use equation 1.3 to estimate the solar radius r^2 from its luminosity and effective temperature. show that the gravitational acceleration g at the surface is about 30 times larger than that on earth. L=4 phi R^2 SB θ T^4

Since (-6, -8) is not a solution to both equations in the system, it is not a solution to the system of equations.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Now in the given question ,

We can check if (-6, -8) is a solution to the system of equations by plugging in these values for x and y in each equation and verifying if both equations are true.

For the first equation y = (1/2)x - 3, if we substitute x = -6 and y = -8, we get:

-8 = (1/2)(-6) - 3

-8 = -3 - 3

-8 = -6

This is not true, so (-6, -8) is not a solution to the first equation.

For the second equation y = (5/2)x + 7, if we substitute x = -6 and y = -8, we get:

-8 = (5/2)(-6) + 7

-8 = -15 + 7

-8 = -8

This equation is true, so (-6, -8) is a solution to the second equation.

Since (-6, -8) is not a solution to both equations in the system, it is not a solution to the system of equations.

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The ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius is 1/3 or 1:3.

The volume of a cone and a cylinder are formulas that are commonly used in geometry. The volume of a right circular cone with height h and base radius r is given by:

V₁ = (1/3)πr^2h

The formula for the volume of a right circular cylinder with height h and base radius r is given by:

V₂ = πr^2h

To find the ratio of the volume of a cone to the volume of a cylinder with the same height and base radius, we can divide the volume of the cone by the volume of the cylinder:

V₁/V₂ = [(1/3)πr^2h]/[πr^2h]

We can simplify this expression by canceling out the factors of π, r^2, and h:

V₁/V₂ = 1/3

Therefore, the ratio of the volume of a cone to the volume of a cylinder with the same height and base radius is 1/3. This means that a cone with the same height and base radius as a cylinder has a volume that is one-third that of the cylinder.

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The point-slope form of a linear equation is:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

Using the given point (2, 0) and slope 1, we can substitute into the equation:

y - 0 = 1(x - 2)

Simplifying, we get:

y = x - 2

So the equation in point-slope form of the line that passes through the point (2, 0) with slope 1 is y = x - 2.

The area of polygon ABCD is 31 square units.

Coordinating refers to the process of organizing or synchronizing different elements or parts to work together in a harmonious and efficient manner towards a common goal or objective. In other words, coordinating involves bringing together various people, resources, activities, or tasks in a way that maximizes their effectiveness and minimizes any conflicts or inefficiencies.

We can find the area of polygon ABCD using the formula for the area of a quadrilateral:

Area = 1/2 * |(x1y2 + x2y3 + x3y4 + x4y1) - (y1x2 + y2x3 + y3x4 + y4x1)|where (x1, y1), (x2, y2), (x3, y3), and (x4, y4) are the coordinates of the vertices of the quadrilateral in order.

Substituting the coordinates of the given vertices, we get:

Area = 1/2 * |(5*(-3) + (-1)2 + (-1)6 + 5(-3)) - (-3(-1) + (-1)5 + 2(-1) + 6*5)|

Simplifying this expression, we get:

Area = 1/2 * |(-15 - 2 - 6 - 15) - (3 + 5 - 2 + 30)|

Area = 1/2 * |-38 - 24|

Area = 1/2 * |-62|

Area = 31

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Answer:

Step-by-step explanation:

You want to identify the rate of change of a graph that has points 1 week apart horizontally and 4 cm apart vertically.

The rate of change (m) of a curve on a graph is the ratio of rise to run.

Here, the graphed points differ by 4 cm vertically, and 1 cm horizontally. The rate of change is ...

  m = rise/run = (4 cm)/(1 week) = 4 cm in 1 week

  = 4/1 = 4 . . . . . centimeters per week

The rate of change can be described as ...

Answer:

Step-by-step explanation:

Just divide the amount he expects to earn between the payment for each working hour.

