Which table represents a function

Answer:

1

A bag contains 7 red balls and 3 green balls. Two balls are taken from the bag. Find the probabilities that they are:

(a)

both red

(b)

both green

(c)

one red and one green.

Show me

2

Weather experts estimate the probability of rain any day as

0.6 if it rained the previous day

0.3 if it did not rain the previous day.

Find the probability that a dry day is followed by,

(a)

two more dry days,

(b)

two wet days,

(c)

a wet day and then a dry day.

Show me

Exercises

1

A bag contains 3 red counters and 4 blue counters. Two counters are taken out of the bag. Find the probability that:

(a)

both counters are red,

Check

(b)

both counters are the same colour,

Check

(c)

the counters are different colours.

Check

2

A card is drawn at random from a full pack of playing cards. It is not put back. A second card is then drawn from the same pack.

(a)

Find the probability that:

(i)

both cards are hearts,

Check

(ii)

only one card is a heart,

Check

(iii)

neither card is a heart.

Check

(b)

Find the probability that:

(i)

both cards are sevens,

Check

(ii)

neither card is a seven,

Check

(iii)

at least one seven is obtained.

Check

3

The probability that a football team win their next match is:

⎧

⎨

⎩

0.3 if they won their last match,

0.8 if they lost their last match.

(a)

Find the probability that if a match is lost, the next two will be won.

Check

(b)

Find the probability that if a match is won, the next two will also be won.

Check

4

A pack of 24 cards contains 12 red cars, 8 yellow cards and 4 pink cards. In a game a player has to select two cards, one after the another. Find the probabilities that a player selects,

(a)

2 red cards,

Check

(b)

2 yellow cards,

Check

(c)

2 pink cards,

Check

(d)

2 cards that are the same colour,

Check

(e)

a pink card and a yellow card in any order.

Check

5

Nisha buys a bag of sweets. The bag contains 3 orange, 17 strawberry and 10 cherry flavour sweets. Nisha eats 3 sweets. Find the probability that she has:

(a)

not eaten an orange sweet,

Check

(b)

eaten 3 sweets of the same flavour,

Check

(c)

only eaten strawberry flavour sweets.

Check

6

Two yachts A and B regularly race against each other. In rough weather the probability that A wins is 0.8 and in fine weather 0.4. The probability of fine weather at a race is 0.7.

(a)

What is the probability that A wins a race?

Check

(b)

If there is a best of 3 races competition, what is the probability that A wins the competition?

Round up to 2 decimal places.

Check

7

Brian enjoys swimming. If it is a sunny day the probability that he swims is 0.9. It the day is not sunny, the probability that he swims is 0.65.

The probability that tomorrow will be sunny is 0.8.

Draw a tree diagram to illustrate this information.

Calculate the probability that Brian will not swim tomorrow.

Check

8

Wes gives Bronwen a box of 25 mixed sweets. 12 of the sweets have soft centres, 8 have toffee centres and 5 have hard centres. All of the sweets have identical wrappers. Bronwen chooses 2 sweets at random.

(a)

What is the probability that Bronwen will choose 2 toffee centred sweets?

Check

After they have eaten 3 soft centred sweets and 2 toffee centred sweets, Wes chooses 3 sweets at random from the 20 sweets that are left.

(b)

What is the probability that Wes will choose a soft centred sweet, followed by a toffee centred sweet, followed by a hard centred sweet?

Check

When there are only 10 sweets left, 3 have soft centres, 4 have toffee centres and 3 have hard centres. Bronwen chooses two sweets at random.

(c)

What is the probability that neither of the sweets will have a hard centre?

Check

9

The fast food chain Macduff's is running a competition.

You obtain a card with 12 circles covered up.

You are allowed to scratch off up to three circles.

You win if 2 or more PALM TREES are revealed.

You lose if two or more CRABS are found.

If you win, you scratch off one of the three squares to show your prize.

Step-by-step explanation:

Given condition will be represented by linear equation 5x+10y=90.

What is linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Total trail hiked=90miles

mountain trail=5mile

canal-trail=10mile

x represent the number of times Maria hiked the mountain trail, and  y represent the number of times Maria hiked the canal trail

Therefore,

Linear equation will be 5x+10y=90

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Answer:

y = (1/4)x + 3

Step-by-step explanation:

I have put my answer in slope-intercept form as that is usually the most common. Inputing the slope as "m" into the equation "y=mx+b" and substituting the x and y coordinates given to find b gives the equation "2=(1/4)(-4)+b" By solving this we get "b=3" to finish the equation.

Answer:

y=1/4x+3

Step-by-step explanation:

y-2=1/4(x-(-4))

y-2=1/4(x+4)

y-2=1/4x+1

y=1/4x+1+2

y=1/4x+3

Answer:

4

Step-by-step explanation:

Answer:

96 tiles

Step-by-step explanation:

The kitchen floor is rectangular on shape.

The dimensions of the kitchen floor were 8 feet by 12 feet.

Hence, Area of a rectangle = Length × Width

Length = 8ft

Width = 12ft

Hence:

Area = 8ft × 12ft

= 96 ft²

If each tile was 1 square foot, the number of tiles he would need is

1 ft² = 1 tile

96 ft² = x

Cross Multiply

1ft² × x = 96 ft² × 1 tile

x = 96 ft² × 1 tile/1 ft²

x = 96 tiles

Therefore, Mark's father would need 96 tiles

Answer:

Choice D.

Step-by-step explanation:

5.2

Answer:

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

Step-by-step explanation:

Answer:

x = -4; y = 2

Step-by-step explanation:

The solution is the point of intersection of the two lines.

The lines intersect at point (-4, 2).

Answer: x = -4; y = 2

Answer:

x = -4; y = 2

Step-by-step explanation:

the are the answers to both of the statements

The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.

If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050

The population is given to be increasing exponentially, which means it will follow the equation:

\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.

We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:

\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)

Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.

Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:

\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)

where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)

where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)

Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)

To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):

\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.

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Answer:

Step-by-step explanation:

From the question, we are informed that 15⋅324=4,860. Thee exact product of 1.5⋅3.24 will be:

= 1 × 5 × 3 × 24

= 360

The answer will therefore be 360

No, it doesn't show that single individuals under the age of 25 have more insurance claims than the nationwide percent reported by the big insurance firm.

Hypothesis

Null hypothesis : H0: p = 0.68

Alternative hypothesis : Ha: p > 0.68

A random sample of 53 claims showed that 41 were made by single people under the age of 25.

Thus; p^ = 41/53 = 0.7736

The test statistic is

z = (p^ - p_o)/√(p_o(1 - p_o)/n)

z = (0.7736 - 0.68)/√(0.68(1 - 0.68)/41)

z = 0.0936/0.07285

z = 1.28

The p-value from z-score calculator, using z = 1.28, one tail hypothesis and significance level of 0.05,we have;

P(z > 1.28) = 0.100273

The p-value gotten is greater than the significance value and so we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

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Answer:

below

Step-by-step explanation:

uG =(12sin45)/sin85

A radian is a unit of measurement that quantifies the size of an angle by considering the length of the arc it subtends on a circle with a radius of 1.

To visualize this, let's consider a circle with a radius of length 'r.' If we were to trace an arc along the circumference of this circle with a length equal to 'r,' the angle subtended by that arc at the center of the circle is one radian. In other words, a radian is the measure of the angle that corresponds to an arc of length 'r' on a unit circle (a circle with a radius of 1).

In standard position, an angle is said to be in its standard position when its vertex coincides with the origin of a coordinate plane, and its initial side is along the positive x-axis. Radians are often employed to measure angles in standard position because they allow us to directly relate the angle's measurement to the coordinates of points on the unit circle.

Additionally, radians help us divide the circle into quadrants. A quadrant is one of the four sections into which the circle is divided by the x-axis and y-axis. Each quadrant spans an angle of 90 degrees or π/2 radians. By using radians, we can more precisely describe the location of a point on the unit circle and calculate trigonometric ratios.

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Answer:

9 dollars and 40 cents

Step-by-step explanation:

Answer:

It is 9 dollars and 40 cents :)

Markov analysis is used for analyzing the performance and reliability of complex systems, while replacement charts are used for optimizing the replacement timing of deteriorating assets.

Markov Analysis:

Markov analysis is a probabilistic model that is used to predict the future state of a system based on its current state.

