Take as input two opposite corners of a rectangle: (x1,y1) and (x2,y2). Finally, the user is prompted for the coordinates of a third point (x,y). Find whether the point (x,y) lies inside the rectangle.

Answer:

(-37+43)-44=x

Step-by-step explanation:

i put the parentheses only because of PEMDAS. it's a pretty straightfoward question. To put it in an expression however, I'm not sure. Best of luck!

Answer:

x=14

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

The answer is x=14.

Step-by-step explanation:

In order to determine the answer, we have to solve for x, that is, we have to free the "x" variable in any side of the equation. We have to do the same procedure for any variable, independent of the amount of variables in the equation.

Solving the expression for x:

[tex]5+\frac{4}{7}*(21+3x)=41\\\frac{4}{7}*(21+3x)=41-5\\\\21+3x=\frac{36}{\frac{4}{7} } \\\\21+3x=\frac{36*7}{4}\\3x=63-21\\3x=42\\x=\frac{42}{3}= 14[/tex]

The solution for x is x=14.

Answer:

The system of equations is

[tex]f=4n[/tex]  and  [tex]f=n+27[/tex]

Fred's age is 36 years old and Nathan's age is 9 years old

Step-by-step explanation:

Let

f -----> Fred's age

n ----> Nathan's age

we know that

[tex]f=4n[/tex]-----> equation A

[tex]f=n+27[/tex] ----> equation B

equate the equations and solve for n

[tex]4n=n+27\\4n-n=27\\3n=27\\n=9[/tex]

Find the value of f

[tex]f=4(9)=36[/tex]

therefore

Fred's age is 36 years old and Nathan's age is 9 years old

Answer:

The system of equations is f=4n  and  f=n+27

Step-by-step explanation:

Answer:

Last year, the average cost of a traditional Thanksgiving dinner was $48.91.

Step-by-step explanation:

If this year the cost of a traditional Thanksgiving dinner was decreased by 1.76% compared to last year, then

last year cosr - 100%

this year cost - 100%-1.76%=98.24%

So,

$x - 100%

$48.05 - 98.24%

Write a proportion:

[tex]\dfrac{x}{48.05}=\dfrac{100}{98.24}[/tex]

Cross multiply:

[tex]98.24x=48.05\cdot 100\\ \\98.24x=4,805\\ \\x\approx 48.91[/tex]

Last year, the average cost of a traditional Thanksgiving dinner was $48.91.

Final answer:

The average cost of a traditional Thanksgiving dinner in the last year was approximately $48.91, calculated by dividing this year's cost of $48.05 by the percentage decrease converted to a decimal (1 - 0.0176).

Explanation:

To calculate the average cost of a traditional Thanksgiving dinner in the last year, given this year's average cost and the percentage decrease, we can use the formula original price = discounted price / (1 - discount rate). The discount rate in this case is the percentage decrease in cost, expressed as a decimal. Given that this year's average cost is $48.05 and the decrease is 1.76%, we first convert the percentage to a decimal by dividing by 100, which gives us 0.0176.

The formula becomes:

original price = $48.05 / (1 - 0.0176)

original price = $48.05 / 0.9824

original price = $48.91 approximately

Therefore, the average cost of a traditional Thanksgiving dinner in the last year was about $48.91.

Answer:

I am trying on this but I can solve you the 10th question

Answer:

12.4 miles, N84.4°E

Step-by-step explanation:

Split the translation over the components parallel to the direction S>N and W>E, then calculate the sum of both components, and get magnitude and direction of the movement. Here's my calculation, double check them regardless.

For the first hour, it travels [tex] 8.5 cos 37.5 [/tex] north and [tex] 8.5 sin 37.5 [/tex] east. Once the wind changes, it flies [tex] 6*1.5 cos (180-52.5) = 9 cos 127.5 [/tex] "north" ( the actual movement is southbound, which will appear calculating the cosine and getting a negative number) and [tex]6*1.5 sin (180-52.5) = 9 sin 127.5 [/tex]. The complete movement is 1.2 miles N and 12.3 miles E. The total movement is, with the Pythagorean theorem, 12.4 miles total, and the angle it forms with the north direction is the [tex]tan^{-1} \frac{12.3}{1.2} = 84.4°[/tex].

