7. Choose Efficient Methods A circular patio has a circumference of 53.38 feet. What is the area of the patio? Use 3.14 for an approximation for T. Round to the nearest tenth.​

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =65 \end{cases}\implies a=\cfrac{(65)\pi (20)^2}{360} \\\\\\ A=\cfrac{650\pi }{9}\implies A\approx 226.89[/tex]

The only value of k that allows us to write √50 + √k as a single term is

k = 25.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To be able to write the expression √50 + √k as a single term, we need to find a perfect square that is a factor of both 50 and k.

Prime factorizing 50, we get 50 = 2 * 5².

Since 50 contains a factor of 2, any perfect square factor of 50 must also contain a factor of 2. The only perfect square factor of 50 that contains a factor of 2 is 2*5² = 50 itself.

Now we need to find a perfect square that is a factor of k and contains a factor of 5. This can be done by prime factorizing k and seeing if any of the factors can be squared and still contain a factor of 5.

Let's try some values of k:

If k = 5, then √k = √5, which is not a perfect square, so it won't work.

If k = 25, then √k = 5, which is a perfect square that contains a factor of 5, so we can write √50 + √25 as 5√2 + 5 = 5(√2 + 1).

If k = 125, then √k = 5√5, which is not a perfect square, so it won't work.

Therefore, the only value of k that allows us to write √50 + √k as a single term is k = 25.

So, √50 + √25 can be written as 5(√2 + 1).

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Answer:

area of the triangle BCD is

1/2.8.10 sq unit

=40 sq unit

BCD is a right angle triangle

so, BC^2+CD^2=BD^2

=> 8^2+10^2=BD^2

=> 64+100=BD^2

=> BD^2=164

=> BD=√164=2√41

BD=2√41 unit

1/2.BD.x=40

=> x=40.2/BD

=> x=80/2√41=40/√41

Equation (12x² - 6x)(4x - 2) simplifies to 12x(2x - 1)².

We can start by factoring out the greatest common factor from both terms, which is 6x:

(12x² - 6x)(4x - 2) = 6x(2x - 1)(4x - 2)

Next, we can simplify the expression by factoring out the common factor (4x - 2) from the remaining terms (2x - 1):

6x(2x - 1)(4x - 2) = 6x(2x - 1) × 2(2x - 1)

Now we have two factors that are the same, (2x - 1), so we can combine them by multiplying them together:

6x(2x - 1) × 2(2x - 1) = 12x(2x - 1)²

Therefore, (12x² - 6x)(4x - 2) simplifies to 12x(2x - 1)².

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Given question is incomplete, the complete question is below

Assuming that x ≠ 1/2, simplify (12x² - 6x)(4x - 2).

Step-by-step explanation:

The domain of the new function remains the same as the domain of the original function because it only affects the coefficient of x, not the values of x itself.

However, the range of the new function changes because increasing the coefficient a shifts the entire graph of the function upwards. Specifically, the range of the new function becomes y ≥ 2 since the minimum value of the function is now 2, which occurs when x = 0.

Therefore, the correct answers are:

The domain stays the same.

The range becomes y ≥ 2.

The single transformation that maps shape triangle a onto shape b is  [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

From the figure, we have the following highlights

Both triangles are congruent

Triangle B is 5 units down from triangle A

Triangle B is 5 units left of triangle A

The above highlights mean that the triangle A must be translated 5 units left and 5 units down to get triangle B.

This is represented as (x,y) -> (x - 5, y - 5)

By vector representation, we have: [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

Hence, the single transformation that maps shape a onto shape b is  [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

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Answer:

B

Step-by-step explanation:

Using the data:

6 students sent 0-4 emails

4 students sent 5-9 emails

2 students sent 10 - 14 emails

3 students sent 15-19 emails

Option B graphs this data correctly

Answer:b

Step-by-step explanation:

have a nice day

The price markup when we bought products for $50.00 and sold for $67.00 is c. 34%.

Price markup is the amount by which the selling price of a product is increased from its cost price.

It is expressed as a percentage of the cost price.

We would use the below formula to find out the price markup:

Markup = (Selling price - Cost price) / Cost price * 100%

Here,

cost price = $50.00

selling price = $67.00.

