex]

Next, we need to factor the quadratic expression inside the parentheses. We can do this by finding two numbers whose product is -56 (the constant term) and whose sum is -35 (the coefficient of the t term). The numbers are -7 and 8:

[tex]-4(4t^{2} - 35t - 14) = 0[/tex]

-4(4t + 7) (t - 2) = 0

Now we have a product of three factors that equals zero. According to the zero-product property, this means that one of the factors must be zero:

[tex]4t + 7 = 0 or t - 2 = 0[/tex]

Solving for t in each equation, we get:

[tex]4t = -7 or t = 2[/tex]

[tex]t = -7/4 or t = 2[/tex]

Since time cannot be negative, the only solution that makes sense is t = 2. Therefore, it takes the flare 2 seconds to hit the water.

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Answer:

the answer is 5........

Answer: I rechecked and confirmed the answer. The answer is 5.

There is no solution to the given system of equations. Therefore, the system is inconsistent.

How to solve the equation using substitution method?

To solve this system of equations using the substitution method, we need to solve one of the equations for one of the variables, and then substitute that expression into the other equation. Let's solve the first equation for y:

2x - y = 7

-y = -2x + 7

y = 2x - 7

Now we substitute this expression for y into the second equation:

-6x + 3y = 21

-6x + 3(2x - 7) = 21

-6x + 6x - 21 = 21

-21 = 21

This is a contradiction, and there is no solution to the system of equations. Therefore, the system is inconsistent.

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The probability that a passenger is traveling for business is 67.1%.

The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.

The probability that a passenger is traveling for business can be calculated by adding the number of passengers traveling for business and dividing by the total number of passengers:

P(traveling for business) = (274 + 397) / 1000 = 0.671

Therefore, the probability that a passenger is traveling for business is 0.671 or approximately 67.1%.

b. The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business can be calculated as follows:

P(laptop | traveling for business) = number of passengers with a laptop and traveling for business / number of passengers traveling for business

P(laptop | traveling for business) = 236 / 671 = 0.352

Therefore, the probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.

c. It should be noted that to determine if there is an association between bringing a laptop on a flight and traveling for business, we can compare the proportion of passengers who bring a laptop when traveling for business versus when not traveling for business. If the proportions are different, it suggests an association.

P(laptop | traveling for business) = 0.352

P(laptop | not traveling for business) = 0.093

The proportions are different, which suggests an association between bringing a laptop on a flight and traveling for business.

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Answer:

1.  m∠5 + m∠6 = 180°

2. ∠ 2+ ∠ 3 = ∠ 6

3. m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

IF ITS WRONG CONTACT ME AND I WILL FIX IT

Answer:

1. 60 ft^2

2. 175 cm^2

3. 36 cm^2

4. ≈ 121 cm^2

Step-by-step explanation:

1.

First, let's find the area of the whole rectangle:

A (whole) = 7 × 12 = 84 ft^2

Then, we have to find the area of the smaller rectangle which is inside the whole rectangle:

A (smaller) = 3 × 8 = 24 ft^2

Finally, let's subtract the area of the smaller rectangle from the area of the whole rectangle and we'll get the answer:

A (shaded) = 84 - 24 = 60 ft^2

.

2.

The opposite side lengths of a rectangle are equal

First, we can find the shorter side's length of each shorter rectangle:

(16 - 9) / 2 = 3,5 cm

A shorter side of the larger rectangle would be:

16 - 9 = 7 cm

Now, we can find the area of two smaller rectangles that are on top of the larger one:

A (2 smaller rectangles) = 9 × 3,5 × 2 = 63 cm^2

Also, we have to find the area of the larger rectangle:

A (larger) = 16 × 7 = 112 cm^2

In order to find the area of the shaded region, we have to add both of these areas together:

A (shaded) = 63 + 112 = 175 cm^

.

3.

Given:

h = 12 cm

b (triangle's base) = 9 cm

a (rectangle's longer side) = 6 cm

c (rectangle's shorter side) = 3 cm

Find: A (shaded) - ?

