Write the equation of the line in fully simplified slope-intercept form.
-12-11-10-9-8-7
6
5
+
co
12
55555
11
10
9
-2-1-
TO
-9
-10
-11
"12
(4
4 5 6 7 8 9 10 11 12

The estimated winners' prize in 2040, assuming the same rate of increase per year, is approximately $54,680,580,063,400.

The initial value is $150, and the final value is $1,163,000. The number of years between 1895 and 2007 is 2007 - 1895 = 112 years.

Using the formula for percentage increase:
Percentage Increase = [(Final Value - Initial Value) / Initial Value] * 100
= [(1,163,000 - 150) / 150] * 100
= (1,162,850 / 150) * 100
= 775,233.33%

Therefore, the winners' check increased by approximately 775,233.33% over the period from 1895 to 2007.

To estimate the winners' prize in 2040, we assume the same rate of increase per year. We can use the formula:
Future Value = Initial Value * (1 + Percentage Increase)^Number of Years

Since the initial value is $1,163,000, the percentage increase per year is 775,233.33%, and the number of years is 2040 - 2007 = 33 years, we can calculate the future value:

Calculating this expression:
Future Value = 1,163,000 * (1 + 775,233.33%)^33

Using a calculator or computer software, we can evaluate this expression to find the future value. Here's the result:

Future Value ≈ $1,163,000 * (1 + 77.523333)^33 ≈ $1,163,000 * 47,051,979.42 ≈ $54,680,580,063,400

Therefore, based on the assumed rate of increase per year, the estimated winners' prize in 2040 would be approximately $54,680,580,063,400.

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A common at-home workout that features high-intensity cardio, and strength-building exercises, and focuses on total body fitness might be a 21-day or 60-day "challenge". Thus, the correct option is C.

Body fitness may be defined as an ability of a person to perform daily physical activities with normal performance, endurance, and strength. This fitness assists the individual in the regulation of disease, fatigue, and stress and reduced inactive behavior.

People who performed high-intensity cardio, and strength-building exercises, in their home and focus on total body fitness must be actively involved in the 21-day or 60-day "challenge".

A 21-day or 60-day "challenge" would be self-selected by an individual in order to maintain their overall physical fitness.

Therefore, the correct option for this question is C.

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The effect of an infinitesimally small increase in income on the consumer's maximized utility is zero. The consumer will continue to consume the same optimal bundle of goods, and their utility will not change.

To compute the effect of an infinitesimally small increase in income on the consumer's maximized utility, we can use the concept of marginal utility.

The consumer's utility function is given as U(x1, x2) = x1^2 * x2^3, where x1 represents the quantity consumed of good 1 and x2 represents the quantity consumed of good 2.

The consumer faces prices p1 = 4 and p2 = 5, and has an income of $200. We want to analyze the effect of a small increase in income on the consumer's maximized utility.

To find the consumer's optimal consumption bundle, we can set up the utility maximization problem subject to the budget constraint.

The optimization problem can be formulated as:

Maximize U(x1, x2) = x1^2 * x2^3

subject to the budget constraint: p1 * x1 + p2 * x2 = income

Substituting the given prices and income, we have:

4x1 + 5x2 = 200

To solve this problem, we can use the Lagrange multiplier method. Taking the partial derivatives of the objective function and the constraint, we obtain:

∂U/∂x1 = 2x1 * x2^3 = λ * 4

∂U/∂x2 = 3x1^2 * x2^2 = λ * 5

Dividing the two equations, we get:

(2x1 * x2^3) / (3x1^2 * x2^2) = 4/5

Simplifying, we have:

2x2 / 3x1 = 4/5

Cross-multiplying and rearranging, we get:

10x2 = 12x1

Dividing by 2, we have:

5x2 = 6x1

This equation represents the consumer's optimal consumption bundle.

Now, let's analyze the effect of an infinitesimally small increase in income on the consumer's maximized utility. Since the increase in income is infinitesimally small, it can be represented by δY, where δ represents a very small change.

To compute the effect, we need to compute the derivative of the utility function with respect to income (dU/dY) and evaluate it at the consumer's optimal consumption bundle.

Taking the derivative of the utility function with respect to income, we have:

dU/dY = ∂U/∂x1 * ∂x1/∂Y + ∂U/∂x2 * ∂x2/∂Y

Since x1 and x2 are the quantities of goods consumed, their derivatives with respect to income are 0.

Therefore, dU/dY = 0.

