Find the surface area of a hexagonal pyramid with a apothem of 3 square root of 2 and height of 3

(a) If we draw 2 letters from a bag containing 26 letters of alphabet, and we return the letters in between the draws, the probability of drawing a "W" both the time is 1/676.

(b) If we toss two-cubes numbered 1 to 6 each time, then probability that we toss a 6 on first cube and a odd number on second cube is 1/12.

Part (a) : The letters in between the draws are returned, which means each draw is independent of the other.

So, the probability of drawing a "W" on any single draw is 1/26.

The probability of drawing a "W" both times is written as :

P(W and W) = P(W) × P(W) = (1/26) × (1/26) = 1/676,

Therefore, the probability of drawing a "W" both times is 1/676.

Part (b) : The probability of getting a 6 on the first-cube is = 1/6, and

The probability of getting an "odd-number" on the second cube is = 3/6, (because there are 3 odd numbers out of a total of 6 numbers).

The probability of 6 on first-cube and odd number on second, cube is written as ;

⇒ P(6 and odd) = P(6) × P(odd) = (1/6) × (3/6) = 1/12,

Therefore, the required probability is 1/12.

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This is an example of a correlation between the two variables, where they tend to change together in a predictable way, but it does not necessarily imply causation.

This is an example of a correlation between the two variables. When two variables are correlated, they tend to change together in a predictable way. In other words, when one variable goes up, the other tends to go up as well, or when one variable goes down, the other tends to go down as well.

It's important to note that correlation does not necessarily imply causation. Just because two variables are correlated, it does not mean that one causes the other. There may be other factors that influence both variables, or the correlation may be coincidental. To establish causation, a more rigorous study design and analysis is required.

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Answer:

1. 25.74

2. 13.13

3. 9.31

4. 13.47

Step-by-step explanation:

1. solution: C=  (A^2 + B^2 - 2 ab cosy) = C= (10^2 + 19^2 - 2 * 10 * 19 cos (122 degrees) = 25.73654 rounded to the nearest 10 is 25.74

2. Solution: C= (A^2 + B^2 - 2 ab cosy) = C= (14^2 + 8^2 - 2 * 14 * 8 * cos (67 degrees) = 13.13302 rounded to the nearest 10 is 13.13

3. Solution: C=(A^2 + B^2 - 2 ab cosy) = C= (15^2 + 13^2 - 2 * 15 * 13 * cos (38 degrees) = 9.30998 rounded to the nearest 10 is 9.31

4. Solution: C=(A^2 + B^2 - 2 ab cosy) = C= (34^2 + 26^2 - 2 * 34 * 26 * cos (21 degrees) = 13.46959 rounded to the nearest 10 is 13.47

Hope this helped  

Answer:

x = 2, y = -3 and z = 1.

Step-by-step explanation:

3x+4y-z=-7  ............. A

X-5y+2z=19 ..............B

5x+y-2z=5  ...............C

Adding equations B and C to eliminate z:

6x - 4y + 0 =  24

6x - 4y = 24.............D

Now we multiply Equation A by 2:-

6x + 8y - 2z = -14

Now adding this to equation B, ( again to eliminate z) we get equation E:

7x + 3y = 5 -----------E

Bring down equation D:

6x - 4y = 24.............D

Multiplying  E by 4 and D by 3:

28x + 12y = 20

18x - 12y = 72

Adding:

46x = 92

x = 2.

and substituting in equation D

6(2)- 4y = 24

-4y = 12

y = -3.

Finally we find z by substituting in equation A:

3(2) + 4(-3) - z = -7

-z = -7 - 6 + 12

-z = -1

z = 1.

The required value of the x is 13 in the measures of the angle.

Given that,

Line A and B are parallel lines and intersect by a transversal line.

Here,

If a pair of parallel lines intersect by the transversal line then their corresponding angles are equal in measure,

Thus, we get;

8x + 2 = 14x - 76

6x = 78

x = 78 / 6

x = 13

Thus, the required value of the x is 13 in the measures of the angle.

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The minimum value of the given function is 3 at x=-5.

