kyra coverted some australian dollars to pounds she received £67.50
kyra coverted some australian dollars to pounds she received £67.50

The circumference of the given circle is 14π mm.

We have,

The circumference of a circle with radius r is given by the formula:

C = 2πr

In this case,

The radius of the circle is given as 7 mm.

Substituting the value of r in the above formula.

C = 2π(7) mm

Simplifying this expression, we get:

C = 14π mm

Therefore,

The circumference of the given circle is 14π mm.

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Therefore, the dimensions of the rectangular plot are either 20 meters by 11 meters or 11 meters by 20 meters.

Let's assume that the length of the rectangular plot is x meters. Then the width would be (220/x) meters because we know that the area is 220 square meters.

The perimeter of the rectangular plot would be:

2x + 2(220/x) = 62

Simplifying this equation, we get:

2x^2 + 440 = 62

2x^2 - 62x + 440 = 0

x^2 - 31x + 220 = 0

Factoring this equation, we get:

(x - 20)(x - 11) = 0

Therefore, x = 20 or x = 11.

If x = 20, then the width would be 11 and if x = 11, then the width would be 20.

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Evaluating the function we can see that:

a) f(7) is equal to f(-7)

b) f(-10) is greater than f(3).

Here we have the quadratic function f(x) = x²

A) First we need to evaluate the function in x = 7 and x = -7 to see which one gives a larger value.

f(7) = 7² = 49

f(-7) = (-7)² = 49

Then neither of these two is greater, because are the same value.

B) now we need to evaluate in x = -10 and x = 3

f(-10) = (-10)² = 100

f(3) = 3² = 9

We can see that f(-10) is greater.

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The sample space has 13 outcomes.

We have to given that;

A player randomly selects a marble from a bag.

And, In the bag which has 5 blue marbles, 6 red, 1 orange, and 1 yellow.

Since, The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Now, We can formulate;

Total number of marbles = 5 + 6 + 1 + 1

Total number of marbles = 13

Hence, there are 13 possible outcomes for the player's selection.

Therefore, We get;

The sample space has 13 outcomes.

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Answer:

$21.78

Step-by-step explanation:

2.79 X 5 = 13.95

13.95 + 7.83 = 21.78

The answers are explained below.

Given are the questions to be solved with the help of proportionality,

Let the unknown values be x,

a) 32 / x = 8 / 6

x = 24

Hence the height of the tree is 24 ft.

b) 3.5 / 5 = x / 3

x = 2.1

Hence the cups of flour needed is 2.1 cups.

c) 2 / 90 = 5 / x

x = 225

Hence 5 cubic ft sand will weigh 225 lbs.

d) 18.50 / 35 = 12.50 / x

x = 23

Hence $12.5 will costs for 23.

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The expected gain or loss from playing the game 15 times is -$75.00, indicating an expected loss of $75.00.

To determine the expected gain or loss from playing the game 15 times, we need to calculate the expected value.

The probability of getting three tails (winning) in a single coin toss is (1/2) * (1/2) * (1/2) = 1/8, since each coin toss is independent and has a 1/2 probability of landing tails.

The probability of losing in a single coin toss is 1 - 1/8 = 7/8.

If we play the game 15 times, the expected number of wins is (1/8) * 15 = 15/8, and the expected number of losses is (7/8) * 15 = 105/8.

The amount gained from winning is $10, and the amount lost from losing is $2.

Therefore, the expected gain or loss can be calculated as follows:

Expected gain or loss = (Expected number of wins * Amount gained) - (Expected number of losses * Amount lost)

= (15/8 * $10) - (105/8 * $2)

Simplifying this expression, we find:

Expected gain or loss = $187.50 - $262.50

= -$75.00

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ANSWER:

(-4,-4)

EXPLANATION:

Just simply multiply the two points by 2. Since -2*2 is equal to -4, then the answer would be (-4, -4).

The attributes, measurements used, and observations of the data are listed  below:

Attributes:

- Light bulb

- Wattage (number of watts of electricity used)

Measurements used:

- Watts (units of measurement for the amount of electricity used by a light bulb)

Observations:

- The data shows the wattage for different types of light bulbs.

- The wattage varies widely among different types of light bulbs.

- Incandescent bulbs have the highest wattage, followed by halogen bulbs, fluorescent bulbs, and LED bulbs.

- The wattage for each type of bulb can vary within a certain range, with some bulbs having higher or lower wattage than others within the same category.

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Answer:

Step-by-step explanation:

The rectangular equation that represents the polar equation r = (cot²θ)(csc θ) is y³ = x², which is an option (d).

The polar equation r = (cot²θ)(csc θ) can be written in rectangular form using the relationships x = r cos θ and y = r sin θ.

Substituting these expressions into the polar equation, we get:

r = (cot²θ)(csc θ)

r = (cos θ/sin θ)²(1/sin θ)

r = cos² θ/sin³ θ

x = r cos θ = cos³ θ/sin³ θ

y = r sin θ = cos² θ/sin² θ

As per the variable of x and y,

y³ = x².

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The sum of the measures of the angle of a triangle is 180 degrees.

The given triangle is a type of triangle and the type of triangle a scalene triangle.

For a scalene triangle, the measure of the three sides are unequal and the sum of the interior angle of a triangle is 180 degrees.

Hence the measure of the angles <A, <B and <C are all less than 90 degrees since they are all acute angles.

We can therefore conclude that:

m<A + m<B + m<C = 180 degrees

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A 95% confidence set for two or more coefficients is a set that contains: D) the population values of these coefficients in 95% of randomly drawn samples.

A 95% confidence set for two or more coefficients is a set that contains the same values as the 95% confidence intervals constructed for the coefficients. This means that the set includes all possible values for the coefficients that are consistent with the observed data and the level of uncertainty indicated by the confidence level. It is important to note that the confidence set is not guaranteed to contain the true population values of the coefficients in 95% of randomly drawn samples, as the true values are unknown.

The confidence set provides a range of plausible values that can be used for inference and decision making. The concept of a 95% confidence set.

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Answer:Yes, because ∛84 = ∛(2 × 2 × 3 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 84 is an irrational number.

Step-by-step explanation:

Answer: i think so

Step-by-step explanation:

Answer:

The area is 12.57, rounded to the nearest then is 13.

Step-by-step explanation:

A=πr2=π·22≈12.56637

Answer:

180 cm³

Step-by-step explanation:

split the side (the side facing us) into three rectangles. one rectangle immediately beneath top step, next under middles step and so on.

area under top step = (2 + 2 + 2) X 3 = 18.

area under middle step = (2 + 2) X 3 = 12

area under bottom step = 2 X 3 = 6

total area of this side (cross-section) = 18 + 12 + 6 = 36.

volume = 36 X length

=  36 X 5

= 180 cm³

Answer:

50.85% increase

Step-by-step explanation:

The formula for % change is (new-old)/old.

So (89-59)/59 = 30/59 = 0.5084745763 = 50.85% increase

Answer:

y=-[tex]\frac{9}{7}[/tex]

Step-by-step explanation:

Answer:

150 square inches

Step-by-step explanation:

The formula is A=2(wl+hl+hw)

Plug in the values.

2(9+33+33)

Evaluate.

=150

(Assuming both the length and width is 3)

Step-by-step explanation:

1:3    means you need to find 1 /(1+3) = 1/4 th of the way to 5,8 from -2,0

x:   from -2 to +5 is 7 units     1/4th * 7 = 7 /4   added to -2

              is  - 1/4

y: from 0 to 8    is 8 units   1/4 th * 8  = 2 added to 0   is   2

(-1/4 , 2)

the maximum value of the function is y = -1 + 6cos(2π/7(26.75-5)) = 5.

The function y = -1 + 6cos(2π/7(x-5)) is a periodic function with a period of 7. The maximum value of the function occurs when the cosine function reaches its maximum value of 1.

So, we need to find the value of x that makes the argument of the cosine function equal to an odd multiple of π/2, which is when the cosine function is equal to 1.

2π/7(x-5) = (2n + 1)π/2, where n is an integer

Simplifying this equation, we get:

x - 5 = (7/4)(2n + 1)

x = 5 + (7/4)(2n + 1)

Since the function has a period of 7, we can restrict our attention to the interval [5, 12].

For n = 0, we get x = 5 + 7/4 = 23/4

For n = 1, we get x = 5 + (7/4)(3) = 26.75

For n = 2, we get x = 5 + (7/4)(5) = 33.25

For n = -1, we get x = 5 + (7/4)(-1) = 1.75

For n = -2, we get x = 5 + (7/4)(-3) = -4.75

Out of these values of x, the only one that lies in the interval [5, 12] is x = 26.75.

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The answer for (1) is 31, the answer for (2) is 25, and the answer for (3) is 17.

It is given that:

In a secondary school class, 23 pupils study Economics, 6 pupils study both Government and Economics. 48 pupils study either Government or Economics or both.

Based on the information we can draw a Venn diagram:

From the Venn diagram:

A + B = 17 + 6

A + B = 23

B = 6

A + B + C = 48

A = 23 - 6 = 17

C = 48 - 17 - 6

C = 25

The total number of pupils who only study Government = 25

The total number of pupils who study Government = 25 + 6 = 31

The total number of pupils who study Economics only = 17

Thus, the answer for (1) is 31, the answer for (2) is 25, and the answer for (3) is 17.

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The probability that the sample contains exactly two defective parts from a production process with a 6% defect rate is 0.0299. Option B is answer

To find the probability, we can use the binomial probability formula. The formula is P(X=k) = (n C k) * (p^k) * ((1-p)^(n-k)), where n is the sample size, k is the number of successes (defective parts), p is the probability of success (defect rate), and (n C k) represents the combination formula.

In this case, n = 5 (sample size), k = 2 (number of defective parts), and p = 0.06 (probability of a part being defective). Plugging these values into the formula, we get P(X=2) = (5 C 2) * (0.06^2) * ((1-0.06)^(5-2)) = 10 * 0.0036 * 0.8464 = 0.0299.

Therefore, the probability that the sample contains exactly two defective parts is 0.0299 (Option B).

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The test statistic if the sample proportion is 20/50 and the hypothesized proportion was 0.5 is:  -1.414.

Using z-test formula to determine the test statistic

z = (p - P) / [tex]\sqrt[/tex]((P(1-P))/n)

Where:

p = sample proportion = 20/50 = 0.4

P = hypothesized proportion = 0.5

n= sample size = 50

Let plug in the formula

Test statistic  = (0.4 - 0.5) / [tex]\sqrt[/tex]((0.5(1-0.5))/50)

Test statistic = (-0.1) / [tex]\sqrt[/tex]((0.25)/50)

Test statistic = (-0.1) / [tex]\sqrt[/tex](0.005)

Test statistic = (-0.1) / 0.0707

Test statistic = -1.414

Therefore the test statistic  is -1.414.

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a.

i. The initial value (IV) is 37.

ii. The percent increase or decrease is 4%.

b.

i. The initial value (IV) of the function is -0.7.

ii. The percent decrease is 40%.

a.

i. The initial value (IV) of the function is 37.

ii. The percent increase or decrease is 4%, because the base of the exponential function is 1.04, which is 1 plus 4% (0.04).

b.

i. The initial value (IV) of the function is -0.7.

ii. The percent decrease is 40%, because the base of the exponential function is 0.6, which is 60% (0.6) of the initial value (-0.7).

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The complete question:

1. For each equation, find the initial value and the percent increase or decrease.

a. f(x) = 37(1.04)ˣ

i. IV:__

ii. % Inc/Dec:_

b. f(x) = (-0.7) (0.6)ˣ

i. IV:

ii. % Inc/Dec:___

Answer:

198 in²

Step-by-step explanation:

triangle (A=1/2)bh [A=1/2(22×8)] b=22 H=8

rectangle (A=bh) [A= 22×5] B=22 H=5

triangle = 88

rectangle = 110

So, 88+110 = 198

By probability , Tom can arrange his 5 red and 5 white books in an alternating pattern in 48 ways

There are 5 red books and 5 white books to arrange in an alternating pattern on the shelf.

To do this, Tom can start with either a red or a white book. If he starts with a red book, he can arrange the rest of the books in 4! (4 factorial) ways. Similarly, if he starts with a white book, he can arrange the rest of the books in 4! ways. Therefore, the total number of ways Tom can arrange the books in an alternating pattern is 2 x 4! = 48.

Tom can arrange the 10 books in an alternating pattern by starting with either a red or a white book. If he starts with a red book, he can arrange the rest of the books in 4! ways, and if he starts with a white book, he can also arrange the rest of the books in 4! ways. Therefore, the total number of ways to arrange the books is 2 x 4! = 48.

Tom can arrange his 5 red and 5 white books in an alternating pattern in 48 ways.

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(a) The people that did not own a car are 13

(b) The sentence to describe the problem is "13 of every 20 people do not own a car"

Given that

Number of friends = 20

Percentage that do not own a car = 65%

Using the above as a guide, we have the following:

People = 65% * 20

Evaluate

People = 13

Writing a sentence to describe the problem, we have:

The statement is given as

65% of people do not own a car".

This can be rewritten as

"13 of every 20 people do not own a car"

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The radius of the golf ball is given as follows:

2.1 feet.

The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

The volume of the ball in this problem is given as follows:

V = 38.7 cubic feet.

Hence the radius of the ball is obtained as follows:

r³ = 3 x 38.7/4π

r³ = 9.2389

[tex]r = \sqrt[3]{9.2389}[/tex]

r = 2.1 feet

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