an arched window is in the shape of a rectangle surmounted by a semicircle. if the perimeter is 5 m, what should the radius of the semicirculoar part be if the window is to admit as much light as possible?

The answer for the equation should be 46

Answer:

the answer is 25

hope it is right

please mark as brainliest

The line that connects the coordinates (6, -1) and is parallel to the line denoted by the equation 8x + 3y = 15 has the standard form equation 8x + 3y = 45.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

Standard version of the equation is Ax + Bx = C.

A, B, and C are constants where

In light of this, the slope intercept form y = mx + b

m = slope, and b = y-intercept

8x+ y = 15

3y= -8x+15

y= -8/3x + 5

slope = -8/3

The line passes through (6, -1)

-1 = -8/3 (6)+b

-1 = -48/3+ b

-1  = -16 +b

b = -1+16

b = 15

Therefore,

y =-8/3x + 15

8/3 x+ y = 15

8x + 3y = 45

Hence, The equation in standard form of the line that passes through the point (6, -1) and is parallel to the line represented by 8x + 3y= 15 is

8x + 3y = 45.

To know more about standard form of an equation, visit:

https://brainly.com/question/16646502

#SPJ4

The dimensions of the box with a volume of 1000 cm3 that has a minimal surface area are  10 cm* 10 cm*10 cm.

Let's define the dimensions of the box as x, y and z.  The surface area of the box is given by:  2(xy + xz + yz). We want to minimize the surface area.  Since the volume is 1000 cm3, we know xyz = 1000.  Therefore, the surface area of the box is given by:

2(xy + xz + yz) = 2(1000/x + 1000/y + 1000/z),  We need to minimize 2(1000/x + 1000/y + 1000/z) subject to xyz = 1000.  This is a constrained optimization problem.  We can solve this problem using Lagrange multipliers.  Let L(x, y, z, λ) be the Lagrangian given by:

L(x, y, z, λ) = 2(1000/x + 1000/y + 1000/z) + λ(xyz - 1000), To find the minimum, we need to find the critical points of the Lagrangian.  Taking the partial derivatives of L with respect to x, y, z, and λ, we get:

∂L/∂x = -2000/x² + λyz = 0

 ∂L/∂y = -2000/y² + λxz = 0

∂L/∂z = -2000/z² + λxy = 0  

∂L/∂λ = xyz - 1000 = 0

From the last equation, we get xyz = 1000.  Substituting this value in the first three equations, we get:

 ∂L/∂x = -2000/x² + 2000/x = 0

∂L/∂y = -2000/y² + 2000/y = 0  

∂L/∂z = -2000/z² + 2000/z = 0

Solving these equations, we get x = y = z = 10.  Therefore, the dimensions of the box with minimal surface area and volume of 1000 cm3 are x = y = z = 10 cm.

To know more about surface area refer to  the link  brainly.com/question/2835293

#SPJ4

Answer:

Available credit = $2,416.42

Step-by-step explanation:

$1,374.90

$266.21

39.46

$903.01

Sum = $2,583.58

$2,583.58 was spent. Subtract this from $5,000 to find Marianne's available credit.

$5,000

- $2,583.58

Available credit = $2,416.42

If a graph have 12 vertices and 3 connected components, then  the largest number of edges it might have is 45.

What is vertex?

One of the items joined together in a graph is referred to as a vertex (or node). Edges or links are the connections between the vertices in any graph.

As given in the question,

The vertices (n) = 12,

Connected components (k) = 3

let m be the number of edges it the graph might have,

The number of edges in the graph can be calculated by the following formula:

[tex]m \le \frac{(n-k+1) \times (n-k)}{2}[/tex]

putting the values from the question,

[tex]m \le \frac{(12-3+1) \times (12-3)}{2}[/tex]

[tex]m \le \frac{(10) \times (9)}{2}[/tex]

[tex]m \le 45[/tex]

By the above equation, we can say that maximum number edges of is 45.

To know more about vertex, go to link

https://brainly.com/question/525947

#SPJ4

On your entire strategy at the expiration of the contract if the stock price at that time is $81.50 then the profit is $2189.

A portfolio is a collection of financial investments like stocks, bonds, commodities, cash and cash equivalents, including closed-end funds and exchange traded funds.