Answer:

a.[tex]P(E_1/A)=0.0789[/tex]

b.[tex]P(E_2/A)=0.395[/tex]\

c.[tex]P(E_3/A)=0.526[/tex]

Step-by-step explanation:

Let [tex]E_1,E_2,E_3[/tex] are the events that denotes the good drive, medium drive and poor risk driver.

[tex]P(E_1)=0.30,P(E_2)=0.50,P(E_3)=0.20[/tex]

Let A be the event that denotes an accident.

[tex]P(A/E_1)=0.01[/tex]

[tex]P(A/E_2=0.03[/tex]

[tex]P(A/E_3)=0.10[/tex]

The company sells Mr. Brophyan insurance policy and he has an accident.

a.We have to find the probability Mr.Brophy is a good driver

Bayes theorem,[tex]P(E_i/A)=\frac{P(A/E_i)\cdot P(E_1)}{\sum_{i=1}^{i=n}P(A/E_i)\cdot P(E_i)}[/tex]

We have to find [tex]P(E_1/A)[/tex]

Using the Bayes theorem

[tex]P(E_1/A)=\frac{P(A/E_1)\cdot P(E_1)}{P(E_1)\cdot P(A/E_1)+P(E_2)P(A/E_2)+P(E_3)P(A/E_3)}[/tex]

Substitute the values then we get

[tex]P(E_1/A)=\frac{0.30\times 0.01}{0.01\times 0.30+0.50\times 0.03+0.20\times 0.10}[/tex]

[tex]P(E_1/A)=0.0789[/tex]

b.We have to find the probability Mr.Brophy is a medium driver

[tex]P(E_2/A)=\frac{0.03\times 0.50}{0.038}=0.395[/tex]

c.We have to find the probability Mr.Brophy is a poor driver

[tex]P(E_3/A)=\frac{0.20\times 0.10}{0.038}=0.526[/tex]

Final answer:

The probability that Mr. Brophy is a good, medium, and poor risk driver given he has had an accident is approximately 0.079, 0.395, and 0.526 respectively, as calculated using Bayes' theorem.

Explanation:

Using Bayes' theorem, we can find out the probability that Mr. Brophy is a good, medium, or poor risk driver given that he has had an accident:

Let's denote A as the event of having an accident and Gi, Mi, Pi as the events of Mr. Brophy being a good, medium, or poor risk driver respectively.

The total probability of an accident, P(A), is given by:

P(A) = P(A|Gi)P(Gi) + P(A|Mi)P(Mi) + P(A|Pi)P(Pi)

P(A) = (0.01)(0.30) + (0.03)(0.50) + (0.10)(0.20) = 0.003 + 0.015 + 0.02 = 0.038

The probability of Mr. Brophy being a good driver given he had an accident, P(Gi|A), is:

P(Gi|A) = (P(A|Gi)P(Gi)) / P(A) = (0.01)(0.30) / 0.038 ≈ 0.079

The probability of Mr. Brophy being a medium risk driver given he had an accident, P(Mi|A), is:

P(Mi|A) = (P(A|Mi)P(Mi)) / P(A) = (0.03)(0.50) / 0.038 ≈ 0.395

The probability of Mr. Brophy being a poor risk driver given he had an accident, P(Pi|A), is:

P(Pi|A) = (P(A|Pi)P(Pi)) / P(A) = (0.10)(0.20) / 0.038 ≈ 0.526

Answer:

The answer to your question is:  4w + 50

Step-by-step explanation:

Data

w = wide ft

length = w + 25

perimeter = ?

Process

Find the perimeter

Perimeter = 2 wide + 2 length

Perimeter = 2w + 2(w + 25)

Perimeter = 2w + 2w + 50

Perimeter = 4w + 50

The length of a fence around a rectangular park with width 'w' feet and length 'w + 25' feet would be 4w + 50 feet according to the perimeter formula for rectangles.

The length of the rectangular park is given as w + 25 feet, where w represents the width of the park. The length of a fence surrounding the park, including the gates, would cover the entire perimeter of the park. The formula to find the perimeter of a rectangle is 2*(length + width).

Substitute the given dimensions into the formula, the fence length therefore would be 2*(w + (w + 25)). Simplifying this equation gives us 2*(2w + 25) which is equal to 4w + 50. Thus, the length of the fence, including the gates, that surrounds the rectangular park is 4w + 50 feet.

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Answer:

  40.56 ft

Step-by-step explanation:

The perimeter is the sum of the lengths of the "sides" of this figure. Starting from the left side and working clockwise, the sum is ...

  P = left side (8 ft) + top side (10 ft) + semicircle (1/2×8 ft×π) + bottom side (10 ft)

  = 28 ft + 4π ft

  = (28 +12.56) ft

  P = 40.56 ft

Answer:

Top part lenght= 24 ft.

Middle part= 72 ft.

Bottom part = 144 ft.

Step-by-step explanation:

First we assign varibales to each rocket part

top part length= x;

middle part length= y;

bottom part length= z;

Then from the reading we can write the next equations:

X=1/6 Z; (1)

Y=1/2 Z; (2)

X + Y +Z = 240 (3)

Then solving, we replace x and y, in the equation (3)

1/6 z + 1/2 z + z = 240

Multiply by 6 both sides:

6/6 z + 6/2 z + 6 z = 1440

z + 3 z + 6 z = 1440

Then grouping similar terms

10 z = 1440

z= 144

Then replacing in (1) and (2)

Y=1/2 *144=72

X=1/6*144= 24

Answer:

OPTION A.

OPTION D.

OPTION E.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the  slope and "b" is the y-intercept.

The  Standard form of the equation of the line is:

[tex]Ax + By = C[/tex]

Where "A" is a positive integer, and "B" and "C" are integers.

Choose two points from the table and find the slope with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

Points:

[tex](1,27)\\\\(4,24)[/tex]

So we get that the slope is:

[tex]m=\frac{24-27}{4-1}=-1[/tex]

Let's substitute the slope and the coordinates of the point (1,27) into  [tex]y=mx+b[/tex] and then solve for "b":

[tex]27=(-1)(1)+b\\\\27+1=b\\\\b=28[/tex]

Then, we get that the equation of the line in Slope-Intercept form is:

[tex]y=-x+28[/tex] or [tex]28-x=y[/tex]

In order to write it in Standard form, we can add "x" to both sides of the equation:

[tex]y+x=-x+28+x\\\\x+y=28[/tex]

We can solve for "x" by subtracting "y" from both sides of the equation:

[tex]x+y-y=28-y\\x=28-y\\\\28-y=x[/tex]

Answer:

A,D, and E

Step-by-step explanation:

[tex]\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}] [/tex]

[tex]\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}][/tex]

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

   [tex] \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}][/tex]

The solutions are[tex]\( z = 5e^{i(\frac{9\pi}{4})} \), \( z = 5e^{i(\frac{17\pi}{4})} \), \( z = 5e^{i(\frac{25\pi}{4})} \), and \( z = 5e^{i(\frac{33\pi}{4})} \).[/tex]

To find the solutions of the equation [tex]\( z^4 = -625 \) in the given range of argument, we first rewrite the equation in polar form. Let \( z = re^{i\theta} \), where \( r \) is the magnitude of \( z \) and \( \theta \) is its argument.[/tex]

The equation becomes:

[tex]\[ (re^{i\theta})^4 = -625 \]\[ r^4e^{4i\theta} = -625 \]Now, since the right side is a negative real number, we can express it in polar form as \( -625 = 625e^{i\pi} \). So we have:\[ r^4e^{4i\theta} = 625e^{i\pi} \][/tex]

Comparing the magnitudes and arguments on both sides, we get:

[tex]\[ r^4 = 625 \]\[ 4\theta = \pi \]Solving for \( r \) and \( \theta \):\[ r = \sqrt[4]{625} = 5 \]\[ \theta = \frac{\pi}{4} \][/tex]

However, we need solutions in the given range of argument, which is between [tex]\( 270^\circ \) and \( 360^\circ \). Since \( \frac{\pi}{4} \) is approximately \( 45^\circ \) or \( \frac{\pi}{4} \), we need to add multiples of \( 2\pi \) to this angle to get solutions within the desired range.[/tex]

The solutions are:

[tex]\[ z_1 = 5e^{i(\frac{\pi}{4} + 2\pi)} \]\[ z_2 = 5e^{i(\frac{\pi}{4} + 4\pi)} \]\[ z_3 = 5e^{i(\frac{\pi}{4} + 6\pi)} \]\[ z_4 = 5e^{i(\frac{\pi}{4} + 8\pi)} \]Simplifying the angles:\[ z_1 = 5e^{i(\frac{9\pi}{4})} \]\[ z_2 = 5e^{i(\frac{17\pi}{4})} \]\[ z_3 = 5e^{i(\frac{25\pi}{4})} \]\[ z_4 = 5e^{i(\frac{33\pi}{4})} \][/tex]

Finally, we can convert these back to rectangular form if needed:

[tex]\[ z_1 = 5\left(\cos\frac{9\pi}{4} + i\sin\frac{9\pi}{4}\right) \]\[ z_2 = 5\left(\cos\frac{17\pi}{4} + i\sin\frac{17\pi}{4}\right) \]\[ z_3 = 5\left(\cos\frac{25\pi}{4} + i\sin\frac{25\pi}{4}\right) \]\[ z_4 = 5\left(\cos\frac{33\pi}{4} + i\sin\frac{33\pi}{4}\right) \][/tex]

You can compute the approximate values of these complex numbers and round them to the nearest thousandth if necessary.

Complete Question;

Find the solution of the following equation whose argument is strictly between [tex]$270^\circ$[/tex] , degree and [tex]$360^\circ$[/tex] , degree. Round your answer to the nearest thousandth.  [tex]\[z^4 = -625z\][/tex]

Answer:

Step-by-step explanation:

The radius is half the diameter, so is ...

  r = d/2 = 15 cm/2 = 7.5 cm

The area formula is ...

  A = πr²

Filling in the radius, we have ...

  A = π·(7.5 cm)² = 56.25π cm² ≈ 176.7 cm² . . . area

__

The circumference formula is ...

  C = πd

Filling in the diameter, we have ...

  C = π·(15 cm) = 15π cm ≈ 47.1 cm . . . circumference

Answer:

Here's ur answer

Step-by-step explanation:

Answer:

width = 23 inches

length = 57 inches

Step-by-step explanation:

Let x inches be the width of the rectangular solar panel.

So,

width = x inches

3 times the width = 3x inches

12 inches shorter than 3 times the width = 3x - 12 inches

length = 3x - 12 inches

The perimeter of the rectangle is

[tex]P=2(\text{Width}+\text{Length})[/tex]

Hence,

[tex]160=2(x+3x-12)\\ \\160=2(4x-12)\\ \\80=4x-12\ [\text{Divided by 2}]\\ \\4x=80+12\\ \\4x=92\\ \\x=23\ inches\\ \\3x-12=3\cdot 23-12=69-12=57\ inches[/tex]

Answer:

31 emails, but I can't do a # number line.

Step-by-step explanation:

Answer: There are 31 emails left in her inbox.

Step-by-step explanation:

Since we have given that

Number of emails in her inbox = 78

Number of emails she deleted = 47

We need to find the number of emails that are left in her inbox.

So, for left we would use "Subtraction operator"

So, Number of emails left in her inbox = Number of emails in her inbox - Number of emails she deleted.

[tex]=78-47\\\\=31[/tex]

Hence, there are 31 emails left in her inbox.

Answer: 380

Step-by-step explanation: Did you mean to ask how much time it took him? If he’s doing 4 races each being 95 miles it would simply be 95 x 4 = 380

The total distance driven by Walt is calculated by multiplying the length of each race (95 miles) by the number of races (4), giving a total of 380 miles.

Walt averages 98 miles per hour, each race is 95 miles long, and he completed 4 races. To find the total distance driven by Walt, we only need to know how long each race is and how many races Walt completed because the speed at which Walt drives does not affect the total distance he covered in the race. Therefore, to get the total distance, we simply multiply the length of each race by the number of races. In this case, Walt drove 95 miles x 4 = 380 miles in total.

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Answer: Option c.

Step-by-step explanation:

We know that the first month's interest payment was $477.82, therefore, we can calculate the Annual interest multiplying this first month's interest payment by 12:

[tex]Annual\ interest=\$477.82*12\\\\Annual\ interest=\$5,733.84[/tex]

Dividing it by the interest rate (Remember that [tex]7.125\%=\frac{7.125\%}{100}=0.07125[/tex]), we get:

[tex]\frac{\$5,733.84}{0.07125}=\$80,474.94[/tex]

Finally, since Kate and Bill secured a loan with a 75% loan-to-value ratio, we get:

[tex]\frac{\$80,474.94}{0.75}=\$107,299.92 \approx\$107,300[/tex]

Answer:

n=2/5 or 0.4

Step-by-step explanation:

thx mate brainliest plzz

Consumer goods are goods produced with the help of Capital goods.

Capital Good=Machine and Machine Parts, Parts which are used in manufacture of a tool,

Consumer Good=Chocolate, Different Commodities, Car.

Capital goods last for longer period of time, whereas Consumer goods are manufactured again and again with the help of same Capital goods.

It is given that, we want to increase production of consumer goods to a total of 6 units.

Producing 7.5 ,units of capital goods is too high for producing 6 unit of Consumer good, as Capital good last for Longer duration of time.

Answer:

  CD = 40

Step-by-step explanation:

Since D is the midpoint, the entire length CE is twice the length of CD, so we have ...

  2×CD = CE

  2×(5x) = 9x +8

  x = 8 . . . . . . . . subtract 9x and simplify

Then the length of CD is ...

  CD = 5x = 5·8 = 40

Answer:

3rd graph

Step-by-step explanation:

Hi, the answer would be the 3rd graph because each given set is shown on that coordinate relation.

Hope this helps, I attached the graph in case my explanation was confusing.

Third graph represents the set B = (1, 2), (2, 1), (3, 0), (4, -1).

Here, Set of points given as,

B = (1, 2), (2, 1), (3, 0), (4, -1).

We have to check the graph which represents the given set.

How to show points on graph?

Points are identified by stating their coordinates in the form of (x, y).

Where x is coordinate of x - axis and y is coordinate of y - axis.

Now,

Set of points given as,

B = (1, 2), (2, 1), (3, 0), (4, -1).

⇒ Third graph represents the set B = (1, 2), (2, 1), (3, 0), (4, -1).

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Answer:

Step-by-step explan 3x+2x+20+4x-20=180. 9x=180 X=180÷9. X=20

Answer:

The answer to your question is below

Step-by-step explanation:

I think it will easy to understand if we graph this information but let's explain it without the graph.

According to the information given, we know that f(x) represents the number of baskets and x the number of players at the practice.

So, if we have the point (12, 36) we can conclude that during practice there were 12 players and there were 36 baskets.

For me, it makes sense.

Answer: Yes. The input and output are both possible

Step-by-step explanation:

The reason why is because f(x) stands for y and in parenthe this is how it looks like(x,y) and if you put the numbers in you have (12,36) 12 stands for the number of players and f(x) or y stands for the number of baskets made.

Answer:

Area = length * width

11.25 sq ft = 4.5 ft * width

width = 11.25 / 4.5

width = 2.5 feet

5/2 feet = 2.5 feet

answer is D

Step-by-step explanation:

Answer:

[tex]dAB=10\ units[/tex]

Step-by-step explanation:

we know that

The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

A(1, 1) and B(7, −7)

Let

(x1,y1)=A(1, 1)

(x2,y2)=B(7, −7)

substitute the given values in the formula

[tex]dAB=\sqrt{(-7-1)^{2}+(7-1)^{2}}[/tex]

[tex]dAB=\sqrt{(-8)^{2}+(6)^{2}}[/tex]

[tex]dAB=\sqrt{64+36}[/tex]

[tex]dAB=\sqrt{100}[/tex]

[tex]dAB=10\ units[/tex]

Answer:  The required distance between the points between A(1, 1) and B(7, −7) is 10 units.

Step-by-step explanation:  We are given to explain the distance formula. Also, to calculate the distance between A(1, 1) and B(7, −7).

