For the problem n 2/3 which of the following are always true

Amy is left with 60% of the money she had initially.

Let's break down the problem step by step:

Amy had $80 to spend on a filter.

She spent 20% of the money on a filter, which is 0.20 * $80 = $16.

After purchasing the filter, she paid $16 to a plumber to install it.

So far, Amy has spent a total of $16 + $16 = $32.

To find out how much money Amy is left with, we subtract the amount she has spent from the initial amount she had:

$80 - $32 = $48

Amy is left with $48.

To determine the percentage of the money she is left with, we can calculate what portion of the initial amount she still has:

($48 / $80) * 100 = 60%

Therefore, Amy is left with 60% of the money she had initially.

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Answer:

Step-by-step explanation:

a1 = - 7

d = 4

an = a1 + (n - 1) * d

an = - 7 + (n - 1) * 4

an = - 7 + 4n - 4

an = -11 + 4n

Try this out. Let n = 3

a3 = -11 + 4*3

a3 = - 11 + 12

a3 = 1   Which is what the series says.

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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Given:

The height h of an object after t seconds is

\(h=-16t^2+48t+210\)

The height of a neighboring 50-foot tall building is modeled by the equation h=50.

The time (t) when the object will be at the same height as the building is found to be t = –2 and t = 5.

To find:

The statement which describes the validity of these solutions.

Solution:

We have,

\(h=-16t^2+48t+210\)

Here, t is the time in seconds.

For t=-2,

\(h=-16(2)^2+48(-2)+210\)

\(h=-64-96+210\)

\(h=50\)

For t=5,

\(h=-16(5)^2+48(5)+210\)

\(h=-400+240+210\)

\(h=50\)

So, the value of h is 50 at t=-2 and t=5.

We know that time is always positive so it cannot be negative value. It means t=-2 is not possible.

The solution t = 5 is the only valid solution to this system since time cannot be negative.

Therefore, the correct option is C.

There are 15 different positive divisors (greater than 1) for the number m³pt. Here m, p, and t are distinct prime numbers. This is obtained by the prime factorization method.

The following are the steps to find the number of positive factors of a number:

Step 1: Find the L.C.M of the number by using the prime factorization method. For example: consider the number 24. Then, its prime factorization is as follows:

24 = 2 × 2 × 2 × 3

Step 2: Same bases should be added in powers. So, the factors we can write as

24 = 2³ × 3¹

Step 3: To find the number of positive factors of the number, the exponents of the prime factors is multiplied by adding 1.

I,e., N = (3 + 1)(1 + 1) = 4 × 2 = 8.

So, there are 8 factors for the number 32. They are 1, 2, 3, 4, 6, 8, 12, and 24.

It is given that, m, p, and t are distinct positive prime numbers.

Then, the number of positive divisors greater than 1 for the number m³pt are

m³× p × t

Since m, p, and t are prime factors, we can multiply their power by adding 1 to them. I.e.,

N = (3 + 1) (1 + 1) (1 + 1) = 4 × 2 × 2 = 16

So, there are a total of 16 factors for the given number (including 1). So, the number of factors greater than 1 is 16 - 1 = 15.

Therefore, there are 15 different positive divisors greater than 1 for the number having prime factors as m³pt.

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Step-by-step explanation:

The slope is the ratio of change in number of cups to change in hours:

The y-intercept is the number of cups at zero hour:

The line would be:

Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

\(\qquad\qquad\displaystyle \huge Answer\)

Let's check if (3 , 6) is the point of intersection of the given lines ~

\( \qquad \displaystyle \: y = 4x - 2\)

and

\( \qquad \displaystyle \: y = \frac{1}{2} x + 5\)

If the point is the point of intersection of these two lines, then it should satisfy both the equations ~

let's try each of them, using x coordinate of point.

\( \qquad \displaystyle \: y = 4(3) - 2\)

\( \qquad \displaystyle \: y = 12 - 2\)

\( \qquad \displaystyle \: y = 10\)

So, the point didn't actually satisfy one of the equation. hence we can infer that the given statement is wrong.