[tex]Hours -to-babysit=\frac{168}{6}=28[/tex]

Hermes must babysit 28 hours to earn $168 for his new videogame

After divide, the value of expression (-9∠30 ) ÷ (-3∠-30) is

⇒ (-9∠30 ) ÷ (-3∠-30) = 3

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ (-9∠30 ) ÷ (-3∠-30)

Now, We can divide the expression as;

⇒ (-9∠30 ) ÷ (-3∠-30)

⇒ (-9∠30 ) / (-3∠-30)

⇒ - 9/- 3

⇒ 3

Thus, After divide, the value of expression (-9∠30 ) ÷ (-3∠-30) is

⇒ (-9∠30 ) ÷ (-3∠-30) = 3

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The correct answer is −8p − 5q. This is because when multiplying two numbers, the two signs are combined.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


Since both −4 and (2p − 5q) are negative, the resulting product is also negative. To calculate the expression, it is simply a matter of multiplying the two numbers together: −4 * (2p − 5q) = −8p − 5q.

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Answer:

C

Step-by-step explanation:

in the triangle with respect to the 50° angle, the side opposite is c and the adjacent side is 14.

thus using the tangent ratio in the right triangle

tan50° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{c}{14}[/tex] ( multiply both sides by 14 )

14 × tan50° = c , then

c ≈ 16.7  ( to 1 decimal place )

In this problem, the cosine function is used to solve for the length of side C in a right-angled triangle, because the angle and the adjacent side are known. According to trigonometry, the cosine for an angle is the length of the adjacent side divided by the hypotenuse.

In the given right-angled triangle, since the length of side C (hypotenuse) is unknown and one of the acute angles (50 degrees) is known, you should use the cosine function to solve for the length of side C. According to Trigonometry, cosine of an angle (in a right-angled triangle) is equal to the adjacent side divided by the hypotenuse. Hence, cos(50) = 14 / C. You could solve this equation for C.

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The required for a. Genevieve must multiply the original dimensions with a lower scale factor lower than 1 while for b. Genevieve must multiply the original dimensions with a lower scale factor of more than 1.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
To create a smaller model that fits in a scale model of the entire city, Genevieve will need to use a smaller scale. She can calculate the new measurements by dividing the dimensions of the original model by the desired scale factor. For example, if she wants the new model to be half the size of the original, she would divide all dimensions by 2.

To create a slightly larger model for the entrance of the old library building, Genevieve can use a larger scale. She can calculate the new measurements by multiplying the dimensions of the original model by the desired scale factor. For example, if she wants the new model to be 10% larger than the original, she would multiply all dimensions by 1.1.

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Answer:    7:17

Step-by-step explanation:

Ate breakfast 7:05

Clock stopped 12 minutes before

7:05 + 12 = 7:17

The function that models the data is y = 42 ([tex]\frac{1}{2}[/tex])ˣ.

Exponential functions are functions where the independent variable, x is in the exponent.

From the graph, it is clear that it is an exponential function.

Exponential functions will be of the form y = k bˣ.

We have the point (0, 42).

Substituting the point,

k b⁰ = 42

k = 42, since any number raised to 0 is 1, b⁰ = 1.

So the function is y = 42 bˣ.

Substituting the point (1, 21),

42 b¹ = 21

b = 21 / 42

b = 1/2

So the function is y = 42([tex]\frac{1}{2}[/tex])ˣ.

Hence the function is y = 42([tex]\frac{1}{2}[/tex])ˣ.

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From the given information, the mean is 0.3025, the median is 0.3065, and the mode is 0.277 and 0.321.

To find the mean, we need to add up all the values and divide by the total number of values:

Mean = $\frac{0.302 + 0.278 + 0.321 + 0.283 + 0.311 + 0.312 + 0.320 + 0.276 + 0.275 + 0.281 + 0.305 + 0.277 + 0.308 + 0.303 + 0.322 + 0.317 + 0.305 + 0.291 + 0.321 + 0.277}{20} \approx 0.3025$

To find the median, we need to arrange data in the order from smallest to largest:

0.275, 0.276, 0.277, 0.277, 0.278, 0.281, 0.283, 0.291, 0.305, 0.305, 0.308, 0.311, 0.312, 0.317, 0.320, 0.321, 0.321, 0.322, 0.303, 0.302

There are 20 values, so median is average of the 10th and 11th values:

Median = $\frac{0.305 + 0.308}{2} = 0.3065$

To find the mode, we look for the value that appears most frequently. In this case, there are two modes: 0.277 and 0.321.

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The evaluated values,

(1) 0.38 × 10³ = 380

(2) 0.38 × 100,000 = 38000

(3) 0.38 × 10 = 3.8

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Three expressions are,

0.38 × 10³

0.38 × 100,000

0.38 × 10

Solving,

(1) 0.38 × 10³ = 0.38 x 1000 = 380

(2) 0.38 × 100,000 = 38000

(3) 0.38 × 10 = 3.8

Therefore, the evaluations are given above.

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The coordinates of the point 'r' that lies along the directed segment from j (10, -5) to k (-2, -3) are equal to the ( 2/3 , -4 ).

We have, coordinates of the point r that lies along the directed line segment from j (10, -5) to k (-2, -3). The ratio of partitions of segment = 2 : 7

Internal section formula, Let consider M(x, y) be the point which divides line segment PQ internally in the ratio m : n. Then, the coordinates of M are calculated by below formula,

M = {[(mx₂ + nx₁ )/(m+n)], [(my₂ + ny₁)/(m+n)]}

j(10, -5) = (x₁,y₁), k(-2,-3) = (x₂,y₂)

Now we can determine the co-ordinate of r by substituting all values, Also, m : n = 2 : 7

r = {[2(10) + 7(-2)/ 2+7 ],[(3(-5) +7(- 3))/2+7 ]}

={[ (20 - 14)/9 ],[(-15 - 21) / 10]}

={6/9 , - 36/9}

= ( 2/3 , -4 )

Hence, required coordinates of r are ( 2/3 , -4 ).

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Answer:

The recursive formula for this sequence is y(n) = 2 * y(n-1). Starting with y(1) = -3, this formula produces the sequence of -3, -6, -12, -24, -48, and -96.

The missing side length is 7 yd.

The object given is made up of two rectangles. The width of the upright rectangle is to be determined. In order to determine this value, the mathematical operation that would be used is subtraction.

Subtraction is the process of determining the difference between two or more numbers. The sign that is used to represent subtraction is -.

Width of the upright rectangle = 15 - 8 = 7 yd

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A copy machine takes 4.75 minutes to make 171 copies.  

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. Division is the reciprocal of multiplication.

Time taken by the copy machine to take 36 copies = 1 minute.

Since 36 copies can be printed every minute, you could divide 171 by 36 to determine the time needed to make 171 copies.

[tex]\frac{171}{36}[/tex] = 4.75 minutes.

Time taken to print 171  copies is 4.75 minutes.

Hence, a copy machine takes 4.75 minutes to make 171 copies.

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Answer:

28 centimeters (cm) is equal to 280 millimeters (mm).

Step-by-step explanation:

This conversion can be done by multiplying the number of centimeters by 10 since there are 10 millimeters in 1 centimeter. So, 28 cm x 10 mm/cm = 280 mm.

The required ratio of Quantricide to water is 1 fl oz of Quantricide to 64 fl oz of water.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Since we are mixing 2 fl oz of Quantricide with one gallon of water, the ratio of Quantricide to water is, 2 fl oz : 1 gallon

However, it is common to express ratios in simplified form, so we can convert the units of gallons to fluid ounces to get a ratio in terms of fluid ounces,
1 gallon = 128 fl oz (since 1 gallon contains 128 fluid ounces)

So, the ratio of Quantricide to water in terms of fluid ounces is:

2 fl oz : 128 fl oz

This ratio can be simplified by dividing both sides by 2:

1 fl oz : 64 fl oz

Therefore, the ratio of Quantricide to water is 1 fl oz of Quantricide to 64 fl oz of water.