A stock is a security that represents the ownership of a fraction of the issuing corporation. Units of stock are called "shares" which entitles the owner to a proportion of the corporation's assets the owner equal to how much stock they own.

We know that,

Profit on the strategy

        = Profit on the shares + Profit from long calls + Profit from short puts

        = 200(81.50 - 70) + 200(Max(81.50-72,0)-5.75) + 300(-Max(68 - 81.50,0)+2.87)

        = 2300 + 750 - 861

        = 2189

Therefore profit on strategy is $2189.

To know more about profit here

https://brainly.com/question/17093483

#SPJ4

The solutions for the given equation are [tex]2+\sqrt{31}[/tex] and [tex]2-\sqrt{31}[/tex]. These are calculated by applying the quadratic formula since the given equation is a quadratic equation.

The quadratic formula is used for finding the roots of a quadratic equation in the form of ax² + bx + c = 0.

The formula is,

x  = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

The given equation is

x² - 27 = 4x

On rewriting the equation, we get

x² - 4x - 27 = 0

thus, it is in the form of ax² + bx + c = 0. So, this is a quadratic equation.

Then, applying the quadratic formula for finding roots is nothing but its solutions.

Where a = 1; b = -4; c = -27

⇒ x = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

      = [tex]\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-27)} }{2(1)}[/tex]

      = (4 ± [tex]\sqrt{16+108}[/tex])/2

      = (4 ± [tex]\sqrt{124}[/tex])/2

      = (4 ± 2[tex]\sqrt{31}[/tex])/2

      = 2 ± [tex]\sqrt{31}[/tex]

So, the roots of the given equation are 2 + [tex]\sqrt{31}[/tex] and 2 - [tex]\sqrt{31}[/tex].

Learn more about the quadratic formula here:

https://brainly.com/question/9929333

#SPJ1

Step-by-step explanation:

"to solve for h" just means to transform the equation, so that instead of V we get h alone on one side of the equation.

V = pi×r²×h

h = V / (pi×r²)

that's it.

for the slope question :

the slope is the factor of x (2/3 and 3/2) and indicates how steep the line is. and it is expressed as y/x ratio defining how many units y changes, when x changes a certain amount of units.

the bigger the number, the steeper the line.

so, the 4th answer option is correct. g(x) is steeper than f(x).

the lines are not parallel, because they do not have the same slope.

they are not perpendicular, because perpendicular slopes turn the y/x ratio upside down AND flip the sign.

e.g. the perpendicular slope of 2/3 would be -3/2.

The slope of all lines parallel to the line 3x + 7y = -7 is 3/7.

To find the slope of the line 3x + 7y = -7, we can use the slope-intercept formula y = mx + b, where m is the slope.

We can rearrange the equation 3x + 7y = -7 to the slope-intercept form 7y = -3x -7.

We can then divide both sides of the equation by 7 to get the slope, m = -3/7.

Therefore, the slope of all lines parallel to the line 3x + 7y = -7 is 3/7.

Learn more about slope here

https://brainly.com/question/3605446

#SPJ4

The probability that they finish within 10 minutes of each other here their times are independent

i.e P( -10 < X₂ - X₁ < 10) where X₂ - X₁ = D Normally distributed, is 0.78 ..

Let X₁ be a random variable as taylor cleans the exterior of each car.

mean , μ₁ = 20 ,

standard deviations, σ₁ = 4.8

let X₂ be a random variable as sam cleans the interior of each car.

mean, μ₂ = 18

standard deviations, σ₂ = 6.4

If the two random variables are normal, then their difference , X₂ - X₁ also be normal.

As two normal variables here are normally distributed, therefore the distribution of the difference between the two variables here is given as: X₂ - X₁ = X

with mean, μ = μ₂ - μ₁ = 2

standard deviations, σ = σ₁² + σ₂²

= 6.4² + 4.8² = 64

To any bivariate Normal distribution of (X₁,X₂) Thus the variable

Z = (X−μ)/σ = (X₂−X₁ −(μ₂ - μ₁))/(√σ₁² + σ₂²)

= X - 2 /√64 = (X - 2 )/8

The probability here is computed as:

P( -10 < X₂ - X₁ < 10) = approx P(∣D∣<10)

where D is difference between their finishing times. Converting it to a standard normal variable, we have here:

= P( (-10 - 2) / 8 < Z < (10 - 2) / 8)

= P( -1.5 < Z < 1)

= P(Z < 1 ) - P(Z < -1.5)

Getting it from standard normal tables,

= 0.8431 - 0.0668

= 0.7763

Therefore 0.7763 is the required probability here.

