Winston is baking a pie. The diameter of the pie is 12 inches. What is the area of the pie? Use 3. 14 for pi and round your answer to the nearest tenth

Therefore , the solution of the given problem of angles comes out to be m∠G= 63° is the response to the second component of the query.

The curved lines which make up the ends of a skew are divided by its highest and bottom walls using Cartesian measurements. There is a possibility who two poles will collide at an intersection. Another result of two objects interacting is an angle. They most closely mimic dihedral shapes. Two line beams can be arranged in different ways between their extremities to form a two-dimensional curve.

Here,

m∠E + m∠F + m∠G = 180°

Additionally, we are aware that mE = (5x + 6)°, mF = (4x - 6)°, and mG = (5x - 2)°. When we enter these numbers into the formula above, we obtain:

=> (5x + 6)° + (4x - 6)° + (5x - 2)° = 180°

When we simplify and find x, we obtain:

=> 14x - 2 = 180

=> 14x = 182

=> x = 13

Now that we know the three vectors' values:

=> m∠E = (5x + 6)° = (5(13) + 6)° = 71°

=> m∠F = (4x - 6)° = (4(13) - 6)° = 46°

=> m∠G = (5x - 2)° = (5(13) - 2)° = 63°

In light of this, mE = 71°, mF = 46°, and mG = 63°.

The first portion of the question has the following solution:

=>  m∠EFG = m∠E + m∠F + m∠G = 71° + 46° + 63° = 180°.

m∠G= 63° is the response to the second component of the query.

To know more about angles visit:

https://brainly.com/question/14569348

#SPJ1

If the balance will be $1370.55 after 6 years, then The balance will be $1711.03 after approximately 14.3 years.

The formula for calculating the balance in a continuously compounded account is:

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

Where:

A = final balance

P = principal (initial deposit)

e = Euler's number (approximately 2.71828)

r = annual interest rate

t = time in years

We know that the initial deposit is $1000 and the balance after 6 years is $1370.55, so we can use these values to solve for the annual interest rate:

[tex]1370.55 = 1000*e^{6r}[/tex]

⇒ [tex]ln(\frac{1370.55}{1000}) = 6r[/tex]

⇒ [tex]r = \frac{ln(\frac{1370.55}{1000})}{6}[/tex]

⇒ [tex]r = 0.0345[/tex]

Now we can use the same formula to find out when the balance will be $1711.03:

[tex]1711.03 = 1000*e^{(0.0345*t)}[/tex]

⇒ [tex]ln(\frac{1711.03}{1000}) = 0.0345*t[/tex]

⇒ [tex]t = \frac{ln(\frac{1711.03}{1000})}{0.0345}[/tex]

⇒ t = 14.3 years.

To know more about interest

brainly.com/question/28792777

#SPJ4

The values of the expression when using the completing the square method is given below

To complete the square for x²-16x+c, we need to add and subtract the square of half the coefficient of x, which is (-16/2)² = 64. So:

x² - 16x + c = (x - 8)² - 64 + c

To complete the square, we added (-16/2)² = 64, but we subtracted it again to keep the expression equivalent. Therefore, c - 64 is the value that completes the square.

Similarly, for x² + 7x + c, we add and subtract (7/2)² = 49/4:

x² + 7x + c = (x + 7/2)² - 49/4 + c

So c - 49/4 completes the square.

For x²- 9x, we add and subtract (9/2)² = 81/4:

x² - 9x = (x - 9/2)² - 81/4

Therefore, c - 81/4 completes the square.