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The Volume of Pyramid is 512 in³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume.

Given:

Hypotenuse= 10 inch

leg length= 8 inch

Using Pythagorean Theorem

h² = 10² - 8²

h²= 100 - 64

h = 6 inch

So, the Volume of Pyramid

= lwh/3

= 6 x 16 x 16 /3

= 2 x 196

= 512 in³

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Since we rejected the null hypothesis, you can consider opening a restaurant at that location.

In order to determine whether the mean income of the sample is sufficient to support the type of upscale restaurant you wish to open, we can perform a hypothesis test.

The null hypothesis (H₀) is that the mean income of the population near the potential location is $85,000 or less.

The alternative hypothesis (Ha) is that the mean income of the population near the potential location is greater than $85,000.

Using a one-sample t-test to test this hypothesis, since the population standard deviation is unknown and the sample size is relatively small (n = 50).

Let's assume that the sample mean income is $90,000 and the sample standard deviation is $10,000.

The test statistic can be calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / √n))

t = ($90,000 - $85,000) / ($10,000 / √50))

t = 2.50

The degrees of freedom for this test are n-1 = 49. Using a significance level of 0.05 and a one-tailed test, the critical t-value is 1.676.

Since the calculated t-value (2.50) is greater than the critical t-value (1.676), we can reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean income of the population near the potential location is greater than $85,000.

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Answer:

A radius is half of a diameter

To find the radius, divide the diameter by 2

If you don't have a π button on your calculator, you should use 3.14159 (for accuracy) instead.

The segment that goes all the way across the circle through the center point is called the diameter.

A radius is half of a diameter.

To find the radius, divide the diameter by 2.

If you don't have a π button on your calculator, you should use an approximation, such as 3.14, instead (for accuracy).

Given two lines with slopes m<1 and m<2, the slope of a third line that is perpendicular to these lines would be the negative reciprocal of either slope. The negative reciprocal of m<1 is -1/m<1 and the negative reciprocal of m<2 is -1/m<2.

Since m<1 = 38 degrees, the negative reciprocal of m<1 would be -1/38.

And since m<2 = 78 degrees, the negative reciprocal of m<2 would be -1/78.

So, if m<3 is the slope of a line perpendicular to the lines with slopes m<1 and m<2, then m<3 could be either -1/38 or -1/78, depending on which slope is chosen.

Part A: Let x be the number of rides you can enjoy at the South Florida Fair. The total cost of admission and rides cannot exceed the $52 you have, so we can write the following inequality:

32.50 + 0.60x ≤ 52

Part B: We can solve the inequality by first subtracting 32.50 from both sides:

0.60x ≤ 19.50

Then, we can divide both sides by 0.60 to isolate x:

x ≤ 32.5

Therefore, the maximum number of rides you can enjoy at the South Florida Fair is 32 rides, since you need to pay for admission and cannot exceed the $52 you have to spend.

The coordinates of D on the given line segment is  (8/3, 0).

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2}[/tex]

and

[tex]y = \dfrac{q+n}{2}[/tex]

We are given that;

y = 3x – 8

Now,

When a line cuts the x-axis, its y-coordinate is always 0. Therefore, we can substitute y = 0 into the equation y = 3x - 8 and solve for x:

0 = 3x - 8

3x = 8

x = 8/3

Therefore, the point D has coordinates (8/3, 0).

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The constraint 3X₁²  + 7X₂ ≤ 45 has a degree of two and it cannot be used as constraint in a linear programming problem.

The correct answer is an option (e)

We know that a linear constraint in linear programming occurs when linear components are added or subtracted. Also the resulting expression must either increase, decrease, or be exactly equal to a right-hand side value.

Any constraint of a linear programming problem is referred to as linear if all of its terms are of the first order.