Equation of the line - 8 + x = 4y - 16

x- intercept, at y = 0:

y- intercept, at x = 0:

The points are (0, 2) and (- 8, 0), plot them and connect to get the graph.

The graph that connects points (-8,0) and (02) is shown below

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

-8+x=4y-16

x- intercept, at y = 0:

- 8 + x = 4(0) - 16

x = - 16 + 8

x = - 8

y- intercept, at x = 0:

- 8 + 0 = 4y - 16

4y = 16 - 8

4y = 8

y = 2

The points are (-8,0) and (02)

So, the graph that connects points (-8,0) and (02) is shown below

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a. $3,000 at 5% APR for 8 years = $4,469.47., b. Semiannual: $4,494.49. Bimonthly: $4,503.50., c. 10% APR: Annual - $4,878.14; semiannual - $4,913.67; bimonthly - $4,924.25., d. 16 years, 5%APR:$5,918.94.,e.increase future sums.



( a. )To calculate the future sum, we use the formula for compound interest: FV = P(1 + r/n)^(nt). Plugging in the values, we have FV = $3,000(1 + 0.05/1)^(1*8) = $3,000(1.05)^8. ( b. ) For semiannual compounding, n = 2. Therefore, FV = $3,000(1 + 0.05/2)^(2*8) = $3,000(1.025)^16. For bimonthly compounding, n = 6. So, FV = $3,000(1 + 0.05/6)^(6*8) = $3,000(1.008333)^48.

( c.) Using an APR of 10%, we repeat the calculations in parts a and b. For part a, FV = $3,000(1 + 0.10/1)^(1*8) = $3,000(1.10)^8. For part b with semiannual compounding, FV = $3,000(1 + 0.10/2)^(2*8) = $3,000(1.05)^16. And for bimonthly compounding, FV = $3,000(1 + 0.10/6)^(6*8) = $3,000(1.016667)^48. ( d.) For a time horizon of 16 years and an APR of 5%, we use the formula in part a: FV = $3,000(1 + 0.05/1)^(1*16) = $3,000(1.05)^16.

 e. Comparing the results, we observe that higher interest rates and longer holding periods lead to larger future sums. Additionally, more frequent compounding (bimonthly) generates higher future sums compared to semiannual or annual compounding, highlighting the power of compounding over shorter intervals.

Therefore,interest  is  a. $3,000 at 5% APR for 8 years = $4,469.47., b. Semiannual: $4,494.49. Bimonthly: $4,503.50., c. 10% APR: Annual - $4,878.14; semiannual - $4,913.67; bimonthly - $4,924.25., d. 16 years, 5% APR: $5,918.94., e. Higher rates, compounding, longer time horizons increase future sums

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The equation of parabola will be x² = 3y.

A parabola is a curve which forms by joining all the points which are at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).

Given is a parabolic headlamp has a bulb placed at the focus. A cross-section of the parabola is 6 cm deep and 12 cm wide.

The general equation of a parabola that opens up with vertex at the origin as -

x² = 4py

We have -

x = 6 cm

y = 12 cm

So, we can write -

36 = 4p x 12

4p = 3

p = 3/4

So the equation of parabola would be -

x² = 4py

x² = 4(3/4)y

x² = 3y

The equation of the parabola will be x² = 3y

Therefore, the equation of parabola will be x² = 3y.

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To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)

where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.

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(a) It is a designed study because the manager intentionally installs different incentive programs to determine their effect on productivity. On the other hand, (b) is an observational study as it involves monitoring and measuring the relationship between sulfur dioxide levels and the facility's load without any manipulation of variables.

(a) The study described in (a) is a designed study. This is because the manager deliberately installs different incentive programs in each of the nine plants with the intention of determining the effect of each program on the overall productivity of the facility. By manipulating the independent variable (incentive programs), the manager is attempting to establish a cause-and-effect relationship between the programs and productivity. The study design allows for control over the variables and enables comparisons to be made between the different incentive programs.

