Determine whether the triangles are similar. If similar, state how (SA, SSS, or SAS), and write a similarity statement

Thus, the probability of being dealt a full house with an Ace of Hearts is 0.0457% (rounded to 4 decimal places).

To calculate the probability of being dealt a full house with an Ace of Hearts in a standard 52-card deck, we can use the following formula:

=(number of ways to get a full house with an Ace of Hearts) / (total number of 5-card poker hands)

The total number of 5-card poker hands is C(52,5) = 2,598,960.

To count the number of ways to get a full house with an Ace of Hearts, we need to consider the following:

We choose 2 of the remaining 3 Aces from the deck: C(3,2) = 3

We choose 2 of the 12 remaining ranks for the other 2 cards: C(12,2) = 66

For each rank, we need to choose 2 cards from the 4 of that rank: C(4,2) = 6

Therefore, the number of ways to get a full house with an Ace of Hearts is 3 x 66 x 6 = 1,188.

Thus, the probability of being dealt a full house with an Ace of Hearts is:

1,188 / 2,598,960 ≈ 0.000457 = 0.0457% (rounded to 4 decimal places)

To know more about probability,

https://brainly.com/question/31599842

#SPJ11

We can begin by noting that 153° is the supplement of 27°, meaning that the sum of the two angles is 180°.

From this, we can use the fact that the sine function has a period of 360° to express the sine of 153° in terms of the sine of 27°. Specifically, we know that the sine of an angle and its supplement are equal, but the sine of an angle and its complement are not. Therefore, we can write: sin 153° = sin(180° - 27°) = sin 27°So we can say that sin 153° = t, since we were given that sin 27° = t. This result allows us to express the sine of 153° in terms of t, which was the goal of the problem.  In summary, we used the fact that 153° is the supplement of 27°, and the periodicity of the sine function, to express sin 153° in terms of sin 27° = t. This led us to the solution sin 153° = t, which provides a way of expressing the value of 153° in terms of t.

Learn more about supplement here: brainly.com/question/15320080

#SPJ11

(a) Isla's trading cards are 125% of Lily's trading cards.

(b) Lily's trading cards are 80% of Isla's trading cards.

Given that,

There are 225 trading cards and Lily has 180 trading cards.

To calculate the percentage of Isla's trading cards compared to Lily's,

We can use this formula:

⇒ Isla's trading cards / Lily's trading cards x 100%

Plugging in the values we get:

⇒ (225 / 180) x 100% = 125%

Therefore,

Isla's trading cards are 125% of Lily's trading cards.

b) To calculate the percentage of Lily's trading cards compared to Isla's, we can use the formula:

⇒ Lily's trading cards / Isla's trading cards x 100%

Plugging in the values we get:

(180 / 225) x 100% = 80%

Therefore,

Lily's trading cards are 80% of Isla's trading cards.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

6 x 7 = 42

6 x 8 = 48

6 x 9 = 54

So, 12, 18, 24, 30, 36, 42, and 48.

I assume "between" means we aren't including 6 and 54.

The true statement is,

⇒ The joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.

Now, Based on the given table, the statement that is true about the joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.

Since, The given table shows that in the first column, under the ninth grade row, there are 18 students who prefer math and in the third column, under the 11th grade row, there are 15 students who prefer science.

Hence, There are no joint frequencies given that add up to 23, so the only true statement among the options is the first one.

Thus, The true statement is,

⇒ The joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer answer is b dont trust the otha dude

Step-by-step explanation:

The distribution that t follows is the maximum of three independent exponential distributions with a mean of 5 minutes each.

Each block takes an exponential amount of time with a mean of 5 minutes, which means that the time it takes to compile each block follows an exponential distribution with a rate parameter of 1/5. Since the blocks are being compiled independently of each other, the time it takes to compile all three blocks is the maximum of the three independent exponential distributions.

This distribution is known as the maximum of exponential distributions or the generalized extreme value distribution with a shape parameter of 0 and scale parameter of 5 minutes. Therefore, t follows a generalized extreme value distribution with a shape parameter of 0 and scale parameter of 5 minutes.

To know more about distributions visit:

https://brainly.com/question/29062095

#SPJ11

Answer:112 players

Step-by-step explanation:

To solve the problem, we can use the formula:

Total number of players = Number of teams × Number of players per team

Since there are 14 teams with 8 players each, we have:

Total number of players = 14 × 8 = 112

Therefore, there are 112 players in the soccer league.

