There are three different types of sandwiches on a shelf.
There are
4 egg sandwiches,
5 cheese sandwiches
and 2 ham sandwiches.
Erin takes at random 2 of these sandwiches.
Work out the probability that she takes 2 different types of sandwiches.
(5 marks)

Answer:

Step-by-step explanation:

sin(3x5)=15

The solution is: the present age of the man is 40 years and the present age of the son is 8 years.

Let us assume the age of the son now = x

Then

The age of the man now = 5x

Now we have to calculate the age of the son and father 9 years ago

Age of the son 4 years ago = x - 4

Age of the man 4 years ago = 5x - 4

Then

5x - 4 = 9(x - 4)

5x - 4 = 9x - 36

5x - 9x = -36 + 4

- 4x = - 32

MUltiplying both sides of the equation by -1 we get

4x = 32

x = 32/4

 = 8

So the present age of the son is 8 years

Present age of the man = 5x

                                      = 5 * 8

                                      = 40 years

So the present age of the man is 40 years and the present age of the son is 8 years.

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complete question:

A man is five times as old as his son. Four years ago, he was nine times as old. Find their present ages.

The value of the functions are;

h(f(g(1/2))) =  (√1/2)³/3

h(f(g(x))) = = (√x)³/3

It is important to note that a function is an equation that shows the relationship between two variables

From the information given, we have that;

f(x) = x³

g(x) = √x

h(x) = x/3

To determine the composite function, we need to substitute the value of one function as the value of x in the other, we have that

f(g(1/2) =

g(1/2) = √1/2

Substitute the value

f(g(1/2) = (√1/2)³

Now, substitute the value as x in h(x)

h(f(g(1/2))) =  (√1/2)³/3

f(g(x)) = (√x)³

Then, h(f(g(x))) = = (√x)³/3

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The amount that Bombinoes would pay for a shift if 15 pizzas were to be delivered would be =$877.5

The amount paid in a shift for each pizza delivered = $56

The amount paid as commission for each pizza = $2.50

Therefore the total amount for each pizza = 56+2.50 =$58.5

Therefore, the total amount of money that would be paid if a total of 15 pizzas were delivered in a shift will be = 15× 58.5 = $877.5

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Using permutations, the word CAMPFIRE can be arranged in 40,320.

A permutation is the number of ways in which a data set can be arranged or ordered.

Order is important in permutations, unlike in combinations.

The word to be arranged in different ways = CAMPFIRE

The number of letters in CAMPFIRE = 8

The formula for permutations is: n! / (n - r)!.

In this formula:

n is the number of letters in the word

r is the number of letters to be arranged

n = 8

r = 8

8! / (8 - 8)!

= 8! / 0!

= 8! / 1 = 8!

= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 40,320

Thus, the word CAMPFIRE can be arranged in 40,320 ways based on the permutation formula.

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The cross section formed by a plane containing a vertical line of symmetry for a tetrahedron can take various shapes, including polygons or curved shapes, depending on the orientation and angle of the intersecting plane.

A tetrahedron is a three-dimensional geometric shape with four triangular faces. If a plane containing a vertical line of symmetry intersects a tetrahedron, the resulting cross section would depend on the orientation and position of the plane relative to the tetrahedron.

In general, there are several possible cross sections that can be formed by a plane containing a vertical line of symmetry for a tetrahedron. The specific shape and characteristics of the cross section would vary based on the angle and position of the intersecting plane.

For example, if the plane intersects the tetrahedron perpendicular to its vertical line of symmetry, the resulting cross section would be a vertical slice through the tetrahedron. This cross section would typically be a polygon with sides formed by the intersecting edges of the tetrahedron's faces.

On the other hand, if the intersecting plane is at an angle to the vertical line of symmetry, the resulting cross section would have a different shape. It could be a tilted polygon or even a curved shape, depending on the orientation of the intersecting plane and the specific angles of intersection.

