The intensity of light at its source is 100%. The intensity ,I at a distance d centimetres from the sources is given by the formula I = 100d exponent -2. Use the formula to determine the intensity of the light 18cm form the source

Answer: yield = ($70 / $875) x 100% = 8% (rounded to the nearest hundredth)

Step-by-step explanation:

To calculate the yield on a corporate bond, we need to use the following formula:

yield = (annual coupon payment / bond price) x 100%

In this case, the bond has a face value of $1000 and pays a fixed interest rate of 7%. The bond was purchased at a discount price of $875. The annual coupon payment can be calculated as:

annual coupon payment = face value x coupon rate = $1000 x 7% = $70

Using the formula above, we can calculate the yield as:

yield = ($70 / $875) x 100% = 8%

Therefore, the yield on this corporate bond is 8% rounded to the nearest hundredth.

The minimum score an applicant must achieve in order to receive consideration for admission to the university is 678.

To solve this problem, we need to find the score x such that the area to the right of x under the standard normal curve is 0.1 (since the 90th percentile corresponds to the top 10% of scores).

Using a standard normal table (also known as a Z-table), we can find the z-score that corresponds to the area of 0.1. The closest value we can find in the table is 1.28. This means that 10% of the scores fall above a z-score of 1.28.

Now we can use the formula for converting a z-score to an x-score:

z = (x - mu) / sigma

where mu is the mean and sigma is the standard deviation of the distribution. Substituting the given values, we have:

1.28 = (x - 550) / 100

Solving for x, we get:

x = 100(1.28) + 550 = 678

Therefore, the minimum score an applicant must achieve in order to receive consideration for admission to the university is 678.

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The correct choice is A: (2,2,4) | 10x dx + 18y dy + 8z dz = 21 (0,0,0)

To check whether the differential form is exact, we need to calculate its curl:

curl(F) = (∂Q/∂y - ∂P/∂z)i + (∂R/∂z - ∂Q/∂x)j + (∂P/∂x - ∂R/∂y)k

Here, P = 10x, Q = 18y, and R = 8z. Substituting these values, we get:

curl(F) = (0 - 0)i + (0 - 0)j + (0 - 0)k = 0

Since the curl of F is zero, the differential form is exact. We can find a potential function f such that F = ∇f.

To find f, we integrate the differential form along any path from (0,0,0) to (2,2,4)

f(2,2,4) - f(0,0,0) = ∫CF · dr

where CF is the given differential form and the integral is taken along the path C. We can choose a simple path, such as a straight line from (0,0,0) to (2,2,4):

r(t) = ti + tj + 2tk, 0 ≤ t ≤ 1

Then CF · dr = 10x dx + 18y dy + 8z dz = (10t)i + (18t)j + (16t)k dt

Substituting for x, y, and z in terms of t, we get:

CF · dr = 10ti dt + 18tj dt + 16tk dt = d(5t^2 + 9t^2 + 8t^2/2)

Therefore, f(2,2,4) - f(0,0,0) = (5(1)^2 + 9(1)^2 + 8(1)^2/2) - (5(0)^2 + 9(0)^2 + 8(0)^2/2) = 21

Hence, the value of the integral is:

∫CF · dr = f(2,2,4) - f(0,0,0) = 21

Therefore, the correct choice is A: (2,2,4) | 10x dx + 18y dy + 8z dz = 21 (0,0,0)

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To compute the variance of a geometric distribution with parameter p, we first need to understand the geometric distribution itself.

The geometric distribution represents the number of trials required for the first success in a sequence of Bernoulli trials, where each trial has a success probability of p.

The variance of a geometric distribution with parameter p can be calculated using the formula:

Variance = (1 - p) / p^2

Please note that the Taylor expansion "=1+r+ ir -1" you mentioned does not seem to be relevant to the calculation of the variance of a geometric distribution. The correct formula for the variance is provided above.

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ANOVA assumes that the observations from different groups (methods) are independent of each other.

i) The sample mean costs for the three methods are equal

A. False

Explanation: ANOVA tests the hypothesis that the population means of the three methods are equal, not the sample means.

ii) The daily costs from each method are from a Normal distribution

A. True

Explanation: ANOVA assumes that the data within each group (method) are normally distributed.

iii) The daily costs for each method are independent.

