Q6) The diagram shows a pyramid. The apex of the pyramid is V.
Each of the sloping edges is of length 6 cm.
A
6 cm
2 cm
B
2 cm с
F
6 cm
The base of the pyramid is a regular hexagon with sides of length 2 cm.
O is the centre of the base.
B
2 cm
E
2 cm C
Calculate the height of V above the base of the pyramid.
Give your answer correct to 3 significant figures.

The volume of the composite figure is 837.33 cubic units.

The area or capacity of a cone is determined by its volume. A cone's circular base tapers from a flat base to a point known as the apex or vertex in three dimensions. A cone is made up of a collection of line segments, half-lines, or lines that link the apex—the common point—to each point on the base, which is on a plane without the apex. A cone may be thought of as a collection of irregularly shaped circular discs placed on top of one another with the ratio of their radii remaining constant.

The volume of any composite figure is the addition of the volume of all the shapes present in the figure.

Here, the composite solid is made of 2 cones and a cylinder.

The volume of cone is:

V = 1/3(πr²h)

For cone with height 12 and r= 4:

V = 1/3(π)(4)²(12)

V = 200.96 cubic units.

For cone with h = 8 and r = 4:

V = 1/3(π)(4)²(8)

V = 133.97

The volume of cylinder is:

V = πr²h

V = (3.14)(4)²(10)

V = 502.4 cubic units.

The volume of the composite solid is:

Total volume = 200.96 + 133.97 + 502.4

Total volume = 837.33 cubic units.

Hence, the volume of the composite figure is 837.33 cubic units.

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Answer:

Step-by-step explanation:

For Diane's account:

Year 1: Interest = $70,000 x 0.03 = $2,100

Year 2: Interest = ($70,000 + $2,100) x 0.03 = $2,163

Year 3: Interest = ($70,000 + $2,100 + $2,163) x 0.03 = $2,227.89

For Henry's account:

Year 1: Interest = $70,000 x 0.03 = $2,100

Year 2: Interest = $70,000 x 0.03 = $2,100

Year 3: Interest = $70,000 x 0.03 = $2,100

For the first year, both Diane and Henry earn the same interest of $2,100. However, for the second and third years, Diane earns more interest than Henry. Therefore, Diane earns more interest for each year after the first year

Initially, while maintaining the very same [tex]x-[/tex]coordinates, the negative reflect across the [tex]x-axis[/tex] modifies the signs of all locations' [tex]y-[/tex]coordinates.

A negative value is one that always has a value lower than zero and is denoted by the minus (-) symbol. In a number line, negative values are displayed just left of zero.

If a number is higher than zero, it is considered positive. Or less zero numbers are referred to as negative numbers. If a number is bigger than that or equal to zero, it is not negative. If a number falls below or equal to zero, it is non-positive.

This transforms Figure [tex]1[/tex] into a new figure with points [tex](-2, -5), (-2, -4), (-3, -4), (-3, -2), (-5, -2), (-5, -5)[/tex].

Next, the [tex]180^{0}[/tex] rotation about the origin swaps the signs of both [tex]x[/tex] and [tex]y[/tex] coordinates of each point. This results in the final figure with points [tex](2, -5), (2, -4), (3, -4), (3, -2), (5, -2), (5, -5)[/tex].

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The probability that the person chosen is a woman is 0.51.

The probability that the person chosen favors pink or purple is 0.67.

The probability that a person that favors turquoise is a man is 0.66.

Probability is the odds that a random event would occur. The odds that the event occurs has a probability value that lies between 0 and 1. The more likely it is that the event would happen, the closer the probability value would be to 1.

The probability that the person chosen is a woman = number of women / total number of people = 152 / 300 =  0.51.

The probability that the person chosen favors pink or purple = (number of people who favor pink / total number of people) + (total number of people that favor purple / total number of people) = (50 /300) + (50 / 300) =  0.67.

The probability that a person that favors turquoise is a man = men who favor turquoise / total number of people who favor turquoise = 79/120 = 0.66

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Answer:

6188 ways

Step-by-step explanation:

there ate 5 objects to be choosen and there is no replacement of the object therefore you got

17 choices for the first selection of the object and 16 objects for the selection of the second object and so on until you get 13 objects for the last selection

totally you have 5 selections also arrangement does not matter there fore you have 17!/12!5! which is 6188

note we used 5! cause there are 5 placed objects and 12! are unplaced objects

note

that you have used one so you have to deduct one every time you use one

Answer:

54°

Step-by-step explanation:

AB = BC = CD = AD (Because all sides of a rhombus are equal)

Let's consider the triangle DBC:

BC = DC => ∠DBC = 36°

The angle DCB is equal to:

180° - 36*2 = 180° - 72° = 108°

In a parallelogram, opposite angles are equal.