This means that an infinitesimally small increase in income has no effect on the consumer's maximized utility. The consumer will continue to consume the same optimal bundle of goods, and their utility will remain unchanged.

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Answer:

3.7

Step-by-step explanation:

The lenght of an arc with a radius of 3m and substended angle of 70 degrees is 3.7meters

The length of an arc is expressed as:

L = r theta

Given the following parameters

r = 3m

theta = 70 degrees = 70π/180

L = 3(70π/180)

L = 3.7 metres

Hence the lenght of an arc is 3.7meters

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Answer:

-2x-6

Step-by-step explanation:

Distribute -2x -2(3) = -2x-6

To find the density of the metal, we need to calculate the mass of the metal and the volume of the metal.

Step 1: Calculate the mass of the metal:

Mass of metal = Mass of cylinder with all its contents - Mass of empty graduated cylinder

Mass of metal = 390.98 g - 45.7 g

Mass of metal = 345.28 g

Step 2: Calculate the volume of the metal:

Volume of metal = Final volume of water + metal - Initial volume of water

Volume of metal = 70.7 mL - 42.0 mL

Volume of metal = 28.7 mL

Step 3: Calculate the density of the metal:

Density = Mass of metal / Volume of metal

Density = 345.28 g / 28.7 mL

Density ≈ 12.01 g/mL

Therefore, the density of the metal is approximately 12.01 g/mL.

To determine the density of the metal, we use the principles of water displacement. The student first measures the mass of the empty graduated cylinder and records it as 45.7 g. Then, 42.0 mL of water is added to the cylinder, which has a known density of 1.00 g/mL. After placing the metal into the cylinder, the student measures the final volume of water and metal as 70.7 mL.

To calculate the mass of the metal, we subtract the mass of the empty cylinder from the mass of the cylinder with its contents. This gives us a mass of 345.28 g. To calculate the volume of the metal, we subtract the initial volume of water (42.0 mL) from the final volume of water and metal (70.7 mL), resulting in a volume of 28.7 mL.

Finally, we can calculate the density by dividing the mass of the metal (345.28 g) by the volume of the metal (28.7 mL). The density of the metal is approximately 12.01 g/mL.

Using the water displacement method, the student successfully determined the density of the unknown piece of metal.

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The value for x in the given equation x = (1.38-1.21)/1.23 is 0.1382.

The density of the metal is 10.56 .

To solve for x in the given equation x = (1.38-1.21)/1.23 ,follow the steps below:

Subtract the values in the parenthesis: 1.38-1.21=0.172.

Divide the result from step 1 by the divisor: 0.17/1.23=0.138(rounded off to 3 decimal places).

Therefore, the solution for x in the given equation x = (1.38-1.21)/1.23 is 0.1382.

Now to find the density of the metal, the volume of the metal must be found by subtracting the volume of the water from the final volume of water and metal (which gives the volume of the metal). Also, the mass of the metal must be found by subtracting the mass of the cylinder and water from the mass of the cylinder, water, and metal.

With these values the density can be found by dividing the mass by the volume of the metal.To find the volume of the metal, subtract the volume of the water from the final volume of water and metal:

70.7 mL - 42.0 mL = 28.7

Therefore, the volume of the metal is 28.7 .

To find the mass of the metal, subtract the mass of the cylinder and water from the mass of the cylinder, water, and metal:

390.98 g - 45.7 g - 42.0 g = 303.28

Therefore, the mass of the metal is 303.28 .

Now that the volume and mass of the metal have been found, the density can be calculated by dividing the mass by the volume:

density = mass/volume= 303.28 g/28.7 mL= 10.56

Therefore,  the density of the metal is 10.56 .

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Answer:

  85.9 m

Step-by-step explanation:

The law of sines can help figure this.

The remaining angle in the triangle is ...

  180° -75° -68° = 37°

This is the angle opposite the leg from the surveyor to the second marker. Referencing the attachment, we have ...

  b/sin(B) = c/sin(C)

  b = sin(B)·c/sin(C) = 132.3·sin(37°)/sin(68°) ≈ 85.873 . . . meters

The surveyor is about 85.9 meters from the second marker.

Answer:

Step-by-step explanation:

6 5/10 - 1 7/10

= (6 - 1) + (5/10 - 7/10)

= 5 + 5 - 7/10

= 5 + -2/10

= 5 + -2 ÷ 2/10 ÷ 2

= 5 + -1/5

= 4 4/5

Extra:

Can i hav brainliest plz it would help alot :D

Answer The small triangles each have an area of 12m^2 and the big rectangle had an area of 80m^2. This would mean that the combined area is 104m^2

Step-by-step explanation: The rectangle shape can be found by multiplying 8 by 10 to get 80m^2. The two triangles can be found by multiplying 4 (half of 8) by 6 and then dividing it by two. This would mean that the small triangles each have an area of 12.