Answer:

Step-by-step explanation:

x^4+13^x^2+36=4x^3+36

4x+26x+36=4x^3+36

30x+36=12x+36

30x=12x

so,x=1

Answer:

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

∠ADC and ∠ABC subtend the same arc AC, hence ∠ABC is double the measure of ∠ADC:

To find the ratio of the volumes of two similar right cylinders, we need to know the ratio of their heights and radii. We can use the fact that the ratio of their surface areas is 36:121 to determine this. So, the ratio of the volumes of the two right cylinders is 216:1331.
Let the height and radius of the first cylinder be h1 and r1, respectively, and the height and radius of the second cylinder be h2 and r2, respectively. Then, we can write:
(2πr1h1)/(2πr2h2) = 36/121
Simplifying this equation, we get:
r1h1/r2h2 = 18/121
Since the cylinders are similar, we know that their ratios of heights and radii are equal. So, we can write:
r1/r2 = h1/h2 = x
Substituting this into our equation above, we get:
x^2 = 18/121
x = √(18/121) = 3/11
Therefore, the ratio of the volumes of the two cylinders is:
(r1^2h1)/(r2^2h2) = (r1/r2)^2(h1/h2) = (3/11)^2 = 9/121
In other words, the volume of the second cylinder is 121/9 times the volume of the first cylinder. Answer more than 100 words.
The ratio of the surface areas of two similar right cylinders is 36:121. To find the ratio of their volumes, we can use the fact that when two similar solids have a ratio of their surface areas (A1:A2), the ratio of their volumes (V1:V2) is the cube of the ratio of their corresponding linear dimensions (L1:L2).
First, let's find the ratio of the linear dimensions:
√(A1/A2) = √(36/121) = 6/11
Now, cube the ratio of the linear dimensions to find the ratio of their volumes:
(6/11)^3 = (6^3)/(11^3) = 216/1331
So, the ratio of the volumes of the two right cylinders is 216:1331.

To know more about Ratio visit:

https://brainly.com/question/29467965

#SPJ11

The distance d from P to the point (0,0) is √x²+x.

What is the distance formula?

The d-distance between two places is calculated using the distance formula. The distance formula determines how far apart two areas are from one another. The dimensions of these points are unlimited.

Here, we have

Given: Let P(x,y) be a point on the graph of y=√x.

We have to find the distance d from P to the point (0,0)(0,0) as a function of x.

Since P = (x,y) is on the graph of y =√x,

P can be expressed as (x,√x).

Now, we apply the distance formula and we get

d = √[(x - 0)² + (√x - 0)²]

d = √x²+x

Hence, the distance d from P to the point (0,0) is √x²+x.

To learn more about the distance formula from the given link

https://brainly.com/question/28551043

#SPJ4

We need to convert the normal distribution of caffeine consumption to a standard normal distribution using the z-score formula. We can then look up the corresponding area under the standard normal distribution curve using a z-table.

Explanation:

To convert the normal distribution of caffeine consumption to a standard normal distribution, we use the z-score formula:

z = (x - μ) / σ

where x is the value we want to convert to a z-score, μ is the mean of the normal distribution, and σ is the standard deviation of the normal distribution.

In this case, we want to find the z-score for x = 240, μ = 240, and σ = 49:

z = (240 - 240) / 49 = 0

Since the z-score is 0, we can look up the area to the left of z = 0 in the standard normal distribution table. This area represents the percentage of adults who consume less than 240 mg of caffeine daily.

From the standard normal distribution table, we can see that the area to the left of z = 0 is 0.5000. Therefore, approximately 50% of adults consume less than 240 mg of caffeine daily.

So, the percent of adults who consume less than 240 mg of caffeine daily is 50%.

To learn more about mean click here, brainly.com/question/31101410

#SPJ11

These tests would allow us to determine if the observed sample mean of $934 is significantly different from the claimed average of $1250, providing evidence to support or reject the alternative hypothesis.

To test the claim made by the IRS representative that the average deduction for medical care is $1250, we can formulate the null and alternative hypotheses as follows:

Null Hypothesis (H0): The average deduction for medical care is $1250.

Alternative Hypothesis (H1): The average deduction for medical care is lower than $1250.