(b) The study described in (b) is an observational study. This is because the electric utility is hiring a consultant to monitor the discharge from its smokestack on a monthly basis and relate the level of sulfur dioxide in the discharge to the load on the facility's generators. The researchers in this case are not actively intervening or manipulating any variables. They are simply observing and measuring the relationship between sulfur dioxide levels and the facility's load. The study does not involve any manipulation of variables or random assignment, making it an observational study.

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Answer:

Yes, A,B, and F is correct

Step-by-step explanation:

-- Gage Millar, Algebra 2 Tutor

Answer:

y = 6

may help you i think so

To determine the validity of the argument that "Mr. Einstein wears glasses", given that "some professors wear glasses", trapezium

a Venn diagram can be constructed.The Venn diagram is given below: A rectangle is drawn to represent all professors. A circle inside the rectangle represents professors who wear glasses. This is because "Some professors wear

glasses."Inside the circle, another circle represents the group of people who wear glasses. Mr. Einstein is included in this circle because "Mr. Einstein wears glasses."Thus, the argument is valid since Mr. Einstein is included in the group of professors who wear glasses.

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To determine the validity of the argument that "Mr. Einstein is a professor," we can use a Venn diagram. Here's how to

do it:Step 1: Draw two overlapping circles, one for "Professors" and one for "People who wear glasses."Step 2: Label the circle for professors "P" and the circle for people who wear glasses "G."Step 3: Write "Some professors wear glasses" in the area where the circles overlap.Step 4: Write "Mr. Einstein wears glasses" in the area that represents

people who wear glasses but are not professors.Step 5: We cannot conclude that Mr. Einstein is a professor based solely on these premises since there are people who wear glasses but are not professors. Therefore, the argument is invalid.Here is a visual representation of the

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Answer:

∠GIH or ∠HIG

Explanation:

Just make sure the vertex of the angle is the middle letter. In this case, it is I.

Answer : 2

Step-by-step explanation:

Slope is a ratio, Slope = rise/run. This can also be described as "the change in Y" / "The change in X"

So, using the table, find the rate of change in the y-values and the x-values.

y = mx + b

slope : m

x=-7, y=2 : -7m + b = 2 (1)

x=-6, y=4 : -6m + b = 4 (2)

(2)-(1) => m= 2

Answer:

4.5 x 0.72

Step-by-step explanation:

I AM ASSUMING THAT YOU FORGOT TO ADD 2 AFTER 0.7 IN 4.5 x 0.7

Answer:

50

Step-by-step explanation:

cause its right trust me i dont wanna waist ur time writing something that i know ur no gonna read

Answer:

lol

Step-by-step explanation:

\((x - 4) {}^{2} + (y - 1) {}^{2} = r {}^{2} \)

passes through ( 4 , -4 )

\((4 - 4) {}^{2} + ( - 4 - 1) {}^{2} = r {}^{2} \)

\(r {}^{2} = ( - 5) {}^{2} \)

\(r {}^{2} = 25\)

\(r = \sqrt{25} = 5\)

Your radius is 5 units

\(c = 2\pi \: r \\ c = 2 \times 3.14 \times 5 \\ c = 31.4\)

Place your center at the point x=4 and y=1

Then take your radius 5 units by going straight down left right or up by 5 units

AND DRAW

Answer:

x=55.5

Step-by-step explanation:

2x=111

Isolate x by dividing both sides by 111

x=55.5

The number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.

Fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

\(\dfrac{a}{b}\)

Here (a) is the numerator and (b) is the denominator.

Last week, Ken ran 10 laps around the lake. Heather ran 2/3 as many laps around the lake as Ken did. Thus, the number of laps heather ran is,

\(x=\dfrac{2}{3}\times10\\x=\dfrac{20}{3}\)

Hence, the number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.

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Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

it is suggested that students allocate around 2-3 hours of study time per credit hour per week for a college-level course. However, the actual study time required may vary based on individual learning styles, prior knowledge, and the specific requirements set by professors or institutions.

Let's apply this general guideline to your scenario:

One three-credit class that is less demanding:

Assuming 2-3 hours of study per credit hour, for a three-credit class, you would ideally spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Two three-credit classes that are typically demanding:

Similarly, for each of the two three-credit classes, you would spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Since you have two such classes, the total time would be:

2 * (6-9) hours = 12-18 hours per week.

