Y is directly proportional to x
When y=30 x=6
work out an equation connecting y and x

From the calculations, we can see that each of the external angles of the polygon would have a measure of  60 degrees.

The external angles of a polygon are the angles formed by extending one side of the polygon and forming a new angle with the adjacent side. To find the external angle of a polygon, you can use the following formula:

External angle = 360° / number of sides

In this case we have been told that what we have is a hexagon thus;

4xternal angle is; 360/6

= 60 degrees

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Answer:

The mean is 19.6. you have to add up all the numbers given and divide it by the number of numbers which in this case it's 18+18+19+21+22=98

98/5=19.6

The median is the middle number when you arrange the numbers in order therefore it's 19

The mode is that number which appears the multiple time in the numbers given therefore it's 18

The probability of rolling a number less than 7 would be written as 1/1 or simply 1.

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.

Without additional information, it's impossible to determine the probability of an event being less than 7. We need to know the context of the situation and the possible outcomes that can occur to calculate the probability.

However, if we assume that the context is related to rolling a fair six-sided die, then the probability of rolling a number less than 7 is 1 because all the possible outcomes (1, 2, 3, 4, 5, and 6) are less than 7.

In fraction form, the probability of rolling a number less than 7 would be written as 1/1 or simply 1.

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The probability of getting a card less than 7 would be 0.75. So, p( less than 7) in fraction form will be 3/4.

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.

The given cards are numbered as:

s = [4,5,6,7]

n(s) = 4

The event here is the probability of picking the cards less than 7

Cards less than 7 i.e. 4,5,6

n(e) = 3

Probability of picking the card lesser than 7 is:

P(e) = n(e)/n(s)

P(e) = 3/4

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The complete question is as follows:

You pick a card at random. 4 5 6 7 What is P(less than 7)? Write your answer as a fraction or whole number.

p = probability.

The nurse should administer 19.958 mg of furosemide per dose to the toddler.

To use the unitary method, we need to convert the toddler's weight from pounds to kilograms, as the dose is given in mg/kg/day.

1 lb = 0.45359237 kg (conversion factor)

Therefore, the toddler's weight in kilograms is

22 lb x 0.45359237 kg/lb = 9.979 kg (rounded to three decimal places)

Now we can calculate the total daily dose of furosemide for the toddler

4 mg/kg/day x 9.979 kg = 39.916 mg/day (rounded to three decimal places)

Since the dose is divided into 2 equal doses daily, each dose would be half of the total daily dose

39.916 mg/day ÷ 2 = 19.958 mg/dose (rounded to three decimal places)

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Let's start by finding out how much money Keiko spent on coffee. She started with an $80 gift card and ended up with $43.15 left, so she spent:

$80 - $43.15 = $36.85

We also know that the coffee costs $7.37 per pound. Let's use "x" to represent the number of pounds of coffee Keiko bought. Then we can set up an equation:

$7.37x = $36.85

To solve for x, we can divide both sides by $7.37:

x = $36.85 ÷ $7.37

x = 5

So Keiko bought 5 pounds of coffee.

Answer:

1080

Step-by-step explanation:

the perimeter of the field is 2(80) + 2(100) or 360

if he goes around the field 3 times then its 3*360 or 1080

~lmk if u got Qs

Answer:

A is definitely correct and possibly C as well

Step-by-step explanation:

Wyatt is correct so it’s not B or D and E doesn’t make sense.

The value of the given integral function is 10 and option d is the correct answer.

Any function that may be drawn without removing the pen from the page is said to be continuous. Formally, a function f(x) is continuous at a point c if all three of the following criteria are true:

Definition of f(c) (i.e., c is in the domain of f).

When x gets closer to c, f(x) reaches its maximum.

The limit of f(x) as x gets closer to c equals f. (c).

A function is said to be continuous if it is continuous over its whole domain. In mathematics and the sciences, continuous functions have a wide range of useful features and applications.