In this case, the taxpayer who believes that the real figure is lower has collected a sample of 32 random families. The sample mean is $934, and the sample standard deviation is $619. The null hypothesis assumes that the average deduction is $1250, while the alternative hypothesis suggests that it is lower than $1250.

To statistically test these hypotheses, we can use a one-sample t-test or a z-test, depending on the sample size and whether the population standard deviation is known.

Know more about alternative hypothesis here:

https://brainly.com/question/30404845

#SPJ11

Inequality for number line 1:  x ≤ -15

Inequality for number line 2:  ≥ 15

Inequality for number line 3: x ≥ 10

Inequality for number line 4: x ≤ -10

For the given number lines

We know that,

Inequalities specify the connection between two non-equal numbers. Equal does not imply inequality.

Typically, we use the "not equal symbol" to indicate that two values are not equal.

But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

For number line 1:

Since the line is starting from -15 and tending toward infinity of negative

So inequality be x ≤ -15

For number line 2:

Since the line is starting from 15 and tending toward infinity of positive

So inequality be x ≥ 15

For number line 3:

Since the line is starting from 10 and tending toward infinity of positive

So inequality be x ≥ 10

For number line 4:

Since the line is starting from 10 and tending toward infinity of positive

So inequality be x ≤ -10

To learn more about inequality visit:

https://brainly.com/question/30231190

#SPJ1

The area of the part of the plane 5x + 2y + z = 10 that lies in the first octant is 5 square units.

To find the area of the part of the plane 5x + 2y + z = 10 that lies in the first octant, we need to first find the coordinates of the three points where the plane intersects the coordinate axes.

Setting x = 0, we get 2y + z = 10, so the plane intersects the y-axis at the point (0, 5, 0).

Setting y = 0, we get 5x + z = 10, so the plane intersects the x-axis at the point (2, 0, 0).

Setting z = 0, we get 5x + 2y = 10, so the plane intersects the z-axis at the point (0, 0, 5).

We can see that the triangle formed by these three points lies entirely in the first octant.

To find the area of this triangle, we can use the formula for the area of a triangle given its vertices:

A = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Plugging in the coordinates of the three points, we get:

A = 1/2 * |(0)(5 - 0) + (2)(0 - 5) + (0)(0 - 0)| = 1/2 * |-10| = 5

Learn more about area at: brainly.com/question/30307509

#SPJ11

The rate at which the area of the circle is increasing at the moment when the circumference of the circle is 27/2 inches is 9 inches squared per second.

derivative of the circle's area with respect to time.

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.

Given that the radius is increasing at a constant rate of 2/3 inches per second, we can express this as dr/dt = 2/3.

We are also given that the circumference of the circle is 27/2 inches. The formula for the circumference of a circle is C = 2πr.

Plugging in the given circumference value, we have 27/2 = 2πr. Solving for r, we get r = (27/4π) inches.

Now, we can differentiate the area formula with respect to time:

dA/dt = d/dt (πr^2)

= 2πr(dr/dt)

Substituting the values, we have:

dA/dt = 2π(27/4π)(2/3)

= (27/2)(2/3)

= 9 inches squared per second

Know more about circumference of the circle here;

https://brainly.com/question/17130827

#SPJ11

a) Yes, this provide strong evidence that more than 15% of college students in America have at least one sibling

b) Type of error might you have committed is type 1 error.

We can use the sample proportion of students with at least one sibling (20/100 = 0.2) to calculate a test statistic, which measures how far the sample proportion is from the null hypothesis. In this case, we can use a one-sample proportion z-test to calculate the test statistic:

z = (p1 - p) / √(p * (1 - p) / n)

where p1 is the sample proportion, p is the null hypothesis proportion, and n is the sample size.

Using the values from your question, we get:

z = (0.2 - 0.15) / √(0.15 * 0.85 / 100) ≈ 1.18

We can use a standard normal distribution to find the p-value, which is the probability of getting a test statistic as extreme as the one we observed, assuming the null hypothesis is true. The p-value can be calculated as:

p-value = P(Z > z)

where Z is a standard normal random variable.

Using a calculator or a table of standard normal probabilities, we can find that the p-value is approximately 0.12.

To make a decision about whether to reject or fail to reject the null hypothesis, we compare the p-value to a significance level, which is a threshold that we set to determine how much evidence we need to reject the null hypothesis.