To factor x²- 14x, we can factor out x:

x² - 14x = x(x - 14)

To factor x² + 30x, we can factor out x:

x² + 30x = x(x + 30)

To factor x²- 9x, we can factor out x:

x² - 9x = x(x - 9)

To solve x² + 10x = 16 by completing the square, we first add and subtract (10/2)² = 25:

x² + 10x + 25 - 25 = 16

(x + 5)² = 41

x + 5 = ±√41

x = -5 ±√41

To solve x² - 3x = 7 by completing the square, we first add and subtract (3/2)² = 9/4:

x² - 3x + 9/4 - 9/4 = 7

(x - 3/2)² = 37/4

x - 3/2 = ±√(37/4)

x = 3/2 ±√(37/4)

To solve x² + 15x = 12 by completing the square, we first add and subtract (15/2)² = 225/4:

x² + 15x + 225/4 - 225/4 = 12

(x + 15/2)² = 129/4

x + 15/2 = ±√(129/4)

x = -15/2 ±√(129/4)

a. Let L be the length of the wading pool. Then its width is L - 12. The height is 1 foot, so the volume is:

V = L(L - 12)(1) = L² - 12L

b. To complete the square for the expression L² - 12L, we add and subtract (12/2)² = 36:

L² - 12L + 36 - 36 = (L - 6)² - 36

So the volume can be written as:

V = (L - 6)² - 36

To find the dimensions of the wading pool that give a volume of 108 cubic feet, we set V = 108 and solve for L:

(L - 6)² - 36

Learn more about completing the square on;

https://brainly.com/question/13981588

#SPJ1

The Airbus A320 Sullenberger was piloting typically cruises at about 550 miles, or 807 ft per minute. His greatest horizontal range would have been between 4.4 and 6.0 nautical miles.

In certain circumstances, you may trade your miles for items like cash back and gift cards in addition to using them to pay for flights. Most of the time, redeeming airline points is straightforward. By entering into your account while making your reservation with most flights, you may use your points to get a free ticket.

You may also determine distance in miles unless you already know your speed and how long it takes to go a particular distance. Just double the time by the speed.

To know more about miles visit:

https://brainly.com/question/10153316

#SPJ1

The equation that can be used to find the sale price, s, of the pizza is S = 0.8(15).

It is the final amount paid for a product or service and is often lower than the original asking price.

This equation uses the percentage discount of 20%, which can be represented as 0.8, to find the sale price.

To calculate the sale price, the equation multiplies the regular price of $15 by the discount, 0.8.

0.8*15 =12

Therefore, the sale price of the pizza is $12.

The other equations are not correct because they do not take into account the percentage discount of 20%.

S = 0.1(15) does not consider the discount of 20%, as it is multiplying the regular price of $15 by 0.1, which is equivalent to 10%, not 20%.

Similarly, S = 0.115 is incorrect because it is multiplying the regular price of $15 by 1.15, which is equivalent to 115%, not 20%.

Lastly, S=0.8 15 is incorrect because it is not multiplying the regular price of $15 by the discount of 20%, which is 0.8.

For more questions related to discount

https://brainly.com/question/7459025

#SPJ1

a) The probability of hitting the black circle inside the target is closer to zero.

b) The probability of hitting the white portion inside the target is closer to one.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total area of the region is given as follows:

10² = 100 units squared.

The black circle has a radius of one unit(as the diameter is of 2 units), hence it's area is given as follows:

A = 3.14 x 1²

A = 3.14 units squared.

Then the probability of hitting the black circle is of:

3.14/100 = 0.0314 -> closer to zero.

The probability of hitting the white circle is given as follows:

1 - 0.0314 = 0.9686 -> closer to one.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.

What is an exponential function?

The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The context that represents exponential growth is "A town's population grows at a rate of 4% every year."

Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.

As the population grows, the growth rate also increases, resulting in an exponential increase over time.

Let P(t) be the population of the town after t years, where t is a positive integer.

The exponential function that models the population growth is -

[tex]P(t) = P0 \times (1 + r)^t[/tex]

where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.

In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.

Therefore, the exponential function for the town's population growth is -

[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]

Simplifying the expression, we get -

[tex]P(t) = P0 \times 1.04^t[/tex]

This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.

In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).

Therefore, the exponential growth is displayed by town's population growing 4% every year.

To learn more about exponential function from the given link

brainly.com/question/12626186

#SPJ1

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:

P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Using the binomial formula, we can calculate each of these probabilities:

P(X=k) = (n choose k) p^k (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.

P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608

P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322

P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013

P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003

Therefore,

P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

To know more about probability visit:

https://brainly.com/question/12431044

#SPJ1

The surface area of the prism is 264m²

A prism is a solid shape that is bound on all its sides by plane faces. There are different types of prism but the specific one we will be talking about here is triangular based prism.

The surface area of a prism is obtained by adding the area of the faces. Therefore surface area = 2B +ph

area of the base = 1/2 bh

= 1/2 × 6 × 8

= 1/2 × 48

= 24m²

using Pythagoras theorem, the hypotenuse of the triangle = √ 6²+8²

= √ 36+64

= √100 = 10m

perimeter of the base = 6+8+ 10

= 24m

Therefore SA = 2×24 + 24 × 9

= 48 + 216

= 264m²

learn more about surface area of prism from

https://brainly.com/question/1297098

#SPJ1

When it comes to the sale of products such as pet food, the veterinary practice is at an advantage over feed stores and grocery stores because they have better knowledge and understanding about the pet food, and they have established trust with their customers.

Pet food is a nutrient-rich food specially designed for domestic animals, like dogs, cats, and other pets. It is made from various animal and plant-based sources, such as beef, fish, and corn. Since pet food is designed to meet the nutritional needs of the pets, it must be balanced and complete to provide them with the necessary nutrients they need to be healthy and active.

Veterinarians are at an advantage over feed stores and grocery stores when it comes to the sale of pet food because they have the knowledge and expertise about the pet food. They are aware of the specific nutritional requirements of the pets and the various pet food brands available in the market. They can provide advice and recommendations to pet owners on what type of pet food is best suited for their pets based on their age, breed, and health conditions.

                             Moreover, veterinary practices have established trust with their customers. When customers know they can rely on a particular veterinary practice for quality products and trustworthy advice, they are more likely to shop there repeatedly.

To know more about veterinary practice:

https://brainly.com/question/27817241

#SPJ11

A) Jane's share is 12% of X, which is equal to 0.12X.

B) the total cost of the insurance is $20,691.67

C)  the employer's share is $18,208.67.

Total cost is the collective term for the cost of production as a whole, which encompasses both fixed and variable costs. The expense necessary to produce a good is referred to in economics as the total cost. There are two parts that make up the total cost: a set price The expense is what never changes.

Let X be the total cost of Jane's individual health care, then:

A) Jane's share is 12% of X, which is equal to 0.12X.

B) We know that Jane's deduction from each biweekly paycheck is $95.50, so she pays a total of:

$95.50 * 26 = $2,483

This amount is equal to 0.12X, so we can set up an equation:

0.12X = $2,483

Solving for X, we get:

X = $20,691.67

Therefore, the total value of the insurance is $20,691.67.

C) The employer's share is the difference between the total cost of the insurance and Jane's share:

Employer's share = Total cost - Jane's share

Employer's share = $20,691.67 - $2,483

Employer's share = $18,208.67

Therefore, the employer's share is $18,208.67.

To know more about Total cost visit:

https://brainly.com/question/30355738

#SPJ1

Jane's share of the total cost of her individual health care is $795.83, The total value of the insurance is $795.83 + 0.88x and the employer's share is 0.88x.

What is cost?

In mathematics, cost refers to the amount of resources (such as money, time, effort, or materials) that are required to produce or obtain something.

A) To find Jane's share of the total cost of her individual health care, we can use the information that she contributes 12% of the cost, and that this is a $95.50 deduction from each of her biweekly paychecks.

Let x be the total cost of Jane's individual health care. Then:

12% of x = $95.50

0.12x = $95.50

x = $95.50 / 0.12

x = $795.83

Therefore, Jane's share of the total cost of her individual health care is $795.83.

B) To find the total value of the insurance, we can add up both Jane's share and the employer's share.

If Jane is contributing 12% of the total cost, then the employer is contributing the remaining 88% of the cost. So the employer's share can be calculated as:

88% of x = 0.88x

The total value of the insurance is then:

Total value = Jane's share + Employer's share

Total value = $795.83 + 0.88x

C) To calculate the employer's share, we can use the same information as above. The employer is contributing 88% of the total cost, so:

88% of x = 0.88x

Therefore, the employer's share of the total cost of Jane's individual health care is $0.88x, or approximately $700.33 (if we use the value of x that we found in part A).

To learn more about cost visit:

https://brainly.com/question/25109150

#SPJ1

Answer:

Mark ate 3.3 times the square inches of pizza than Joannie ate.

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr (where r is the radius). If the circumference of a small pizza is 12π inches, then its radius is:

[tex]\implies \sf Radius_{small\;pizza}=\dfrac{circumference}{2\pi}=\dfrac{12\pi}{2\pi}=6\;inches[/tex]

The formula for the area of a circle is A = πr² (where r is the radius).

Therefore, the area of a small pizza is:

[tex]\implies \sf Area_{small\;pizza}=\pi \cdot 6^2=36\pi \; in^2[/tex]

If the small pizzas are cut into 6 congruent pieces, the area of one slice of small pizza is:

[tex]\begin{aligned}\implies \sf Area_{small\;slice}&=\sf \dfrac{Area_{small\;pizza}}{6}\\\\&=\dfrac{36 \pi}{6}\\\\&=6 \pi \; \sf in^2\end{aligned}[/tex]

Therefore, the area of one slice of small pizza is 6π square inches.

[tex]\hrulefill[/tex]

The diameter of a circle is twice its radius.

If the diameter of a large pizza is 16 inches then its radius is:

[tex]\implies \sf Radius_{large\;pizza}=\dfrac{diameter}{2}=\dfrac{16}{2}=8\;inches[/tex]

The formula for the area of a circle is A = πr² (where r is the radius).

Therefore, the area of a large pizza is:

[tex]\implies \sf Area_{large\;pizza}=\pi \cdot 8^2=64 \pi \; in^2[/tex]

If the large pizzas are cut into 8 congruent pieces, the area of one slice of large pizza is:

[tex]\begin{aligned}\implies \sf Area_{large\;slice}&=\sf \dfrac{Area_{large\;pizza}}{8}\\\\&=\dfrac{64 \pi}{8}\\\\&=8 \pi \; \sf in^2\end{aligned}[/tex]

Therefore, the area of one slice of large pizza is 8π square inches.

[tex]\hrulefill[/tex]

If Joannie eats 2 slices of small pizza, the square inches of pizza she ate is:

[tex]\implies \sf Joannie=2 \times 6 \pi = 12 \pi\;in^2[/tex]

If Mark eats 5 slices of large pizza, the square inches of pizza he ate is:

[tex]\implies \sf Mark =5 \times 8 \pi = 40\pi\;in^2[/tex]

To calculate how many times greater are the square inches of pizza that Mark ate than the square inches of pizza that Joannie ate, divide the area Mark ate by the area Joannie ate:

[tex]\implies \sf \dfrac{40 \pi}{12 \pi} = \dfrac{10}{3}=3.3\;(nearest\;tenth)[/tex]

Therefore, Mark ate 3.3 times the square inches of pizza than Joannie ate.

Answer:

remember, in order to calculate the weight on earth, we need to multiply the mass of the object with the force of Gravity (9.8 m/s^2 on earth)

so, her weight would be:

48 x 9.8 = 470.4 >>>>>>> Will be 470 if we round it to the nearest whole number.

Step-by-step explanation: Hope this helps. Mark me brainliest!! :)))

Answer: 470

Step-by-step explanation:

Answer:

To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.

Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.

Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.

Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.

Sum the first 26 terms of the series is needed  to get an approximation of its sum with an error of less than 0.01.

The question asks about the series 1 - 1/3 1/5 - 1/7 and the number of terms required to approximate its sum with an error of less than 0.01.

We will use the formula for the nth partial sum of an alternating series with terms that decrease in magnitude as n increases. The formula for the nth partial sum of such a series is :Sn = a1 - a2 + a3 - ... + (-1)^(n+1)an where a1, a2, a3, ... are the terms of the series.

If we can find the smallest value of n for which the absolute value of the (n+1)th term is less than 0.01, then the sum of the first n terms will be within 0.01 of the actual sum. We can use the formula for the nth term of the series to find such a value of n.

We have a series of the form:a1 - a2 + a3 - ... + (-1)^(n+1)an where a1 = 1, a2 = 1/3, a3 = 1/5, and so on. The nth term of this series is:an = (-1)^(n+1)/(2n - 1).Therefore, we want to find the smallest value of n for which : |an+1| < 0.01, where an+1 = (-1)^(n+2)/(2(n+1) - 1)

Simplifying this inequality, we get:|(-1)^(n+2)/(2(n+1) - 1)| < 0.01, Multiplying both sides by 2(n+1) - 1 and simplifying, we get:1/(2(n+1) - 1) < 0.01.

Taking the reciprocal of both sides and simplifying, we get:2(n+1) - 1 > 100. Therefore, we want to find the smallest integer value of n such that:2(n+1) > 101n+1 > 50.5n > 49.5n > 50. The smallest integer value of n that satisfies this inequality is n = 26. Therefore, we need to sum the first 26 terms of the series to get an approximation of its sum with an error of less than 0.01.

To know more about arithmetic progression click here :

https://brainly.com/question/14278705

#SPJ11

Answer: Rectangular prism & Cylinder

Step-by-step explanation: In geometry, a rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The line segment joining the two centers is the axis, that denotes the height of the cylinder.

As the given abc is a right triangle with points a(2, 5), b(2, 0), and c(x, 0). The area of 'abc' is 25 square units. and the equation of AC is x = 5√5.

The equation of ac has to be found. Since triangle ABC is right-angled, it can be shown that

                  AC² = AB² + BC²

    Finding the lengths of AB and BC before using the Pythagorean theorem to find AC.

    Using the distance formula,

                     AB =√(5²+0²)

                           = √25

                          = 5,

           And BC = √(x²+0²)

                         = √x²

                          = x.

  Area of a right triangle = ½(base × height)

          Here base = AB and height = BC,

              So,  ½ × 5 × x = 25

                            ⇒ 5x = 50

                              ⇒ x = 10

       Now, to find AC, use the Pythagorean Theorem.

                      AC² = AB² + BC²

                             = 5² + 10²

                             = 25 + 100

                             = 125AC

                             = √125

                             = 5√5

     Thus, the equation of AC is x = 5√5. Answer: x = 5√5.

Learn more about the Area of a right triangle at: https://brainly.com/question/17335144

#SPJ11

In Linear pair, 52°  is the value ∠AZJ .

What is Linear pairs?

When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's total angles are always equal to 180 degrees.

                                   A pair of adjacent angles is said to be a linear pair if the total of the two angles' (measured) angles is 180°. This means that a linear pair of angles always adds up to 180°. The linear pair of 30°, for instance, is 150°; the linear pair of 70°, 110°; etc.

∠JZF or ∠HZG

Linear pairs form supplementary angles.

 ∠AZJ = ∠AZH - ∠HZA

           = 90° - 38°

  ∠AZJ = 52°

Learn more about Linear pairs

brainly.com/question/17525542

#SPJ1

An expression for the number of amoebas after 24 hours is 1 × 2²⁴ = 16,777,216

Single-celled creatures knοwn as amοebas reprοduce asexually. An amοeba begins tο reprοduce when its genetic material dοubles, twο nuclei are fοrmed, and it begins tο alter shape by develοping a thin "waist" in the centre. Typically, this prοcedure gοes οn until the cells are finally divided intο twο.

Amοeba reprοduce typically asexually thrοugh a prοcess called binary fissiοn. The cell splits intο twο daughter cells οf equal size fοllοwing the replicatiοn οf its genetic material by mitοtic divisiοn.

a. It is given that an amοeba divides tο fοrm twο amοebas after οne hοur sο there are 2 amοebas after 1 hοur.

b. It is given that οne hοur later, each οf the twο amοebas divides tο fοrm twο mοre amοebas sο there are 2×2=4 amοebas after 2 hοurs.

c. The number οf amοebas is dοubling after each hοur since each amοeba divides intο twο amοebas every hοur. This means that the number οf amοebas after 6 hοurs can be fοund by multiplying the οriginal number οf amοebas, which was 1, by 2 six times. The number οf amοebas after 6 hοurs is then 1 × 2⁶ = 2⁶= 64 amοebas.

d. Using the same pattern frοm part (c), the number οf amοebas after 24 hοurs is 1 × 2²⁴ = 2²⁴ = 16,777,216 amοebas.

Expression = 1 × 2²⁴ = 16,777,216

To know more about expression visit:

https://brainly.com/question/14083225

#SPJ1

The 90% confidence interval for the population proportion is (0.1171, 0.1829).

To calculate the confidence interval, we first need to find the point estimate of the population proportion. The point estimate is the sample proportion which is given by:

p-bar = x/n = 60/400 = 0.15

where x is the number of items that failed the test and n is the sample size.

Next, we need to find the margin of error, which is given by:

ME = z*√(p_bar(1-p_bar)/n)

where z is the z-score corresponding to the confidence level, p_bar is the sample proportion, and n is the sample size.

For a 90% confidence level, the z-score is 1.645 (using a standard normal distribution table). Substituting the values, we get:

ME = 1.645*√(0.15(1-0.15)/400) = 0.0329

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:

CI = p_bar ± ME = 0.15 ± 0.0329 = (0.1171, 0.1829)

Therefore, we are 90% confident that the true population proportion of items that will fail the test is between 0.1171 and 0.1829.

Learn more about Confidence Interval:

https://brainly.com/question/15712887
#SPJ4

The given statement "The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line" is true because it provides the best fit line.

The simple linear regression equation estimates the relationship between two variables - a dependent variable (y) and an independent variable (x) - by fitting a straight line through the data points.

The line is chosen so that the sum of the squared deviations (also known as the sum of squared errors or SSE) between the observed values of y and the predicted values of y on the line is minimized.

In other words, the simple linear regression equation finds the line that is closest to all the data points in terms of the vertical distance between the points and the line.

This line is chosen to minimize the sum of squared deviations because it provides the best estimate of the relationship between x and y, and it allows for the prediction of y values for a given x value.

Thus, minimizing the sum of squared deviations is a crucial aspect of the simple linear regression equation because it ensures that the line of best fit provides the most accurate estimate of the relationship between the variables.

To learn more about regression click on,

https://brainly.com/question/31037753

#SPJ4

In the given right angled triangle, using Pythagorean theorem, the value of x is 12.73 units.

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the length of the squares on the other two sides add up to the length of the square whose side is the hypotenuse, or the side across from the right angle. This theory can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:

a² + b² =c²

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.

In the given right angled triangle, using Pythagorean theorem,

x² = (9[tex]\sqrt{2}[/tex] )²+ (9[tex]\sqrt{2}[/tex] )²

x² = 81×2

x = [tex]\sqrt{162}[/tex]

x = 12.73 units

Therefore, the value of x will be 12.73 units.

To know more about Pythagorean Theorem, visit

https://brainly.com/question/343682

#SPJ1

The sample space for rolling the game piece is S = {A, B, C, D}

In mathematics, a set is a well-defined collection of distinct objects, which can be anything like numbers, letters, people, or even other sets. A set is usually denoted by curly braces {} enclosing its elements separated by commas. For example, the set of natural numbers less than or equal to 5 can be denoted as {1, 2, 3, 4, 5}.

Sets can also be described by various methods such as by listing its elements, by set-builder notation, or by using a Venn diagram to visualize relationships between sets. A set can have any number of elements, including none (empty set), and can also have infinite number of elements.

Sets can be combined through set operations such as union, intersection, and complement. The union of two sets A and B is a set that contains all the elements that belong to either A or B (or both). The intersection of two sets A and B is a set that contains all the elements that belong to both A and B. The complement of a set A is the set of all elements that are not in A.