The equations with same value of x as (3/5)(30x - 15) = 72 is 18x - 9 = 72, 3(6x - 3) = 72 and x = 4.5

An equation shows the relationship between two or more numbers and variables.

Given the equation:

(3/5)(30x - 15) = 72

Opening the parenthesis:

18x - 9 = 72

Factorizing the equation:

3(6x - 3) = 72

Dividing through by 3:

6x - 3 = 24

6x = 27

Dividing through by 6:

x = 4.5

The solution to the equation (3/5)(30x - 15) = 72 yields x = 4.5

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I believe the answer is x= 12

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Answer:

2=3408493-=2=9

Step-by-step explanation:

Answer:

c) 29

Step-by-step explanation:

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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Answer:

True

Explanation:

A proportion states the equality of two fractions. It is an equation that shows that two fractions are equivalent to each other.

Looking at the given statement;

10 altos for every 16 sopranos, 5 altos for every 8 sopranos.

This can be expressed as;

And we can see that the two fractions are equivalent, if we divide the numerator and denominator of the 1st fraction by 2 we'll have the 2nd fraction.

Answer: \(\frac{1}{\sqrt[3]{x} }\)

Step-by-step explanation:

Since the base of the exponents are the same, we can go ahead and subtract the exponents.

\(\frac{x^{\frac{5}{6}} }{x^{\frac{7}{6} }}\)               [subtract exponents]

\(x^{-\frac{2}{6} }\)             [simplify exponent]

\(x^{-\frac{1}{3}}\)             [write in radical form]

\(\frac{1}{\sqrt[3]{x} }\)

Answer:

\(4(a + 2) - 2(a - 8) = 24 \\ 4a + 8 - 2a + 16 = 24 \\ 2a + 24 = 24 \\ 2a = 24 - 24 \\ a = \frac{0}{2} \\ \\ a = 0\)

I hope I helped you^_^

Answer:

Marco had 45 dollars on the card when he received it.

Step-by-step explanation:

So we see that r = 0. Therefore, the equation of the circle is just:

(x - 2)^2 + (y - 9)^2 = 0

Company revenue quadratic function.

Angel

The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?

To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:

r(x) = a(x - h)^2 + k

where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

We can use the given revenue values to set up a system of three equations:

2.7 = a(0 - h)^2 + k

3.4 = a(1 - h)^2 + k

2.7 = a(6 - h)^2 + k

Subtracting the first equation from the second, and the first equation from the third, we get:

0.7 = a(1 - h)^2

0 = a(6 - h)^2

Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:

6 - h = 10

which gives us h = -4.

Substituting h = -4 into the first equation, we get:

2.7 = a(0 - (-4))^2 + k

2.7 = 16a + k

Substituting the revenue value for 2005, we get:

3.9 = a(3 - (-4))^2 + k

3.9 = 49a + k

Solving for a and k, we get:

a = -0.1

k = 4.3

Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:

r(x) = -0.1(x + 4)^2 + 4.3

The vertex of this function is at (-4, 4.3).

Angel

What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?

We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:

3 - 4 + 5 - 6 + ... + 101

We can group the terms into pairs:

(3 - 4) + (5 - 6) + ... + (99 - 100) + 101

Each pair of terms adds up to -1, so we can simplify the expression to:

-1 -1 -1 ... -1 + 101

where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:

-50 + 101 = 51

Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.

Angel

What is 12 7/8 - 56/17?

To subtract mixed numbers like 12 7/8, we first need to convert it to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction, and adding the result to the numerator. This gives us:

12 7/8 = (12 × 8 + 7)/8 = 103/8

Now we can subtract 56/17 from 103/8. To do this, we need to find a common denominator for the two fractions. The least common multiple of 8 and 17 is 136, so we can rewrite the fractions with this denominator:

103/8 = (103/8) × (17/17) = 1751/136

56/17 = (56/17) × (8/8) = 448/136

Now we can subtract the two fractions:

1751/136 - 448/136 = (1751 - 448)/136 = 1303/136

We can simplify this fraction by finding a common factor to divide both the numerator and denominator. Since both 1303 and 136 are relatively prime, we cannot simplify it any further. Therefore, the final answer is:

12 7/8 - 56/17 = 1303/136

Angel

A circle in the xy-plane has a diameter with endpoints (2,4) and (2,14). An equation of this circle is (x-2)^2+(y-9)^2=r^2 ,where r is a positive constant. What is the value of r?

