A stack of 12 sheets of gypsum board are 10.5 inches thick. If all the boards are uniform, how thick is each board?

The value of x from the given figure is 3. Hence, proved.

Given that, ∠XVW=∠W.

When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles. They are also known as "Vertically opposite angles" due to the fact that they are perpendicular to one another.

∠XVW = ∠W   (Given)

∠XVW = ∠ZVY  (Vertical angles theorem, vertical angles are congruent.)

∠ZVY = ∠W  (Transitive property of congruence)

m ∠ZVY = m ∠W (Angle congruence postulate)

8x+13=75x+28 (Substitution property of equality)

5x=15 (Subtraction property of equality)

x=3 (Division property of equality)

The value of x from the given figure is 3. Hence, proved.

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40 Km/h will be the average speed of the lorry for the overall journey from factory P to Q and again from factory Q to P.

The distance between the factories can be calculated by the Speed-Time relation.

Total Distance = Total Speed x Total Time = 45Km x 2 = 90Km

To calculate the Average Speed, Total Distance and Total Time are the essential parameters.

Total Distance = 90 + 90 = 180Km

Total Time = 2 + 2.5 = 4.5h

As per the formula of Average speed:

                          Average speed = Total Distance/ Total Time

                           Average speed = 90+90Km / 4.5h

                                                      = 40Km/h

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Answer:

3

The answer is three cuase I did the math but it's hard to explain on here

The elevation at which the diver takes the picture is -14 3/4 feet if, on a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

On a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.

Let x be the elevation at which the diver takes the picture.

The value of x can be found as follows:

x = -20 3/4 + 6

x = -83/4 + 6

x = (-83 + 24)/6

x = -59/6

Or

x = -14 3/4 feet

Thus, the elevation at which the diver takes the picture is -14 3/4 feet if, on a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.

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The number of ways to select a sample of 2 computer chips so that at least one of the chips is defective is 9876 ways.

The box contains 400 computer chips. Of these 400 chips 24 are defective and 376 are good.

A quality control inspector samples 2 computer chips.

The number of ways to select at least 8 defective chip is:

n (At least 8 defective chip) = n (1 defective chip) + n (2 defective chips)+n (3 defective chips)+n (4 defective chips)+n (5 defective chips)+n (6 defective chips)+n (7 defective chips)+n (8 defective chips)

The number of ways to select 1 defective chip is:24C1*400C1=24*400=9600  ways.

The number of ways to select 2 defective chips is: 24C2*400C0=276*1=276ways.

n (At least 1 defective chip) = n (1 defective chip) + n (2 defective chips)

                                             = 9600+276

                                             = 9876

Thus, the number of ways to select a sample of 2 computer chips so that at least one of the chips is defective is 9876 ways.

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Answer:

78.8

Step-by-step explanation:

The solution to the fraction -1/2 + 1/6 is -1/3

The expression is given as

-1/2 + 1/6

Rewrite the terms of the expression as equivalent fractions

So, we have the following equation

-1/2 + 1/6 = -3/6 + 1/6

Take the LCM of the equation

So, we have the following equation

-1/2 + 1/6 = (-3 + 1)/6

Evaluate the sum

So, we have the following equation

-1/2 + 1/6 = -2/6

Simplify the quotient

-1/2 + 1/6 = -1/3

Hence, the value of the fraction is -1/3

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The point (9, 16) is on the line.

Given,

The equation of the line = y = 4/3x + 4

We have to find whether the given points are on this line or not.

For that substitute the points into the equation.

That is,

Point (6, 13)

x = 6 and y = 13

Equation;

y = 4/3x + 4

13 = 4/3 x 6 + 4

13 = 8 + 4

13 ≠ 12

That is, the point (6, 13) is not in the line.

Next,

Point (9, 16)

x = 9 and y = 16

Equation;

y = 4/3x + 4

16 = 4/3 x 9 + 4

16 = 12 + 4

16 = 16

Therefore, the point  (9, 16) is in the line.

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Answer:

J. - (x-7)(x + 4)

Step-by-step explanation:

The  amount of taxes owed on a taxable income of $49,652 is 10,293.44.

The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate. With a marginal tax rate of 10%, tax would be deducted from the following dollar of income at a rate of 10%.