It involves the use of Markov chains to model the transitions between different states of a system over time.

Markov analysis is commonly used when the equipment or system under consideration can be in multiple states with varying probabilities of transition.

It is suitable for analyzing systems that have a continuous or non-repairable nature, such as complex machinery, infrastructure, or systems with multiple failure modes.

The primary objective of Markov analysis is to assess the reliability, availability, and performance of the system and make decisions regarding maintenance, replacement, or repair strategies.

Replacement Chart:

A replacement chart, also known as a replacement model or replacement policy, is a decision-making tool used to determine the optimal time to replace a piece of equipment or system.

It involves comparing the costs associated with continuing to use the existing equipment (including maintenance and repair costs) with the costs of replacing it.

The replacement chart provides a visual representation of the costs over time and helps identify the point at which replacement becomes more cost-effective than continued use.

Replacement charts are commonly used for assets that are subject to wear and tear, aging, or deterioration over time, such as vehicles, machinery, or equipment with a defined lifespan.

The primary objective of a replacement chart is to minimize costs associated with the asset's life cycle by optimizing the replacement timing.

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The correct answer is (4) All of the above (1, 2, and 3).

When using ANOVA to evaluate models, among the important considerations are:

The ANOVA table is not the fitted model itself but rather an attempt to partition credit for the model's predictive power across the different variables,

Interpreting the ANOVA table requires more subtlety when there is correlation among model predictors, and there can only be one correct ANOVA table for any given model in the context of an observational study.

Hence, the correct answer is (4) All of the above (1, 2, and 3).

ANOVA, short for Analysis of Variance, is a statistical method for comparing the means of two or more groups. It is utilized to compare whether there are any statistically significant differences between the group means.

The ANOVA table is not the fitted model itself but rather an attempt to partition credit for the model's predictive power across the different variables. Interpreting the ANOVA table requires more subtlety when there is correlation among model predictors.

There can only be one correct ANOVA table for any given model in the context of an observational study.

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Answer: 6.782

Step-by-step explanation:

Answer:

B

Step-by-step explanation:B

According to the Pythagorean Theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs of a right triangle.

In other words, \(a^2 + b^2 = c^2\) for the triangle depicted below.

The right triangle's legs, a and b, are perpendicular sides, and the hypotenuse, c, is the side that faces away from the right angle.

Construction projects and almost anything involving right triangles, such as roofing for homes, are common uses for this application.

Hypotenuse² = Base² + Perpendicular²

The Pythagorean Theorem is used in a variety of computations. For instance, it may be used to determine the height and distance of straight and fallen trees, as well as the steepness of hills and mountains.

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$16,200

1) Coletando los datos

Valor presente: 5,000

rate: 9%

Tiempo: 36 meses

2) Escribindo la formula y despues aplicando los datos, tienemos:

Mira que subtraemos de lo Valor Futuro, el Principal. A -P = i

3) Entonces el interés simple és $16,200

Answer:

New price: $255.50

Step-by-step explanation:

First you multiply 365x.30

Then you'll get 109.5

Sub that from 365 and you'll get $255.50

Answer:

6 1/4

Step-by-step explanation:

1/2 = 2/4

2/4 + 3/4 = 5/4 which is 1 1/4 simplified.

Then add the whole numbers, 2 + 3 = 5

5 + 1 1/4 = 6 1/4

Tomas rides 6 1/4 miles everyday.

Answer:

It is 24 inches

Step-by-step explanation:

Multiply 24  by 8 to get 192. Then multiply 8 by 3 to get you answer.

:)

Answer:

i believe it’s no. sorry if i’m wrong!

Step-by-step explanation:

To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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Answer:

Angle g = 90°

Angle between x and G = 30°

Angle x= 180-(90+30)

= 180-120=60°

Hello!

The perimeter is the sum of all sides of the figure. As we know, this is rectangular parking with a length equal to 69m. Look at the figure below:

As we know the definition of the perimeter, we can sum all sides, look:

Answer for A:

width of the parking lot = 58m.

We'll solve it in a similar way.

The area of a rectangle is obtained using the formula:

Replacing the values, we'll obtain:

Answer for B:

length of the pool = 78m.

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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