First, let's find the area of the triangle:

[tex]a(triangle) = \frac{1}{2} \times b \times h[/tex]

[tex]a(triangle) = \frac{1}{2} \times 9 \times 12 = 54 \: {cm}^{2} [/tex]

Now, we have to find the area of the rectangle:

[tex]a(rectangle) = a \times c = 6 \times 3 = 18 \: {cm}^{2} [/tex]

In order to find the area of the shaded region, we have to subtract the rectangle's area from the triangle's area:

[tex]a(shaded) = 54 - 18 = 36 \: {cm}^{2} [/tex]

.

4.

Given:

r (radius) = 7 cm

a (rectangle's longer side) = 11 cm

b (rectangle's shorter side) = 3 cm

Find: A (shaded) - ?

First, let's find the area of the circle:

[tex]a(circle) = \pi {r}^{2} = \pi \times {7}^{2} = 49\pi \: {cm}^{2} [/tex]

Now, we have to find the area of the rectangle:

[tex]a(rectangle) = a \times b = 11 \times 3 = 33 \: {cm}^{2} [/tex]

In order to find the shaded area, we have to subtract the rectangle's area from the circle's area:

[tex]a(shaded) = 49\pi - 33 ≈ 121 \: {cm}^{2} [/tex]

1. First, we need to find the volume of the hemisphere bowl:

V_bowl = (2/3)πr^3

V_bowl = (2/3)π(6 cm)^3

V_bowl = 288π cm^3

Since water fills two-fifths of the volume, we can find the volume of water:

V_water = (2/5)V_bowl

V_water = (2/5)(288π cm^3)

V_water = 115.2π cm^3

2. Now, we need to find the radius and height of the cone to which the water is poured. Let's call the radius of the cone r and the height h. We know that the volume of the cone is equal to the volume of the water in the bowl:

V_cone = V_water

(1/3)πr^2h = 115.2π

r^2h = 345.6

We also know that the depth of the water in the cone is 12 cm, so h = 12 cm. Substituting this value into the equation above, we get:

r^2(12 cm) = 345.6

r^2 = 28.8

r ≈ 5.36 cm

So, the radius of the cone is approximately 5.36 cm, and the height is 12 cm.

The solution for the system of equation is (8, 1), Hence the correct option is c.

The given system of equations is:

–3x + 2y = –22

–5y = –4x + 27

We can solve for x and y using elimination method:

–3x + 2y = –22

⇒ -3x + 2y = -22

–5y = –4x + 27

⇒  –4x + –5y = - 27

Eliminate x,

-3x + 2y = -22

-4x  - 5y = -27

That is

-12x + 8y = -88

-12x - 15y = −81

0  −7y = −7

or

-7y = -7

y = 7/7

y = 1

Solve for x by substituting the value of y in –3x + 2y = –22

–3x + 2(1) = –22

–3x + 2 = –22

–3x  = –22 - 2

–3x  = −24

x = 24/3

x = 8

Thus, The solution for the system of equation is (8, 1), Hence the correct option is c.

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Complete question:

Select the statement that correctly describes the solution to this system of equations.

–3x + 2y = –22

–5y = –4x + 27

A

There is no solution.

B

There are infinitely many solutions.

C

There is exactly one solution at (8, 1).

D

There is exactly one solution at (1, 8)

We know that the area of a parallelogram is given by the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given the area and the base, and we need to find the height.

We can rearrange the formula to solve for h: h = A/b

Plugging in the given values, we get:

h = 14.4 sq ft / 4.5 cm

Note that the units are different for area and base, so we need to convert them to the same units. Let's convert the base to feet, since the area is given in square feet:

h = 14.4 sq ft / (4.5 cm / 30.48 cm/ft) [converting cm to ft]

h = 14.4 sq ft / 0.148 ft

h ≈ 97.3 cm

Therefore, the height of the parallelogram is approximately 97.3 cm.

Therefore , the solution of the given problem of unitary method comes out to be  -10 and 8 are the two numbers that sum up to -16 and multiply to -80.

This generally recognized ease, preexisting variables, and any crucial elements from the initial Diocesan customizable query may all be used to complete the task. If therefore, you might have another chance to interact with the item. Otherwise, major influences on algorithmic evidence will cease to exist.  