Then the angle DAB = DCB = 108°

Also, we know that the diagonals of a rhombus are the bisectors of the angles from which they come.

So, the angle DAE = EAB = 108° / 2 = 54°

Answer:

7. 23      

8. (3 - 8) x 5

Step-by-step explanation:

I think the second one is right but I know the first one is.

The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.

Step 1:

The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:

P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38

= (38/38) - (26/38) = 12/38 = 0.316

So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.

Step 2:

The average waiting time can be calculated by finding the expected value of the probability density function:

E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt

= [(t²)/(238)] from 0 to 38

= (38²)/(238) = 19

Therefore, the average waiting time is 19 minutes.

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Answer:

a

Step-by-step explanation:

The line segment AB and CB are perpendicular to each other.

Check whether the slopes of the lines are the negative reciprocals of one another to see if they are perpendicular to one another. The steps are as follows:

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There are 3 seniors who take Math and Spanish, but not Physics.

What is Venn Diagram?

A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.

To solve this problem, we can use a Venn diagram to organize the information given about the students.

First, we know that there are 150 seniors in total, so we can label the outer rectangle of the Venn diagram as having a total of 150 students.

Next, we can label the three circles as Math, Spanish, and Physics, with the numbers given in the problem:

80 seniors take Math, so we label the Math circle with 80.

41 seniors take Spanish, so we label the Spanish circle with 41.

54 seniors take Physics, so we label the Physics circle with 54.

We also know that 10 seniors take Math and Spanish, 19 take Math and Physics, 12 take Physics and Spanish, and 7 take all three. We can label these overlaps in the Venn diagram as follows:

The overlap of Math and Spanish is 10.

The overlap of Math and Physics is 19.

The overlap of Physics and Spanish is 12.

The overlap of all three is 7.

To find the number of seniors who take Math and Spanish, but not Physics, we need to subtract the number of seniors who take all three (because they are counted in all three circles) and the number of seniors who take Math, Spanish, and Physics (because they are counted in the overlap of all three circles). Then we add the number of seniors who take only Math and Spanish (because they are not counted in the Physics circle).

Using the formula for the number of elements in the union of three sets, we have:

Math or Spanish or Physics = Math + Spanish + Physics - (Math and Spanish) - (Math and Physics) - (Spanish and Physics) + (Math and Spanish and Physics)

So, the number of seniors who take Math and Spanish, but not Physics is:

Math and Spanish - (Math and Spanish and Physics) + (Math or Spanish or Physics - (Math + Spanish + Physics) + (Math and Spanish and Physics))

= 10 - 7 + (80 + 41 + 54 - 2(10) - 2(19) - 2(12) + 7)

= 3

Therefore, there are 3 seniors who take Math and Spanish, but not Physics.

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Answer:

2.

a) log base 10 of 100

b) The expression means that 10 to the 2nd power equals 100.

c) 2

3.

4. It would make sense that the value is between 1 and 2 because 10 to the 1st power is 10, and 10 to the 2nd power is 100. 50 is between 10 and 100 so the value would have to be between 1 and 2. This works because logs are the inverse function to exponentiation.

a) 2.6021

b) 3 and the value is exact because the base 10 in the log expression is technically the exponent when you convert it to exponent form. This works because logs are the inverse function to exponentiation. So 10 to the 3rd power would give you exactly 1000.

Answer:

Relating SSE to Other Statistical Data



Answer:

7.  300 miles

8. 60 miles

9. 5 miles

10. 1000 meters

Step-by-step explanation:

7.

We Take

60 x 5 = 300 miles

So, Ruth drives 300 miles in 5 hours.

8.  

5 miles = 10 minutes

1 mile = 2 minutes

2 hours = 120 minutes

We Take

120 / 2 = 60 miles

So, Carl drive 60 miles in 2 hours

9.

1 hour and 25 minutes = 85 minutes

We Take

85 / 17 = 5 miles

So, Nick travels 5 miles in an hour and 25 minutes.

10.

100 meters = 2 minutes

50 meters = 1 minute

We Take

50 x 20 = 1000 meters

So, Stan swims 1000 meters in 20 minutes.

Answer:

7. 300 miles/hours
8. 60 miles in 2 hours
9. 5 miles in 2 hours and 25 mins.

10. 1000 meters in 20 minutes.

Step-by-step explanation:

7. 60 x 5= 300 miles/hours

8. 5 miles in 10 minutes so in 2 hours it will be 5 x 12 = 60 miles in 2 hours

9.  5 miles in 2 hours and 25 mins.

10. 1000 meters in 20 minutes.

Descriptive statistics are the most useful in life. Descriptive statistics provide information about a data set and can help to summarize and interpret data. Specifically, I find the mean and median to be the most useful.

Descriptive statistics involves the use of measures such as the mean, median, mode, and range, as well as graphical representations of the data, such as histograms, box plots, and scatter plots.

The mean is the average of a set of data and is useful for summarizing and interpreting data. For example, when I am studying for a test, I often use the mean of my practice test scores to understand my overall performance.

The median is the middle value of a set of data and is useful for understanding the spread of the data. For example, when I am tracking my monthly expenses, I often use the median to understand how much I am spending each month. By taking the median of my monthly expenses, I can get an idea of which expenses are taking up the most of my budget.

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Answer:

(f - g)(x) = -4x² + x - 8

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

            = x - 8 - (4x²)

            = -4x² + x - 8

Answer:

  C. RP = 4.5

Step-by-step explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given  three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

  C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

  AB : BC : CA = 10 : 9 : 6

  QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.

Answer:

Matt would walk 8 miles in to hours.

Step-by-step explanation:

15 minutes is 1/4 of an hour, meaning it would be 1/8 of 2 hours.

1 mile times 8 = 8 miles

Hope that helps!

The process to show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied is shown below.

We prove this using the Pigeonhole Principle, which states that if n items are placed into m containers, and n > m, then at least one container must contain more than one item.

Let us consider the 16 people seated in a row of 20 chairs. Each person occupies one chair, so there are 20 - 16 = 4 empty chairs in the row.

We assume that empty chairs as containers, and people as items that need to be placed into containers.

Since there are more items (people) than containers (empty chairs), there must be at least one group of 2 or more consecutive empty chairs.

Now, let's consider the complement of this statement: Suppose there are no groups of 4 consecutive chairs that are occupied. Then, each group of 4 consecutive chairs contains at most 3 people.

We partition the row of chairs into groups of 4 consecutive chairs.

So, there are 20 - 3 = 17 such groups. By the statement above, each of these groups contains at most 3 people. Therefore, the total number of people seated in the row is at most 17×3 = 51.

But, we know that there are actually 16 people seated in the row. This is a contradiction, since 51 < 16. Therefore, our assumption that there are no groups of 4 consecutive chairs that are occupied must be false, and we have proved that some group of 4 consecutive chairs must be occupied.

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Answer:

I HOPE ITS HELPFUL

Step-by-step explanation:

Cost price of 300 articles = ₹1500Hence cost of each item = 1500/300 = ₹5With 20% profit, selling price of each item = 5 * 120/100 = ₹6Hence, total selling price of 260 items = 260 * 6 = ₹1560Selling price of balance items = 6/2 = ₹3Total selling price for balance items = 40 * 3 = ₹120Total selling price = 1560 + 120 = ₹1680Profit gained = 1680 - 1500 = ₹180Profit percentage = 180/1500 * 100 = 12

Answer:

[tex]{ \sf{a = \frac{0.012}{0.633 -0.063 } }} \\ \\ { \sf{a = \frac{0.012}{0.57} }} \\ \\ { \sf{a = 0.021 \: (2 \: s.f)}}[/tex]

The solution to the compound inequality -3+b> 7 OR b +9 <17 is given as follows:

b < 8 or b > 10.

The inequality for this problem is defined as follows:

-3+b> 7 OR b +9 <17.

The or operation means that the we must solve each operation separately, and then the solution set to the compound inequality is given by the union of the solution set of each of the inequalities.

The solution set for the first inequality is given as follows:

-3+b> 7

b > 10.

The solution set for the second inequality is given as follows:

b + 9 < 17

b < 8.

Hence the solution for the entire inequality is of:

b < 8 or b > 10.

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Answer:

invertible

Step-by-step explanation:

If A is invertible then ∣A∣ =0

Answer:

6

Step-by-step explanation:

We know that a dozen is the value of 12 so to find half a dozen we simply need to half it!

This means that there are 6 eggs in a half dozen.

FUN FACT:

A baker's dozen is 13, one more than a regular dozen!

Hope this helps, have a lovely day!

The given statements are true or false are shown below, about linear system has n variables and m equations, then the augmented matrix has n rows.

First, let's write how A and C look like.

A = [C|b], where b is the constant matrix.

(a) False.

Example

[tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\\end{array}\right][/tex]

We can see that z = t and so we have infinitely many solutions but there's no row of zeros.

(b) False.

Example

[tex]\left[\begin{array}{cc}1&0&0\1&1&0&0\\\end{array}\right][/tex]

Here; x1 = 1 and x2 = 1 is a unique solution and we have a row of zeros.

(c) True.

In the row-echelon form, the last row is either a row of zeros or a row that contains a leading 1. If the row has a leading 1, then there is a solution. Since we assume there is no solution, then the row must be a row of zeros.

(d) False.

Example

[tex]\left[\begin{array}{cc}1&3\\0&0\end{array}\right][/tex]

Here; x₁ = 1 − 3t and x2 = t. Thus, the system is consistent.

(e) True.

Suppose we have a typical equation in a system

а1x1 + A2X2 + ··· + anxn = b

Now, if b≠0 and x1 = x2 = ··· = x₂ = 0, then the system is Xn inconsistent. But, if b = 0, then we have a solution.

(f) False.

Example

[tex]\left[\begin{array}{cc}1&2&0&0\end{array}\right][/tex]

If a = 0, then it's consistent(infinitely many solutions) but if a 0, then it's inconsistent.

(g) Ture.

Since the rank would be at most 3 and this will lead to a free variable (4 columns in C and the rank is 3, so there is at leat 1 free variable). Thus, the system has more thatn one solution.

(h) True.

Because the rank is the number of leading 1's lying in different rows and A has 3 rows. Thus, the rank ≤ 3.

(i) False.

Because we could have a row of zeros in C and a leading 1 in A. In other words, a31 = a32 = A33 = A34 = 0 and c3 1. This makes the system inconsistent.

(j) True.

If the rank of C = 3, then there will be a free variable and this means the system is consistent.

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Complete question:

In each case either show that the statement is true, or give an example showing it is false. (a) If a linear system has n variables and m equations, then the augmented matrix has n rows. quations • ( *b) A consistent linear system must have infinitely many solutions. . (c) If a row operation is done to a consistent linear system, the resulting system must be consistent. (d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent.

To rewrite a number with a radical in the denominator without the radical, we can use the conjugate of the denominator. The conjugate of a binomial expression a + b is a - b, and the conjugate of a - b is a + b.

Suppose we have a number with a radical in the denominator, such as 1/√2. To rewrite this without the radical, we multiply the numerator and denominator by the conjugate of the denominator, which is

√2: 1/√2 = (1/√2) * (√2/√2) = √2/2

Note that the product of the denominator and its conjugate is always a difference of squares, which can be simplified to an integer without a radical.

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Answer: the distribution to the x and the 3 makes the solution 4

Step-by-step explanation: i got you broski

Answer:

13/8

Step-by-step explanation:

You first find the lcm of 8 and 4 which is 8

Then make a dividing line (/) with the lcm as the numerator.

After which you start diviing the lcm by each denominator of the two terms, and then multiplying with their numerators:

8/8 x 7 + 8/4 x 3 all over the lcm which is 8

(1 x 7 + 2 x 3)/8

(7 + 6)/8

13/8

The length of the top of the bookcase should be approximately 25 inches to display the soap carving collection with an area of 300 in².

To find the length of the top of the bookcase (which we'll call "b"), we need to know the area of the collection of soap carvings and the formula for the area of a rectangle:

Area = length x width

We're given the area of the soap carving collection (300 square inches), and we know that the soap carvings will be displayed on top of the bookcase, which is a rectangle.

Let's assume that the width of the bookcase is 1 unit (we can choose any unit we want, as long as we're consistent). Then we can write:

300 = b x 1

Simplifying this equation, we get:

b = 300/1

b = 300

So the length of the top of the bookcase should be 300 inches. However, this assumes that the width of the bookcase is only 1 inch, which is quite narrow.

If we assume a more reasonable width of, say, 12 inches, then we can write:

300 = b x 12

Simplifying this equation, we get:

b = 300/12

b = 25

So the length of the top of the bookcase should be 25 inches (if the width of the bookcase is 12 inches).

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