The most common significance level is 0.05, which means that we are willing to accept a 5% chance of rejecting the null hypothesis when it is actually true.

In this case, the p-value (0.12) is greater than the significance level (0.05), so we fail to reject the null hypothesis. This means that we do not have strong evidence to conclude that more than 15% of college students in America have at least one sibling based on this sample.

Now, let's talk about the type of error that we might have committed when testing the hypothesis. In hypothesis testing, there are two types of errors: type I error and type II error.

A type I error occurs when we reject a true null hypothesis, and a type II error occurs when we fail to reject a false null hypothesis.

To know more about hypothesis here

https://brainly.com/question/29576929

#SPJ4

Answer:

0.1 is the correct answer of this questions

Answer:4 is incorrect

Step-by-step explanation:

Answer:

4 is incorrect

Step-by-step explanation:

.

The length of the diameter of the circle is 50 inches.To find the length of the diameter of the circle, we can use the formula that relates the length of an arc to the angle it subtends and the radius of the circle.

The formula is: arc length = radius * angle

In this case, we are given that the arc length is 80 inches and the angle is 3.2 radians. Let's assume the radius of the circle is 'r'.

Plugging in the given values, we have:

80 = r * 3.2

To solve for 'r', we divide both sides of the equation by 3.2:

r = 80 / 3.2 = 25

So, the radius of the circle is 25 inches.The diameter of a circle is twice the radius, so:

Diameter = 2 * radius = 2 * 25 = 50 inches.

For such more questions on Diameter:

https://brainly.com/question/358744

#SPJ11

Hello !!

kᵃ x kᵇ = kᵃ⁺ᵇ

kᵃ ÷ kᵇ = kᵃ⁻ᵇ

4¹⁰ x 4⁵ ÷ 4⁹

= 4¹⁰⁺⁵ ÷ 4⁹

= 4¹⁵ ÷ 4⁹

= 4¹⁵⁻⁹

= 4⁶

Increasing the number of scores in the samples for an independent-measures t-statistic has the effect of increasing the likelihood of rejecting the null hypothesis while having little or no effect on measures of effect size.

As the sample-size increases, the t-statistic becomes more robust and accurate, which leads to a more precise estimate of the population parameter. This increased precision reduces the variability in t-statistic, which makes it easier to detect small differences between the means of the independent groups.

With a larger sample size, the t-statistic's sampling distribution approaches a normal-distribution, allowing for more reliable statistical inference. This results in a narrower confidence interval and a smaller p-value, increasing the likelihood of rejecting the null hypothesis when there is a true difference between the groups.

Therefore, increasing number of scores in samples enhances power of independent-measures t-statistic.

Learn more about T-Statistic here

https://brainly.com/question/19583193

#SPJ4

The historian is engaged in the process of data collection, which is the first step in the data analysis process. In this case, the historian is collecting marriage records from the archives to estimate the average age at which men married in the United States in 1956.

   Once the historian has collected the data, he will move on to the next steps in the data analysis process, which include data preparation, data analysis, and interpretation of results. In data preparation, the historian will clean, transform, and organize the data so that it is ready for analysis. In data analysis, he will use statistical methods to analyze the data and answer his research question. Finally, in interpretation of results, he will draw conclusions from the analysis and communicate his findings.

To learn more about data analysis click here : brainly.com/question/30094947

#SPJ11

The historian is engaged in the process of data collection, which is the first step in the data analysis process. In this case, the historian is collecting marriage records from the archives to estimate the average age at which men married in the United States in 1956.

  Once the historian has collected the data, he will move on to the next steps in the data analysis process, which include data preparation, data analysis, and interpretation of results. In data preparation, the historian will clean, transform, and organize the data so that it is ready for analysis. In data analysis, he will use statistical methods to analyze the data and answer his research question. Finally, in interpretation of results, he will draw conclusions from the analysis and communicate his findings.

To learn more about data analysis click here : brainly.com/question/30094947

#SPJ11

well, we know the store is having a 20% off sale, so if you go and buy a few items and the total cost is X, well, since the items are on sale, you won't be paying 100% of X, you'll be paying only 100% - 20% = 80% of X, hmmm how much is 80% of X anyway?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of X}}{\left( \cfrac{80}{100} \right)X}\implies 0.80X \\\\[-0.35em] ~\dotfill\\\\ ~\hspace{12em}\stackrel{ \textit{total amount} }{A}~~ = ~~0.80X[/tex]

The computations for the p-value of a hypothesis test about a population mean rely on the mathematical properties of the t-distribution and the sample statistics.