Here,

We can use the knowledge that if two numbers x and y multiply to a constant k and add to a constant z to solve this issue by writing:

=> xy=k and x+y=z

We have k = -80 and z = -16 in this instance. Thus, we can say:

=>  xy = -80

=>  x + y = -16

=>  (x + y)² = (x + y)² + (x + y)².

=>  (x + y)² = (-16)2 = 256 x, 2 + 2xy + y, 2 = (x + y), 2 - 4xy, which equals 256 - 4(-80) = 576.

Thus, we can say:

=>  x² + 2xy + y² = 576

=> [tex]x^{2} - 160x + y^{2} = 576[/tex]

=>[tex](-10) - 160(-10) + 8^{2} = 576[/tex]

Since x = -10 and y = 8 satisfy the equation, this is correct. Therefore, -10 and 8 are the two numbers that sum up to -16 and multiply to -80.

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There is not enough Evidence to support the claim that more than 20% of users of the pain medication will develop nausea.

To test the claim that more than 20% of users of a pain medication will develop nausea, we can use a hypothesis test with a significance level of 0.05. The null hypothesis (H0) would be that the proportion of users who develop nausea is less than or equal to 0.20, while the alternative hypothesis (Ha) would be that the proportion is greater than 0.20.

To conduct the test, we can use the binomial distribution since we are looking at the number of successes (subjects who develop nausea) out of a fixed number of trials (total number of subjects). We can calculate the expected number of successes under the null hypothesis by multiplying the total number of subjects (239) by the assumed proportion (0.20). This gives an expected number of 47.8 subjects who would develop nausea.

We can then use a one-sample z-test to compare the observed proportion of subjects who developed nausea (52/239 = 0.218) to the expected proportion under the null hypothesis (0.20). The test statistic is calculated as (0.218 - 0.20) / sqrt(0.20 * 0.80 / 239), which is approximately 1.08.

With a significance level of 0.05 and one-sided test, the critical value for the z-statistic is 1.645. Since the calculated test statistic (1.08) is less than the critical value (1.645), we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the claim that more than 20% of users of the pain medication will develop nausea.

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Answer:

Step-by-step explanation:

After answering the given question, we can conclude that As a result, the probability of receiving an odd or a divisor of 54 is one, or 100% confidence.

Probability is a gauge of how likely an occurrence is to occur. It is represented by a figure between 0 and 1, with 0 representing an unlikely occurrence and 1 representing an inevitable event. Switching a fair coin and coin turns has a chance of 0.5 or 50% because there are two equally likely results. (Heads or tails). Probability theory is a branch of mathematics that studies random occurrences rather than their characteristics. It is applied in many areas, including statistics, economics, science, and engineering.

There are three equally probable results from the spinner: 1, 2, and 3. To determine the likelihood of receiving an odd or divisor of 54, we must tally the number of events that meet this requirement.

54 has divisors of 1, 2, 3, 6, 9, 18, 27, and 54. Only one, three, and nine are unusual. As a result, the potential results that are either odd or divisors of 54 are 1, 3, and 2.

P(odd or divisor of 54) = P(1) + P(2) + P(3) + P(9) = 1/3 + 1/3 + 1/3 + 0 (because 9 is not a spinning choice) = 1

As a result, the chance of receiving an odd or a divisor of 54 is one, or 100% confidence.

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The volume of a rectangular box or basket can be calculated using the formula:

V = l x w x h

where l is the length, w is the width, and h is the height of the box or basket.

In this case, the height of the basket is 6 inches, the width is 4 inches, and the length is 12 inches. Therefore, we can substitute these values into the formula and calculate the volume:

V = l x w x h

V = 12 x 4 x 6

V = 288 cubic inches

Therefore, the volume of the rectangular basket is 288 cubic inches.

The volume of the basket is 288 cubic inches.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

The volume of a rectangular prism can be calculated

= length x  width x height.

Given that the height is 6 inches, the width is 4 inches, and the length is 12 inches, the volume of the basket can be calculated as:

Volume = Length x Width x Height

Volume = 12 inches x 4 inches x 6 inches

Volume = 288 cubic inches

Therefore, the volume of the basket is 288 cubic inches.

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the inn had the greatest number of guests in December 2023, with 1428 guests staying at the inn during that month.

To find the month with the greatest number of guests, we need to find the maximum value of N(x) over the range of x from 0 to 11 (representing January to December).

We can find the maximum value of N(x) by taking the derivative of N(x) with respect to x, setting it equal to zero, and solving for x. However, since N(x) is a quadratic function, we can also use the vertex formula to find the x-value of the vertex of the parabola.

The vertex formula states that the x-value of the vertex of the parabola   [tex]y = ax^2 + bx + c[/tex] is given by [tex]x = -b/2a[/tex] .

In this case, N(x) is a quadratic function with a = -10%, b = 120, and c = 120. Plugging these values into the vertex formula, we get:

[tex]x = -b/2a = -120/(2\times -10%) = 60[/tex]

Since x represents the number of months after January 2019, the month with the greatest number of guests is the 60th month after January 2019, which is December 2023.

To find the number of guests who stayed at the inn during that month, we can plug x = 11 (representing December) into the formula for N(x):

[tex]N(11) = -10%(11^2) + 120(11) + 120[/tex]

[tex]= -0.1(121) + 1320 + 120[/tex]

[tex]= -12.1 + 1440[/tex]

[tex]= 1427.9[/tex]

Since the number of guests must be a whole number, we round 1427.9 to the nearest integer, which is 1428.

Therefore, the inn had the greatest number of guests in December 2023, with  [tex]1428[/tex] guests staying at the inn during that month.

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16) The number of guests during that month was 720.

17) In the year 2003, there were 4,600 triplet and higher order births.

18) The greatest average viewership occurred in the year 2015, with 17.95 million viewers per game.

16) How to find the month during which the inn had the greatest number of guests?

To find the month during which the inn had the greatest number of guests, we need to find the maximum value of the quadratic function N(x) = -10x² + 120x + 120.

We can begin by finding the x-coordinate of the vertex of this quadratic function, which is given by x = -b/2a, where a = -10 and b = 120.

x = -b/2a = -120/(2×(-10)) = 6

So the vertex of the quadratic function is at x = 6.

To find the maximum value of the function, we can evaluate N(6):

N(6) = -10(6)² + 120(6) + 120 = 720

So the inn had the greatest number of guests during the 6th month, which represents June 2019. The number of guests during that month was 720.

17) How to find the year when the number of triplet and higher order births was greatest?

To find the year when the number of triplet and higher order births was greatest, we need to find the maximum value of the function N(t). The formula for the maximum value of a quadratic function is -b/2a, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term.

In this case, a = -0.266 and b = 6.974. So, the t-value for the maximum number of triplet and higher order births is t = -b/(2a) = -6.974/(2×(-0.266)) = 13.12

Rounding this value to the nearest whole number, we get t = 13.

Therefore, the year when the number of triplet and higher order births was greatest is 1990 + 13 = 2003

To find the maximum number of triplet and higher order births, we substitute t = 13 into the function N(t):

N(13) = -0.266(13)² + 6.974(13) + 27.056 = 45.7 (in hundreds)

Rounding this value to the nearest whole number, we get 46.

Therefore, in the year 2003, there were approximately 4,600 triplet and higher order births

18) How to find the vertex of the quadratic function A(x)?

We can start by finding the vertex of the quadratic function A(x) to determine the year in which the greatest average viewership occurred:

The x-coordinate of the vertex of the quadratic function A(x) is given by x = -b/2a, where a = -0.59 and b = 3.5. Substituting these values,

x = -3.5/(2*(-0.59)) = 2.966

This means that the vertex occurs approximately 2.966 years after 2012, which corresponds to the year 2015.

To find the maximum average viewership, we can simply plug in x = 2.966 into the function A(x):

A(2.966) = -0.59(2.966)² + 3.5(2.966) + 12.71 ≈ 17.95 million viewers per game

Therefore, the greatest average viewership occurred in the year 2015, with approximately 17.95 million viewers per game.