By locating the vertex of the parabola that the function defines, we may determine the lowest or maximum value of G(x).

The x-coordinate of the vertex may be determined by using the formula x = -b/(2a), where a and b are the coefficients of the quadratic components in the function.

In this case, a = 3 and b = 30, so:

x = -b/(2a) = -30/(2*3) = -5

Now we can find the y-coordinate of the vertex by plugging in x = -5 into the function:

[tex]G(-5) = 3(-5)^2 + 30(-5) + 78 \\= 3(25) - 150 + 78 \\= 3(25) - 72 \\= 3(25 - 24) \\= 3(1) \\= 3[/tex]

Therefore, the minimum value of G(x) is 3 and there is no maximum value.

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A pie chart is effective for demonstrating percentages that make up a whole. It shows the proportions of a whole by dividing it into slices, where the size of each slice represents the percentage of the whole that it represents.

Pie charts are commonly used to represent data such as market share, budget allocations, or demographic breakdowns.

They are useful for quickly conveying the relative sizes of different categories within a dataset.

However, pie charts may not be as effective for showing trends over time, where things are located on a map, or relationships between variables, as other types of graphs such as line charts, maps, or scatter plots may be more appropriate for these purposes.

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Answer:

x=12

Step-by-step explanation:

given: 9(x-11)=9

Distribution: 9x-99=9

Simplify:(common denominator is 9) x-11=1

x=12

Step-by-step explanation:

multiply the 9 in the brackets, so the equation will be 9x-99=9.

next move -99 to the other side and change its sign

making the equation 9x=108

now diveide both sides by 9 to leave x alone.

x=12 is the final answer;)

The equations that represent exponential growth are [tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t,[/tex] [tex]P = 1700(1.07)^t[/tex] and the equations that represent exponential decay are [tex]A = 80(1/2)^t, A = 1600(0.8)^t,[/tex] and [tex]P = 1700(0.93)^t.[/tex]

The mathematical function used to calculate the exponential growth or decay of a given set of data is an exponential function. we can calculate changes in population, loan interest charges, bacterial growth, radioactive decay, or the spread of disease by using the exponential functions.

An exponential function is of the form:

[tex]f(x) = a ^x[/tex]

The function represents an exponential decay If b < 1

The function represents an exponential growth If b > 1

From the given data about equations, we have;

Exponential Growth is;

The equation with the values b < 1 is:

[tex]A = 20,000(1.08)^t[/tex]

[tex]A = 40(3)^t[/tex]

[tex]P = 1700(1.07)^t[/tex]

Exponential Decay is;

The equation with the values b > 1 is:

[tex]A = 80(1/2)^t[/tex]

[tex]A = 1600(0.8)^t[/tex]

[tex]P = 1700(0.93)^t[/tex]

Therefore, The equations that represent exponential growth are[tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t[/tex], and[tex]P = 1700(1.07)^t[/tex]  the equations that represent exponential decay are [tex]A = 80(1/2)^t[/tex], [tex]A = 1600(0.8)^t\\[/tex], and [tex]P = 1700(0.93)^t.[/tex]

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The complete question is

Which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table

Answer:

[tex] \sqrt{ {( - 3 - ( - 5))}^{2} + {( - 4 - 2)}^{2} } [/tex]

[tex] \sqrt{ {2}^{2} + {( - 6)}^{2} } [/tex]

[tex] \sqrt{4 + 36} = \sqrt{40} = 2 \sqrt{10} [/tex]

The area of the given tile is 36.5 cm² which is in the form of trapezoid

A trapezoid is a four-sided geometric shape with one pair of parallel sides.

The two non-parallel sides are usually referred to as the "legs" and the other two sides are the "bases".

A trapezoid can be either isosceles or non-isosceles depending on the angles of the legs. A trapezoid can also be equilateral if all four sides have equal lengths.

The area of the tile can be calculated by using the formula for the area of a trapezoid, A = (a+b)/2× h

where a and b represent the parallel sides, and h represents the height.

In this case, a = 5 cm, b = 6 cm, and h = 3 cm

A = (5 + 6)/2 × 3

= 36.5 cm².

Hence, the area of the given tile is 36.5 cm²

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230.26

"How so?"

First of all, formulate: 70.2% x 328

Then convert the percentage to decimals: 0.702 x 328

Now calculate the quotient: 230.256 and round it: 230.26

I apologize if anything is incorrect! Have a good day and good luck! <3

Answer: 230.58

Step-by-step explanation:

To find 70.2% of 328, we multiply 70.2% (or 0.702 as a decimal) by 328:

0.702 x 328 = 230.5776

Rounding this to the nearest hundredth gives:

230.58

Therefore, 70.2% of 328 rounded to the nearest hundredth is 230.58.

Answer:

Step-by-step explanation:

If he puts smarty back

because it's an "and" multiply by the 2 possibilities

4/12 *4/12

=1/3 *1/3

=1/9

If does not put smarty back

4/12 *3/11

=1/3*3/11

=3/33

both sides are equal, we can conclude that n = 150/29 is the correct solution.

What is an Equations?

Equations consist of two algebraic expressions separated by an equal (=) sign, representing the equality between the expressions on the left and right sides. Solving equations helps to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol, a statement cannot be considered an equation and is instead considered an expression.

(2n)/3 + 1 = (7n)/15 + 3 // subtract 1 from both sides

(2n)/3 = (7n)/15 + 2 // multiply both sides by 15 to eliminate fractions

10n = 3(7n)/5 + 30 // multiply both sides by 3

10n = 21n/5 + 30 // subtract 21n/5 from both sides

50n/5 - 21n/5 = 30 // simplify fractions

29n/5 = 30 // multiply both sides by 5/29

n = 150/29

To check the solution, we substitute n = 150/29 back into the original equation and see if both sides are equal:

(2n)/3 + 1 = (7n)/15 + 3

(2(150/29))/3 + 1 = (7(150/29))/15 + 3

100/29 + 1 = 70/29 + 3

129/29 = 129/29

Since both sides are equal, we can conclude that n = 150/29 is the correct solution.

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The annual interest rate of the account is 3.5%

From the question, we have the following parameters that can be used in our computation:

Principal = 12000

Time = 14 years

Amount = 17880

The amount of simple interest is calculated using

A = P(1 + RT)

Substitute the known values in the above equation, so, we have the following representation

12000 * (1 + R * 14) = 17880

So, we have

(1 + R * 14) = 1.49

This gives

14R = 0.49

Divide

R = 3.5%

Hence, the interst is 3.5%

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so let's say A(-3 , -10) and B(9 , 5), so that point C partitions it in a 1 : 2 ratio from A to B

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-3,-10)\qquad B(9,5)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-3,-10)=1(9,5)[/tex]

[tex](\stackrel{x}{-6}~~,~~ \stackrel{y}{-20})=(\stackrel{x}{9}~~,~~ \stackrel{y}{5}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-6 +9}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-20 +5}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ 3 }{ 3 }~~,~~\cfrac{ -15}{ 3 } \right)\implies C=(1~~,~-5)[/tex]

Answer:

7.21x3.86/10.09

7 x 4 / 10

28 / 10

2.8

Answer: not compleatly sure but its possibly C  

The most appropriate one-sample test of hypothesis to test the belief that the average tenure of a U.S. worker is 4.6 years is option (c) a lower one-tailed test.

The reason for this is that the article states a specific average tenure of U.S. workers (4.6 years), and the hypothesis we want to test is whether this average tenure is lower than this value or not. We are not interested in whether the average tenure is higher than 4.6 years, so a two-tailed test or an upper one-tailed test would not be appropriate.

Therefore, we would use a lower one-tailed test to test the null hypothesis that the average tenure of U.S. workers is 4.6 years or higher, against the alternative hypothesis that the average tenure is lower than 4.6 years. We would then use statistical analysis to determine whether the evidence supports rejecting the null hypothesis in favor of the alternative hypothesis.