To learn more about Normal probability distribution, refer:

https://brainly.com/question/6476990

#SPJ4

Complete question:

Sam and Taylor own and operate a car wash service. Sam cleans the interior of each car and Taylor cleans the exterior. The time it takes Sam to finish the interior has a mean of 20 minutes with a standard deviation of 6.4 minutes. The time it takes Taylor to finish the exterior has a mean of 18 minutes with a standard deviation of 4.8 minutes. Both of their finishing times are approximately normally distributed.

Suppose we select a car at random, and define the random variable D as the difference between their finishing times. We can assume that their times are independent.

Find the probability that they finish within 10minutes of each other.

You may round your answer to two decimal places.

P\left(|D|<10\right)\approxP(∣D∣<10)≈P

Tomika and Mark claim a medical deduction in the amount of $1,839.8.

To determine how much Tomika and Mark can claim as a medical deduction, you first need to calculate the number of medical expenses that are covered by their insurance.

The first step is to calculate medical insurance :

Medical insurance = 7.5 % of $101,598

Medical insurance = 7.5% x $101,598

Medical insurance =  $7,619.88.

Medical deduction claim = $7,619.88 - (100% - 60%)x $3,800

Medical deduction claim = $7,619.88 - 40% x $3,800

Medical deduction claim = $7,619.88 - $1,520

Medical deduction claim = $6,099.88

Therefore, they can claim a medical deduction in the amount of $1,839.8.

To learn more about medical claim deduction click here:

https://brainly.com/question/21335691

#SPJ1

The slope of the line passing through the two points [tex](-1,3)[/tex] and [tex](4,7)[/tex] is [tex]\frac{4}{5}[/tex]

The formula for finding the slope when two points are given

[tex]y=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\y=\frac{7-3}{4-(-1)} \\y=\frac{4}{4+1} \\y=\frac{4}{5}[/tex]

The slope of the line is [tex]\frac{4}{5}[/tex]

Learn more about slope from

https://brainly.com/question/3605446

#SPJ4

The linear function decreases when x is between –6 and 0.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+2. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=5 and b=2.

A function can be classified as:

From the graph is possible to see that the function decreases when x is between –6 and 0 because the values of y decrease with the increasing of x-values.

Read more about decreasing linear function here:

https://brainly.com/question/27716206

#SPJ1

Answer:

£52.8

Step-by-step explanation:

£8.80 per hour

1 hour £8.80

£8.80×6 hours

=£52.8

Answer:

£52.80 after 6 hours

Step-by-step explanation:

8.80*6=52.8 which means £52.80.

Answer:

Based on the given polynomial, g(x) = 5x + 17x5, it is a polynomial of the sixth degree because it contains six terms (one constant term, one linear term, and one quintic term). Thus, another name for this polynomial is a sixth-degree polynomial.

Step-by-step explanation:

The value of  P(G<2.5) is 14.23%.

What is observation?

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. Using scientific tools to perceive and record data is another way that observation may be used in science.

The [tex]$z$[/tex]-score for this observation of 2.30 is:

Z= (2.3-2.8)/0.7=-1.71

The table shows a value of 0.8577 , and because this z-score is negative, this is the proportion greater than a GPA of 2.30. So the proportion less than 2.30 is 1-0.8577 =0.1423 . Expressing it mathematically we have:

[tex]$$\begin{aligned}P(X \leq 2.7) & =P(Z \leq-1.07) \\& =1-P(Z \geq-1.07) \\& =1-P(Z \leq 1.07) \\& =1-0.8577 \\& =0.1423=14.23 \%\end{aligned}$$[/tex]

To learn more about proportion visit:https://brainly.com/question/28041973

#SPJ1

Answer:

The diagram shows a line of reflection, labeled as "line r," and a point B on one side of the line. The image of point B, labeled as B', is shown on the other side of the line.

If point A is on line r, then the image of A would be A itself because a reflection in line r means that all points on the line remain unchanged.

If point B is not on line r, then line r would be the perpendicular bisector of line segment BB'. This means that line r would pass through the midpoint of line segment BB' and be perpendicular to it. The image of point B would be on the opposite side of line r from the original point B, but the distance between B and B' would remain the same.

a. The diagram that represents this situation is given by the image shown at the end of the answer.

b. The height of the building is of: 33.4 feet.

The three trigonometric ratios are defined as follows:

As shown by the diagram given at the end of the answer, this situation is represented by a right triangle in which:

Then the height of the building is calculated as follows:

tan(24º) = x/75

x = 75 x tangent of 24 degrees

x = 33.4 feet. -> height of the building.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

Answer:

.33m+65=C

Step-by-step explanation:

to solve the equation you will need to multipy .33 x the amount of miles drove after you get the answer for that you will need to add 65 then thats your final answer

In terms of relative growth rate Exponential growth is characterized by a constant relative growth rate.

Exponential growth is the process of increasing quantity over time. Occurs when the instantaneous rate of change of a quantity over time is proportional to the quantity itself. The exponential growth model has the form

y (t) = C eᵏᵗ, where k is the rate constant.

Relative Growth Rate:Relative growth rate (RGR) is the rate of growth relative to size. That is, the rate of growth per unit time relative to the size at that point in time and y'(t)/y(t) is the relative growth rate of a function y at time t.

1/y dy/dt = 1/y d(C eᵏᵗ)/dt

= 1/y(kC eᵏᵗ)

= 1/y ( ky) ( since, y (t) = C eᵏᵗ)

= k

Therefore a constant relative growth rate.

To learn more about Exponential growth model, refer:

https://brainly.com/question/13223520

#SPJ4

Complete question:

In terms of relative growth rate, what is the defining property of exponential growth? Choose the correct answer below.

A. The relative growth rate at time t is the slope of the exponential function at time t.

B. dy dt If y represents a population, then the relative growth rate can be represented by dy/dt

C. The relative growth rate is proportional to the size of the population

D. The relative growth rate is constant.

Answer:

4.82803

Step-by-step explanation:

3 x 1.6

Answer:So looking at this question, we have two variables (1 - a glass of milk; 2 - a snack bar) and two equations to use to solve for the two variables. Remember that for any number of variables, you need that same number or more equations to solve for the variables.Let's say that a glass of milk is represented by g and a snack bar is represented by s.So we essentially have two equations here:4 glasses of milk + 3 snack bars = 88 carbs, or:4g + 3s = 882 glasses of milk + 4 snack bars = 74 carbs, or:2g + 4s = 74Now that we have this, we can solve for our equations. There are two ways to do this:SUBSTITUTION - solve for one variable, then substitute it inLet's solve for g using the second equation. First, we'll isolate g by subtracting 4s from both sides.2g = 74 - 4sNext, we can divide the whole equation by 2 to solve for g.g = 37 - 2sNow, we can substitute this into the first equation for g and solve for s.4g + 3s = 884(37 - 2s) + 3s = 88148 - 8s + 3s = 88148 - 5s = 88 (now subtract 88 from both sides and add 5s to both sides)60 = 5ss = 12Now we can use this to solve for g in the original equationg = 37 - 2sg = 37 - 2(12) = 37 - 24 = 13ELIMINATION - eliminate one variable to solve for the other, then use that to solve for the firstLet's look at our two equations4g + 3s = 882g + 4s = 74Let's eliminate the variable g first by multiplying the second question by -2.4g + 3s = 88-4g - 8s = -148If we add these two equations together, we get-5s = -60Divide both sides by -5 and we gets = 12Now, we can plug s into either equation to solve for g as we did above.

Answer:

P=69

Step-by-step explanation:

Percentage Of people Prefers to die at home in developed countries is 30%

Lets have Brief explanation

What is scientific research?

Scientific research is research carried out using organised, constructed scientific techniques for data collection, analysis, and interpretation.

There is growing scientific research regarding the choices people would prefer to make regarding their care as they approach death.

According to a number of studies, between 50% and 70% of patients undergoing treatment for a serious illness also state that they would prefer to die at home.

Even though many people would prefer to get care and pass away at home, hospital death is nonetheless common in many nations.

According to the research, between 25% and 30% of people want to die at home, and the classic scenario involves 30% of people.

Percentage Prefer to die at home = 30%

To learn more about scientific research visit: brainly.com/question/6139379

#SPJ4

Answer:

both cost the same price of 6 dollars for each

Step-by-step explanation:

we can make a system of equation

d- daylilies

o- ornamental glass

5d+5o=60

8d+5o=78

-8d.      -8d

5o=78-8d

5d+78-8d=60

-3d+78=60

     -78. -78

-3d= -18

/-3.   /-3

d=6

5(6)+5o=60

30+5o=60

-30.      -30

5o=30

/5.  /5

o=6

they both are 6 dollars each

hopes this helps

The sample size be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence is 4148 , the correct option is (b)    .

In the question ,

it is given that ,

the confidence interval is 99% .

let us consider ,

A sociologist wishes to estimate the percent of the U.S. population living in poverty .

Here , preliminary estimate of population has been ,

p = q = 0.50 .

for given , 99% confidence interval z = 2.756 .

the error percent is 2% , the means E = 0.02  .

So , the required sample size (n) can be calculated using the formula ,

n = (0.50)(0.50)(2.576/0.02)²

n = 0.25 * 16589.44

n = 4147.36

n ≈ 4148 .

Therefore , the sample size is 4148 .

The given question is incomplete the complete question is

A sociologist wishes to estimate the percentage of the U.S. population living in poverty. What size sample should be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence ?

(a) 2401

(b) 4148

(c) 1692

(d) 2.575

Learn more about Sample Size here

https://brainly.com/question/28942039

#SPJ4

The slope of the equation, given, is the pace at which a car enters a garage. Hence, it is 3.56, or around 4 automobiles per hour. Option D is the correct answer.

In statistics, a straight line of correlation between two variables is referred to as a linear relationship (or linear association). The mathematical equation y = mx + b can be used to represent linear relationships graphically.

Jamal is the owner of a parking garage and is attempting to determine the correlation between the number of automobiles in the garage and the hour of the day. He discovers that he can represent this using a linear relationship between 4 am and 10 am. y = 3.56x + 2 is the model's equation.

To learn more about a linear relationship

https://brainly.com/question/11663530

#SPJ4

The complete question of the above answer is

Jamal owns a parking garage and is trying to find the relationship between the hour of the day and the number of cars in the garage. He finds that between 4 am and 10 am he can model this with a linear relationship. The equation for this model is y = 3.96x + 2. About how many cars are entering the garage every hour?

A) 1

B) 2

C) 3

D) 4

The mean square for error in the ANOVA provides an estimate of the variance of an individual treatment average.

What is a variance?

Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance serves as a proxy for dispersion, or the degree to which a set of numbers deviates from their mean.

Here, We have

The mean square for error in the ANOVA provides an estimate

ANOVA = Analysis of VarianceThe correct answer is (B)

The mean square for error (MSE) in the analysis of variance (ANOVA) provides an estimate of the variance of an individual treatment average.

Unlike option C which refers to an individual observation,

option B refers to a group of observations that are classified into a single treatment sample.

The MSE measures (gives an estimate of) the variation within this treatment sample. In this case, the variation is in the average or the mean. This could be average texture, average strength, average penetration, etc.

Hence, the mean square for error in the ANOVA provides an estimate of the variance of an individual treatment average.

To learn more about the variance from the given link

https://brainly.com/question/25639778

#SPJ4

Answer:

The only answer that does not have a 2 digit quotient would be 6,701÷36.

Answer:

--------------------------

s varies directly as t:

If s is 20 when t is 4, find the value of k:

The equation is:

When s is 30, then t is:

Answer:

Thus, t = 6 if s = 30.

Step-by-step explanation:

Given that,

→ The value of s is 20 when t is 4.

Now value of s when t is 1,

→ s = (20/4)t

→ [ s = 5t ]

Then value of t when s is 30,

→ 5t = 30s

→ t = (30/5)s

→ t = 30/5

→ [ t = 6 ]

Hence, the value of t is 6.