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Answer: (a) To shift the graph of f(x)=9^x 2 units upward, we can add 2 to the function. Therefore, the new equation is:

y = 9^x + 2

(b) To shift the graph of f(x)=9^x 4 units to the right, we can replace x with (x - 4). Therefore, the new equation is:

y = 9^(x - 4)

(c) To reflect the graph of f(x)=9^x about the x-axis and the y-axis, we can replace x with (-x) and take the negative of the function. Therefore, the new equation is:

y = -9^(-x)

Step-by-step explanation:

The expression that correctly name the angle below is ∠K, So correct option is C.

In geometry, an angle is a figure formed by two rays, or half-lines, that originate from a common endpoint, which is called the vertex. The rays can be thought of as emanating from the vertex and extending infinitely in opposite directions.

The measure of an angle is typically given in degrees, where a full circle is 360 degrees. Angles can be classified according to their size:

An acute angle is less than 90 degrees.

A right angle measures exactly 90 degrees.

An obtuse angle is greater than 90 degrees but less than 180 degrees.

A straight angle measures exactly 180 degrees.

A reflex angle is greater than 180 degrees but less than 360 degrees.

A full angle measures exactly 360 degrees.

Angles can also be classified based on their position relative to other angles or lines:

Adjacent angles share a common vertex and one common side.

Complementary angles add up to 90 degrees.

Supplementary angles add up to 180 degrees.

Vertical angles are formed by two intersecting lines and are opposite each other.

The expression that correctly name the angle below is ∠K.

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The answer C is accurate since the formula that correctly identifies the angle below is ∠K.

An angle is a figure in geometry made up of two rays, or half-lines, that start from a single endpoint known as the vertex. You can imagine the rays coming from the vertex and continuing in opposing directions indefinitely.

A whole circle has 360 degrees, hence an angle is commonly measured in degrees. Angles can be grouped based on their size:

Any angle that is below ninety degrees is considered acute.

Obtuse angles are those that are greater than 90 degrees but below 180 degrees.

The length of a straight angle is 180 degrees.

A reflex angle is one that is above 180 degrees and less than 360 degrees.

Angles can also be categorised according on where they are situated in relation to other angles or lines:

Adjacent angles have one shared side as well as a common vertex.

Complementary angles add up to 90 degrees.

The sum of all supplementary angles is 180 degrees.

Two intersecting lines that are opposite one another form vertical angles.

The formula K accurately identifies the angle below.

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Answer:

Step-by-step explanation:

Value of y can be found using the tan ratio of the angle.

tan 26.5 = opposite/adjacent

.49858161 = y/24

mulitply each side by 24

11.97 = y

Answer: The value of y=116.28ft

Step-by-step explanation:

tan x = opposite side/adjacent side

let x=26.5 degree

opposite side= y

adjacent side=24ft

Therefore,

 tan(26.5) = y/24

y = tan(26.5) * 24

tan(26.5) = 4.8450

y = 4.8450*24

y = 116.28ft

The values that complete the missing segments are shown below

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

Blue segment = length of the rectangle

Where

length of the rectangle = radius of circle

So, we have

Blue segment = 12 units

Similarly, we have

Violet segment = width of rectangle

So, we have

Violet segment = 18 units

The green segment is the base circumference

So, we have

Green segment = 2 * 22/7 * 12

Green segment = 75.4 units

The orange segment is the diameter

So, we have

Orange segment = 2 * 12

Orange segment = 24

The area of one base is

Area of one base = 22/7 * 12^2

Area of one base = 452.4

The area of one rectangle is

Area of rectangle = 12 * 18

Area of rectangle = 216

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Answer:

15/100

Step-by-step explanation:

8/10 is equal to 80/100

95/100 - 80/100 = 15/100

Barbara Smith made $6,492 in total last month from her $42,800 in sales, 14% Commission, and her $500 monthly wage.

To calculate the total amount that Barbara Smith earns from A-1 Chemical Supply, we need to find her monthly salary, commission on sales, and then add them together.

1. Monthly Salary: Barbara receives a fixed monthly salary of $500.

2. Commission on Sales: To find her commission, we'll use the formula:
Commission = (Sales Amount) * (Commission Rate)

Barbara's sales for last month were $42,800, and she earns a 14% commission. To calculate the commission:
Commission = ($42,800) * (14/100)

3. Total Earnings: Add the monthly salary and commission to find Barbara's total earnings for the month.
Total Earnings = Monthly Salary + Commission

Now, let's calculate the commission and total earnings.