A. True

Explanation: ANOVA assumes that the observations within each group (method) are independent of each other.

iv) The sample standard deviations of the costs for each method are equal.

A. False

Explanation: ANOVA tests the hypothesis that the population variances of the three methods are equal, not the sample standard deviations.

v) The daily costs for the different methods are independent.

A. True

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The slope between the points, (2, -4) and (-1, -12), is calculated as:

m = 8/3.

To find the slope between two points that lie on a line, we would apply the slope formula below:

Slope of a line (m) = change in y / change in x = (y2 - y1) / (x2 - x1) = rise / run.

Given the following points:

(2, -4) = (x1, y1)

(-1, -12) = (x2, y2)

Plug in the values:

Slope of the line (m) = change in y / change in x = (-12 -(-4)) / (-1 - 2)

m = -12 + 4 / -3

m = -8/-3

Slope between the two points (m) = 8/3

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The area of the concrete patio is 280.86 ft²

The area of a circle of radius R is:

A = pi*R²

Where pi = 3.14

And for half a circle the area is half of that.

Here we can see that the diameter is (26 + 3/4) ft

so the radius is:

R = (26 + 3/4)/2 ft

R = (13 + 3/8) ft

Replacing that in the area formula we will get:

A = 0.5*3.14*(13 + 3/8)² = 280.86 ft²

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Theoretically, you should expect to get 5 questions correct by randomly guessing on a 10-question true/false quiz.

Since this is a true/false quiz with 10 questions, if you were to guess randomly on each question, you would have a 50/50 chance of getting each question correct. Therefore, the probability of guessing correctly on any one question is 0.5.

Let X be the number of questions you guess correctly. Since each question is independent of the others, we can use the binomial distribution to calculate the expected value of X.

The formula for the expected value of a binomial distribution is:

E(X) = n * p

where n is the number of trials (in this case, the number of questions) and p is the probability of success on each trial (in this case, the probability of guessing a question correctly, which we calculated to be 0.5).

So, plugging in the numbers:

E(X) = 10 * 0.5 = 5

Therefore, theoretically, you should expect to get 5 questions correct if you randomly guess on each question. However, since the minimum score to pass is 60%, you would need to get at least 6 questions correct to pass.

To answer your question, let's consider the terms "minimum score", "questions", and "true/false". You have a true/false quiz with 10 questions, and you need a minimum score of 60% correct to pass. Since you're randomly guessing, the probability of getting each question correct is 50% or 0.5.

Now, let's calculate the expected number of correct questions, X. To do this, we multiply the probability of getting a question correct (0.5) by the total number of questions (10):

X = 0.5 * 10

X = 5

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Answer:

A. The cost of purchasing one pencil.

Step-by-step explanation:

The slope of the line, m, represents the rate of change in cost per pencil. In other words, it represents how much the cost increases or decreases for each additional pencil purchased. To find the slope, we can use the formula:

m = (change in cost) / (change in number of pencils)

You can calculate the slope m by using two points from the table and the formula for slope: m = (y2 - y1) / (x2 - x1), where x1 and y1 are the coordinates of the first point and x2 and y2 are the coordinates of the second point. For example, using the first two points from the table (3, 1.05) and (7, 2.45),

Using the data from the table, we can calculate:

m = ($2.45 - $1.05) / (7 - 3)

m = $1.40 / 4

m = $0.35

Therefore, the slope of the line is $0.35 per pencil.

The slope of the line represents the rate of change in cost with respect to the number of pencils. In this case, m represents the cost of purchasing one pencil.

The independent variable in the regression analysis that will be conducted is the Grade Point Average (G) of university graduates.

It is considered the independent variable because it is the predictor or explanatory variable that is believed to have an effect on the dependent variable, which is the salary offered (W). The regression analysis will help to estimate the relationship between the two variables and provide a mathematical equation that can be used to predict the expected salary for a given Grade Point Average.

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True. The causal theory of perception is the view that our experiences, such as our sensations and ideas, are caused by physical objects acting on our sense organs.