Markup = (67.00 - 50.00) / 50.00 * 100%

Markup = 17 / 50 * 100%

Markup = 0.34 * 100%

Markup = 34%

Therefore, the price markup is 34%.

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The quotient of the rational expression is [tex]A = \frac{4(x+2)}{(x-2)}[/tex]

Given data ,

Let the first expression be represented as p

Let the second expression be represented as q

And , A = p / q

[tex]p= {\frac{(x^{2}-4) }{(x+3)}[/tex]

[tex]q= {\frac{x^{2}-4x+4 }{4x+12} }[/tex]

where , [tex]A = \frac{\frac{(x^{2}-4) }{(x+3)} }{\frac{x^{2}-4x+4 }{4x+12} }[/tex]

On simplifying , we get

[tex]A = \frac{4(x^{2} -4)}{(x-2)^{2} }[/tex]

Now , taking the common terms in the equation , we get

[tex]A = \frac{4(x-2)(x+2)}{(x-2)(x-2)}[/tex]

[tex]A = \frac{4(x+2)}{(x-2)}[/tex]

Hence , the equation is [tex]A = \frac{4(x+2)}{(x-2)}[/tex]

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Answer:

Step-by-step explanation:

−UPDATE!! The answer is 1/3 so harray

Answer:

Eli speed is above the speed limit by 14.374km/h

Step-by-step explanation:

Eli speed=40mph

speed limit =50km/h

converting Eli speed to 40mph to km/h

E=64.374km/h

Eli speed- speed limit=64.374-50=14.374km/h

According to Amelia's results, 42% of students prefer coffee in the morning. If the margin of error is ±0.072, between 689 and 978 students at the school prefer coffee.

To calculate percentage;

total coffee takers/ total number of students surveyed x 100.

TCT= 63  TSS = 150 which then becomes 63/150x 100 = 42

To calculate margin of error;

TCT/TSS - ME  and TCT/TSS + ME, which becomes

63/150 + 0.072 = 0. 49

63/150 - 0.072 = 0.35

Next we calculate the the highest and lowest number by saying;

0.49 x total number of students in the school  1,981 =

0. 35 x total number of students in the school  1,981 =

The above answer is in response to the full question below;

There are a total of 1,981 students enrolled at Amelia's high school. Amella surveyed 150 of the students regarding their morning drink preference. Her results are recorded in the table.

Drinks                               number

Milk                                     45

Juice                                   18

Coffee                                 63

Smoothie                            11

Others                                 13

Complete the statement.

According to Amelia's results, [DROP DOWN 1] prefer coffee in the morning. If the margin of error is ±0.072, between [DROP DOWN 2] and [DROP DOWN 3) students at the school prefer coffee.

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On solving the query we can say that Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

We may use the following formula to create a confidence interval for the population proportion:

CI is equal to pz/2*(p(1-p)/n)

where:

p = sample percentage

Based on the ordinary normal distribution, z/2 is the z-score for the degree of confidence (with a 98% confidence level, z/2 = 2.33).

sample size, n

Given:

The population proportion's 98% confidence interval is as follows:

CI = (0.4392, 0.7138)

Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.

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On solving the query we can say that Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.

What is function?

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

We may use the following formula to create a confidence interval for the population proportion:

Cl is equal to pz/2"(p(1-p)/n)

where:

p = sample percentage

Based on the ordinary normal distribution, z/2 is the z-score for the degree of confidence (with a 98% confidence level, z/2 = 2.33).

sample size, n

Given:

The population proportion's 98% confidence

interval is as follows:

CI = (0.4392, 0.7138)

Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.

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Answer: 2

Step-by-step explanation:

Hace 2+3=5 collares. Para cada collar usa 2/5 por eso

5(2/5)=2

Answer:

216g³

Step-by-step explanation:

(6g)³

6³ = 216

g³ = g³

So, (6g)³ simplify will be 216g³

We are given that a hose in the front yard can fill the pool in 30 minutes and a hose in the back yard can fill it in half the time (so 15 minutes). We are asked to find the time, we'll call "t," it takes for both hoses together to fill up the pool.

We can create a rational equation, [tex]\frac{1}{30}+\frac{1}{15}=\frac{1}{t}[/tex]. Solve to "t"

[tex]\frac{1}{30}+\frac{1}{15}=\frac{1}{t} \Longrightarrow \frac{1}{30}+\frac{1}{15}*\frac{2}{2} =\frac{1}{t} \Longrightarrow \frac{1}{30}+\frac{2}{30} =\frac{1}{t} \Longrightarrow \frac{3}{30} =\frac{1}{t}[/tex]

[tex]\Longrightarrow \frac{1}{t}=\frac{3}{30} \Longrightarrow \frac{1}{t}=\frac{1}{10} \Longrightarrow \boxed{t=10 \ min}[/tex]

Thus, b is the correct option.

The  n'th Taylor Polynomial centered at c is given as  f(z) = 21

An nth degree Taylor polynomial is a way of approximating a function with a partial sum of additions and multiplications.

the general formula for An nth degree Taylor polynomial is Function, f(x) = 1/x², n = 4, c = 5

Using the Taylor polynomial formula,

Pₙ(x) = (x) = f(a) + f′(a)(x − a) + f′′(a)/2! × (x − a)2 + f′′′(a)/3! × (x − a)3 + f(4)(a)/4! × (x − a)4 + ... + f(n) (a)/n! × (x − a)n

The function and its derivatives are:

f(x) =  1/x²

f′(x) = 4² + 5

f′′(x) = 21

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Sample space for the given experiment is:

OGRI, OGRS, OGII, OGIS, OPRI, OPRS, OPII, OPIS, GGRI, GGRS, GGII, GGIS, GPRI, GPRS, GPII, GPIS.

In probability theory, the sample space is the set of all possible outcomes of a random experiment or process. The sample space of an experiment refers to the set of all possible outcomes that can occur when the experiment is conducted. In this case, the experiment is choosing toppings for a salad at a restaurant. The sample space would consist of all possible combinations of the toppings and dressings that can be chosen.

There are two choices for the extra toppings: olives or garbanzo beans. There are also two choices for the meat: pepperoni or shrimp. Lastly, there are two choices for the dressing: ranch or Italian.

To find the sample space, we can list out all possible combinations of these choices. Using the given letters to represent each choice, the sample space would be:

{OGI, OGI, OPI, OPS, ORI, ORG, OGS, OPI, OPS, OSI, OSG, OSI, GGI, GPI, GPS, GRI, GRG, GGS, GGI, GPI, GPS, GSI, GSG, GSI}

This set contains all 24 possible outcomes that can occur when selecting toppings and dressing for the salad.

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Complete question:

If the claim is approved, the homeowner's insurance policy will pay an amount of for the damages.

Given that,

Annual premium = $650

Deductible = $1,350 per claim.

Amount of damage formed in windstorm = $35,500

Amount of the damage that the insurance company will pay is the amount of the damage which deducts the deductible amount.

Amount insurance company pays = $35,500 - $1,350 = $34,150

Hence the amount paid by the company is $34,150.

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Answer:

the train can travel 4/15 of the distance between two cities in one hour

Answer:

B. $436,72

Step-by-step explanation:

500,000 = R * ((1 - (1 + 0.02/12)^(-12*40)) / (0.02/12))

Resolviendo para R, obtenemos:

R = 436.72

Por lo tanto, Jesse necesitará invertir $436.72 en su IRA cada mes para alcanzar su meta de $500,000 en 40 años, suponiendo una tasa de interés del 2% compuesto mensualmente. La respuesta correcta es la opción B.

The area of the shaded region is given as follows:

0.0475.

Here, we have to obtain probabilities using the normal distribution:

The z-score of a measure X of a variable that has mean symbolized by  and standard deviation symbolized by  is obtained by the rule presented as follows:

Z = X - μ / σ

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.

Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.

The mean and the standard deviation for the IQ scores are given as follows:

μ = 100, σ = 15

The shaded region is the area to the right of 125, hence it's area is one subtracted by the p-value of Z when X = 125, hence:

Z = (125 - 100)/15

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

Hence:

1 - 0.9525 = 0.0475.

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Missing Information

The shaded region is the area to the right of 125.

Stefanie bought 14 erasers.

Let's call the number of erasers Stefanie bought x.

We know that Stefanie paid $ 1.25 for the pencils, and she bought x erasers that each cost $ 0.50. So the total cost of the erasers is 0.5x.