For instance, if a person has a taxable income of $24,750, they will pay taxes on the first $19,900 of that income at a rate of 10%, and on the remaining $5,000 at a rate of 12%.

Given:

Income= $49652

The above amount lies in the range of 41176- 89075 which has tax rate pf 22%.

So, the amount of taxes

= 49652 x 22%

=49652 x 22/100

= 49652 x 0.22

= 10,293.44

Hence, the amount of taxes owed on a taxable income of $49,652 is 10,293.44.

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Answer:

$6,600.44

Step-by-step explanation:

$49,652 falls into the 22% bracket.

Basically you take the taxable amount from each bracket and then multiply each by the corresponding marginal tax rate.

Then we take the income $49,652 and subtract it by the maximum of the last tax bracket which would be $41,175.

$49,652 - $41,175 = $8,477.

Multiply this by 22% = 1,864.94 then add the other brackets' taxes owed which should total to $6,600.44

The nurse should program the infusion pump to deliver 21.6ml/hour

Given the following:

Drug propofol prescribed is 8mcg/kg/min

Drug dispensed in 100mg in 50ml NS

Weight of patient is 198 pounds

Converting pounds in Kg:

198 pounds is (1 pound is 0.45Kg)

89.8 equivalent to 90Kg

Converting 8mcg/kg/min into mg/kg/min:

8mcg is 0.008mg so it becomes 0.008mg/kg/min

Patient weight is 90 kg , so required drug is:

90x0.008=0.72 mg/min

Now 50ml has 100mg, so 1ml has 2mg

We want to give 0.72mg, so if there is 2mg in 1 ml how much will be 0.72 mg for, by doing cross multiplication we get as below:

2mg in 1 ml

0.72=?

=0.72x1/2

=0.36ml

Now we have to give 0.36ml/min

Infusion pump has rate in ml/ hour, as 1 hour has 60 min, we multiply 0.36x60=21.6ml/hour

Hence, Infusion pump delivered 21.6ml/hour

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Answer: $2.80 a day

Step-by-step explanation:

you would need to save at least $2.80 a day, just take the total (19.60) and divide it by the number of days you have till its due, in this case a week (7 days) than divide. 19.20/7= 2.8

PX ≅ QX, as ΔGXP ≅ ΔIXQ is congruent by the AAS property.

Given, GHIJ is a parallelogram.

Given, HP ≅ JQ

GH ≅ JI, as both are on opposite sides it is a congruency property.

GP ≅ QI, the definition of congruency.

GP + PH ≅ JQ + QI, segment addition property.

∡PXG ≅ ∡ IXQ, vertical angles are congruent.

GH || JI, opposite sides are parallel

∠ PGH ≅ ∠QIX, alternate interior angles

PX ≅ QX, corresponding parts of congruent triangles are congruent.

ΔGXP ≅ ΔIXQ is congruent by the AAS property.

Therefore, PX ≅ QX

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Answer: 11/4n + 2 = -3 +3/2n

Step-by-step explanation:

1) Solve the given equation

-5n + 31 = -14n -5

9n = -36 (Move like terms)

n = -4

2) Solve every other equation until match

1a)

11/4n + 2 = -3 +3/2n

11/4n = -5 + 6/4n (Change fraction and move like terms)

5/4n = -5 (minus fraction)

n =  -4 Correct

Answer: 6:30

Step-by-step explanation: every number you count by 5 and the short hand is the hour hand.

The required equation of the line is 5x + y + 17 = 0.

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. Equations are used to describe geometric shapes in Cartesian geometry. Because the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions, the goal has shifted: instead of directly stating the solutions or counting them, which is impossible, one utilizes equations to investigate the features of figures. This is the fundamental concept of algebraic geometry, a significant branch of mathematics. An equation consists of two expressions joined by an equals sign ("="). The expressions on each side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side."

The equation of the line is given below:

y - 3 = -5(x - 4)

or, y - 3 = -5x - 20

or, 5x + y + 17 = 0

Hence, the required equation of the line is 5x + y + 17 = 0.

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Answer:

x = 1

Step-by-step explanation:

3(5x-2)=3x+8-2x

Apply the Distributive Property

15x - 6 3x+8 - 2x

Combine like terms

15x-6= x+8

Rearrange variables to the left side of the equation

15x-x=8+6

Combine like terms

14x 8+6

(I don't know if you want me to answer it)

Answer:

then answer is never going to give you up never going to let you down

Answer:

  1/3

Step-by-step explanation:

You want to know the slope of the line through points (10, 4) and (7, 3).

