An urn contains six red balls, five black balls, and four green balls. If two balls are selected at random without replacement from the urn, what is the probability that a red ball and a black ball will be selected. Please explain how to do it

To find the slant height of a square pyramid, we can use the Pythagorean theorem. The theorem should be applied as follows: A² = (y² + h²), to solve for A which is the slant height. Radical form implies that the answer will include the square root symbol.

The question asks to find out the slant height x of a square pyramid. In order to do that, we have to invoke the Pythagorean theorem (x² + y² = h²). Here, x represents the slant height, y could be the half of the side of the base of the pyramid and h is the height from the base to the tip of the pyramid. Assuming that the pyramid is a right pyramid, the Pythagorean theorem applies.

So, the equation becomes A² = y² + h², where A is the slant height we are looking for. We solve for A to get, A = √(y² + h²). This is your slant height in radical form.

Please note you would need specific values for y and h to compute the numerical value of A.

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The Polynomial Remainder Theorem in mathematics states that the remainder of dividing a polynomial P(x) by (x - a) is P(a). This theorem is linked to the Binomial theorem for series expansions and is useful in graphing and solving polynomials and quadratic equations.

The Polynomial Remainder Theorem is a concept in mathematics associated with series expansions and equation graphing. This theorem states for a given polynomial P(x) and a number a, when P(x) is divided by the binomial (x - a), the remainder is P(a). This is a crucial concept when graphing polynomials, as understanding the remainder can assist in predicting the behavior of the polynomial curve. The theorem is tied to the Binomial theorem which provides a series expansion for expressing powers of a sum of terms (a + b)^n in terms of a and b.

To solve quadratic equations, which are second-order polynomials, the Polynomial Remainder Theorem can also be utilized. It can further clarify the solutions of quadratic functions when they are graphed. Furthermore, in the realm of function graphing, the theorem aids in visualizing how different terms contribute to the shape of the polynomial curve.

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Answer:

The measure of ∠X is 135°

Step-by-step explanation:

Given that angles X and Y are supplementary and also angle X is 3 times the measure of angle Y.

we have to find the measure of angle X.

Since X and Y are the supplementary therefore these add up to 180° i.e

[tex]\angle X+\angle Y=180\°......(1)[/tex]

Also angle X is 3 times the measure of angle Y i.e

[tex]\angle X=3\angle Y[/tex]

Substitute this value in equation (1), we get

[tex]3\angle Y+\angle Y=180\°......(1)[/tex]

[tex]4\angle Y= 180\°[/tex]

[tex]\angle Y=\frac{180\°}{4}=45\°[/tex]

[tex]\angle X=3\times 45\°=135\° [/tex]

Hence, the measure of ∠X is 135°

Answer:

Option 1  

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

Step-by-step explanation:

Given :

The outcomes are :             1         2         3        4        5

The Relative Frequency : 0.05   0.35   0.26   0.13    0.21

To find : Which statement about Pilar's experiment is true?

Solution :

We can see the outcomes do not appear to be equally likely.

Since 0.05 and 1 are not close in number range along with the other options.

So, The outcomes do not appear to be equally likely.

Uniform probability model - A model in which every outcome has equal probability.

But in given case, Probabilities in Pilar's experiment does not support a uniform probability model.

So, A uniform probability model is not a good model to represent probabilities in Pilar's experiment.

Therefore, Option 1 is correct.

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

To determine whether a uniform probability model is appropriate, we need to assess if each outcome has the same likelihood of occurring. In a uniform probability model, if there are 'n' possible outcomes, each outcome has a probability of 1/n.

In Pilar's experiment, she selects a card 46 times, and we are given the relative frequencies of the outcomes 1 through 5. If the outcomes were equally likely, we would expect each number to have a relative frequency of approximately 1/5, since there are 5 different numbers.

Let's calculate the expected relative frequency for each number if the outcomes were equally likely:

Expected relative frequency for each number = 1/5 = 0.2.

Now, let's compare this with the given relative frequencies:

These relative frequencies are not close to the expected relative frequency of 0.20 for a uniform distribution. Since the relative frequencies vary significantly from one another, 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 Pilar's experiment.

Hence, the correct conclusion is that the outcomes do not appear to be equally likely, and thus a uniform probability model is not suitable for representing the probabilities in Pilar's experiment.

The complete question is Whole numbers are written on cards and then placed in a bag. Pilar selects a single card, writes down the number, and then places it back in the bag. She repeats this 46 times.

Pilar calculates the relative frequency of each number card.

Outcome 1 2 3 4 5

Relative Frequency 0.05 0.35 0.26 0.13 0.21

Which statement about Pilar's experiment is true?

A) The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment.

B) The outcomes appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment.

C) The outcomes do not appear to be equally likely, so a uniform probability model is a good model to represent probabilities in Pilar's experiment.

D) The outcomes appear to be equally likely, so a uniform probability model is a good model to represent probabilities in Pilar's experiment.

The missing number will be 108. The sequence is; 4, 12, 36,108, 324, 972, 2916.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The given sequence is;

4, 12, 36,108, 324, 972, 2916

It is observed from the sequence that the following sequence follow a specific rule in which the progressive term is multiplied by a factor of 3.

[tex]\rm 4 \times 3 = 12 \\\\ 12 \times 3 = 36 \\\\ 36 \times 3 =108[/tex]

Hence, the missing number will be 108.

Learn more about the sequence here:

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The distributive property of multiplication is a very useful property that lets you simplify expressions in which you are multiplying a number by a sum or difference. The property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of the products – in this case, 6(5) – 6(2).

Remember that there are several ways to write multiplication. 3 x 6 = 3(6) = 3 • 6.

3 • (2 + 4) = 3 • 6 = 18.

Distributive Property of Multiplication over Addition

The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2.

3(10 + 2) = ?

According to this property, you can add the numbers and then multiply by 3.

3(10 + 2) = 3(12) = 36. Or, you can first multiply each addend by the 3. (This is called distributing the 3.) Then, you can add the products.

The multiplication of 3(10) and 3(2) will each be done before you add.

3(10) + 3(2) = 30 + 6 = 36. Note that the answer is the same as before.

You probably use this property without knowing that you are using it. When a group (let’s say 5 of you) order food, and order the same thing (let’s say you each order a hamburger for $3 each and a coke for $1 each), you can compute the bill (without tax) in two ways. You can figure out how much each of you needs to pay and multiply the sum times the number of you. So, you each pay (3 + 1) and then multiply times 5. That’s 5(3 + 1) = 5(4) = 20. Or, you can figure out how much the 5 hamburgers will cost and the 5 cokes and then find the total. That’s 5(3) + 5(1) = 15 + 5 = 20. Either way, the answer is the same, $20.

The two methods are represented by the equations below. On the left side, we add 10 and 2, and then multiply by 3. The expression is rewritten using the distributive property on the right side, where we distribute the 3, then multiply each by 3 and add the results. Notice that the result is the same in each case.

Final answer:

To test whether the proportion of babies born in September is higher than the expected proportion of 1/12, we can use hypothesis testing. Given a sample of 150 students, with 21 of them born in September, we calculate the test statistic, compare it to the critical value, and make a decision.

Explanation:

To test whether the proportion of babies born in September is higher than the expected proportion of 1/12, we can use hypothesis testing. Let's set up the hypotheses:

Null Hypothesis (H0): The proportion of babies born in September is equal to 1/12.

Alternative Hypothesis (Ha): The proportion of babies born in September is greater than 1/12.

We can use a one-sample proportion test to test these hypotheses. Given that we have a simple random sample of 150 students at your school and 21 of them were born in September, we can calculate the sample proportion: 21/150 = 0.14.

Next, we calculate the test statistic using the formula: test statistic = (sample proportion - null proportion) / standard error. The null proportion is 1/12 = 0.0833, and the standard error is √[(null proportion * (1 - null proportion)) / sample size]. Calculating the test statistic gives us: test statistic = (0.14 - 0.0833) / √[(0.0833 * (1 - 0.0833)) / 150] = 2.92 (rounded to two decimal places).

Finally, we compare the test statistic to the critical value(s) at a chosen significance level to make a decision. The critical value(s) depend on the significance level and the direction of the alternative hypothesis. If the test statistic falls in the rejection region (i.e., it is greater than the critical value), we reject the null hypothesis and conclude that the proportion of babies born in September is higher than 1/12.

Answer:

b. [tex](-3,6)[/tex]

Step-by-step explanation:

We have been given that triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up.

To find the coordinates of B', we will shift x-coordinate of point B to left by 3 units and y-coordinate of point B to 1 unit up.

After the given transformation the coordinates of point B' would be:

[tex]B(0,5)\rightarrow B'((0-3),(5+1))\rightarrow (-3,6)[/tex]

Therefore, the coordinates of point B' are [tex](-3,6)[/tex] and option 'b' is the correct choice.

Answer:

The image of the point (4, -2) is (2, 4).

Step-by-step explanation:

Since, the rule of rotation 270 degree clockwise about the origin is,

[tex](x,y)\rightarrow (-y,x)[/tex]

Where, (-y,x) is the image of the point (x,y),

Thus, by the above rule,

[tex](4,-2)\rightarrow (-(-2), 4)[/tex]

Hence, the image of the point (4, -2) is (2, 4).

The new coordinates of Point H' will be (6, -5) after the translation.

Triangle ABC is translated on the coordinate plane below to create triangle A'B'C':

If parallelogram EFGH is translated according to the same rule that translated triangle ABC.

In the triangle, point A is moved 5 units to the right side and down 6 units.

If we count the same amount of space right side and down from point H, we will end up on a point (6, -5).

Therefore, The new coordinates of Point H' will be (6, -5) after the translation.

Learn more about translation;

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The practical domain of the function p(h) = 40h - 250 for Vonda's weekly pay is between 30 and 32 hours, inclusive, with increments of 0.25 hours. These values represent all the possible hours Vonda can work in a week.

To determine the practical domain of the function p(h) = 40h - 250, we need to consider the range of hours that Vonda works. The problem states that Vonda works between 30 and 32 hours per week, and her hours are rounded to the nearest quarter hour. Therefore, the possible values for h (in hours) are:

Hence, the practical domain of the function p(h) is all the values between 30 and 32, inclusive, measured in quarter-hour increments.

Answer:

below the x axis

Step-by-step explanation:

i took the test

Final answer:

Jana has completed 11/12 or 11 out of 12 of her homework so far.

Explanation:

To find out how much of her homework Jana has finished so far, we need to add together the fractions of her homework completed at school and before dinner.

Jana finished 1/4 of her homework at school and 2/3 of it before dinner.

To add fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we can convert both fractions to have a denominator of 12.

1/4 is equivalent to 3/12, and 2/3 is equivalent to 8/12.

Now, we can add the fractions: 3/12 + 8/12 = 11/12.

Therefore, Jana has completed 11/12 or 11 out of 12 of her homework so far.

Answer:

The length of DD' is [tex]\sqrt{29}[/tex] or 5.39 units.

Step-by-step explanation:

The distance formula is

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

From the given figure it is clear that the coordinates of D are (2,0) and coordinates of D' are (7,2).

Using distance formula we get

[tex]DD'=\sqrt{(7-2)^2+(2-0)^2}[/tex]

[tex]DD'=\sqrt{25+4}[/tex]

[tex]DD'=\sqrt{29}[/tex]

[tex]DD'\approx 5.39[/tex]

Therefore the length of DD' is [tex]\sqrt{29}[/tex] or 5.39 units.

Answer:  The answer is (C) Place the point of the compass on point C and draw an arc that intersects AC and BC.

Step-by-step explanation:  Given that Russ is constructing the inscribed circle for △ABC and he has already used his compass and straightedge to complete the part of the construction shown in the given figure. We are to find his next step.

Since Russ has already constructed the angle bisector of ∠B, so next he shoul construct the angle bisector of either ∠A or ∠C. Since the steps for constructing angle bisector of ∠A are not in the options, so he should go with ∠C. For that, he must place the point of the compass on the point C and draw an arc that intersects AC and BC.

Thus, (C) is the correct option.