40 Members of arwick youth club go on a trip to a leisure centre they go in minibuses that can each seat up to 15 people. It costs £30 for each minibus and £150 for the group to have use of the leisure centre. How much will the trip cost per person

Answer:

• x-intercept: (-1.5, 0).

• y-intercept: (0, 1).

Explanation:

Given the function:

(a)x-intercept

The x-intercept is the value of x at which f(x)=0.

When f(x)=0

The x-intercept is located at (-1.5, 0).

(b)y-intercept

The y-intercept is the value of f(x) at which x=0.

When x=0

The y-intercept is at (0, 1).

(c)Graph

The graph of f(x) is given below:

Answer:

-1

Step-by-step explanation:

the slope of the line is given by the equation m=(y2-y1)/(x2-x1)

here the line passes with the coordinate (-2,0),(0,-2)

m=(-2-0)/(0-(-2))

 = -2/2

 = -1

The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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The y3(t) ≠ y1(t) + y2(t), the system is not linear.

To show that the system is not linear, we need to check if it follows the properties of linearity: superposition and homogeneity.

A counter-example can help demonstrate that these properties do not hold for the given system.
System definition: y(t) = |a(t-1)|
Let's consider two arbitrary inputs a1(t) and a2(t) with their respective outputs y1(t) and y2(t):
1. y1(t) = |a1(t-1)|
2. y2(t) = |a2(t-1)|
Now let's apply the superposition principle:
a3(t) = a1(t) + a2(t)
Let's find the output y3(t) for a3(t) and check if it's equal to y1(t) + y2(t):
y3(t) = |a3(t-1)| = |a1(t-1) + a2(t-1)|
Now let's check if y3(t) = y1(t) + y2(t):
y1(t) + y2(t) = |a1(t-1)| + |a2(t-1)|
Since we cannot guarantee that |a1(t-1) + a2(t-1)| = |a1(t-1)| + |a2(t-1)| for all possible inputs a1(t) and a2(t), we can conclude that the given system is not linear.

Here is a counter-example:
Let a1(t) = 1 for all t and a2(t) = -1 for all t.
Then, a3(t) = a1(t) + a2(t) = 0 for all t.
The outputs will be:
1. y1(t) = |a1(t-1)| = |1|
2. y2(t) = |a2(t-1)| = |-1|
3. y3(t) = |a3(t-1)| = |0|
Now, let's compare y3(t) with y1(t) + y2(t):
y3(t) = 0, but y1(t) + y2(t) = 1 + 1 = 2.

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Answer:

1428.28

Step-by-step explanation:

Answer:

A sample of 595 should be obtained.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

Estimate of 0.55

This means that \(\pi = 0.55\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

What sample size should be obtained if she wishes the estimate to be within a margin of error of 0.04?

This is n for which M = 0.04. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 1.96\sqrt{\frac{0.55*0.45}{n}}\)

\(0.04\sqrt{n} = 1.96\sqrt{0.55*0.45}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.55*0.45}}{0.04}\)

\((\sqrt{n})^2 = (\frac{1.96\sqrt{0.55*0.45}}{0.04})^2\)

\(n = 594.2\)

Rounding up,

A sample of 595 should be obtained.

The volume of the circular cylinder be,

⇒ 62.8 mm³

Given that,

For a circular cylinder,

Height = 5 mm

Radius = 2 mm

Then we have to find the volume of this circular cylinder

Since we know that,

The right circular cylinder is a cylinder with circular bases that are parallel to each other. It's a three-dimensional form. The axis of the cylinder connects the centers of the cylinder's two bases.

This is the most frequent sort of cylinder encountered in daily life. The oblique cylinder, on the other hand, does not have parallel bases and resembles a skewed construction.

volume of circular cylinder = πr²h

Here we have,

r = 2 mm

h = 5 mm

Now put the values into the formula we get,

Volume = π x 2² x 5

             = 62.8 mm³

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The value of x is 24 and different angles of hexagon will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

An angle is a geometric shape that is defined as the amount of rotation that occurs between two straight lines or planes. Angles are measured in degrees, with 360° representing a full circle.

We need to apply the inverse tangent function to determine the angle at which the sun strikes the flagpole. We are aware that the triangle's adjacent side is 42 feet long and its opposite side is 25 feet tall (the height of the flagpole) (the length of the shadow).

Given the figure is hexagon,

the sum of angles of a hexagon is 720,

Upon adding the given angles,

mA = (7x-8)°

mB (4x+46)°

mC = (5x)

mD = (6x+12)°

mE = (x+7)°

mF = (5x-9)°

⇒ 7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720

⇒ 28x + 48 = 720

⇒ 28x = 672

⇒ x = 24

Therefore, the angles will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

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Answer:

v = 5

Step-by-step explanation:

Collect like-terms:

\(8v = 3v + 25\)

\(8v - 3v = 25\)

\(5v = 25\)

Divide both sides by 5 to make v the subject:

\(v = 5\)

Answer:

(a) 3, (b) 96, (c) No

Step-by-step explanation:

(a) Since we have \(p = 150 - 6q^2\) and \(p = 10q^2 + 2q\), we can set up a quadratic equation by \(150 - 6q^2 = 10q^2 + 2q\), moving all values to one side.

The equation is: \(16q^2 + 2q - 150 = 0\).

Let's use the quadratic formula to find q,

we obtain that \(q = 3\) or \(q = -3.125\)

We can ignore \(-3.125\) because supplying a negative quantity is impossible.

Hence, the answer of (a) is 3

(b) Simply substitute \(q = 3\) into either equations given in the question to find p, and the answer of (b) is 96.

(c) We want to find if there is an exact quantity that makes the TR exactly 1500.

We substitute TR = 1500,

\(1500 = 85q - 2q^2\)

Use the quadratic formula again, and we will find that the answer is "undefined".

As a result, there is not output level in which the total revenue is exactly 1500.

Answer:

Length = 5 feet

Breadth = (5/3) feet

Height(depth) = 2 feet

Volume of the entire tank = Length x Breadth x Height  

                                         = \(5 \times \frac{5}{3} \times2 = \frac{50}{3}\)   ----------(1)

Water is filled upto a height of (1/3) feet

Volume of water in the tank = Length x Breadth x Height  

                                           = \(5 \times \frac{5}{3} \times \frac{1}{3} = \frac{25}{9}\)     -------------(2)

Volume of space needed to be filled = (1) - (2)

                                                         = \(\frac{50}{3} -\frac{25}{9} = \frac{150-25}{9} = \frac{125}{9} cubic feet\)

                                           OR

Height of tank needed to be filled = 2 - (1/3) = (5/3) feet

Volume of space =  Length x Breadth x Height of empty tank

                           =  \(5 \times \frac{5}{3} \times \frac{5}{3} = \frac{125}{9} cubic \ feet\)

Answer:

C. 1/10

Step-by-step explanation:

Answer: Yes, this is a linear function between P and M.

Step-by-step explanation:

We can define a function as a relation between two or more variables, like y = f(x).

This function, maps the elements x (the input) into elements y (the output).

We have a rule for a function: Each input x can be mapped into only one output y.

In this case, we have:

P = 0.15*M + 20.

Let's prove that each value of M is related to only one value of P.

Suppose that, for a given M0, we have:

0.15*M0 + 20 = p1

and also for M0, we have:

0.15*M0 + 20 = p2

This means that p1 = p2, so we can not have different outputs for the same input.

This is a linear relation, so each value of M is related to only one value of P.

Then this is a function P(m) = 0.15*M + 20.

Answer:

597.25 m

Step-by-step explanation:

We need to find 77% of 775.66 m.

It can be calculated as follows :

\(77\%\times 775.66\\\\=\dfrac{77}{100}\times 775.66\\\\=597.25\ m\)

So, 77% of 775.66 m is equal to 597.25 m.

Answer:

100 wizards in magic club

Step-by-step explanation:

20% of 120 is 20 so

120-20=100

Answer: 583333 1/3

Step-by-step explanation:

you divide 1 3/4 millioin/3 = 583333 1/3

Answer:

The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

Step-by-step explanation:

What is probability?

Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.

To find which 2 books describe a pair of dependent events:

A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.

Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.

Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.

Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.

Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

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The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Using law of cosine and Pythagorean theorem, the length of BC is 18 foot and CD is 12.3 foot

a) To find the length of support member BC, we can use the Law of Cosines:

BC^2 = AC^2 + AB^2 - 2 * AC * AB * cos(m/C)

where m/C is the measure of angle C. We know that m/A = 40° and m/D = 45°, so m/C must be the supplementary angle to the sum of these angles:

m/C = 180° - (m/A + m/D) = 180° - (40° + 45°) = 95°

Substituting known values into the Law of Cosines equation, we have:

BC^2 = 10^2 + 8^2 - 2 * 10 * 8 * cos(95°)

BC^2 = 100 + 64 + 160

BC^2 = 324

BC = sqrt(324) = 18

So, the length of support member BC is 18 feet to the nearest hundredth of a foot.

b) To find the length of cable CD, we can use the Pythagorean Theorem:

CD^2 = BC^2 + AC^2 - 2 * BC * AC * cos(m/A)

Substituting known values into the equation, we have:

CD^2 = 18^2 + 10^2 - 2 * 18 * 10 * cos(40°)

CD^2 = 324 + 100 - 360 * cos(40°)

CD^2 = 424 - 360 * cos(40°)

Using the cosine formula, we can find the value of cos(40°):

cos(40°) = cos(90° - 40°) = sin(40°)

And using a reference table or calculator, we find that sin(40°) = 0.766

So, substituting the value of cos(40°) back into the equation for CD^2, we have:

CD^2 = 424 - 360 * 0.766

CD^2 = 424 - 276.56

CD^2 = 147.44

CD = sqrt(147.44) = 12.3

So, the length of cable CD is 12.3 feet to the nearest hundredth of a foot.

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\(7.24 * 10^4 - 7.21 * 10^3\) in scientific notation is \(6.519 * 10^4\).

What is scientific notation?

Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.

To subtract these two numbers, we need to make sure they have the same exponent. We can do this by rewriting \(7.21 * 10^3\) as \(0.721 * 10^4\) (since \(7.21 * 10^3 = 0.721 * 10^4\)).

Now we can perform the subtraction:

\(7.24 * 10^4 - 0.721 * 10^4 = 6.519 * 10^4\)

Therefore, \(7.24 * 10^4 - 7.21 * 10^3\) in scientific notation is \(6.519 * 10^4\).

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We will see that the probabilities are:

First, the probability of getting a particular color of marker is given by the quotient between the number of markers of that color and the total number of markers

There are:

9 red markers.

5 blue markers.

14 yellow markers

8 green markers.

For a total of: 9 + 5 + 14 + 8 = 36.

a) P(yellow, then red)

First, the probability of getting a yellow marker is:

p = 14/36.

Then the probability of getting a red marker (notice that now there are 35 markers in total) is:

q = 9/35.

Then the joint probability is:

P(yellow, then red) = p*q = ( 14/36)*(9/35) = 0.1

b) P(blue, then green)

First, the probability of getting a blue marker is:

p = 5/36.

After, the probability of getting a green marker is:

q = 8/35.

So the joint probability is:

P(blue, then green) = (5/36)*(8/35) = 0.03

c) P(both red).

First, the probability of getting a red marker is:

p = 9/36

Now there are 8 red markers and 35 markers in total, so the probability of getting another red marker is:

q = 8/35

The joint probability is:

P(both red) = (9/36)*(8/35) = 0.06

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Answer: C. 3 cups

Step-by-step explanation:

Given: In recipe for 5 people, Required Gulf shrimp = \(1\dfrac14\) cups

Since, \(1\dfrac14=\dfrac{5}{4}\)

Required Gulf shrimp = \(\dfrac54\) cups

Then, for 1 people Gulf shrimp required = \(\dfrac{5}{4}\div 5\)

\(=\dfrac54\times\dfrac{1}{5}\)

\(=\dfrac14\) cup

For 12 people, it is required = \(12\times\dfrac14 = 3\text{ cups}\)

Hence, 3 cups of gulf shrimp is required for new recipe.

So, correct option is C. 3 cups

Answer:

2(2w) + 2(w) = 390

6w = 390

w = 65

2w or l = 130 feet

Answer:

The probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525

Step-by-step explanation:

\(Mean = \mu = 3.25 inches\)

Standard deviation = \(\sigma = 0.15 inches\)

We are supposed to determine the probability that a randomly chosen part has diameter of 3.5 inches or more

\(P(Z \geq 3.5)=1-P(z<\frac{x-\mu}{\sigma})\\P(Z \geq 3.5)=1-P(z<\frac{3.25-3.5}{0.15})\\P(Z \geq 3.5)=1-P(z<-1.67)\)

Refer the z table for p value

\(P(Z \geq 3.5)=1-0.0475\\P(Z \geq 3.5)=0.9525\)

Hence  the probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525