Therefore, the correct option is (c) a lower one-tailed test

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Answer:

If 4 units equal 16 ounces, we can find the value of 1 unit by dividing both sides by 4:

4 units = 16 ounces

4 units ÷ 4 = 16 ounces ÷ 4

1 unit = 4 ounces

So, 1/4 x 16 ounces = 4 ounces.

4/1 is the answer in fraction :)

The three equations are:

3x = 30.3

30.3 - x = 27.3

3x + 30.3 = 63.6

We have,

Equation 1:

3x = 30.3

Solving for x, we can divide both sides by 3:

x = 10.1

Equation 2:

30.3 - x = 27.3

Solving for x, we can subtract 27.3 from both sides:

x = 3

Equation 3:

3x + 30.3 = 63.6

Solving for x, we can first subtract 30.3 from both sides:

3x = 33.3

Then, we can divide both sides by 3:

x = 11.1

Thus,

The three equations are:

3x = 30.3

30.3 - x = 27.3

3x + 30.3 = 63.6

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The exact spread of the t-distribution depends on the number of degrees of freedom. (Option A)

The t distribution is a probability distribution that is used in hypothesis testing and confidence interval estimation when the population standard deviation is unknown. It is similar to the standard normal distribution, but its spread (or variability) depends on the sample size and the number of degrees of freedom (df).

The degree of freedom (df) is a parameter that determines the shape of the t distribution. It is defined as the number of observations in the sample minus one (df = n-1), where n is the sample size. As the sample size increases, the t distribution becomes closer to the normal distribution, which has infinite degrees of freedom.

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The radius of the circle as given is; 3.

The center of the circle as given is; (-4, 1).

It follows from the task content that the center and radius of the given circle image and radius are to be determined.

Recall, the center-radius equation of a circle takes the form;

(x - h)² + (y - k)² = r² where center is; (h, k) and radius is r.

By observation of the graph as well as the given equation of the circle, the pair of coordinates for the center is; (-4, 1).

Also, since the radius is the distance from the center to any point on the circumference of the circle; the radius of the circle is; 3.

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The value of

1. sin(tetha) = 8/√89

2. cos(tetha) = 5/√89

3. sec(tetha) = √89/5

4. cosec(tetha) = √89/8

5. cot( tetha) = 5/8

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(tetha) = opp/hyp

tan(tetha) = opp/adj

cos(tetha) = adj/hyp

This means that, since tan(tetha) = 8/5 , the adj is 5 and the opp is 8

Using Pythagorean theorem,

hyp = √opp²+adj²

hyp = √8²+5²

hyp = √64+25

hyp = √89

therefore;

sin(tetha) = 8/√89

cos(tetha) = 5/√89

sec(tetha) = 1/cos(tetha) = √89/5

cosec(tetha) = 1/sin(tetha) = √89/8

cot (tetha) = 1/tan(tetha) = 5/8

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The total amount that the invisible man will pay for the chair is $9, 240.

Seeing as this is simple interest, the total amount paid for the chair would be the total amount the man pays the bank after 5 years:

= Principal borrowed x Interest rate x Time

= 6, 600 x 8 % x 5

= 6, 600 x 40 %

= $ 2, 640

The total amount the invisible man would pay is:

= Cost of chair + Interest over 5 years

= 6, 600 + 2, 640

= $ 9, 240

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Karim and Ali have different conclusions about the closure property for whole numbers and integers because when two whole numbers are subtracted, the result may not be a whole number, but when two integers are subtracted, the result is always an integer. Therefore, integers are closed under subtraction, but whole numbers are not.

Karim and Ali, both  have different conclusions about the closure property for whole numbers and integers because of their definitions.

Whole numbers are defined as all positive integers, including zero. When two whole numbers are subtracted, the result may not be a whole number because the result may be a negative number.

For example, when 3 is subtracted from 2, the result is -1, which is not a whole number.

Integers, on the other hand, are defined as all positive and negative whole numbers, including zero. When two integers are subtracted, the result is always an integer because the result may be a negative or positive number, but it will always be a whole number.

For example, when 3 is subtracted from 2, the result is -1, which is still an integer.