Distance formula :  The distance between any two two points with co-ordinates (a, b) and (c, d) is given by

[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]

Therefore, the distance between the points A(1, 1) and B(7, −7) is given by

[tex]D\\\\=\sqrt{(7-1)^2+(-7-1)^2}\\\\=\sqrt{36+64}\\\\=\sqrt{100}\\\\=10.[/tex]

Thus, the required distance between the points between A(1, 1) and B(7, −7) is 10 units.

Answer:

4 boys, 3 girls

Step-by-step explanation:

brothers of John ⇒ x

sisters of John ⇒ y

John has as many brothers as sisters:

brothers of Emily ⇒ x + 1 (Emily have the same amount of brother as John, plus one (John))

sisters of Emily ⇒ y -1 (Emily have the same amount of sister as John, minus one (herself))

Emily has twice as many brothers as sisters:

Now we have a system of 2 equations and 2 variables

x=y (I)

2y - 2 = x + 1 (II)

____________

Replace x in equation II

2y - 2 = y + 1

2y - y = 2 + 1

y = 3

____________

Replace y in equation I

x = y = 3

That mean that John have 3 brothers plus himself, there is 4 boys in the family and John have 3 sister, so there is 3 girls in the family

John and Emily are both girls as they have 0 brothers and 0 sisters in the family.

Let's use variables to represent the number of brothers and sisters John and Emily have. Let b represent the number of brothers and s represent the number of sisters.

From the given information, we know that John has as many brothers as sisters. So, b = s.

We also know that Emily has twice as many brothers as sisters. So, b = 2s.

We can solve this system of equations to find the values of b and s. Substituting the value of b from the second equation into the first equation, we get 2s = s. Therefore, s = 0.

Since John and Emily are siblings, and John has as many brothers as sisters (0 sisters), it means John has 0 brothers as well. So, the family consists of only John and Emily, who are both girls.

Answer:

10

Step-by-step explanation:

20/2=10

Answer:10

Step-by-step explanation:

Answer:

The answer is 10

Step-by-step explanation:

The side length cannot be negative, hence the side length of the patio will be 10 feet

Give the expression that represents the statement given as:

[tex](s+4)^2 = 196[/tex]

We need to get the length of the side of the patio "s"

[tex](s+4)^2 = 196\\s+4 = \pm\sqrt{196}\\s+4=\pm14[/tex]

Subtract 4 from both sides

[tex]s+4-4=14-4\\s=14-4\\s =10ft[/tex]

Since the side length cannot be negative, hence the side length of the patio will be 10 feet

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Answer: 0.3061.

Step-by-step explanation:

Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean [tex]\mu[/tex], the actual temperature of the medium, and standard deviation [tex]\sigma[/tex].

Let X be the random variable that represents the reading of the thermometer.

Confidence level : [tex]=95\%[/tex]

We know that the z-value for 95% confidence interval is 1.96.

Then, we have

[tex]-1.96<\dfrac{X-\mu}{\sigma}<1.96[/tex]      [tex]z=\dfrac{X-\mu}{\sigma}[/tex]

[tex]\Rightarrow\ -1.96\sigma<X-\mu<1.96\sigma[/tex]  

But all readings are within 0.6° of [tex]\mu[/tex].

So, [tex]1.96\sigma=0.6[/tex]  

[tex]\Rightarrow\ \sigma=\dfrac{0.6}{1.96}=0.30612244898\approx0.3061[/tex]

Hence, the required standard deviation will be  

The confidence level is 95% in normal distribution then The value of standard deviation is 0.3061.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

Given

The temperature reading from a thermocouple placed in a constant temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ.

Let x be the random variable that represents the reading of the thermometer.

The confidence level is 95%. Then the z-value for 95% confidence level interval is 1.96.

Then we have

[tex]-\ \ 1.96 \ < \dfrac{x- \mu}{\sigma} < 1.96\\-1.96 \sigma < x- \mu \ < 1.96 \sigma[/tex]

But all the readings are within 0.6° of μ. Then

[tex]1.96 \sigma = 0.6\\[/tex]

On solving

[tex]\sigma = \dfrac{0.6}{1.96}\\\\\sigma = 0.306122 \approx 3061[/tex]

Thus, the standard deviation is 0.3061.

More about the normal distribution link is given below.

https://brainly.com/question/12421652