According to this causal theory of perception, when an object in the external world acts on our sense organs, it causes certain neural processes to occur, which in turn give rise to our conscious experiences. The causal theory of perception holds that there is a causal relationship between physical objects in the external world and our conscious experiences. When an object interacts with our sense organs, it causes certain neural processes to occur in our brain, which ultimately give rise to our conscious experiences of the object. So, the physical object is the cause, and our conscious experience is the effect.

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f = h - 6 and 5f = 8h + 7 are the system of equations to find f and h

We have to form a system of equations

Let F be no of pages in each science fiction comic book

Let h h be the no of pages in each super hero comic

To find f,

5f = 8h + 7

this is because no of pages in all science fiction is 7 times more than total in super hero bopks

Then f = h - 6

this is because  the science fiction has fewer pages than 6 compared to supoer heroes

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The circular cookie cake have an area of 200.96 in², and thus 100.48 square inches will make up its half.

The area of a circle is π multiplied by the square of the radius. The area of a circle when the radius 'r' is given is πr².

Area of circle = πr²

π = 3.14

radius = 2 m {half the diameter}

Area of the circular cookie = 3.14 × 8 in × 8 in

Area of the circular cookie = 200.96 in²

square inches to make up half the cookie = 200.96 in²/2

square inches to make up half the cookie = 100.48 in²

Therefore, the circular cookie cake have an area of 200.96 in², and thus 100.48 square inches will make up its half.

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Answer: 27

Step-by-step explanation:

This is a cube so all of the lengths have the same lengths.

3x3x3=27

3x3=9

9x3=27

Evaluating this triple integral will give us the volume of the solid bounded below by the cone z and bounded above by the sphere xyz.

To find the volume of the solid bounded below by the cone z and bounded above by the sphere xyz, we can use a triple integral.

First, we need to determine the limits of integration for each variable.

For z, the lower limit is 0 (since the solid is bounded below by the cone z), and the upper limit is the equation of the sphere, which is x^2 + y^2 + z^2 = r^2 (where r is the radius of the sphere). Solving for z, we get z = sqrt(r^2 - x^2 - y^2).

For y, the limits are -sqrt(r^2 - x^2) to sqrt(r^2 - x^2), which represents the cross-section of the sphere at a given value of x.

For x, the limits are -r to r, which represents the entire sphere.

Therefore, the triple integral to find the volume of the solid is:

V = ∭dV = ∫∫∫ dzdydx

Where the limits of integration are:

-∫r^2-x^2-y^2 to ∫sqrt(r^2-x^2-y^2) for z
-∫sqrt(r^2-x^2) to ∫-sqrt(r^2-x^2) for y
-∫-r to ∫r for x

The integrand, dV, represents an infinitesimal volume element in Cartesian coordinates.

Evaluating this triple integral will give us the volume of the solid bounded below by the cone z and bounded above by the sphere xyz.

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x < -1/2 is the solution of the inequality -2x+7>8

The given inequality is  -2x+7>8

We have to find the solution

Subtract seven from both sides

-2x>8-7

-2x>1

Divide both sides by 2

-x>1/2

so x<-1/2 is the solution

Hence, x < -1/2 is the solution of the inequality -2x+7>8

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What is solution of inequality -2x+7>8?

The only equation that met the condition is x² + (y + 8)² = 36

Analytic Geometry is a branch of mathematics that deals with the study of geometry using algebraic methods. It involves using coordinate systems to describe geometric figures and to express geometric properties in terms of algebraic equations.

In particular, the study of equations of circles is a fundamental topic in analytic geometry. A circle is a set of points in a plane that are equidistant from a fixed point called the center. In the coordinate plane, a circle with center (a, b) and radius r can be described by the equation:

(x - a)² + (y - b)² = r²

where x and y are the coordinates of any point on the circle.

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Answer:

Function operation and function composition are two fundamental concepts in mathematics that are commonly used in algebra, calculus, and other branches of mathematics.