Therefore, Karim and Ali have different conclusions because whole numbers are not closed under subtraction, but integers are closed under subtraction.

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The 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings is (3.36, 13.78).

To construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings, we can use a two-sample t-test with equal variances.

Let x₁ be the number of blocked intrusions per day before the change of firewall settings, and let x₂ be the number of blocked intrusions per day after the change of firewall settings. We have

x₂ = (56+47+49+37+38+60+50+43+43+59+50+56+54+58)/14 = 50.36

x₂ = (53+21+32+49+45+38+44+33+32+43+53+46+36+48+39+35+37+36+39+45)/20 = 40.95

s₁ = standard deviation of x₁ = 8.23

s₂ = standard deviation of x₂ = 8.98

The pooled standard deviation, sp, is given by

sp = √(((n₁-1)s₁² + (n₂-1)s₂²)/(n₁+n₂-2))

where n₁ and n₂ are the sample sizes. Since we assume equal variances, we use the formula for the pooled standard deviation. Substituting the values, we get:

sp = √(((14-1)8.23² + (20-1)8.98²)/(14+20-2)) = 8.63

The t-statistic for the difference between the means is given by

t = (x₁ - x₂) / (sp × √(1/n₁ + 1/n₂))

Substituting the values, we get

t = (50.36 - 40.95) / (8.63 × √(1/14 + 1/20)) = 2.28

We can use a t-distribution with degrees of freedom = n₁ + n₂ - 2 = 32 and a significance level of α = 0.05 to find the confidence interval. The confidence interval is given by

(x₂ - x₂) ± tsp√1/n₁ + 1/n₂)

Substituting the values, we get

(50.36 - 40.95) ± 2.0458.63√(1/14 + 1/20) = 8.57 ± 5.21

= (3.36, 13.78)

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The given question is incomplete, the complete question is:

The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56,47,49,37,38,60,50,43,43,59,50,56,54,58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53,21,32,49,45,38,44,33,32,43,53,46,36,48,39,35,37,36,39,45. construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances).

Answer:

  0.13824

Step-by-step explanation:

You want the probability of exactly 4 successes in 6 trials if the probability of success in each trial is 0.4.

The probability of k successes in n trials with each having a probability of success of p is given by the formula ...

  P(k of n) = nCk·p^k·(1-p)^(n-k)

  P(4 of 6) = 6C4·0.4^4·0.6^2 = 15·0.0256·0.36 = 0.13824

The probability of exactly 4 successes is 0.13824.

__

Additional comment

The binomial coefficient nCk is computed as ...

  nCk = n!/(k!(n-k)!)

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1)The probability that the team will pull a hamstring muscle = 0.240. 2)The probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game = 0.020.

Given that hamstring injuries on the team follow an exponential distribution with an average time between injuries of 342 minutes, we can use the formula for the exponential distribution to answer the following questions:

1)The time duration of a game is 90 minutes. Therefore, the probability of a hamstring injury occurring during a game can be calculated as follows:

λ = 1/342 injuries per minute (since on average there is one injury every 342 minutes)

t = 90 minutes (duration of a game)

P(X ≤ t) = 1 - e^(-λt)

P(X ≤ 90) = 1 - e^(-1/342 * 90) ≈ 0.2399

So the probability that the team will pull a hamstring muscle in the next game is approximately 0.2399 (or 0.240 when rounded to 4 decimal places).

2)The probability of a hamstring injury occurring between the 15th and 25th minute of the game can be calculated as follows:

λ = 1/342 injuries per minute (since on average there is one injury every 342 minutes)

t1 = 15 minutes (starting time)

t2 = 25 minutes (ending time)

P(t1 < X ≤ t2) = e^(-λt1) - e^(-λt2)

P(15 < X ≤ 25) = e^(-1/342 * 15) - e^(-1/342 * 25) ≈ 0.0199

So the probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game is approximately 0.0199 (or 0.020 when rounded to 4 decimal places).

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Answer:

Vertical translation

Step-by-step explanation: