NEED answer fast, please hurry. If events A and B are independent, and the probability that event A occurs is 83%, what must be true?
The probability that event B occurs is 17%.
The probability that event B occurs is 83%.
The probability that event A occurs, given that event B occurs, is 83%.
The probability that event B occurs, given that event A occurs, is 83%.

$16 are discounted from the regular price of the item.

Given that an item is regularly priced at $40, and it is on sale for 40% off the regular price, to determine how much (in dollars) is discounted from the regular price, the following calculation must be performed:

Therefore, $16 are discounted from the regular price of the item.

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Final answer:

The business woman invested $17,000 in the 3.5% interest account and $21,000 in the 6.5% interest account.

Explanation:

To find how much she invested in each account:

Let x be the amount invested at 3.5% interest and y be the amount at 6.5%.

We can set up a system of equations like this: x + y = $38,000 and 0.035x + 0.065y = $1,960.

Solving this system, we get x = $17,000 and y = $21,000.

Therefore, investment is $17,000 in the 3.5% interest account, $21,000 in the 6.5% interest account

Option: B is the correct answer.

B.  a line perpendicular to <-AB-> through point P.

We know that a line perpendicular to a given line is constructed as follows:

1)  Draw a line segment AB

2) Take a span of compass more than half the length of AB and keep the point of compass first at A and then at B to make a arc above AB.

3) Draw a straight line that passes through the intersection  of arc and line AB such that it meets AB at point P which will act as a midpoint of line AB.

       Hence, the correct option is:

                    Option: B

The equation [tex]d=(m)/(V)[/tex] can be used to calculate the density, [tex]d[/tex], of an object with mass, [tex]m[/tex], and volume, [tex]V[/tex].  [tex](m)/(d)=V[/tex] is an equivalent equation solved for [tex]V[/tex].

To find the equation equivalent to [tex]d= m/V[/tex] solved for [tex]V[/tex], we need to isolate [tex]V[/tex]on one side of the equation.

Given the equation [tex]d= m/V,[/tex] where [tex]d[/tex] represents density, [tex]m[/tex] represents mass, and [tex]V[/tex] represents volume.

To solve for [tex]V[/tex] , we can rearrange the equation:

[tex]d= m/V[/tex]

First, let's get rid of the fraction by multiplying both sides by [tex]V[/tex]:

[tex]d*V=m[/tex]

Now, to isolate [tex]V[/tex], we need to divide both sides by [tex]d[/tex]:

[tex]V= m/d[/tex]

So, the equivalent equation solved for [tex]V[/tex] is:

[tex]V= m/d[/tex]

​This corresponds to option C: [tex]m/d=V.[/tex]

COMPLETE QUESTION:

The equation [tex]d=(m)/(V)[/tex] can be used to calculate the density, [tex]d[/tex], of an object with mass, [tex]m[/tex], and volume, [tex]V[/tex]. Which is an equivalent equation solved for [tex]V[/tex]?

A. [tex]dm=V[/tex]

B. [tex](d)/(m)=V[/tex]

C. [tex](m)/(d)=V[/tex]

D. [tex]m-d=V[/tex]

I substitute 1 in 2

AD²=2*[(17-AD)²+(AD/2)²]----> AD²=2*[289-34AD+AD²+0.25AD²]

AD²=578-68AD+2.50AD²--------> 1.50AD²-68AD+578

1.50AD²-68AD+578=0

 using a graph tool to solve the quadratic equation

see the attached figure

AD1=11.33 in

AD2=34 in----------is not solution because (AB+AD=17)

Solution is AD=11.33 in

AB=17-11.33--------> 17-11.33-----> AB=5.67 in

 the answer is

AD=11.33 in

AB=5.67 in

Final answer:

A person earning $500,000 per year received an additional $16,386 or 3.3% more of their income due to tax changes.

Explanation:

To ascertain how much more a person earning $500,000 per year received due to tax changes, we need to calculate the savings from the first $106,800 at a 2% reduction, in addition to the increased federal tax return of $14,250.

Firstly, we calculate 2% of $106,800:

0.02 × $106,800 = $2,136

Now, we add this to the additional amount received from the tax return:

$2,136 + $14,250 = $16,386

Therefore, a person earning $500,000 per year has received an additional $16,386. To find the percentage this additional amount represents of their income, we perform the following calculation:

($16,386 / $500,000) × 100 = 3.277%

Rounded to the nearest tenth of a percent, it is 3.3%.

The statement completed would be: A person earning $500,000 a year received $16,386 more or 3.3% more of their income.

In order to find the reciprocal of a number, we should just flop it over.

If we're asked to find the reciprocal of a fraction, then the numerator & denominator of the fraction switch places.

If we're asked to find the reciprocal of an expression, then we also flop it over, like so:-

[tex]\pmb{u^2-s^2}\longmapsto\pmb{\displaystyle\frac{u^2-s^2}{1} }\longmapsto\pmb{\displaystyle\frac{1}{u^2-s^2} }[/tex]

Explanation of steps:-

First, I turned the expression into a fraction by adding a denominator of 1.

Then, I flopped it over and found the reciprocal.

Hence, the reciprocal of u²-s² is:-

[tex]\bigstar{\boxed{\pmb{\displaystyle\frac{1}{u^2s^2} }}}[/tex]

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Final answer:

To find the future price of milk after a 54% increase, multiply the current price by 1.54. For 2 gallons of milk costing $2.50 now, the future price will be $3.85.

Explanation:

To calculate the future price of milk after a 54% increase over 3 years, we first need to determine the percentage increase in decimal form and then apply it to the current price. An increase of 54% is equivalent to a multiplier of 1.54 in decimal form.

Therefore, if 2 gallons of milk currently cost $2.50, we calculate the future cost by multiplying $2.50 by 1.54.

Here's the calculation:

Convert the percentage increase to a decimal: 54% = 0.54.

Add 1 to the decimal to account for the total value after the increase: 1 + 0.54 = 1.54.

Multiply the current price of 2 gallons of milk by the increase factor: $2.50 x 1.54 = $3.85.

After a 54% increase, the price for 2 gallons of milk will be $3.85.

To find the distance between Tim and Terry after 18 minutes, you can calculate the distance each has traveled based on their speed and time elapsed. Then subtract their distances to find the total distance between them.

To determine the distance between Tim and Terry after 18 minutes, you can add up the distances each has traveled according to their speeds and time elapsed. Tim covers 90 feet/minute, so in 18 minutes, he would have traveled 90 * 18 = 1620 feet. Terry covers 11 feet/minute, so in 18 minutes, he would have traveled 11 * 18 = 198 feet.

Calculating the total distance between them:

Distance = |1620 - 198| = 1422 feet

e^c=2

Step-by-step explanation:

Final answer:

You can make 19 cheese sandwiches with 38 bread slices and 28 cheese slices.

Explanation:

In this scenario, you have 38 bread slices and 28 cheese slices. The equation for a cheese sandwich is 1 sandwich = 2 slices of bread + 1 slice of cheese. So, if you set the number of bread slices to '2' and the number of cheese slices to '1', you can calculate how many cheese sandwiches you can make.

First, divide the number of bread slices (38) by 2 to get the number of sandwiches that can be made with the bread: 38 / 2 = 19 sandwiches.

Next, divide the number of cheese slices (28) by 1 to get the number of sandwiches that can be made with the cheese: 28 / 1 = 28 sandwiches.

Since you can only make 19 sandwiches with the available bread, the limiting factor is the bread. Therefore, you can make 19 cheese sandwiches with the given amounts of bread and cheese.

Answer: The outcomes appear to be equally likely, so a uniform probability model is a good model to represent the probabilities in Tyra's experiment.

Step-by-step explanation: Probability model, also known as Probability distribution, is a mathematical function that shows the probability of any outcome to occur in an experiment. When those probabilities of occurence  are the same for all possible outcomes, it is a uniform probability distribution.

For example, if you roll a fair dice, the probability of having the number 1 is 1/6; for 2 is also 1/6 and etc,

In Tyra's experiment, when the calculates the frequency of each number card,  the values are closer together. This means that the probability of taking a card with number 1 written on it is almost the same as taking a card with number 2 and so. In conclusion, Tyra's experiment is au uniform probability model.

The statement about Tyra's experiment is:The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent the probabilities in Tyra's experiment.

In probability theory, a uniform probability model is one in which all outcomes in the sample space are equally likely to occur. This means that if there are n possible outcomes, the probability of each outcome is [tex]\( \frac{1}{n} \)[/tex].

In Tyra's experiment, she drew a card from a bag, recorded the number, and then replaced it before drawing again. This process is repeated 62 times, and she calculates the relative frequency of each number card. The relative frequency is the ratio of the number of times a particular outcome occurs to the total number of trials.

The given relative frequencies for outcomes 1 through 5 are as follows:

If the outcomes were equally likely, we would expect the relative frequencies to be the same for all outcomes, especially after a large number of trials like 62. However, the relative frequencies vary from 0.19 to 0.21, indicating that some outcomes are occurring more frequently than others.

Since the relative frequencies are not the same for all outcomes, we can conclude that the outcomes do not appear to be equally likely. Therefore, a uniform probability model, which assumes equal likelihood for all outcomes, would not be a good fit for Tyra's experiment. Instead, the probabilities in Tyra's experiment seem to be non-uniform, and a different probability model that accounts for the varying likelihoods of the outcomes would be more appropriate.

Answer:

n = 2

Step-by-step explanation:

As per statement of the question we will form the equation first.

[tex](\frac{3}{5})n-\frac{4}{5}=(\frac{1}{5})n[/tex]

Now we will solve the given equation to get the solution of n.

[tex](\frac{3}{5})n=\frac{4}{5}+(\frac{1}{5})n[/tex]

[tex](\frac{3}{5})n-(\frac{1}{5})n=\frac{4}{5}[/tex]

[tex](\frac{3-1}{5})n=\frac{4}{5}[/tex]

[tex](\frac{2}{5})n= \frac{4}{5}[/tex]

Now we cross multiply the fractions

(2×5)×n = 4×5

10.n = 20

[tex]n=\frac{10}{5}=2[/tex]

Therefore answer is n = 2

The Complete sentence is shown below.

Two angles are congruent if they are supplements of the same angle (also known as congruent angles).

The Complete sentences will be

∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)

∠EIA  ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)

∠IKL + ∠IKC 180°    (Linear Pair Theorem)

and ∠DLH +  ∠JLD =180° (Linear Pair Theorem)

Then, m∠IKL + m∠IKC = 180°      

Also, ∠IKC  ≅ ∠JLD

m∠IKC = m∠JLD (Subtraction Property OF Congruency)

Thus, m∠IKL + m∠JLD = 180°

As, ∠IKL and ∠JLD are supplementary angles.

But ∠DLH and ∠JLD are supplementary angles.

∠IKL ≅ ∠DLH (Congruent Supplements Theorem)

Learn more about Congruent Supplements Theorem here:

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