For the given function the integral can be written as follows:

[tex]\int\limits^2_{-4} {f(x)} \, dx = \int\limits^0_{-4} {\frac{x^2}{|x|} } \, dx + \int\limits^2_0 {\frac{x^2}{|x|} \, dx[/tex]

[tex]= [\frac{x^2}{2} ]_{-4}^0 + [\frac{x^2}{2} ]_{0}^2\\= 8 + 2\\= 10[/tex]

Hence, the value of the given integral function is 10 and option d is the correct answer.

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The number of cupcakes that were sold in each of the hours between 4 and 6 o’ clock is 24 cupcakes.

Since the total number of cupcakes that were sold is equal to 9 dozen cupcakes.

Total number of cupcakes = 9 * 12 = 108 cupcakes.

Since c is the number of cupcakes that were sold in each of the hours between 4 and 6 o’ clock.

We can write an equation that represents the total number of cupcakes sold as follows:

36 + 24 + c + c = 108

Solve for c:

36 + 24 + c + c = 108

36 + 24 + 2c = 108

60 + 2c = 108

2c = 108 - 60

2c = 48

c = 48/2

c = 24

Therefore, the number of cupcakes that were sold in each of the hours between 4 and 6 o’ clock is 24 cupcakes.

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Answer:

It is known as many things

Step-by-step explanation:

Kite, Dart, Arrowhead. Kites can be concave or convex. It can also be called a reflexed polygon.

Answer:

[tex]the \: shape \: above \: is \: a \\ \: concave \: polygon[/tex]

Answer:

the healthy fruit is 77.07

and the spoiled fruit is 20.19

Step-by-step explanation:

the explanation is a little long but if you want one just ask in the comments and ill edit this

Answer:

34

Step-by-step explanation:

1)Simplify 5−2 to 3

2+5+6+7×3

2)Simplify 7×3  to 21.

2+5+6+21

3)Simplify 2+5  to 7.

7+6+21

4)Simplify 7+6 to 13.

13+21

5)Simplify.

34

Step-by-step explanation:

decimal interest = .06

$ interest = prt

                = $ 1730 * .06 * 4 = $ 415.20

The measure of arc BC is 264°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

Since the triangle is isosceles, this means that angle B = angle C

therefore angle A = 180- ( 24+24)

= 180- 48

= 132°

From the theorem that says that the angle at the circumference is twice the angle at the centre.

therefore arc BC = 2 × 132

arc BC = 264°

therefore the measure of arc BC is 264°

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According to given information, the area of kite is 480 m².

What is area of kite?

The area of a kite can be calculated by multiplying the lengths of its two diagonals and dividing the result by 2:

Area of kite = (diagonal 1 x diagonal 2) / 2

The hypotenuse is usually the slanted line in a triangle.

Area of a kite = pq/2 (p and q = diagonal)

Finding the missing side length of triangle₁

37² = 12² + x² (x = unknown side length)

=> 1369 = 144 + x² (x = unknown side length)

=> 1369 - 144 = x² (x = unknown side length)

=> 1225 = x² (x = unknown side length)

=> x = 35 m

Finding the area:

Area of a kite = pq/2 (p and q = diagonal)

=> Area of a kite = (35 + 5)(12 + 12)/2

=> Area of a kite = (40)(24)/2

=> Area of a kite = 40 x 12 = 480 m².

Therefore, the area of kite is 480 m².

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Step-by-step explanation:

[tex] \sqrt{x} = {x}^{ \frac{1}{2} } [/tex]

Its like because when you try to cut down it would be

[tex] {}^{2} \sqrt{ {x}^{1} } [/tex]

So to simplify things down it would be

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

The nth term from the quadratic sequence  "2, 8, 18, 32, 50,..." Would be 2n², where n reffers to the position of number.

By observation and by trial and error.

The first term, n = 1    = 2*1*1 = 2

Second term, n =2,     = 2*2*2 = 8

Third term , n =3,                = 2*3*3 = 18

Third term, n = 4,       = 2*4*4 = 32

Fourth term, n =5,     2 * 5* 5 = 50

For nth term,        2 *n *n = 2n²

Therefore the nth term of quadratic sequence would be 2n².

Sequences with a term are referred to as quadratic sequences. The fact that the first differences between terms are not equal but the second differences between terms are can be used to identify them.

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Answer:

The answer is B

Step-by-step explanation:

The asymptote of this graph is -4. If you look at the bottom of the graph, the line is going flat to -4, that means it's the asymptote. B has the only option where -4 occurs. Therefore, it's B.

Hope this helps.

The required probability of waiting taxi longer than one hour and waiting for one hour is equals to 0.0821 and 0.1725 respectively.

Use the exponential distribution formula,

For an exponentially distributed random variable X with mean μ, the probability density function is given by,

f(x) = (1/μ) × e^(-x/μ)

And the cumulative distribution function is ,

F(x) = P(X ≤x)

      = 1 - e^(-x/μ)

Mean time between taxi arrivals is 24 minutes,

Rate parameter

λ = 1/μ

  = 1/24.

Probability of waiting longer than one hour for a taxi,

Probability that the time between arrivals is greater than 60 minutes. Using the cumulative distribution function,

P(X > 60)

= 1 - P(X ≤ 60)

= 1 - (1 - e^(-60/24))

= e^(-2.5)

≈ 0.0821

Probability of waiting longer than one hour for a taxi is approximately 0.0821.

Already been waiting for one hour,

the time you have to wait for the next taxi to arrive is 10 minutes.

Using the cumulative distribution function,

P(X ≤70 | X > 60)

= P(60 < X ≤ 70) / P(X > 60)

= (1 - e^(-70/24) - (1 - e^(-60/24))) / e^(-60/24)

≈ 0.1725

Therefore, the probability of waiting longer than one hour for a taxi is and that a taxi arrives within the next 10 minutes waiting for one hour is equals to 0.0821 and 0.1725 respectively.

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The above question is incomplete, the complete question is:

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 24 minutes. (a) What is the probability that you wait longer than one hour for a taxi? (b) Suppose you have already been waiting for one hour for a taxi, what is the probability that one arrives within the next 10 minutes? Round your answers to 4 decimal places.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=2000(1.08)^{10} \implies A \approx 4317.85[/tex]

a)The probability that at least 10 of the 15 randomly chosen individuals have no citations is 0.6723.  b) the probability that fewer than half of the 15 randomly chosen individuals have at least one citation is 0.3826. c) the probability that the number of individuals among 15 who have at least one citation is between 5 and 10, inclusive, is 0.7278.

Recall that in Exercise 30 (Section 3.3) the pmf of Y, the number of traffic citations for a randomly selected individual insured by a particular company, was given as follows:

Y=y 0 1 2 3 4 5

P(Y=y) 0.52 0.29 0.10 0.05 0.03 0.01

a. We can use the binomial distribution to model the number of individuals among 15 who have no citations, with the probability of success being P(Y=0)=0.52. Then, the probability of at least 10 individuals having no citations is:

P(X >= 10) = 1 - P(X < 10) = 1 - P(X <= 9)

Using a binomial table or calculator, we find that:

P(X <= 9) = 0.3277

Therefore,

P(X >= 10) = 1 - P(X <= 9) = 1 - 0.3277 = 0.6723

b. We can use the binomial distribution again to model the number of individuals among 15 who have at least one citation, with the probability of success being P(Y>0)=1-P(Y=0)=1-0.52=0.48. Then, the probability of fewer than half (less than 7) individuals having at least one citation is:

P(X < 7) = Σ P(X = k), where k = 0,1,...,6

Using a binomial table or calculator, we find that:

P(X < 7) = 0.6174

Therefore,

P(X >= 7) = 1 - P(X < 7) = 1 - 0.6174 = 0.3826

c. We need to find the probability that the number of individuals among 15 who have at least one citation is between 5 and 10, inclusive. We can use the binomial distribution with the probability of success being P(Y>0)=0.48. Then, the probability is:

P(5 <= X <= 10) = Σ P(X = k), where k = 5,6,...,10

Using a binomial table or calculator, we find that:

P(5 <= X <= 10) = 0.7278

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Your question is incomplete, but probably the complete question is :

Exercise 30 (Section 3.3) gave the pmf of Y, the number of traffic citations for a randomly selected individual insured by a particular company. What is the probability that among 15 randomly chosen such individuals

a. At least 10 have no citations?

b. Fewer than half have at least one citation?

c. The number that have at least one citation is between 5 and 10, inclusive?*

When P(opposed | Grade 12) exceeds P(Grade 12 | opposed), the correct response is: P(opposed | Grade 12) P(opposed | Grade 12) (Option C)

An arrangement of things in a particular order is known as a permutation in mathematics. In more detail, an arrangement of a set's members in a certain order is known as a permutation. To give one example, the set 1, 2, 3 contains six permutations: 1, 2, 3, 1, 2, 3, 1, and 3, 2, 1. The formula P(n, r) is frequently used to express permutations, which are the various methods to select r things from a group of n objects and arrange them in a particular order. P(n, r) has the following formula: P(n, r) equals n!/(n-r)!  where the factorial of n is represented by n! (i.e., the product of all positive integers from 1 to n).

given

Using Bayes' theorem, we can contrast P(Grade 12 | opposed) with P(grade 12 | opposed):

Grade 12 opposition formula: P(opposed) = P(Grade 12 opposition) * P(opposed) / P (Grade 12)

The table contains the values we require:

P(grade twelve) = (12+6+11)/(5+3+9+8+12+9+15+16+10+12+6+11) = 0.15 P(opposition) = (3+12+16+6)/(5+3+9+8+12+9+15+16+10+12+6+11) = 0.5 P(opposition | grade twelve) = 6/(12+6+11) = 0.24

Although we do not directly know the value of P(Grade 12 | opposed), we can calculate it using the following formula:

P (12th grade | opposed) = P (12th grade | opposed) * P (12th grade | opposed) / P (12th grade | opposed) = 0.24 * 0.15 / 0.5 = 0.072

As a result, we have:

P (12th grade | opposed) = 0.072 P (12th grade | opposed) = 0.24

When P(opposed | Grade 12) exceeds P(Grade 12 | opposed), the correct response is: P(opposed | Grade 12) P(opposed | Grade 12) (Option C) .

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The sprinkler will water an area of approximately 1519.76 square feet.

Area is the measurement of the size of a surface or region. It is usually measured in square units such as square meters, square feet, or square inches.

The area watered by the sprinkler can be calculated using the formula for the area of a circle:

Area = πr²

where r is the radius of the circle.

In this case, the radius of the sprinkler's spray is given as 22 ft. So, we can substitute this value in the formula:

Area = π(22 ft)²

Area = π(484 ft²)

Area = 1519.76 ft² (rounded to two decimal places)

Therefore, the sprinkler will water an area of approximately 1519.76 square feet.

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Using concrete pavers for the patio flooring is a cost-effective and durable option for Mr. Manley's project. Approximately 176 pavers will be needed to cover the 3.2 m x 5.0 m area of the patio.

Based on Mr. Manley's request for the most economical option for the patio flooring, I would suggest using concrete pavers. Concrete pavers are a durable and cost-effective option for outdoor flooring. They come in various shapes, sizes, and colors, allowing for a range of design options. To calculate the number of pavers needed, we first need to determine the total area of the patio. The formula for the area of a rectangle is length times width, so the area of the patio is 3.2 m x 5.0 m = 16 square meters. Next, we need to determine the size of the pavers. Let's assume we use 30 cm x 30 cm pavers. To cover 1 square meter with these pavers, we will need 11 pavers (100 cm / 30 cm = 3.33 pavers per meter, and 3.33 x 3.33 = 11.11 pavers per square meter, rounded to 11). Therefore, to cover the 16 square meter patio, we will need approximately 176 pavers (11 pavers per square meter x 16 square meters = 176 pavers).

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Part A: Two-way radio A covers approximately 201 square miles.

Part B: Two-way radio B covers approximately 483 square kilometers.

Part C: Two-way radio A covers the larger area.

Part D: The scale factor relationship between the radio coverages is approximately 0.8746.

What is area of circle?

The area of a circle can be found using the formula A = πr², where A is the area and r is the radius of the circle.

Part A: For two-way radio A, the radius is 8 miles, so the area covered by the radio is:

A = π8²

A = 64π

A ≈ 201 square miles

Therefore, two-way radio A covers approximately 201 square miles.

Part B:For two-way radio B, the radius is 11.27 kilometers. We need to convert this to miles in order to use the formula for the area of a circle.

1 kilometer is equal to 0.621371 miles (to 6 decimal places).

So, 11.27 kilometers is equal to: 11.27 km × 0.621371 mi/km = 7.00142 miles

Now, we can find the area covered by two-way radio B:

A = π(7.00142)²

A = 153.94π

A ≈ 483 square kilometers

Therefore, two-way radio B covers approximately 483 square kilometers.

Part C:

We can compare the areas covered by the two-way radios by using their respective areas calculated in Part A and Part B.

Area covered by two-way radio A = 201 square miles

Area covered by two-way radio B = 483 square kilometers

We need to convert the area covered by two-way radio B to square miles in order to compare the two areas. We know that 1 mile is equal to 1.61 kilometers, so:

1 square mile = (1.61)² square kilometers

1 square kilometer = (1/1.61)² square miles

1 square kilometer = 0.386 square miles (rounded to 3 decimal places)

Therefore, the area covered by two-way radio B in square miles is:

483 km²× 0.386 mi²/km² ≈ 186 square miles

Now we can compare the two areas:

Area covered by two-way radio A = 201 square miles

Area covered by two-way radio B = 186 square miles

Since 201 is greater than 186, two-way radio A covers the larger area.

Part D:

To determine the scale factor relationship between the radio coverages, we can compare their radii.

The radius of two-way radio A is 8 miles.

The radius of two-way radio B is 11.27 kilometers, which is approximately 6.997 miles (as calculated in Part B).

The scale factor is the ratio of the radii of the two circles.

So,scale factor = radius of two-way radio B / radius of two-way radio A

scale factor = 6.997 / 8

scale factor ≈ 0.8746

Therefore, the scale factor relationship between the radio coverages is approximately 0.8746.

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Answer:

B

Step-by-step explanation:

The length of the rope in this scenario is 33.912 meters based on given diameter.

To find the length of the rope wound around the cylindrical pipe, we need to take the circumference of the pipe and the number of times the rope is wound around it.

The diameter of the pipe is given as 600 mm, which means the radius is half of that, or 300 mm. To find the circumference, we use the formula C = 2πr, where π is pi (approximately 3.14) and r is the radius. Therefore, the circumference of the pipe is 2 x 3.14 x 300 = 1884 mm.

The rope is wound around the pipe 18 times, so the total length of the rope is 18 times the circumference of the pipe, which is 18 x 1884 = 33,912 mm or 33.912 meters.

To calculate or find the length of the rope wound around the cylindrical pipe, we multiply the circumference of the pipe by the number of times the rope is wound around it. Therefore, the length of the rope in this scenario is 33.912 meters.

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Answer:

Expanding the function:

[tex](x+6)^4\\[/tex]

You should get this:

[tex]x^4+24x^3+216x^2+864x+1296[/tex]

Step-by-step explanation:

Hope it helps

Answer:

Step-by-step explanation:

yes yes no 180 which is an angle of time

Answer:

. yes no.180 is angle of time

Answer: : The point (4,5)

Step-by-step explanation: