**Answer:**

0.875 inches

**Step-by-step explanation:**

Pretty easy. Just divide how many inches thick the boards are by how many there are: inches-thick/amount

Now substitute 10.5/12 and find your answer

0.875 inches thick per board

6. A large community college has professors

and lecturers. The total number of faculty

members is 228. The school reported that

they had 5 professors for every 14 lecturers.

How many of each type of faculty member™

does the community college employ?

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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60% of a number is 66. Which proportion best represents this relationship?

Responses

66b =60100

**Answer:**

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

Using the quadratic formula, find the roots of the equation 3x = 2x² + 1.

A

x = -0.5 and x = −1

B x= 1.5 and x = 0

C

D

x = 2 and x = 1

x = 1 and x = 0.5

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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what is the mean of 45,68,77,90,90,95,100,100,86,90,50,55

**Answer:**

78.8

**Step-by-step explanation:**

Given: GHIJ is a parallelogram.

HP = JQ PQ bisects GI

Prove: PX = QX

Hint: Use subtraction of the side lengths.

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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The figure shows rectangle RSTW. Which of the following conditions satisfies the criteria for rectangles?

i cant upload image

a. m∠SRZ = 40°

b. m∠STZ = 40°

c. m∠SRW = 80°

d. m∠TWR = 80

The **condition **that satisfies the criteria for **rectangles **is

m∠SRZ=40°. **Option A**

This is further explained below.

What is theGenerally, 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

the healthcare provider prescribes propofol (diprivan) at 8 mcg/kg/minute for a client during conscious sedation. the drug is dispensed as a econdary infusion labled, 0.9% normal saline 50 ml with propofol 100 mg/50 ml the client's weight is 198 pounds. the nurse should program the infusion pump to deliver how many ml/hour? (enter numeric value only. if rounding is required, round to the nearest tenth.)

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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There is a proportional relationship between gallons and pints.

A) What is the constant of proportionality to convert gallons to pints? Show your work and/or explain your reasoning.

explain pls

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 fo**r direct proportionality:**

y = bx

where:

y = dependent variable = gallons b =16 = 2b

b = 16/2 = 8

40 = 5b

b = 40 / 5 = 8

56 = 7b

b = 56 / 7 = 8

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HELP!! // Your parents allow you to have Internet access on your cell phone as long as you prepay the bill. If your bill is $19.60 per week, how much would you have to save per day to pay the bill? Describe the process you use to solve the problem.

**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

simplify the expression -1/2 + 1/6

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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What is the slope of the line that passes through the points (10, 4) and (7, 3)?

**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)

ApplicationFor the given points, the slope is ...

m = (3 -4)/(7 -10) = -1/-3 = 1/3

**The slope of the line is 1/3**.

explain the strategy you used to sove this equation 3(5x-2)=3x+8-2x

**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)

Help me because i forgot everything :(

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)

How to solve linear equations on a graph?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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On a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level. She notices a sea turtle above her and rises 6 ft to take its picture. At what elevation does the diver take the picture?

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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9 Write the double that you would use to solve the problem Then solve it. Write your answers in the blanks. 4+5= ? Use the double 4+5=

4+5=9 9x2=18 therefore your answer is 18

What is the complete factorization of

-12 + 3x + 28?

F. (x-4)(x-7)

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

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

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

**Answer:**

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

**Step-by-step explanation:**

What is the constant rate of change of the table below?

10x4 is 40, 20x4 is 80, 30x4 is 120, and 40x4 is 160 so that means the constant rate is 4

Travis got a charging fee of 20$.He has an outstanding charge of 7.50 how much will he need to pay to not get feed by the bank

I think it’s 15 or a lil more less

Please Solve this Algebraic Proof for Geometry!!

2 images attached

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

Given that, ∠XVW=∠W.

What is vertical angles theorem?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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Is 1/1 a terminating or repeating decimal

Terminating Decimal: A decimal number that has digits that end. Examples: 0.25Repeating Decimal: Also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely). e.g 0.16666[tex] \frac{1}{1} = 1[/tex]Therefore 1 is a terminating decimal

A lorry travels at a speed of 45 km/h for 2 hours from factory P to factory Q. Then the lorry takes 30 minutes more for its return journey. Calculate the average speed.

**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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a car has a15 gallon gas tank and gets a maximum average mileage of 24 miles per gallon

**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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Find the equation of the line and passing through (4,3) with slope= -5

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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Use the marginal tax rate chart to answer the question.

Determine the amount of taxes owed on a taxable income of $49,652.

•$4,735.38

•$6,600.44

•$7,709.92

•$10,293.44

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 equation of a line is y=4/3x + 4 . Is the point (6, 13) on the line? [ Select ] Is the point (9, 16) on the line?

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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(1 + 2)3 ÷ (2 + 1) =

**Answer:**

3

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

Select the equation that has the same solution.

brainiest for the best answer. 100 points.

**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**

among all the computer chips produced by a certain factory, 6 percent are defective. a sample of 400 chips is selected for inspection. (a) what is the probability that this sample contains between 20 and 25 defective chips (including 20 and 25)? (b) suppose that each of 40 inspectors collects a sample of 400 chips. what is the prob- ability that at least 8 inspectors will find between 20 and 25 defective chips in their samples?

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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If Jake can type approximately 25 words per minute, how long will it take him to type a 1,000 word paper

**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**

**Hope this Helps!!!**

Write the time in the blank below

The time shown on the clock is 6:30

**Answer: 6:30**

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

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