Which of the following expressions is equivalent to 2x + 3?

6(2)x
8(2)x
the quantity 2 to the power of x end quantity over 6
the quantity 2 to the power of x end quantity over 8

Answer:

7A, 8D

Step-by-step explanation:

The compound interest formula is as followed

[tex]A = P(1+\frac{r}{n} )^{nt}\\[/tex]

A = accumulated amount

P = principle

r = interest rate

n = compounding

t = time

The accumulated amount is represented by f(x).

The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000

The interest rate is 5%. This needs to be converted into a decimal.

5% = 0.05 = r

The money is compounded annually, thus n = 1.

The time is represented by x. x = t.

thus

[tex]f(x) = 2000(1+0.05)^{x}[/tex]

After six years, you simply find f(6), or substitute 6 into x.

f(6) = 2000(1.05)^6 = $2,680.19

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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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:

Step-by-step explanation:

y=652/4

convert decimal to a fraction

46/125=5

multiplying by both sides of the equation by 125/4

y=652/4 = 156 1/4

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

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 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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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:

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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Answer:

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

Given

Major axis of length = 12

Foci at ( 9 ,1 ) and ( -1, 1 )

Find

Equation of an ellipse

Explanation

As we know , major axis = 2a = 12

thus a = 6

the midpoint between the foci is the center , so

the distance between the foci is equal to 2c

now,

so , the equation of an ellipse is

Final Answer

The equation of an ellipse

25 new teachers joined the school such that the new ratio is 1 : 20 .

In mathematics, a ratio illustrates how frequently one number appears in another. For instance, the ratio of oranges to lemons on a fruit platter would be eight to six if there were eight oranges and six lemons.

The total number of students is 2000

The ratio of teachers to students  is 3:80 .

Therefore the number of teachers = 3 × 2000 ÷ 80 = 75

Let x teachers joined the school.

Therefore new ratio = (x+75) : 2000

but the new ratio is 1 : 20

Therefore 1 : 20 = (x+75) : 2000

Simplifying we get:

x + 75 = 100

or, x = 25

Therefore the number of teachers who joined the school is 25 .

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Answer:

Answer is the last graph which shows 10 cookies and 5 brownies.

Step-by-step explanation:

There are more cookies (y-axis) than brownies (x-axis), the slope is 2.0 so the line must be > 45 degrees.  

The z-value for 29 and 34 hours is z(32) = 0, the garages take between 32 hours and 34 hours to erect 34%, the garages take between 29 hours and 34 hours to erect 77.45%, and the garages, 5% take 35.29 hours of time.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

Weston Materials, Inc., a national manufacturer of detached garages, states that erecting the Red Barn type takes two construction workers a mean of 32 hours and a standard variation of 2 hours. Assume that the assembly times are distributed normally.

Calculating the z values for 29 and 34 hours.

z(29) = (29-32)/2 = -3/2

z(34) = (34-32)/2 = 1

z(32) = 0

The percentage of garages take between 32 hours and 34 hours to erect as:

⇒ P(32 < x < 34) = P(0< z < 1) = 0.34

The percentage of garages take between 29 hours and 34 hours to erect as:

⇒ P(29 < x < 34) = P(-1.5 < z < 1) = 0.7745

The percentage of garages take 28.7 hours to erect as:

⇒ z(28.7) = (28.7-32)/2 = -3.3

⇒ P(0 < x < 28.7) = P (-10 < z < -3.3) = 0.00048348...

The z-value corresponds to a 95% left area and only

5% to the right under the curve.

Use z-chart or InvNor(0.95) = 1.645

x-value that corresponds to the z-value.

1.645 = (x-32)/2

x-32 = 2×1.645

x = 35.29 hours

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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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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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Answer:

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

Step-by-step explanation:

The probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams is 0.4339.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 3316 grams - 54 grams = 3262

μ = mean = 3316 grams

σ = standard deviation = 324 grams

z-score = (3262 - 3316) / 324

z-score = -54 / 324

z-score = -0.1667

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = -0.1667

Using interpolation of values,

probability = 0.4339

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Answer:

2:20 pm to 5:57 pm is 3 hours and 37 minutes.

Answer:

3 hours and 37 minutes.

Step-by-step explanation:

5:57

-2:20

= 3:37

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 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 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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Answer: 6:30

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

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: 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:

78.8

Step-by-step explanation: