Mrs may is planning for her son's graduation and decides to invest her bonus money for two years. She invests the money in an institution offering interest that is compounded annually at an interest rate of 5.8% for the first year and 6,5% for the second year.

An annual bonus is a 13th chequered which is equal to a monthly salary without deductions.
She only used one year's annual bonus.
Her annual income is R 336000 after she received an increase of 6.5%.
4.1 calculate her annual income before she received the increase.
4.2 Calculate how much money will be paid out to her after the two year period

The probability of randomly choosing a green marble after you have chosen red is 4.4%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given

A jar has 20 marbles: 3 green, 12 blue, 5 red.

Probability;

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The total number of marbles = 20

The number of green marbles= 3

The number of blue marbles = 12

The number of red marbles = 5

The probability of choosing a red marble = Number of red marbles / Total number of marbles

= 5/20

The probability of choosing a green marble is =  Number of green marbles / New total number of marbles

= 3/19

Therefore,

The probability of randomly choosing a green marble after you have chosen red is;

= 5/20 * 3/19

= 3/68

percentage = 3/68 * 100 = 4.4%

Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%

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Answer:

f(3) = 3 + 1 = 4

Step-by-step explanation:

Since 3 > 0, we need to focus on the part of the function where x > 0. So:

f(3) = 3 + 1 = 4.

Therefore, the probability that a randomly selected family owns a cat is 0.257. Therefore, the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat is 0.778.

Probability is a branch of mathematics that deals with the study of random events or situations. It involves the quantification of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty. The theory of probability provides a framework for making predictions, analyzing data, and making decisions in situations involving uncertainty or randomness.

Here,

Let's use the following events:

D: family owns a dog

C: family owns a cat

From the problem statement, we know:

P(D) = 0.3

P(C|D) = 0.2

P(C) = 0.34

1. To find the probability that a randomly selected family owns a cat, we can use the law of total probability:

P(C) = P(C|D) * P(D) + P(C|not D) * P(not D)

We don't know P(C|not D), but we can find it using the fact that P(not D) = 1 - P(D):

P(C|not D) = (P(C) - P(C|D) * P(D)) / P(not D)

P(C|not D) = (0.34 - 0.2 * 0.3) / (1 - 0.3)

P(C|not D) = 0.2857

Substituting the values:

P(C) = 0.2 * 0.3 + 0.2857 * 0.7

P(C) = 0.257

2. To find the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat, we can use Bayes' theorem:

P(not D|C) = P(C|not D) * P(not D) / P(C)

Substituting the values:

P(not D|C) = 0.2857 * 0.7 / 0.257

P(not D|C) = 0.778

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Complete question:

In a certain community, 30% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 34% of all the families own a cat. What is the probability that a randomly selected family owns a cat? What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

Answer:

  C:  y = -(x +3)² -1

Step-by-step explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

For vertex (h, k), the vertex form equation of a parabola is ...

  y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

  y = a(x -(-3))² + (-1)

  y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

  y = -(x +3)² -1

__

Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

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A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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The variable that was defined and the corresponding inequality to depict the constraints is; r < 140 beats per minute.

We are to define a variable and write an inequality for the given question.

Now, since the variable here is the heart rate, then let us define the varibale with the term r.

Thus, the inequality that represens the given question is written as;

r < 140 beats per minute.

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Answer:

4

\(3.5x - 11 = 3 \\ 3.5x = 3 + 11 \\ 3.5x = 14 \\ x = \frac{14}{3.5} \\ x = 4\)

Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

Answer:

The formula for exponential growth is: Total = Starting value(1 + rate)^time

2018 to 2025 is 7 years:

Step-by-step explanation:

Total = 50,000(1+0.037)^7

Total = 50,000(1.037)^7

Total = 64,479 -(Answer)

Answer: It will one year (or 12 months) before Michael is able to ride the roller coaster.

Step-by-step explanation: Because he grows a half inch every month, this means that It takes him two months to grow one full inch. Because he has to grow six inches, you just multiply 2 by 6 to get 12 months or one year.

Answer:

48-42=6, which is how much Michael needs to grow.

1/2x=6, where x is the number of months

x = 12 months.

1 year = 12 months so the answer is one year.

25 is the answer hope it helps

We have the following:

We can see that time is located on the x axis and the price of gasoline is located on y, we can conclude that in both periods the price increases, but in the first it increases slowly and in the second it increases quickly

Therefore, the answer is:

First, the price of gasoline in New mexico increases slowly, and then it increases quickly

Answer:

b

Step-by-step explanation:

Answer: D) KJ

Step-by-step explanation:

The object shown is a ray. It has a fixed starting point, but does not have an endpoint.

Answer:

B. 0.07

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion of convicted drug pushers is significnalty higher than 20%.

Then, the null and alternative hypothesis are:

\(H_0: \pi=0.2\\\\H_a:\pi>0.2\)

The sample has a size n=144.

The sample proportion is p=0.25.

\(p=X/n=36/144=0.25\)

The standard error of the proportion is:

\(\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.2*0.8}{144}}\\\\\\ \sigma_p=\sqrt{0.001111}=0.0333\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p-\pi}=\dfrac{0.25-0.2}{0.0333}=\dfrac{0.05}{0.0333}=1.5\)

This test is a right-tailed test, so the P-value for this test is calculated as:

\(\text{P-value}=P(z>1.5)=0.066\approx0.07\)

Answer:

332, 333, 334

Step-by-step explanation:

First, we acknowledge that the equation that we need to solve will be "x+(x+1)+(x+2)=999" This is because x represents the smallest of three consecutive numbers whose sum is 999. Simplifying this equation will leave us with 3x+3=999 which is simplified further to 3x=996 and again simplified to x=332. X is the smallest number of the three.