In summary, the cross section formed by a plane containing a vertical line of symmetry for a tetrahedron can take various shapes, including polygons or curved shapes, depending on the orientation and angle of the intersecting plane.

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The conditional statement with a false converse is :

A conditional statement consists of an if-then structure, and its converse can be formed by swapping the hypothesis and conclusion. To illustrate, "If A, then B," becomes "If B, then A" in converse form. Our aim is to devise a truthful condition while simultaneously ensuring that its converse yields a falsehood.

Thus, for instance, we may use the fact that all dogs are classified as mammals to offer a valid conditional statement; regrettably, such a proposition fails under converse statement, since not all mammals share this canine trait. Consider cats, elephants, and whales - they render our converse false.

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Determined by various factors such as sample size, statistical significance, and the chosen level of confidence. the probability that the test will fail to decide that the true value is 72.5 when it is indeed 72.5.  

In order to calculate the probability of a Type II error, one would need to know the specific details of the test being used, such as the sample size, the statistical power of the test, and the chosen level of significance.

In general, the probability of a Type II error increases as the sample size decreases and the level of significance decreases. This means that if the test being used is not sufficiently powered or if the level of confidence is too low, there is a higher probability of failing to detect a true effect.

If the test is not able to accurately determine if the statement is true or not when the actual value is 72.5, then there is a possibility that a Type II error has occurred. The probability of this error depends on the specific details of the test being used and cannot be determined without further information.

The probability of a test failing to decide a certain hypothesis is true, when it is actually true, can be determined using the concept of Type II error or false negative rate. In statistical hypothesis testing, Type II error (β) refers to the probability of failing to reject a false null hypothesis. These factors influence the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false. The power of the test (1 - β) is complementary to the probability of making a Type II error.

In this case, the null hypothesis (H0) could be that the value is not equal to 72.5,

while the alternative hypothesis (H1) states that the value is equal to 72.5.

The probability you are looking for is the Type II error rate when the true value is 72.5.

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Answer: Choice B

Step-by-step explanation:

The formula for the area of a circle is πr², and the radius is 1/2 of the diameter.

In the circle shown, the diameter is 18 m. Since the radius is half the diameter, the circle's radius is 9 m.

Inputting this value into this equation gives us π·9², or 81π. Putting this into a calculator or solving it with an approximation of pi gives us a number close to 254.46 m².

The closest option to that is B, so that is your answer.

The normal distribution curve represents the probability distribution for the proportion of voters who support the new tax on fast food when polling 105 voters at random.

Since the proportion of voters who support a new tax on fast food follows a normal distribution, we can model it using the normal distribution curve. Given that 45% of voters support the tax, the mean proportion of voters who support the tax is 0.45.

The standard deviation can be calculated using the formula:

Standard Deviation = sqrt[(p * (1 - p)) / n]

where p is the proportion of voters who support the tax (0.45) and n is the sample size (105).

Substituting the values, we get:

Standard Deviation = sqrt[(0.45 * (1 - 0.45)) / 105] ≈ 0.0497 (rounded to four decimal places)

Now, we can complete the boxes:

Mean = 0.45 (given)

Standard Deviation = 0.0497 (calculated)

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Answer:

Step-by-step explanation:

Answer:

115.5

Step-by-step explanation:

did the iready

The sampling distribution of the difference in sample proportions will be approximately normal, provided that the sample sizes are large enough and certain conditions are met.

The shape of the sampling distribution can be determined by the Central Limit Theorem (CLT), which states that when sampling from a population, the sampling distribution of a sample statistic approaches a normal distribution as the sample size increases. In the case of the difference in sample proportions, the CLT applies if the sample sizes are large enough for each proportion and if the samples are independent.

When these conditions are met, the sampling distribution of the difference in sample proportions will be approximately normal. The exact shape of the distribution will depend on the population proportions and the sample sizes, but it will be symmetric and bell-shaped. This allows for the use of statistical tests and confidence intervals based on the normal distribution to make inferences about the difference in proportions.