The p-value in statistics is the probability that the null hypothesis will be rejected if it is true. In hypothesis testing, p-values are utilized to determine whether or not the null hypothesis should be rejected. The p-value is calculated utilizing a test statistic that is based on the sample statistics and the assumptions of the null hypothesis.

The significance level, alpha, is usually set at 0.05 or 0.01 in hypothesis testing.A p-value of less than or equal to the significance level (alpha) indicates that the null hypothesis should be rejected

Learn more about hypothesis test at:

https://brainly.com/question/29744953

#SPJ11

Answer: 12.3 cm

Step-by-step explanation:

          We are given the perimeter and all but one of the missing side lengths. The perimeter is equal to all of the side lengths added together. Using this information, we can create an equation to solve for the missing length, ?.

? = 65.9 cm - (9.2 cm + 4.7 cm + 4.7 cm + 2.2 cm + 9.2 cm + 2.2 cm + 12 cm + 4.7 cm + 4.7 cm)

? = 65.9 cm - 53.6 cm

? = 12.3 cm

A positive integer y is a whole number by definition, so we are essentially being asked how many positive integers there are. There are infinitely many positive integers, so the answer to the question is also infinity.

A positive integer y is a whole number if it isn't a bit or a numeric. In other words, it's a number that can be expressed without using  fragments or numbers, and can be written as a finite sum of positive integers. For  illustration, 2, 5, and 10 are whole  figures, but3/4,1.5, and √ 2 are not.   To determine how  numerous different values of y are whole  figures, we need to understand the  parcels of whole  figures.

Whole  figures have two main  parcels they're closed under addition and  addition. This means that when you add or multiply two whole  figures, the result is always a whole number. For  illustration, 2 3 =  5 and 2 × 3 =  6, both of which are whole  figures.   To find how  numerous different values of y are whole  figures, we can start with the  lowest possible value of y, which is 1.

Learn more about whole numbers at

https://brainly.com/question/27934713

#SPJ1

The probability that more than 72% of the sampled UCF students will vote in the presidential election is approximately 0.0475 or 4.75%.

To calculate the probability that more than 72% of the sampled UCF students will vote in the presidential election, we need to use the normal distribution approximation since the sample size is large.

First, we find the mean (μ) and standard deviation (σ) of the sampling distribution using the given population proportion (p) of 0.70 and the sample size (n) of 1250:

μ = p = 0.70

σ = √(p(1-p)/n) = √(0.70 * 0.30 / 1250) ≈ 0.012

Next, we need to standardize the desired proportion of more than 72% (0.72) using the z-score formula:

z = (x - μ) / σ

z = (0.72 - 0.70) / 0.012 ≈ 1.67

Now, we can find the probability using the standard normal distribution table or calculator. The probability that more than 72% of the sampled students will vote in the presidential election is the area under the curve to the right of the z-score of 1.67.

Using the standard normal distribution table or calculator, we find that the probability is approximately 0.0475.

Therefore, the probability that more than 72% of the sampled UCF students will vote in the presidential election is approximately 0.0475 or 4.75%.

To learn more about probability from the given link

https://brainly.com/question/23417919

#SPJ4

The surface area of each cylinder would be = 777.15m²

To calculate the surface area of the given cylinder, the formula that should be use will be written below. That is;

Surface area of cylinder = 2πr²+2πrh

Where;

radius = diameter/2 = 15/2 = 7.5m

height = 9m

Surface area= 2×3.14×7.5×7.5+2×3.14×7.5×9

= 353.25+ 423.9

= 777.15m²

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

Answer:

  24 grams

Step-by-step explanation:

You want the amount remaining of 195 grams of an isotope after 3 half-lives.

Each half-life leaves 1/2 of the amount there was at the beginning of that time period. After 3 half-lives, the amount is (1/2)(1/2)(1/2) = 1/2³ = 1/8 of the original amount.

  (195 g)(1/8) = 24.375 g ≈ 24 g

About 24 grams of the isotope will remain after 3 half-lives.

<95141404393>