Stefanie paid a total of $ 8.25, so we can write an equation:

1.25 + 0.5x = 8.25

1.25 + 0.5x - 1.25 = 8.25 - 1.25

Subtracting 1.25 from both sides, we get:

0.5x = 7

Dividing both sides by 0.5, we get:

x = 7 / 0.5

x = 7 × 2

x = 14

Therefore, Stefanie bought 14 erasers.

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Given question is incomplete, the complete question is below

Stefanie bought a package of pencils for $1.25 and some erasers that cost $0.50 each. She paid a total of $8.25 for these items, before tax. Exactly how many erasers did Stefanie buy?

The probability of opening to a page that is either 8 or 12 is 2/13.

The probability of opening to a page that is either 8 or 12 can be found by adding the individual probabilities of opening to page 8 and page 12. Since there are 13 pages in total, each page has a 1/13 chance of being opened. Therefore, the probability of page number 8 is 1/13, and the probability of opening to page 12 is also 1/13.

The probability of opening to page 8 or page 12 is the sum of the individual probabilities:

P(opening to page 8 or page 12) = P(opening to page 8) + P(opening to page 12)

P(opening to page 8 or page 12) = 1/13 + 1/13

P(opening to page 8 or page 12) = 2/13

Therefore, the probability of opening to a page that is either 8 or 12 is 2/13 or about 0.1538

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Joseph's mom was driving at a rate of 93.75 km/h.

Let's start by using the formula;

distance = rate × time

Let's call the distance that Joseph and his mom traveled "D". Let's also call the time that Joseph and his mom traveled before Joseph's dad caught up "T". Since Joseph's dad traveled for one hour less than Joseph and his mom, his travel time was "T - 1".

We know that Joseph's dad drove for four hours at 75 km/h, so he covered a distance of;

75 km/h × (T - 1) h = 75T - 75 km

We also know that Joseph and his mom traveled for T hours at some rate, which we'll call "R", so they covered a distance of;

R × T = D km

Since they ended up at the same place, we can set these two distances equal to each other;

75T - 75 = D

Rearranging, we get;

D = R × T

Substituting the expression for D, we get;

75T - 75 = R × T

Simplifying;

75 = R - 75/T

We know that R is the rate at which Joseph's mom was driving, and we want to find that rate. We also know that T is the time that she was driving before Joseph's dad caught up. We can solve for R by substituting the values we know;

75 = R - 75/T

75 = R - 75/4

R = 75 + 75/4

R = 93.75 km/h

Therefore, Joseph's mom was driving at 93.75 km/h.

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Step-by-step explanation:

Monte answered 9 questions each worth 4 points =  9x 4 = 36 points

 the rest of the 87 points were three-pointers  ( 87-36) = 51 points

      51 points / ( 3points /question)  = 17 three pointers

Answer: I think the answer is 29 I hope this is helping you

Step-by-step explanation: Since 87 divided by 3 gives an integer which is 29 and 29 times 3 is 87 I think this is the answer I'm not entirely sure but that's what I think

Answer: Donald and 2nd one A

Step-by-step explanation:

After factoring the given expression which is -2bk² - 4bk + 30b, we get -2b(k + 5)(k - 3). So, the correct answer is (a) .

To factor the expression -2bk² - 4bk + 30b, we first need to factor out the greatest common factor of -2b.

-2b(k² + 2k - 15)

Next, we need to factor the quadratic expression k² + 2k - 15.

We can find two numbers that multiply to -15 and add up to 2 by using trial and error or by using the quadratic formula. The two numbers are 3 and -5.

Therefore, we can write:

-2b(k + 5)(k - 3)

Therefore, the correct answer is (a) -2b(k + 5)(k - 3).

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The displacement over the interval is 0 and the distance over the interval is 27 meters

Given that

Velocity, v(t) = 3t² – 6t

Integrate to get the displacement function

So, we have

d(t) = t³ - 3t²

The interval is [0, 3]

So, we have

d(0) = 0³ - 3(0)² = 0

d(3) = 3³ - 3(3)² = 0

The displacement over the interval is 0

Recall that

v(t) = 3t² – 6t

So, we have

v(3) = 9

So, we have

distance = speed * time

This gives

distance = 9 * 3

Evaluate

distance = 27 meters

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