We know that the degree of the linear constraint is one, hence the constraint that does not have a degree of one is not a linear constraint.

Here we can observe that the constraint 3X₁²  + 7X₂ ≤ 45 has a degree of two and it cannot be used as constraint in a linear programming problem.

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The complete question is:

Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem?

a. 2X₁ + X₂ − 3X₃ ≥ 50

b. 2X₁ + √X₂ ≥ 60

c. 4X₁ - 1/3 X₂ = 75

d. 3X₁ + 2X₂ - 3x₃ / X₁ + X₂ + X₃ ≤ 0.9

e. 3X₁²  + 7X₂ ≤ 45

a. The quarter has the smallest spread of data is Q3

b. The quarter has the largest spread of data is Q1

c. The interquartile range (IQR) is 1.5

d. There are more data in the interval 10–13

e. The interval has the fewest data in it is 10 - 12.

In statistics, a box plot is a graphical representation of a set of data that shows its distribution, median, and quartiles. It can be used to quickly and easily identify the range, spread, and skewness of a data set. Now let's take a look at the box plot you provided and answer your questions.

a. The quarter with the smallest spread of data is the second quarter, which ranges from approximately 4 to 6. The spread of this quarter can be calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1), which is approximately 0.5.

b. The quarter with the largest spread of data is the fourth quarter, which ranges from approximately 10 to 13. The spread of this quarter can also be calculated as the difference between Q3 and Q1, which is approximately 2.5.

c. The interquartile range (IQR) is a measure of the spread of the middle 50% of the data and is calculated as the difference between Q3 and Q1. In this case, the IQR is approximately 1.5 (6 - 4.5).

d. To determine whether there are more data in the interval 5-10 or 10-13, we can look at the box plot and see that the box and whiskers cover a larger range for the interval 10-13. Therefore, there are likely more data points in this interval.

e. To determine which interval has the fewest data, we can look at the box plot and see which interval has the smallest box and shortest whiskers. In this case, that would be the interval 10-12, which has a relatively small box and short whiskers compared to the other intervals. Therefore, we can conclude that this interval has the fewest data points.

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a) The solution to the equation with the initial condition is x = 40[tex]e^{(t/1000)}[/tex].

b) Approximately 40, 42, 45, and 49 rabbits on the island after 1, 5, 10, and 15 months.

a) To find the solution to the equation with the initial condition, do we need to solve the differential equation x? = x ? (1/1000)x² with the initial condition x(0) = 40.

Separating variables and integrating, we get:

dx/x = (1/1000) dt

Integrating both sides, we get:

ln|x| = (1/1000) t + C

where C is a constant of integration.

Using the initial condition x(0) = 40, we can solve for C:

ln|40| = C

C = ln|40|

Substituting this value of C, we get:

ln|x| = (1/1000) t + ln|40|

Simplifying, we get:

x = [tex]e^{(ln|40|+(1/1000) t)[/tex] = 40[tex]e^{(t/1000)}[/tex]

Therefore, the solution to the differential equation with the initial condition is x = 40[tex]e^{(t/1000)}[/tex].

b) To find the number of rabbits on the island after 1 month, 5 months, 10 months, and 15 months, we simply substitute the given values of t into the solution and round to the nearest integer.

After 1 month, x = 40[tex]e^{(1/1000)}[/tex] ≈ 40.04, so there are approximately 40 rabbits on the island.

After 5 months, x = 40[tex]e^{(5/1000)}[/tex] ≈ 41.67, so there are approximately 42 rabbits on the island.

After 10 months, x = 40[tex]e^{(10/1000)}[/tex] ≈ 45.26, so there are approximately 45 rabbits on the island.

After 15 months, x = 40[tex]e^{(15/1000)}[/tex] ≈ 49.28, so there are approximately 49 rabbits on the island.

Therefore, there are approximately 40, 42, 45, and 49 rabbits on the island after 1, 5, 10, and 15 months, respectively.

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Answer:

Step-by-step explanation:

133 ft