One four-credit class that is very challenging:

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

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Answer:

u = 24

Step-by-step explanation:

-7/8u = -21

Solve for u

Multiply each side by -8/7

-8/7 *-7/8u = -21 *-8/7

u =3*8

u = 24

Answer:

u = 1/24

Write the equation:

–7/8u = –21

Get rid of fraction:

–7/2^3 • u = –21

–7 = ( – (8u) ) 21

Solve:

–7 = –8u + 21

–7 + 8u = –8u + 8u + 21

–7 + 8u = 21

–7 + 7 + 8u = 21 + 7

8u = 21 + 7

8u = 28

u = 1/24

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The coordinates of the vertices after a dilation with a scale factor of 1/3 centered at the origin is E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).

Dilation is  a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Given that center of the dilation is origin.

Any coordinate (x, y) when dilated to a scale factor k is (kx, ky).

The coordinates of the quadrilateral are E(0, -6), F(9, -6), G(9, 3) and H(0, 3).

Dilation is with a scale factor of 1/3.

So all the coordinates become (1/3x, 1/3y).

E(0, -6) becomes E'(0, -2)

F(9, -6) becomes F'(3, -2)

G(9, 3) becomes G'(3, 1)

H(0, 3) becomes H'(0, 1)

Hence the coordinates are E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).

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The daily turnover for the drink vendor in the secondary school is £352.30, which is closest to option A, £353.20 i.e. Option A is the correct answer

To calculate the daily turnover for the drink vendor in the secondary school, we need to consider the number of drinks sold and the price of each drink. From the given table, we can see that for secondary school, the number of Juice drinks sold is 45, the number of Water drinks sold is 115, the number of Coca-Cola drinks sold is 51, the number of Sprite drinks sold is 45, the number of Milk drinks sold is 12, and the number of Chocolate Milk drinks sold is 32.

Using these numbers, we can calculate the daily turnover for each drink by multiplying the number of drinks sold by the price of each drink. For example, for Juice, the price is given as £1.50 and the number of drinks sold is 45, so the total turnover for Juice is £1.50 x 45 = £67.50. Similarly, we can calculate the daily turnover for each drink sold in the secondary school.

Finally, we add up all the daily turnovers for each drink sold in the secondary school to get the total daily turnover for the drink vendor in the secondary school. The calculated total turnover is £352.30, which is closest to the option A, £353.20.

For the secondary school, the turnover can be calculated as follows:

Juice: £1.50 x 45 = £67.50

Water: £0.80 x 115 = £92.00

Coca-Cola: £1.20 x 51 = £61.20

Sprite: £1.20 x 45 = £54.00

Milk: £1.40 x 12 = £16.80

Chocolate Milk: £1.90 x 32 = £60.80

Total turnover = £352.30

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Answer: a

Step-by-step explanation:a

The distances based on their values, we have:

Distances of approximately 1 to 2 units: (-3, 1) and (-4, -2)

Distances of approximately 3 units: (2, 1) and (1, 2)

Distances of approximately 5 units: (3, 7) and (4, -1), (5, -2) and (3, 3), and (-1, 1) and (4, -1).

Coordinates (3, 4) (3, 7) (5, -2) (-2, 3) (-4, -2) (4, -1)

(2, 1)           3.16    

(5, 2)                   5.39    

(3, 3)                             5.1  

(1, 2)                                             3.16  

(-3, 1)                                                1.41

(-1, 1)                                                        5.1

We may use the distance formula to determine the separation between each pair of coordinates:

Distance is equal to sqrt((x2 - x1) + (y2 - y1))

Using the values to categorise the distances, we have:

About 1 to 2 unit distances are (-3, 1) and (-4, -2)

Distances roughly 3 units apart: (2, 1) and (1, 2) Distances roughly 5 units apart: (3, 7) and (4, -1), (5, -2) and (3, 3), and (-1, 1) and (4, -1).

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