You find a mutual fund that offers approximately 8% APR compounded monthly. How much will you need to invest each month for the next year in order to have $2000?​

Answer:

His shadow would be 3 feet long.

Step-by-step explanation:

Ladder:

\( \frac{50}{25} = 2 \: or \: \frac{2}{1} \)

Mark:

\( \frac{6}{x} \)

Using proportions and ratios formula.

\( \frac{6}{x} = \frac{2}{1} \)

Cross multiply.

6 = 2x

Divide both sides.

3 = x or x = 3

100 points literally down the drain guys

The answer of the given question based on the equation problem is , one coin is worth 5 points and one gem is worth 11 points.

An equation is the  mathematical statement that shows  equality between the two expressions. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The LHS and RHS may contain one or more variables, constants, mathematical operations, and functions.

Let's denote the value of one coin by x and the value of one gem by y. We can set up two equations based on the given information:

3x + 5y = 70 (equation 1)

6x + 2y = 52 (equation 2)

We can use these equations to solve for x and y. One way to do this is to multiply equation 2 by 5 and subtract it from equation 1 multiplied by 2:

6x + 10y = 140 (equation 1 multiplied by 2)

-30x - 10y = -260 (equation 2 multiplied by 5, with signs flipped)

-24x = -120

x = 5

Now that we know that one coin is worth 5 points, we can substitute this value into either of the original equations to solve for y. Let's use equation 1:

3(5) + 5y = 70

15 + 5y = 70

5y = 55

y = 11

Therefore, one gem is worth 11 points.

In summary, one coin is worth 5 points and one gem is worth 11 points.

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The sample variance is 95.875/7.

To calculate the sample variance and sample standard deviation using the definitional formula, you need to follow these steps:

Calculate the squared deviations from the mean.

Sum up the squared deviations.

Divide the sum of squared deviations by (n - 1) for the sample variance, or by n for the population variance.

Take the square root of the variance to find the standard deviation.

Let's go through the calculations for the provided data set step by step:

Data set: 92, 84, 85, 93, 95, 89, 86, 91

Mean: 89.375

Step 1: Calculate the squared deviations from the mean:

Squared deviations: (2.625)^2, (-5.375)^2, (-4.375)^2, (3.625)^2, (5.625)^2, (-0.375)^2, (-3.375)^2, (1.625)^2

= 6.890625, 28.890625, 19.140625, 13.140625, 31.640625, 0.140625, 11.390625, 2.640625

Step 2: Sum up the squared deviations:

Sum of squared deviations = 6.890625 + 28.890625 + 19.140625 + 13.140625 + 31.640625 + 0.140625 + 11.390625 + 2.640625

= 114.7671875

Step 3: Calculate the sample variance:

Sample variance = Sum of squared deviations / (n - 1)

= 114.7671875 / (8 - 1)

= 114.7671875 / 7

= 16.3953125

Step 4: Calculate the sample standard deviation:

Sample standard deviation = √(sample variance)

= √(16.3953125)

= 4.052488554

Therefore, for the given data set, the sample variance is 16.3953125 and the sample standard deviation is approximately 4.0525.

If the largest value of 95 was misrecorded as 93, we need to recalculate the variance and standard deviation.

Data set with corrected value: 92, 84, 85, 93, 93, 89, 86, 91

Mean: 89.125 (recalculated mean without the misrecorded value)

Step 1: Calculate the squared deviations from the mean:

Squared deviations: (2.875)^2, (-5.125)^2, (-4.125)^2, (3.875)^2, (3.875)^2, (-0.125)^2, (-3.125)^2, (1.875)^2

= 8.265625, 26.265625, 17.015625, 15.015625, 15.015625, 0.015625, 9.765625, 3.515625

Step 2: Sum up the squared deviations:

Sum of squared deviations = 8.265625 + 26.265625 + 17.015625 + 15.015625 + 15.015625 + 0.015625 + 9.765625 + 3.515625

= 95.875

Step 3: Calculate the sample variance:

Sample variance = Sum of squared deviations / (n - 1)

= 95.875 / (8 - 1)

= 95.875 / 7

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The slope of Ambrose's indifference curve when his consumption bundle is (36,10) is -36/10.

To find the slope of Ambrose's indifference curve, we need to differentiate the equation of the indifference curve with respect to good 1 (x1) and evaluate it at the consumption bundle (36,10).

The equation of Ambrose's indifference curve is given as:

x2 = constant - 4(x1)^(1/2)

Differentiating both sides of the equation with respect to x1, we get:

0 = -4(1/2)(x1)^(-1/2)dx1 - 4

Simplifying this equation, we have:

-4(x1)^(-1/2)dx1 = 4

Now, we can solve for dx1:

dx1 = -1/(x1)^(1/2)

Substituting the consumption bundle (36,10) into dx1, we get:

dx1 = -1/(36)^(1/2) = -1/6

Finally, we can calculate the slope of the indifference curve by taking the ratio of the change in x2 to the change in x1:

slope = dx2/dx1 = -4/(-1/6) = -4 * (-6) = -24

Therefore, the slope of Ambrose's indifference curve when his consumption bundle is (36,10) is -24.

Note: The given answer choices (-36/10, -6, -16, -10/36, -0.33) do not match the calculated slope of -24.

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Answer:

Please refer to the attached image for a possible graph of given equation.

Step-by-step explanation:

Given the equation:

\(g(x) = x^2 + d\)

Let us write the equation as:

\(y = x^2 + d\) so that we can plot it on xy axis.

The highest power of x is 2.

The given equation resembles with the equation of a parabola.

The vertex form of a parabola is given as:

\(y = a(x - h)^2 + k\)

Here (h,k) is the vertex of parabola.

Vertex of the parabola is the point on the axis of symmetry and is the highest or the lowest point on parabola.

Now, let us compare the given equation of parabola with the standard vertex form of parabola. We get the following values:

a = 1 > 0 hence, parabola will open upwards.

h = 0

k = d

So, the vertex is at O (0,d). It means vertex will be on the y axis.

Now, we are given that d < 0 that means the vertex will be on negative y axis.

Now, let us suppose d = -8, the graph will be as attached in the answer area. Please have a look.

Answer:

yo ma

Step-by-step explanation:

because

Answer:

remember to round numbers to 1 significant figure

Step-by-step explanation:

usually in an exam when you're asked to estimate the answer to a calculation, usually you round each number to 1 sf and then work on from there.

y=5x-6

Hope it helps.

Do comment if you have any query.

Answer:

x = 3y + 1

Step-by-step explanation:

You need to find the relationship between x and y before finding the y-intercept.

0-(-1) = 1

1-0 = 1

2-1 = 1

1-(-2) = 3

4-1 = 3

7-4 = 3

As x increases by 1, y increases by 3.

At x = 0, y is already 1. Thus:

x = 3y + 1

Answer:

Slope-intercept For: \(y = 3x + 1\)

Standard Form: \(9x - 3y = -3\)

Point-slope Form: \(y - 4 = 3(x - 1)\)

Step-by-step explanation:

Slope-intercept Form: \(y = mx + b\)

Standard Form: \(Ax + By = C\)

\(\frac{y}{-3x} = \frac{3x}{-3x} + 1\\-3(-3x + y = 1)\\9x -3y = -3\)

Point-slope Form: \(y_2 - y_1 = m (x - x_1)\)

\((1, 4)\\y - 4 = 3 (x - 1)\)

Answer:

The value of x = 0    

Step-by-step explanation:

Given

To determine

The value of x = ?

If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).

i.e. y → 5×4 =20

It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.

Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.

i.e. x → 4×0 = 0

Thus, the rule of dilation is:

P(x, y) = P'(4x, 4y)

Hence,

B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)

Thus,

The value of x = 0           ∵ 0×4 = 0

The domain and range of the function are [-3, 3] and [-2, 4], respectively and The function values for (a) f(-1), (b) f(0), (c) f(1) and (d) f(2) are 0, -2, 4, and 3, respectively. The total number of words used is 163.

Given that the graph of the function is shown below, the domain and range of the function need to be determined along with finding the function values for (a) f(−1), (b) f(0), (c) f(1) and (d) f(2).Graph of the function:Graph of the function for the given graph of the function, we can observe that the domain of the function is from -3 to 3 as the graph is defined within these limits.In order to find the range of the function, we need to look at the range of the y-coordinates.

The minimum value of y is -2 and maximum value of y is 4.Range of the function: [-2, 4]a) f(-1) means the function value for x = -1. As we can observe from the graph, the point where x = -1 is on the graph of the function is (1, 0). Therefore, f(-1) = 0b) f(0) means the function value for x = 0. As we can observe from the graph, the point where x = 0 is on the graph of the function is (0, -2).

Therefore, f(0) = -2c) f(1) means the function value for x = 1. As we can observe from the graph, the point where x = 1 is on the graph of the function is (2, 4). Therefore, f(1) = 4d) f(2) means the function value for x = 2. As we can observe from the graph, the point where x = 2 is on the graph of the function is (3, 3). Therefore, f(2) = 3

Thus, the domain and range of the function are [-3, 3] and [-2, 4], respectively. The function values for (a) f(-1), (b) f(0), (c) f(1) and (d) f(2) are 0, -2, 4, and 3, respectively. The total number of words used is 163.

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Answer:

Winnipeg.

Step-by-step explanation:

Answer:

Quotient = 3x-5

Remainder = 3

Step-by-step explanation:

For any long division, I use the DMS principle, divide, multiply, subtract.

(x+6) | 3x² + 13 x - 27

First of all, divide the first part of the equation by x. (which is 3x²)

You get 3x.

Now take your 3x and multiply it by (x+6)

You get 3x²+18x. You need to subtract this from your equation.

(3x² + 13 x - 27) - (3x² + 18x) = -5x - 27

One round of DMS complete

Now,

(x+6) | - 5x - 27

We again divide the first part only by x again. You get -5

We multiply -5 by (x+6)

-5x-30.

Let's subtract it from the equation.

(-5x-27) - (-5x-30) = - 5x - 27 + 5x + 30 = 3

Second round of DMS complete.

We cannot divide 3 further by (x+6) so this is it.

The remainder is 3.

Now we take our answers, which is 3x and - 5 and add them to get 3x-5. This is our quotient.

Answer:

9:00 pm, 4th November

Step-by-step explanation:

Since ;

Brisbane is 10 hours ahead of London

New York is 5 hours behind London

Then, Brisbane is (10 + 5)hours ahead of New York.

Then Brisbane is 15 hours ahead of New York

Time and Date Brisbane resident called New York = 12 Noon, 5th November

Time and Date in New York will be :

(12 Noon - 15 hours) = 9:00 pm, 4th November

Answer:

Figure A and B are still congruent to each other. the only change is the size of the shape.

Step-by-step explanation:

Yes, figure A and figure B similar because even though their side lengths are different, their internal angles are the same.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Suppose figure A underwent a dilation to produce figure B.

Now, A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

if Dilation factor  N then image Size is multiplied  by  N

if Scale factor  < 1 then image get reduced

if scale factor > 1  then image get enlarged

scale factor = 1 lead to Same size image

Hence, Figure A and figure B similar because even though their side lengths are different, their internal angles are the same.

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Answer:

-1/2

Step-by-step explanation:

Deone's length was 19.5 inches at birth. Assuming his development proceeds normally, his length should be about 29.5 inches by his first birthday.

We know that According to the Centers for Disease Control and Prevention (CDC), the average length for a boy at birth is around 20 inches, and the average length for a boy at one year of age is around 30 inches.

To estimate Deone's length at one year of age, we use the average growth rate between birth and one year, which is approximately 10 inches.

So , we add 10 inches to Deone's length at birth of 19.5 inches to estimate his length at one year of age:

⇒ Estimated length at 1 year = 19.5 inches + 10 inches = 29.5 inches

Therefore, Deone's length should be about 29.5 inches by his first birthday, assuming that his development proceeds normally.

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so Mai had booming sales of $2500, now her commission used to be 5%, but since she rules it went up to 6%, how much is her commission on that?

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 2500}}{\left( \cfrac{6}{100} \right)2500}\implies 150\)

since her salary which used to be $200 but is now 200 + 25 = $225, so for that week she earned 225 + commission or 225 + 150 = 375.