The calculated ratio for the sine the angle A has its value to be 8/17

The ratio for sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

This ratio is commonly denoted as sin(θ), where θ is the angle of interest.

Mathematically, we can express this as:

sin(θ) = opposite / hypotenuse

Using the above, we have

opposite = 8

hypotenuse = 17

So, we have

sin(A) = 8/17

Hence, the ratio is 8/17

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Answer:

i beleive its A

Step-by-step explanation:

i say its A due to the phrase "no more" is accurate to showing that the 200 is truly "More than or equal too"

The equation of Amir's altitude relative to sea level (in meters) and time (in minutes) is: y=-12x+360.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.

First of all let's write the slope-intercept form of the equation of a line, which is:

y=mx+b

where m is the slope and b is y intercept.

So we just need to find  m and b to solve this problem.

Moreover, this problem tells us that Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. So this rate is the slope of the line, that is:

m=-12

Negative slope because Amir is descending. So:

y=-12x+b

To find b, we need to use the information that tells us that he was at sea level after 30 minutes of driving, so this can be written as the point (30,0
). Therefore, substituting this point into our equation:

y=-12x+b

0=12(30)+b

0=-360+b

b=360

Finally, the equation of Amir's altitude relative to sea level (in meters) and time (in minutes) is:

y=-12x+360.

Therefore  the equation of Amir's altitude relative to sea level (in meters) and time (in minutes) is: y=-12x+360.

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Answer:

37.69

Step-by-step explanation:

Answer:r=7r =9 r=10

Step-by-step explanation:

Answer:

The base is 11 cm.

Step-by-step explanation:

The formula for the area of a triangle is \(A = \frac{1}{2} bh\). If we plug in what we know to this equation, we are left with \(121 = \frac{1}{2} * b * 2b\), which we now need to simplify.

First, we combine like terms.

\(121 = \frac{1}{2} * 2b^{2}\)

Then, we can eliminate the \(\frac{1}{2}\) and \(2\) on the right side of the equation, since they cancel each other out.

\(121 = b^{2}\)

Finally, we take the square root of both sides of the equation and find our answer:

\(11 = b\)

The base length of the triangle with an area of 121 square cm will be 11 cm.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The height of a triangle is twice its base. If its area is 121 square cm.

h =  2b

The base length of the triangle is given as,

121 = 1/2 x 2b x b

121 = b²

b = 11

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The best answer is a. chronological, topical.

the organization type would change from topical to categorical.

In the original outline, the organization of the speech follows a chronological order, where the steps to prepare for a job interview are presented in a sequential manner. Each step builds upon the previous one, creating a logical flow.

If the four main points were changed to part-time job interviews, summer job interviews, college entrance interviews, and full-time job interviews, the organization would still follow a chronological order. Each main point would represent a different type of interview, and within each point, the subpoints would address the specific considerations for that type of interview.

Therefore, the organization type remains chronological, even if the specific content changes.

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Answer: -8

Step-by-step explanation: You do y2 which is -4 subtracted by y1 which is 4 over x2 which is 5 subtracted by x1 which is 4 and since the denominator is 1 it becomes just negative 8

Using the graph of the function, it is found that the lateral limits of the function are as follows:

For \(x \rightarrow 1^{+}\), we look at the values slightly greater than 1, that is, to the right of x = 1, for which the function goes to negative infinity, hence \(f(x) \rightarrow -\infty\).

For \(x \rightarrow 1^{-}\), we look at the values slightly less than 1, that is, to the left of x = 1, for which the function goes to infinity, hence \(f(x) \rightarrow \infty\).

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Answer:

190

Step-by-step explanation:

mean = sum of all the numbers/# of numbers

210 + 160 +200 = 570

570/3 = 190

Answer:

190

Step-by-step explanation:

you divide 570 by 3, which is 190.

The value of the side y is 3√3. Option C

It is crucial to note the different types of trigonometric identities.

They are;

From the diagram shown, we have that;

The angle θ = 60 degrees

The opposite side = y

The adjacent side = 3

Let's use the tangent identity

tan 60 = y/3

Find the value

√3 = y/3

cross multiply

y = 3√3

Hence, the value is 3√3

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Answer:True

There is no way to have a negative because it's the number's distance from zero

The scenarios that can be considered a seller-based discount are:

A. The offer by Wire and Cable

B. Carfna's Fine Foods

C. Mouser Electronics offer

E. Carchex Car Maintenance

A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.

The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.

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Answer:

(-5, 4) The x value is -5, and the y value is 4.

To find the least common denominator (LCD) for the fractions 3/4 and 1/6, we need to determine the smallest multiple that both denominators, 4 and 6, divide evenly into.

To find the LCD, we can list the multiples of both denominators and find the smallest common multiple:

Multiples of 4: 4, 8, 12, 16, 20, 24, ...

Multiples of 6: 6, 12, 18, 24, 30, 36, ...

From the lists above, we can see that the smallest common multiple of 4 and 6 is 12.

Therefore, the least common denominator for 3/4 and 1/6 is 12.

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The answer is:

Work/explanation:

To find the least common denominator for 4 and 6, we find their LCM.

And that is:

\(\textsf{Lcm of 4 and 6 = \textbf{12}}\)

Hence, that is the least common denominator for these two fractions.

Now, let's add them:

\(\sf{\dfrac{3}{4} +\dfrac{1}{6}}\)

\(\sf{\dfrac{3\times3}{4\times3} +\dfrac{1\times2}{6\times2}}\)

\(\sf{\dfrac{9}{12} +\dfrac{2}{12}}\)

Now we go about this by just adding the numerators:

\(\sf{\dfrac{11}{12}}\)

Hence, the answer is 11/12.