The slope of the line through two points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

  m = (3 -4)/(7 -10) = -1/-3 = 1/3

The slope of the line is 1/3.

Answer

It'll take Jake 40 minutes to type the 1,000 word paper.

Explanation

Working at that same speed, let the number of minutes it will take Jake to type 1,000 word paper be x minutes.

25 words = 1 minute

1,000 words = x minutes

We can write a mathematical relationship for this by cross mutiplying

(25) (x) = (1,000) (1)

25x = 1,000

Divide both sides by 25

(25x/25) = (1,000/25)

x = 40 minutes

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The constant of proportionality to convert gallons to pints given the information in the table is 8.

The constant of proportionality is the ratio that equates to variables in a directly proportional relationship. A directly proportional relationship is a relationship where the two variables move in the same direction.

The equation for direct proportionality:

y = bx

where:

16 = 2b

b = 16/2 = 8

40 = 5b

b = 40 / 5 = 8

56 = 7b

b = 56 / 7 = 8

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The graph that results from placing the coordinates on the graph is shown below.

Consequently, the graph's coordinates are (-1,1), (0,3), and (1,5)

We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found. The point where the two lines join is (-3, -4), which is where this equation system's solution lies.

There are 3 methods for graphing a linear equation:

1.displaying the graph of a linear equation using two points.

2.Use a linear equation's slope and y-intercept.

3.using a linear equation's x- and y-intercepts.

So we take 3 values to substitute in place of x like

-1,0,1

values of y we get are

1,3,5

Now placing the co ordinates on the graph we get the following graph,

Therefore, the co-ordinates constituting the graph are (-1,1), (0,3), (1,5)

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The condition that satisfies the criteria for rectangles is

m∠SRZ=40°. Option A

This is further explained below.

Generally, The diagram illustrates the rectangle RSTW, which contains the angle RTW with a measurement of forty degrees.

1. The sides SR and TW are perpendicular to one another as opposed sides of the rectangle. Next, the angles SRZ and RTW are alternative inner angles. The alternative inner angles theorem states that because they are congruent, mSRZ must equal 40 degrees. This option should be selected.

2. The angles STZ and RTW are complimentary to one another (they sum up to 90 degrees), and then

m∠STZ=90°-40°=50°. This choice is not a valid option.

3. The SRW angle represents a right angle (in a rectangle all angles are right angles). According to the textbook definition of a right angle,

m∠SRW=90°. This choice is not a valid option.

4. Angle TWR is a right angle (in a rectangle all angles are right angles). According to the textbook definition of a right angle,

m∠TWR=90°. This choice is not a valid option.

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CQ attached

Answer:

360 miles

Step-by-step explanation:

24*15=360

360 miles can be driven in 15 gallons gas.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For, example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A  car has a15 gallon gas tank.

Now, per gallon = 24 miles driven

So, in 15 gallons, the miles driven

= 24 x 15

= 360 miles.

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Using the quadratic formula we can conclude that the equation 3x = 2x² + 1 has two real roots which are x = 1 and x = 0.5.

The quadratic formula: [tex]x = \frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]

There are two real roots which are x = 1 and x = 0.5.

(Refer to the image attached below for the working)

Therefore, using the quadratic formula we can conclude that the equation 3x = 2x² + 1 has two real roots which are x = 1 and x = 0.5.

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The College employee in total count will be 60 professors and 168 lecturers in the college community.

As given total number of faculty member in the school is 228.

Also we have information that for every 14 lecturers the college community has 5 professors counting ratio.

∴ Let's Combine the number of professor and number of lecturers and make one group as a set.

∴ Total of one set will be 5 + 14 = 19.

Now as we have total 228 members and we have the set value as 19 so we can find the total number of set that can be possible with the given members as follows [tex] \frac{228}{19} = 12 [/tex]

Hence total number of set will be 12.

As one set contains 5 number of professors so 12 sets will contain in total ( 12 * 5 ) = 60 number of professors.

As one set contains 14 number of lecturers so 12 sets will contain in total ( 12 * 14 ) = 168 number of lecturers .

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