The length of the unknown sides of the triangles are as follows:

CD = 10√2

AC = 10√2

BC =  10

AB = 10

Since, Triangle ACD

ΔACD is a right angle triangle.

Therefore, Pythagoras theorem can be used to find the sides of the triangle.

c² = a² + b²

where

c = hypotenuse side = AD = 20

a and b are the other 2 legs

lets use trigonometric ratio to find CD,

cos 45 = adjacent / hypotenuse

cos 45 = CD / 20

CD = 1 / √2 × 20

CD = 20 / √2 = 20√2 / 2 = 10√2

Hence,

20² - (10√2)² = AC²

400 - 100(2)  = AC²

AC² = 200

AC = √200 = 10√2

Triangle ABC

ΔABC is a right angle triangle too. Therefore,

AB² + BC² = AC²

Using trigonometric ratio,

cos 45 = BC / 10√2

BC = 10√2 × cos 45

BC = 10√2 × 1 / √2

BC = 10√2 / √2 =  10

Hence,

(10√2)² - 10² = AB²

200 - 100 = AB²

AB² = 100

AB = 10

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The equation of a parabola with a given focus and directrix is:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

In this equation, (a, b) represents the coordinates of the focus, and c represents the y-coordinate of the directrix. This equation describes a parabola where all points on the parabola are equidistant from the focus and the directrix.

To write the equation of a parabola with a given focus and directrix, we can use the geometric definition of a parabola. A parabola is the set of all points that are equidistant from the focus and the directrix.

Let's assume the focus is denoted as F(a, b) and the directrix is a horizontal line given by y = c. The vertex of the parabola is at the midpoint between the focus and the directrix, which is V(a, (b + c) / 2).

The distance from any point (x, y) on the parabola to the focus F(a, b) is given by the distance formula:

sqrt((x - a)^2 + (y - b)^2)

The distance from the point (x, y) on the parabola to the directrix y = c is given by |y - c|.

According to the definition of a parabola, these two distances are equal. Thus, we can set up the equation:

sqrt((x - a)^2 + (y - b)^2) = |y - c|

Squaring both sides of the equation eliminates the square root:

(x - a)^2 + (y - b)^2 = (y - c)^2

Expanding and rearranging the terms:

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2cy + c^2

Simplifying and canceling out the y^2 terms:

x^2 - 2ax + a^2 + b^2 - 2by = c^2 - 2cy

Rearranging the terms to obtain the standard form of the equation:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Thus, the equation of the parabola with focus F(a, b) and directrix y = c is given by:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Complete Question - Write the equation of a parabola with focus F(a, b) and directrix given by y = c.

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Answer:

Yes!!!

Step-by-step explanation:

Well, 12/3=4 16/4=4

4=4

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UwU

Yes, the conveyors are in a proportional relationship.

Given,

A conveyor belt moves at a constant rate of 12 feet in 3 seconds.

A second conveyor belt moves 16 feet in 4 seconds.

We need to find whether the two conveyors are in proportion relationship.

What is a proportional relationship?

There is a proportional relationship if the ratios of each pair of values are the same.

We have,

- First conveyor belt

12 feet in 3 seconds.

Ratio = 12 / 3 = 4

- Second conveyor belt

16 feet in 4 seconds.

Ratio = 16 / 4 = 4

Ratios are the same.

4 = 4

Thus the conveyors are in a proportional relationship.

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Answer:

48m of fence

Step-by-step explanation:

Area of a square = s²

256 = s²

√256 = s

s = 16

There are 4 sides in a square, however, one side is the house, so in total, you need to find 3 sides.

16 * 3 = 48

a) Consumption = $17 billion.

b) Investment = $6 billion.

c) Phoenicia's government runs a budget deficit.

a. To find Phoenicia's consumption, we can use the equation:

Consumption = 60

P - Private Saving.

Given that private saving is $5 billion, and 60P is $22 billion, we can calculate:

Consumption = $22 billion - $5 billion

= $17 billion.

b. To find the country's investment, we need to subtract government purchases, transfer payments, and taxes from the GDP.