Function operation involves performing arithmetic operations on two or more functions to create a new function. To find the result of f(x) + g(x), we simply add the two functions together:

f(x) + g(x) = (2x - 1) + (x^2 - 9x - 4) = x^2 - 7x - 5

Similarly, we can find g(x) - f(x) and f(x) - g(x) by subtracting one function from the other:

g(x) - f(x) = (x^2 - 9x - 4) - (2x - 1) = x^2 - 11x - 3

f(x) - g(x) = (2x - 1) - (x^2 - 9x - 4) = -x^2 + 11x - 3

Function composition, on the other hand, involves plugging one function into another function to create a new function. To find g(f(x)), we first evaluate f(x) and then plug the result into g(x):

g(f(x)) = g(2x - 1) = (2x - 1)^2 - 9(2x - 1) - 4 = 4x^2 - 25x - 14

Similarly, we can find f(g(x)) by plugging g(x) into f(x):

f(g(x)) = f(x^2 - 9x - 4) = 2(x^2 - 9x - 4) - 1 = 2x^2 - 18x - 9

Now, to answer your question about why we don't need to do both f(x) + g(x) and g(x) + f(x), it's because addition is commutative, which means that the order of the terms doesn't matter. Therefore, f(x) + g(x) is the same as g(x) + f(x). The same is true for subtraction. However, this is not the case for function composition, as plugging one function into another is not commutative.

The equation of line passing through points  (-3,6 ) (-2,9 ) in point slope form is y-6=3(x+3)

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The slope of line passing through  (-3,6 )  and (-2,9 )

m=9-6/-2+3

=3

Point slope form equation is y-y₁=m(x-x₁)

y-6=3(x-(-3))

y-6=3(x+3)

Hence, the equation of line passing through points  (-3,6 ) (-2,9 ) in point slope form is y-6=3(x+3)

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Answer: 4

Step-by-step explanation:

The square yard of rubbers needed for the park is 187.5 yards².

The new park is built in the shape of a trapezium. Let's find the square yard of rubbers to cover the ground.

Therefore,

area of a trapezium = 1 / 2 (a + b)h

where

Therefore,

a = 10 yards

b = 20 yards

h = 12.5 yards

area of a trapezium = 1 / 2 (10 + 20)12.5

area of a trapezium = 1 / 2 (30)12.5

area of a trapezium = 15 × 12.5

area of a trapezium = 187.5 yards²

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Therefore, the predicted number of infections in week 10 is approximately 276 (rounded to the nearest whole number).

To predict the number of infections in week 10, we first need to find the growth factor.

Using the formula for exponential growth, we have:

[tex]N = N0 * (1+r)^t[/tex]

where:

N0 = initial number of infections (week 0) = 20

r = growth rate = 30% = 0.3

t = number of weeks

To find the growth factor (1+r), we add 1 to the growth rate:

1+r = 1 + 0.3 = 1.3

So the formula becomes:

[tex]N = N0 * (1.3)^t[/tex]

To find the number of infections in week 10, we substitute t = 10 into the formula and solve for N:

[tex]N = 20 * (1.3)^{10}[/tex]

= 20 * 13.784

= 275.68

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The reason why the confidence interval for the coefficient of rooms in the multiple regression model can be different from the one in part (b) is that in the multiple regression, we are controlling for the effects of other variables (home size, lot size, and bathrooms) on the dependent variable. This can lead to changes in the null hypothesis and their standard errors compared to a simple linear regression model that only considers one independent variable (rooms).

To calculate the 95% confidence interval for the coefficient of rooms in the multiple regression model, we need to use the t-distribution and the standard error of the estimate. The formula is:

Coefficient of rooms ± t_(α/2,n-k-1) x SE

Where t_(α/2,n-k-1) is the critical value of the t-distribution with n-k-1 degrees of freedom and α/2 significance level (α/2 = 0.025 for a 95% confidence interval), n is the sample size, and k is the number of independent variables in the regression model. SE is the standard error of the estimate, which measures the variability of the data around the regression line.

If the confidence interval does not include zero, we can conclude that the coefficient of rooms is statistically significant at the 0.05 level and has a non-zero effect on the dependent variable (price). If the confidence interval includes zero, we cannot reject the null hypothesis that the population regression coefficient of room is zero, meaning that there is no evidence of a significant relationship between rooms and price.

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The final amount after 2 years of continuous compounding at a 5% annual interest rate is $11.05.

Step By Step Calculation:

Step 1: Convert the annual interest charge from a percent to a decimal. In this case, the yearly interest rate is 5%, so we have:

r = 5% = 0.05

Step 2: Use the formulation for continuous compounding to calculate the final amount A, where P is the initial principal and t is the time in years:

[tex]A = Pe^{(rt)}[/tex]

Substituting the given values, we get:

[tex]A = 10e^{(0.05*2)}[/tex]

Step 3: Simplify the exponential expression through elevating the natural number e to the power of 0.1:

[tex]A = 10e^{0.1}[/tex]

Step four: examine e^0.1 the use of a calculator or by means of the use of the Taylor series expansion for [tex]e^x[/tex]:

[tex]e^x = 1 + x + (x^2/2!) + (x^3/3!) + ...[/tex]

when x = 0.1, we get:

[tex]e^0.1 = 1 + 0.1 + (0.1^2/2!) + (0.1^3/3!) + ... = 1.10517092...[/tex]

Step 5: Multiply the preliminary most important by means of the calculated cost of e^0.1 to get the final quantity:

[tex]A = 10 * 1.10517092 = $11.05[/tex]

Consequently, the final amount after 2 years of continuous compounding at a 5% annual interest rate is $11.05.

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1. The area of the parallelogram is 54 cm².

2. The length measurement that 7.5 cm did not use to find the area.

1. As per the shown figure, it is given that:

Base (B) = 9 cm

Height (h) = 6 cm

The area of the parallelogram can be calculated as:

= B × h square units

Substitute the given values in the above formula,

The area of the parallelogram = 9 × 6

The area of the parallelogram = 54 cm².

2. Here, we did not use a length measurement of 7.5 cm to find the area of the given parallelogram because it is irrelevant to the formula.

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a) Based on the least amount that Austin has been charged in a month as $80.25, the possible numbers of minutes he has used his phone in a month are 102 and 103 minutes.

b) Using m for the number of minutes Austin has used his phone in a month, and solving the inequality for m, m ≥ 102.5.

Inequality is a mathematical statement that two or more algebraic expressions are unequal.

Inequalities can be represented by:

The monthly fee that Austin pays for his phone service = $29

The charge per minute of use (variable cost) = $0.5

The least amount charged Austin per month = $80.25

Let the number of minutes = m

29 + 0.5m ≥ 80.25

Solving the inequality:

29 + 0.5m ≥ 80.25

0.5m ≥ 80.25 - 29

0.5m ≥ 51.25

m ≥ 102.5

m = 102, 103

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The true statements about the distance and average speed of Abigail are

a) As Abigail’s time increases, her distance increases

b) At 2 hours, Abigail has traveled 120 miles

c) At 3 hours, Abigail has traveled 180 miles

Given data ,

A coordinate grid showing Time in hours on the x-axis and Distance from Start in miles.

A line plotted passing through the 2 points at P ( 0 , 0 ) and Q ( 3 , 180 )

Now , the slope of the line is m = ( 180 / 3 ) = 60 miles / hour

So , the equation of line is y = 60x

And , at 2 hours , the distance traveled by Abigail is y = 2 ( 60 ) = 120 miles

And , at 3 hours , the distance traveled by Abigail is y = 3 ( 60 ) = 180 miles

Hence , the statements are true and equation of line is y = 60x

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The complete question is attached below :

A coordinate grid showing Time in hours on the x-axis and Distance from Start in miles. A line plotted passing through the 2 points at (0, 0) and (3, 180).

Abigail drives at an average speed of 60 miles per hour for 3 hours. The graph shows her distance versus time. Which statements are true? Check all that apply.

The area of the figure is 47.67 [tex]cm^2[/tex] round to the nearest hundredth.

We can find the area of the half circle with a diameter of 11 cm.

The formula for the area of a circle is A = πr^2, where r is the radius.

Since the diameter is 11 cm, the radius is half of that, which is 5.5 cm.

Substituting the value of r, we get:

A = π(5.5)^2

A = 30.25π

The area of figure is half of the area of the full circle, so we divide by 2:

A = 15.125π

Rounding to the nearest hundredth, we get:

A ≈ 47.67 [tex]cm^2[/tex]

Thus, the answer is 47.67 [tex]cm^2[/tex].

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