Commission = ($42,800) * (14/100) = $5,992

Total Earnings = $500 (Monthly Salary) + $5,992 (Commission) = $6,492

So, Barbara Smith earned a total of $6,492 last month, including her $500 monthly salary and 14% commission on her $42,800 in sales.

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Answer:

11.75

Step-by-step explanation:

2.5 + 4.25 + 5

Answer:

11.75 chapters in total

Step-by-step explanation:

Given:

2.5, 4.25, 5

The question ask for total

2.5 + 4.25 + 5 = 11.75

The length of the room on the blueprint is 12 inches.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To solve this problem, we first need to find the length of Jean's bedroom in real life.

Let L be the length of Jean's bedroom in real life. According to the problem, the width of the room is 9 feet, so we can write:

9 = 0.25x, where x is the width of the room on the blueprint.

Solving for x, we get:

x = 9/0.25 = 36

So the width of the room on the blueprint is 36 inches.

Since the width of the room on the blueprint is 75% of its length, we can write:

36 = 0.75L

Solving for L, we get:

L = 36/0.75 = 48

So the length of Jean's bedroom in real life is 48 feet.

To find the length of the room on the blueprint, we use the same scale of 0.25 inch = 1 foot. Therefore:

1 foot = 0.25 inch on the blueprint

48 feet = 48 x 0.25 = 12 inches on the blueprint

Therefore, the length of the room on the blueprint is 12 inches.

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Answer:

Step-by-step explanation:

[tex](x-5)-(x + 1)=x-5-x-1=-6[/tex]

[tex](x-5)+ (x + 1)=x-5+x+1=2x-4[/tex]

[tex](x-5)+ (x-1)=x-5+x-1=2x-6[/tex]

[tex](x-5)-(x-1)=x-5-x+1=-4[/tex]

The total earnings for the month if she babysat 10 days would be $360.

Using the mathematical operation of multiplication, the total earnings can be determined as follows:

Multiplication operation involves the multiplicand, the multiplier, and the product.

Hourly pay rate = $4.50

Daily working hours = 8 hours

The number of days worked in the month = 10 days

Total working hours for the month = 80 hours (10 x 8)

Total earnings for the month = $360 ($4.50 x 80)

Thus, we can conclude that she earned $360 gross for the month.

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Assuming that the Hourly pay rate is $4.50 and she worked for 8 hours daily.

Answer:

∠ B = 55°

Step-by-step explanation:

the sum of the 3 angles in triangle = 180° , that is

∠ B + 35° + 90° = 180°

∠ B + 125° = 180° ( subtract 125° from both sides )

∠ B = 55°

the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.

How to solve the probability?

To find the expectation of the game, we need to calculate the probability of winning and losing and multiply them by their corresponding payoffs.

First, let's calculate the probability of rolling a sum of 2 or 12. There is only one way to roll a sum of 2 or 12, which is by rolling a pair of ones or a pair of sixes, respectively. So, the probability of rolling a sum of 2 or 12 is:

P(2 or 12) = P(1,1) + P(6,6) = (1/6) * (1/6) + (1/6) * (1/6) = 1/18

Next, let's calculate the probability of rolling a 7. There are six ways to roll a sum of 7, which are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, the probability of rolling a 7 is:

P(7) = P(1,6) + P(2,5) + P(3,4) + P(4,3) + P(5,2) + P(6,1) = 6 * (1/6) * (1/6) = 1/6

Finally, the probability of losing is:

P(loss) = 1 - P(2 or 12) - P(7) = 1 - 1/18 - 1/6 = 11/18

Now, we can calculate the expectation of the game as follows:

E(X) = (12 * P(2 or 12)) + (5 * P(7)) - (1 * P(loss))

= (12 * 1/18) + (5 * 1/6) - (1 * 11/18)

= 2/9 + 5/6 - 11/18

= 0.22

So, the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.

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Answer: 59598

Step-by-step explanation:

It would be 12C2 for the teachers

and 43C2 for the students

12C2=66

43C2=903

66*903=59598