Since the government purchases are $7 billion, transfer payments are $2 billion, and taxes are also $7 billion, we can calculate:

Investment = GDP - (Government purchases + Transfer payments + Taxes)

= $22 billion - ($7 billion + $2 billion + $7 billion)

= $6 billion.

c. To determine if the government runs a budget surplus or a budget deficit, we can compare government purchases, transfer payments, and taxes.

Given that government purchases are $7 billion, transfer payments are $2 billion, and taxes are also $7 billion, we can calculate:

Budget surplus/deficit = Taxes - (Government purchases + Transfer payments)

= $7 billion - ($7 billion + $2 billion)

= -$2 billion.

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The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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The given system of equations has a unique solution if p is not equal to 2. If p is equal to 2 and q is equal to 4, the system has infinitely many solutions.Therefore, the correct answer is (a) 1 correct.

The given system of equations is:

2x - y = 4

px - y = q

To determine if the system has a unique solution, we need to analyze the coefficients of x and y.In the first equation, the coefficient of y is -1. In the second equation, the coefficient of y is also -1.If the coefficients of y are equal in both equations, the system may have infinitely many solutions. However, if the coefficients of y are different, the system will have a unique solution.

Now, we consider the options:

a) 1 correct: This statement is correct. If p is not equal to 2, the coefficients of y in both equations will be different (-1 in the first equation and -1 in the second equation), and thus the system will have a unique solution.b) 2 correct: This statement is correct. If p is equal to 2 and q is equal to 4, the coefficients of y in both equations will be the same (-1 in both equations), and therefore the system will have infinitely many solutions.

c) 1 and 2 correct: This statement is incorrect because option 1 is true but option 2 is only true under specific conditions (p = 2 and q = 4).d) 1 and 2 are false: This statement is incorrect because option 1 is true and option 2 is also true under specific conditions (p = 2 and q = 4).

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Answer:

x > 3/7

Step-by-step explanation:

7x-5>-2

7x > (-2+5)

x > 3/7

Answer:

x>3/7

Step-by-step explanation:

7x-5>-2  add 5 to both sides

7x>3 divide both sides by 7

x > 3/7

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The Correct choice is :

Answer:

...............

Step-by-step explanation:

...............

Answer:

x = -4/3, 2/3

Step-by-step explanation:

Step 1: Factor

(3x + 4)(3x - 2) = 0

Step 2: Find roots

3x + 4 = 0

3x = -4

x = -4/3

3x - 2 = 0

3x = 2

x = 2/3

Answer:

x₁ = -4/3

x₂ = 2/3

Step-by-step explanation:

9x² + 6x - 8 = 0

9x² + 12x - 6x - 8 = 0

3xx(3x + 4) - 6x - 8 = 0

3xx(3x + 4) - 2(3x + 4) = 0

(3x + 4) × (3x - 2) = 0

3x + 4 = 0 → x = -4/3

3x - 2 = 0 → x = 2/3

Hope this helps! :)

Answer:

\(y=\frac{1}{3}\)

Step-by-step explanation:

Subtract \(7\) from both sides of the equation:

\(-4y+7=35y-6\)

\(-4y+7\)\(-7=35y-6\)\(-7\)

Simplify:

\(-4y+7\)\(-7=35y-6-7\)

\(-4y=35y-6-7\)

\(-4y=35y\)\(-6\)\(-7\)

\(-4=35y\)\(-13\)

\(-4y=35y-13\)

Subtract \(35y\) from both sides of the equation:

\(-4y=35y-13\)

\(-4y\)\(-35y=35y-13\)\(-35y\)

Simplify:

\(-4\)\(-35y=35y-13-35y\)

\(-39y=35y-13-35y\)

\(-39y=35y-13\)\(-35y\)

\(-39y=-13\)

\(-39y=-13\)

Divide both sides of the equation by the same term:

\(-39y=-13\)

\(\frac{-39y}{-39} =\frac{-13}{-39}\)

Simplify:

\(\frac{-39y}{-39} =\frac{-13}{-39}\)

\(y=\frac{-13}{-39}\)

\(y=\frac{-13}{-39}\)

\(y=\frac{1}{3}\)