The center of the circle is the midpoint of the diameter, which is at (2, (4+14)/2) = (2, 9). We can substitute this center point into the equation of the circle to get:

(x - 2)^2 + (y - 9)^2 = r^2

(2 - 2)^2 + (9 - 9)^2 = r^2

0 + 0 = r^2

So we see that r = 0. Therefore, the equation of the circle is just:

(x - 2)^2 + (y - 9)^2 = 0

This describes a single point in the xy-plane, which is the center of the circle. Note that this point is already on the given diameter, so it makes sense that the radius is zero.

Answer:

idc

Step-by-step explanation:

AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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The equation for the asymptote of the graphed function is x = 7

The asymptote is a endlessly tendency to a given value. A vertical one is a tendency to infinity.

Here we can see that there is a vertical asymoptote, notice that in one end the function tends to positive infinity and in the other it tends to negative infinity.

The equation of the line where the asymptote is, is:

x = 7

So that is the answer.

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Answer: A) 4.8 CM

Step-by-step explanation:

Answer:

Increase?

Step-by-step explanation:

Because think about it let's use 1/2 as an example.

1/2 equals .5 now lets add 2 to both the numerator and denominator

3/4 is the result and it also equals .75 which is larger than .5 so that's why the answer is increase.

and u can keep on going on with the method

4/5=.8

If equal amounts are added to the numerator and the denominator of the current ratio, the ratio will always decrease.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Let m be the positive number.

And the ratio is p:q = p/q.

If equal amounts are added to the numerator and the denominator of the current ratio is,

(p+m)/(q+m).

The ratio will always decrease.

Therefore, the ratio will always decrease.

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Answer:

-8 < x ≤ 0

Let's remember what open and closed circle mean:

Open Circle:

Less than ( < ) / Greater than ( > )

Closed Circle:

Greater than or equal to ( ≥ ) / Less than or equal to ( ≤ )

Now, let's review this graph:

Let's call this unknown value 'x'

Reading the graph left to right:

x is greater than -8, but is less than or equal to (Remember!! Closed circle!)

We can right this as:

-8 < x ≤ 0

And that is our answer! If your problem wants a different variable (y, z, q, etc) just put that in place of 'x'

Let me know if this helped!

The measure of the angles are  ∠A = 33°  ,   ∠B = 33° and   ∠C = 114°

Supplementary angles are the angles whose sum is equal to \(180^{o}\).

According to the question we have been given that the three angles that is ∠A , ∠B and ∠C are the supplementary angles that is their sum is 180°.

Let the measure of ∠A = x = ∠B

and the measure of ∠C = 81 + x

Now,

      ∠A + ∠B + ∠C = 180°

Putting the required values we get

        x° + x° + (81 +x )° = 180°

        2x° + 81° + x° = 180°

             3x° = 99°

               x° = 33°

Hence the measure of three angles are

       ∠A = 33°  ,   ∠B = 33° and   ∠C = 114°

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The probability that an adult sampled at random will weigh between 136 pounds and 164 pounds can be calculated using the properties of the normal distribution.

To find the probability, we need to calculate the area under the normal curve between the two weight values. We can convert the given weights into z-scores (standardized scores) using the formula:

z = (x - μ) / σ

where x is the given weight, μ is the mean weight, and σ is the standard deviation.

For the lower weight value of 136 pounds:

z1 = (136 - 146) / 12.7 = -0.79

For the upper weight value of 164 pounds:

z2 = (164 - 146) / 12.7 = 1.42

Now, we can look up the corresponding z-scores in the standard normal distribution table or use a calculator to find the area under the curve between these z-scores. The probability is equal to the difference between these two areas.

Using a standard normal distribution table or calculator, we find the area to the left of z1 (0.2139) and the area to the left of z2 (0.9236). Therefore, the probability of an adult weighing between 136 and 164 pounds is:

P(136 < x < 164) = P(-0.79 < z < 1.42) = P(z < 1.42) - P(z < -0.79) = 0.9236 - 0.2139 = 0.7097

The probability that an adult sampled at random will weigh between 136 and 164 pounds is approximately 0.7097 or 70.97%. This means that there is a 70.97% chance of randomly selecting an adult whose weight falls within this range in the town of Metaluna, assuming the weights follow a normal distribution with a mean of 146 pounds and a standard deviation of 12.7 pounds.

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