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The conversion of the recurring decimals 0.027 and 0.037 to fractions in its simplest form are 0.243/9 and 0.333/9

Let

the fraction = x

0.027

Multiply by 10

0.027 × 10 = x

= 0.27

Subtract 0.027 from 0.27

0.27 - 0.027 = x

0.243 = x

divide by 9

0.243/9 = x

0.037

= 0.037 × 10

= 0.37

Subtract 0.037 from 0.37

0.333 = x

divide by 9

x = 0.333/9

Hence, 0.243/9 and 0.333/9 is the fraction for the recurring decimals 0.027 and 0.037.

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The equation y=1 represents a line Perpendicular to x=0.

The equation x=0 represents a vertical line passing through the point (0,0) on the x-axis. A line perpendicular to this line will be a horizontal line passing through the point (0, c) where c is a constant.

So, the equation of the line perpendicular to x=0 is y = c, where c is any constant.

Among the given options, the equation that represents a horizontal line is:

� = 1 y=1

Therefore, the equation y=1 represents a line perpendicular to x=0.

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To find the area enclosed by the loop of the strophoid r = 2cos(theta) - sec(theta), we need to find the points where the curve intersects itself and integrate the area between them.

First, we find the points where the curve intersects itself by solving the equation r = 2cos(theta) - sec(theta) for theta:

2cos(theta) - sec(theta) = 2cos(theta) - 1/cos(theta)

2cos^2(theta) - 1 = 2cos(theta)

2cos^2(theta) - 2cos(theta) - 1 = 0

Using the quadratic formula, we find:

cos(theta) = (2 ± sqrt(8))/4 = (1 ± sqrt(2))/2

Since r = 2cos(theta) - sec(theta) is undefined when cos(theta) = 0 or cos(theta) = ±1, we only need to consider the two values of theta where cos(theta) = (1 + sqrt(2))/2:

theta1 = arccos((1 + sqrt(2))/2) ≈ 0.2π

theta2 = 2π - arccos((1 + sqrt(2))/2) ≈ 1.8π

To find the area enclosed by the loop, we integrate the area between the two curves r1 = 2cos(theta) - sec(theta) and r2 = 0 from theta1 to theta2:

A = ∫theta1^theta2 (1/2)(r1)^2 dtheta - ∫theta1^theta2 (1/2)(r2)^2 dtheta

= ∫theta1^theta2 (1/2)(2cos(theta) - sec(theta))^2 dtheta - ∫theta1^theta2 (1/2)(0)^2 dtheta

= ∫theta1^theta2 2cos^2(theta) - 4cos(theta)/cos(theta) + 1/cos^2(theta) dtheta

= ∫theta1^theta2 2cos^2(theta) - 4 + cos^2(theta) dtheta

= ∫theta1^theta2 3/2cos^2(theta) - 4 dtheta

= (3/4)sin(theta) - 4theta ∣theta1^theta2

≈ 3.37

Therefore, the area enclosed by the loop of the strophoid is approximately 3.37 square units.

To find the length L of the curve given by x = cos^2t and y = cost, we use the arc length formula:

L = ∫a^b sqrt(dx/dt)^2 + sqrt(dy/dt)^2 dt

In this case, dx/dt = -2sintcost and dy/dt = -sint, so:

L = ∫0^2π sqrt((-2sintcost)^2 + (-sint)^2) dt

= ∫0^2π sqrt(4sin^2tcos^2t + sin^2t) dt

= ∫0^2π sqrt(sin^2t(4cos^2t + 1)) dt

= ∫0^2π sin(t)sqrt(4cos^2t + 1) dt

This integral does not have a closed-form solution, but it can be approximated using numerical methods. Using a calculator or computer, we find that L ≈ 4.4.

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For a related-samples t test, the source of variability attributed to individual differences that remains after difference scores are computed is typically referred to as residual variance.

This residual variance can be thought of as the unexplained variability that is still present in the data even after accounting for the systematic differences between the two related groups. In order to accurately interpret the results of a related-samples t test, it is important to consider not only the mean difference between the two groups, but also the amount of residual variance that remains in the data. The source of variability attributed to individual differences that remains after difference scores are computed is the "within-subjects variability."

Lastly, we can address the within-subjects variability. Although the difference scores help to reduce the impact of individual differences, there will still be some within-subjects variability. This remaining variability is due to factors such as random error, measurement error, or individual response variability that are not completely accounted for by the difference scores. It is important to consider this variability when interpreting the results of a related-samples t-test.

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False. assume condition one has two values, condition two has five values, condition three has three values, and condition four has two values; the number of rules required for the decision table is sixty.

The number of rules required for a decision table can be calculated by multiplying the number of values in each condition. In this case, condition one has two values, condition two has five values, condition three has three values, and condition four has two values. The total number of rules would be the product of these values: 2 x 5 x 3 x 2 = 60.

Therefore, the statement "the number of rules required for the decision table is sixty" is true.

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The probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons, is approximately 0.54.

(a) The probability that the person is traveling on business is 0.7(0.5) + 0.3(0.7) = 0.56.

(b) The probability that the person is traveling for business on a privately owned plane is 0.3(0.7) = 0.21.

(c) The probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons, is given by Bayes' theorem as:

P(private plane | business) = P(business | private plane) * P(private plane) / P(business)

= (0.7 * 0.3) / (0.7 * 0.5 + 0.3 * 0.7) = 0.3 / 0.56 ≈ 0.54.

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The ratio of cos A in the right triangle is 12 / 13.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the ratio of cos A using trigonometric ratios.

Using cosine ratio,

cos A = adjacent / hypotenuse

Therefore,

adjacent side = 12

hypotenuse side = 13

cos A = 12 / 13

Therefore, the ratio is 12 / 13

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The maximum area for each pig pen is 156 square feet. The total length of fencing available is 312 feet. We also know that the two pig pens share a common side, so we can assume that the other three sides of each pen are independent rectangles.

The length of the common side "x" and the width of each pen "y". Since the total area is divided in half by the common side, we can write an equation:
2(xy/2) = x*y
xy = 156
A = xy
y = 156/x
Substituting this expression for y into the formula for the area, we get:

A = x(156/x)
A = 156 - x^2/2
This is a quadratic equation in standard form, with a = -1/2, b = 0, and c = 156. The vertex of the parabola is at x = -b/2a = 0, which means that the maximum area occurs when x is at the midpoint of the fencing available, which is 156/2 = 78

feet.
y = 156/78 = 2

The dimensions of each pig pen are 78 feet by 2 feet, and the maximum area of each pen is:
A = 78*2 = 156 square feet.

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The solution for the given equation is x = 2.

Given is an equation, x+1 / 3 = x/2, we need to solve it,

So, in the questions like this, our first step should be of cross-multiplication,

x+1 / 3 = x/2

Cross-multiplying,

2(x+1) = 3x

Using the distributive law,

2x+2 = 3x

Combining the like terms,

3x-2x = 2

x = 2

There can be many equations made like this,

For example,

1) 9 = 3 + x/4

Solution = 9-3 = x/4

6 = x/4

x = 24

2) 2x+2 / 4 = x-3 / 3

Using Cross-multiplying,

6x+6 = 4x-12

2x = -12-6

2x = -18

x = -9

Hence there are many equations made.

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Answer:

y=10

Step-by-step explanation:

y is inversely proportional to x or y=k. 1/x

where k = constant

or x.y =k where y=60 x=3,

3*60 =180=k

Now, when x=18;

18*y = 180 y=180/18

y=10.

Answer:

8.5

Step-by-step explanation:

Standard deviation = √variance = √72.25 = 8.5

The credit control officer's commission for clearing a loan worth 34000000 would be 510000 based on a commission rate of 15000 for every 1 million cleared.

If a loan worth 34000000 is cleared, the credit control officer would receive a commission based on the total amount cleared. Since the commission rate is 15000 for every 1 million cleared, we can calculate the commission by dividing the loan amount by 1 million and multiplying it by the commission rate.

So, 34000000 divided by 1000000 equals 34. This means that there are 34 million-dollar increments in the loan amount. Multiplying 34 by the commission rate of 15000 gives us a commission of 510000.

Therefore, the credit control officer would receive a commission of 510000 for clearing a loan worth 34000000. It is important to note that this commission may be subject to taxes and other deductions depending on the credit control officer's employment terms and local laws.

In conclusion, the credit control officer's commission for clearing a loan worth 34000000 would be 510000 based on a commission rate of 15000 for every 1 million cleared.

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In circle HI=6 and the length of IJ =4π. The measure of ∠IHJ is 60 degrees.

In a circle, the measure of an angle formed by a chord and a tangent at the point of contact is half the measure of the intercepted arc.

Given that IJ is a chord of the circle, and its length is 4π, we can determine the measure of the intercepted arc using the formula:

Arc length = (central angle / 360 degrees) * circumference of the circle

The circumference of the circle is 2π times the radius, and the radius is half the diameter. Since HI is given as 6, the diameter is 2 * 6 = 12. Therefore, the circumference is 2π * 6 = 12π.

Now, we can calculate the measure of the intercepted arc:

4π = (central angle / 360 degrees) * 12π

Simplifying the equation, we get:

4 = (central angle / 360)

To find the measure of the angle IHJ, we solve for the central angle:

central angle = 4 * 360 = 1440 degrees

Since the measure of ∠IHJ is half the measure of the intercepted arc, ∠IHJ = 1440 / 2 = 720 degrees.

However, angles in a circle are measured from 0 to 360 degrees, so we need to find the equivalent angle within this range:

720 - 360 = 360 degrees

Therefore, the measure of ∠IHJ is 360 degrees, or equivalently, 60 degrees.

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To increase the power of a statistical test, one can increase the sample size or increase the significance level. Option D.

It is necessary to either increase the sample size or raise the significance threshold in order to increase the power of a statistical test while maintaining all other factors constant. Let's investigate the causes of this.

The likelihood of successfully rejecting the null hypothesis in a statistical test is known as power. In other words, it refers to the test's capacity to identify a genuine difference or impact. A Type II mistake happens when we fail to reject the null hypothesis even when it is untrue, hence increasing the power is beneficial because it lowers the likelihood of this occurrence.

The power of a test is improved by increasing the sample size. More data points are provided and sampling variability is decreased with a bigger sample size. The test becomes increasingly capable of detecting subtle effects or variations as there are more observations. Because the test has a better chance of successfully identifying a real effect, the power rises as a result.

Alternately, increasing the strength can be accomplished by raising the significance level, also referred to as the alpha level. The threshold for rejecting the null hypothesis is determined by the significance level. The test is made more forgiving by raising the significance level (for instance, from 0.05 to 0.10), which makes it simpler to reject the null hypothesis.

As a result, the test's power rises as the likelihood that it will find a real effect rises.

It's crucial to keep in mind, though, that raising the significance level also raises the likelihood of making a Type I error, which is to reject the null hypothesis when it is actually true. Since there is a chance of producing more false positives, altering the significance threshold should be done with caution. The right answer is D.

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Answer:

----------------------------

The probability of rolling an even number on a single die is 3/6 or 1/2.

Consider the possible outcomes of rolling the two dice:

So, the only way to not have an even product is if both dice are odd.

The probability of rolling an odd number on a single die is also 1/2, so the probability of rolling two odd numbers is (1/2) x (1/2) = 1/4.

Therefore, the probability of rolling an even product is: