You invested some money in a start-up company, and now your investment has gained 60% and is worth $6,720. how much was your original investment?

Answer:

Ratios are proportional when the numbers in the ratio are multiply or divide by the same number. Ex. 3:5 = 6:10 = 12:20 = 9:15 (cross multiply the fractions and the results are the same 3/5 = 6/10)

Step-by-step explanation:

Answer:

4x+7=3x+7

Step-by-step explanation:

4x+(7-7)=3x+(7-7)

4x=3x

Answer:You can choose 6 different sets of 5 books to read.

Step-by-step explanation:All you need to do is do 30 divided by 5 and you get 6

Im pretty sure its permutation

The expression of the dimensions are 3w - 2 by w

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

The length of a rectangle is 2 less than 3 times as long as the width

Using the following variable definitions, we have

Based on the given information, we can express the length (l) in terms of the width (w):

l = 3w - 2

Hence, the dimensions are 3w - 2 by w

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The length is 4424 miles.

Let's denote the length of the bicyclist's route as "R".

According to the given information, the bicyclist covered 5/7 of his route and an additional 40 miles. This can be expressed as (5/7)R + 40.

It is also mentioned that he has yet to cover 118 miles less than 0.75 of his route. Mathematically, this can be represented as 0.75R - 118.

Since these two expressions represent the same length of the route, we can set them equal to each other and solve for R:

(5/7)R + 40 = 0.75R - 118

To solve for R, we can start by subtracting (5/7)R from both sides of the equation:

40 = 0.75R - (5/7)R - 118

Simplifying further, we have:

40 = (3/4)R - (5/7)R - 118

Combining the terms with R:

40 = [(21/28)R - (20/28)R] - 118

40 = (1/28)R - 118

Adding 118 to both sides:

158 = (1/28)R

Finally, multiplying both sides by 28:

R = 158 * 28

R = 4424 miles

Therefore, the length of the bicyclist's route is 4424 miles.

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The minimum distance the annihilation event could have occurred from the center of the machine is approximately 98.94 nanometers.

To determine the minimum distance the annihilation event could have occurred from the center of the machine, we can use the speed of light as a constant and the time difference between the collisions of the gamma rays.

The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s).

Since the time difference between the collisions of the gamma rays is given as 0.33 nanoseconds, we need to convert this time to seconds. One nanosecond is equal to 1 × 10⁻⁹seconds.

0.33 nanoseconds is equal to 0.33 × 10⁻⁹ seconds.

Now, we can calculate the minimum distance using the equation:

Distance = Speed of light × Time

Distance = 299,792,458 m/s × 0.33 × 10⁻⁹ seconds

Distance ≈ 98.94 nanometers

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Answer:

44 cookies

Step-by-step explanation:

1 scoop = 11 cookies

11 cookies * 4 scoops = 44 cookies

0 items in this array will be found if they are searched.

The correct option is D.

If you perform a binary search on a 5-element array sorted in reverse order, none of the items in the array will be found.

This is because the binary search algorithm relies on the array being sorted in ascending order for its correct functioning.

When the array is sorted in reverse order, the algorithm will not be able to locate any elements.

Thus, 0 items in this array will be found if they are searched for.

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Complex fraction.

Hope this helped!

Answer:

Option D. m<A = 43, m<B = 55, a = 20

Step-by-step explanation:

1. Determination of angle B.

Angle C = 82

Opposite C (c) = 29

Opposite B (b) = 24

Angle B =?

Using Sine rule, we can obtain the value of angle B as follow:

b/Sine B= c/Sine C

24/Sine B = 29/Sine 82

Cross multiply

29 × Sine B = 24 × Sine 82

Divide both side by 29

Sine B = (24 × Sine 82) /29

Sine B = 0.8195

Take the inverse of Sine.

B = Sine¯¹ (0.8195)

B = 55

2. Determination of angle A.

Angle C = 82

Angle B = 55

Angle A =?

The value of angle A can be obtained as follow:

A + B + C = 180 (sum of angle in a triangle)

A + 55 + 82 = 180

A + 137 = 180

Collect like terms

A = 180 – 137

A = 43

3. Determination of side a (Opposite A)

Angle C = 82

Opposite C (c) = 29

Angle A = 43

Opposite A (a) =?

The value 'a' can be obtained as by using sine rule as illustrated below:

a/Sine A = c/Sine C

a/Sine 43 = 29/Sine 82

Cross multiply

a × Sine 82 = 29 × Sine 43

Divide both side by Sine 82

a = (29 × Sine 43) /Sine 82

a = 20

Therefore,

m<A = 43, m<B = 55, a = 20

Answer:

The answer is 56.

Step-by-step explanation:

The formula for a triangle is b×h÷2. So you just input the data. 8×14÷2.

Answer:

x = -3

Step-by-step explanation:

5x + 4y = 1

y = 1 - x

• Substitute (1 - x) into y:

5x + 4(1 - x) = 1

• Distribute:

5x + 4 - 4x = 1

• Combine like terms:

x + 4 = 1

• Subtract the 4 to solve for x:

x = -3

Using the intersecting secants theorem, the value of x in the external part of the secant line is 12.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one  of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment"

From the diagram:

External line segement of the first secant line = 8 cm

First sectant line segment = ( 16 + 8 ) cm

External line segement of the second secant line = x

Second sectant line segment = ( x + 4 ) cm

Using the Intersecting secants theorem:

x × ( x + 4 ) = 8 × ( 8 + 16 )

Solve for x:

x² + 4x = 192

x² + 4x - 192 = 0

Factor using AC method:

( x - 12 )( x + 16 ) = 0

Equate each factor to zero:

( x - 12 ) = 0

x - 12 = 0

x = 12

( x + 16 ) = 0

x + 16 = 0

x = -16

Since, we are dealing with dimensions, we take the positive value:

Hence:

x = 12.

Therefore, the value of x is 12.

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To maximize profit, approximately 83 radial tires and 42 tractor tires should be manufactured, resulting in a maximum profit of approximately $1666.67.

The problem involves finding the optimal number of radial and tractor tires to manufacture in order to maximize profit while considering constraints on cost and rubber availability. By formulating the problem as a linear programming model, we can use algebraic methods to solve it.

The cost constraint is given as $8x + $12y ≤ $1500, where x represents the number of radial tires and y represents the number of tractor tires. Additionally, the rubber constraint is 5x + 20y ≤ 1000, indicating the maximum units of rubber available.

The objective function is to maximize profit, given by P = $10x + $25y. By graphing the feasible region, bounded by the given constraints, we identify the vertices of the polygon. Evaluating the profit function at each vertex, we determine that the maximum profit of approximately $1666.67 is achieved when manufacturing approximately 83 radial tires and 42 tractor tires.

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a. John's indifference map would show a preference for combinations of eggs and toast where the ratio of toast to eggs is 3:2.

b. Xi's indifference map would show an equal preference for different combinations of bread and chocolate, as she is neutral about bread but views chocolate as a good.

c. Ramesti's indifference map would show perfect substitution between tickets to the opera and baseball games, indicating that he is equally satisfied with either option.

d. Ahmad's indifference map would show a diminishing marginal utility for chocolate bars, where his satisfaction decreases after consuming a certain number of chocolate bars in a day.

which is because:

John's indifference map would consist of curves or lines that represent combinations of eggs and toast where the ratio of toast to eggs is 3:2. Each curve or line represents a different level of satisfaction or utility for John. As he moves further away from his preferred ratio of 3:2, his satisfaction decreases.

Xi's indifference map would show straight lines or curves that represent combinations of bread and chocolate where she is indifferent between different combinations. Since she views chocolate as good and is neutral about bread, the lines or curves would be parallel to the chocolate axis, indicating that she values chocolate more than bread.

Ramesti's indifference map would consist of straight lines that represent perfect substitution between tickets to the opera and baseball games. Any combination of tickets along a line would provide the same level of satisfaction for Ramesti, indicating that he is willing to trade one ticket for the other at a constant rate.

Ahmad's indifference map would show a downward-sloping curve that represents diminishing marginal utility for chocolate bars. As he consumes more chocolate bars in a day, the curve would become flatter, indicating that the additional satisfaction he derives from each additional chocolate bar decreases. This reflects his dislike for chocolates after consuming a certain quantity.

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Answer:

Compares 3 meals to 1 day

Step-by-step explanation:

The world has made it a basis that most people eat 3 meals a day.

One meal for Breakfast:

This Time Ranges from 6 to 11 am

One meal for Lunch:

This Time Ranges from 11 to 3 pm

One meal for Dinner:

This Time Ranges from 3-10 pm

Hope I could help! If you need anymore assistance, feel free to ask me!

Answer:9-y

Step-by-step explanation:6-7+3= 9-y

Simplified

Answer:

9-y

Step-by-step explanation:

6-y+3=

6+3-y=

9-y

If you were solving for y, then you need to provide a solution for 6-y+3.

If you were solving for the solution, then you need to give y a value.

If you needed to simplify it, then see my answer.

Answer:

5x^2(2x-7)

Step-by-step explanation:

Hope this helps!

the interest rate for this compound interest account is 1.5%.

Compound interest is the amount of interest calculated on both the principal amount and the interest previously earned by the account. The formula for compound interest accounts can be written as:\(A = P(1 + r/n)^(nt)\) where A is the amount accumulated, P is the principle, r is the interest rate, n is the number of compounding periods per year, and t is the time in years.To find the interest rate, we can use the formula and plug in the given values. We have:A = $90,000, P = $60,000, t = 15 years, and the interest is compounded monthly, so n = 12. Substituting these values into the formula, we get:90,000 = 60,000\(A = P(1 + r/n)^(nt)\))We need to solve for r, the interest rate. First, we can divide both sides of the equation by \(60,000:1.5 = (1 + r/12)^(12*15)\)Next, we can take the natural logarithm of both sides of the equation:ln(1.5) = \(ln[(1 + r/12)^(12*15)]\)Using the property of logarithms that says ln(a^b) = b*ln(a), we can simplify the right side of the equation:ln(1.5) = 12*15*ln(1 + r/12)Now we can divide both sides of the equation by 180 (12*15) to isolate ln(1 + r/12):ln(1.5)/180 = ln(1 + r/12)Finally, we can take the exponent of both sides of the equation to isolate r:(1 + r/12) = \(e^(ln(1.5)/180)r/12 = e^(ln(1.5)/180) - 1r = 12[e^(ln(1.5)/180)\)- 1]Using a calculator, we can evaluate the right side of the equation and round to 3 decimal places to get:r ≈ 0.015 or 1.5%Therefore.

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For a cubic unit cell, there are two planes in the {110} family.

A cubic unit cell is a cube-shaped unit that can represent the repeating unit of a crystal structure. In this type of unit cell, the edges are equal in length and the angles between the edges are 90 degrees.

The {110} family of planes: In a cubic unit cell, the {110} family of planes refers to all the planes that have Miller indices of {110} and its equivalent planes (e.g. {011}, {101}).

The Miller indices specify the orientation of a plane in a crystal lattice, and the family of planes refers to all planes that have similar orientations.

How many planes are in the {110} family? There are two planes in the {110} family of planes in a cubic unit cell.

The planes are perpendicular to each other and intersect at a right angle in the center of the cell. These planes are also parallel to the edges of the cube-shaped unit cell.

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Answer:

32+n

Step-by-step explanation:

32 more than the number n would be 32+n.

Hope this helps!

The function `f(x) = e^-x - ²7` for `x > 0` has an absolute minimum at some `x = a` such that `f'(a) = 0` and `f''(a) > 0`.Here's the solution to find the x-coordinate of the absolute minimum for the function `f(x) = e^-x - ²7` for `x > 0`:We first find the first derivative of `f(x) = e^-x - ²7` with respect to x.`

f'(x) = (-1)e^-x = -e^-x`

To find the critical points of the function, we set the first derivative of the function to zero. We have:`

f'(x) = -e^-x = 0`⇒ `e^-x = 0`⇒ `x = ln 0.

We know that `ln0` is undefined. Thus, there are no critical points of the function.The second derivative of the function `f(x) = e^-x - ²7` with respect to x is `f''(x) = e^-x`.Since `f''(x) > 0` for all x, the function is concave up for all x.Therefore, there is an absolute minimum at some `x = a` such that `f'(a) = 0` and `f''(a) > 0`.Since we found that there are no critical points of the function, there is no absolute minimum for the function. The function `f(x) = e^-x - ²7` for `x > 0` does not have an absolute minimum as there are no critical points of the function. We found that the first derivative of the function is `-e^-x` and the second derivative of the function is `e^-x`. We then set the first derivative of the function to zero and found that there are no critical points of the function.We know that a function has an absolute minimum at some `x = a` such that `f'(a) = 0` and `f''(a) > 0`. Since there are no critical points of the function, there is no absolute minimum for the function. Therefore, the function `

f(x) = e^-x - ²7` for `x > 0`

does not have an absolute minimum.

Thus, we can conclude that the function `f(x) = e^-x - ²7` for `x > 0` does not have an absolute minimum.

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Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-15,4) (2,-10)

The midpoint is

We have the final answer as

Hope this helps you

Answer:

3x

Step-by-step explanation:

You multiply the pervious number with 3 to get the next number

For example 2 times 3 = 6

6 times 3 = 18

18 times 3 =54

54 times 3= 162

So on and so forth

Based on the scatterplots provided, the answer would be A. A power model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.

In the scatterplots of log(weeks) against log(stock price), we can see that the relationship between the two variables is not linear, but rather appears to be curved. This suggests that a power model may be more appropriate, since this type of model can capture non-linear relationships.

A linear model is not suitable in this case, as the relationship between weeks and stock price does not appear to be linear. While the scatterplot of weeks against log(stock price) shows a strong linear relationship, this plot is not as appropriate for estimating the stock price as the plot of log(weeks) against log(stock price).

An exponential model may also be appropriate for capturing non-linear relationships, but the plot of weeks against log(stock price) does not show a strong linear relationship, so it is less appropriate than the plot of log(weeks) against log(stock price).

Overall, based on the provided scatterplots, a power model is the most suitable for estimating the stock price.

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Based on the scatterplots, which type of model is most suitable for estimating the stock price?

A. A power model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.

B. A linear model is suitable because the scatterplot of weeks against log(stock price) shows a strong linear relationship.

C. An exponential model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.

D. An exponential model is suitable because the scatterplot of weeks against log(stock price) shows a strong linear relationship.

The two column proof to show that ABCD is a parallelogram is as shown below

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Statement 1; BD bisects AC

Reason 1; Given

Statement 2; ∠BAC ≅ ∠DCA

Reason 2; Given

Statement 3; AB║ CD

Reason 3; Properties of parallelogram

Statement 4; ∠BEA ≅ ∠CED

Reason 4; Alternate Interior angles

Statement 5: AE ≅ EC

Reason 5: Diagonals of a parallelogram bisect each other

Statement 6: ΔABE ≅ ΔCDE

Reason 6: SAS Congruency postulate

Statement 7: BA ≅ DC

Reason 7: Properties of parallelogram

Statement 8: ABCD is a parallelogram

Reason 8: Corresponding parts of congruent triangles are congruent

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