The sample space for rolling the game piece can be represented by the set of possible outcomes, which are the labels on the faces of the game piece. Therefore, the sample space is:

S = {A, B, C, D}

To know more about sample visit:

https://brainly.com/question/30206035

#SPJ1

The total length of Joe's shape will be the sum of these lengths, which is 12 + 9 + 9 = 30cm.

To find the total length of Joe's shape, we first need to determine the length of each part of the strips.

For the first strip, which is divided into three equal parts, each part will be 36/3 = 12cm long. For the second strip, which is divided into four equal parts, each part will be 36/4 = 9cm long.

To make the shape, Joe will need to use two strips. Let's assume that Joe places the strip with three equal parts horizontally and the strip with four equal parts vertically. He will then need to cut each strip into the appropriate lengths to create the shape.

To create the shape, Joe will need to use one 12cm length from the first strip and two 9cm lengths from the second strip. He will then need to connect these lengths together to create the shape.

These lengths will add up to a total length for Joe's shape of 12 + 9 + 9 = 30 cm.

To know more about length

brainly.com/question/17153671

#SPJ4

Answer:

[tex]26a - 10 = 2(13a - 5)[/tex]

The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10, which is a contradiction. This means that there is no solution to the system of equations.

What is an elimination?

To eliminate one of the variables, we need to manipulate one or both of the equations so that when we add them together, one of the variables is eliminated.

Let's start with the given equations:

18x - 6y = -20

-9x + 3y = 15

We can see that the coefficients of y in both equations are opposite, which means we can eliminate y by adding the two equations together. However, we need to make sure the coefficients of y have the same absolute value, so we'll multiply the second equation by 2:

18x - 6y = -20

-18x + 6y = 30

Now we can add the two equations together:

0x + 0y = 10

This equation simplifies to 0 = 10, which is a contradiction. This means that there is no solution to the system of equations. In other words, the two equations represent two parallel lines that never intersect.

Alternatively, we can recognize that the two equations represent the same line when simplified, since the second equation is simply half of the first equation. In this case, there are infinitely many solutions, since any point on the line satisfies both equations.

To know more about elimination, visit:

https://brainly.com/question/13815753  

#SPJ9

Complete question is: The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10.

Answer:

Step-by-step explanation:

Okay so you've gotta start with the y-intersect. The line hits the y-axis at 7, so your B is 7 (y=mx+7).

Since the line is going down, it's a negative slope, so your m will be a negative (y=-mx+7)

The line matches up exactly with (1,4), which shows the line moving down 3 for every 1 movement to the right. That makes your equation for the line y=-3x+7 or y=-3/1x+7

The probability of selecting a vowel from a hat with letters of the alphabet is 5/26 or approximately 0.1923. There are 5 vowels and 26 total letters.

There are 5 vowels in the English alphabet: A, E, I, O, and U. Therefore, the number of favorable outcomes (i.e., the number of vowels in the hat) is 5.

There are a total of 26 letters in the English alphabet. Therefore, the number of possible outcomes (i.e., the number of letters in the hat) is 26.

The probability of selecting a vowel is the ratio of the number of favorable outcomes to the number of possible outcomes:

P(vowel) = number of favorable outcomes / number of possible outcomes

P(vowel) = 5 / 26

Therefore, the probability of selecting a vowel is 5/26 or approximately 0.1923 (rounded to four decimal places).

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

Answer:

5

26

5/26

19

Step-by-step explanation:

The theoretical probability of drawing a blue marble from a jar containing 21 brown and 19 blue marbles is 19/40, or 0.475.

To calculate this, divide the number of blue marbles by the total number of marbles in the jar. 19 divided by 40 equals 0.475, or 19/40. This means that there is a 47.5% chance of drawing a blue marble from the jar.

The probability of drawing a specific marble from the jar can be expressed using the formula P(A) = n(A)/n(T).

In this example, the probability P(A) is the chance of drawing a blue marble, n(A) is the number of blue marbles (19) and n(T) is the total number of marbles in the jar (40). Therefore, P(A) = 19/40 = 0.475.

To know more about theoretical probability click on below link:

https://brainly.com/question/30604977#

#SPJ11