Find, using the method of volumes by SLICES, the volume of a pyramid of height h with an equilateral triangle base with side a.

Answer:

38 & 27 & 147

Step-by-step explanation:

4) 38cm²

5*4 = 20cm²

2*9 = 18cm²

5) 27m²

6*6 = 36m²

3*3 = 9m²

6) 147in²

14*14 = 196cm²

7*7 = 49in²

Answer:

4)  38 cm²

5)  27 m²

6)  147 in²

Step-by-step explanation:

To calculate the area of each given figure, subtract the area of the cut-out rectangle (marked in blue on the attached diagram) from the area of the larger rectangle.

[tex]\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}[/tex]

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&=9 \cdot 6- (9-5)\cdot 4\\&=9 \cdot 6- 4\cdot 4\\&=54-16\\&=38\; \sf cm^2\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 6\cdot 6- 3\cdot 3\\&=36-9\\&=27\; \sf m^2\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 14\cdot 14- 7\cdot 7 \\&=196-49\\&=147\; \sf in^2\end{aligned}[/tex]

As per the tension the weight of the chain is 2.55 kg

The tension is the force exerted by a rope, cable, or chain on an object to which it is attached.

To solve this problem, we need to understand the relationship between tension and weight. The weight of an object is the force with which it is attracted towards the earth due to gravity.

Using the given magnitude of tension (25 N) for each end, we can rewrite this equation as:

25 N - 25 N = Weight of the section

Simplifying this, we get:

Weight of the section = 0 N

This means that the weight of a small section of the chain is negligible compared to the tension at each end. However, if we consider the entire length of the chain, the weight cannot be ignored.

To calculate the weight of the chain, we need to find its mass. We can do this using the formula:

Mass = (weight of the chain) / (gravitational acceleration)

We know that the tension at each end of the chain has a magnitude of 25 N. Since the chain is in equilibrium, the net force on the chain must be zero. This means that the weight of the chain must be equal to the tension at each end.

Therefore, we can write:

Weight of the chain = 25 N

Now we can use the formula for mass:

Mass = (25 N) / (9.8 m/s²)

Using a calculator, we get:

Mass = 2.55 kg

This confirms that the weight of the chain is indeed equal to the tension at each end, as expected.

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Complete Question:

The tension T at each end of the chain has magnitude 25 N (see the figure). What is the weight of the chain?

The  Equation of Parabola shown in the graph is y=2x².

The general equation of a parabola is given by

y = a(x – h)² + k or x = a(y – k)² +h.

Here (h, k) denotes the vertex. y = a(x – h)² + k is the regular form. x = a(y – k)²+h is the sidewise form.

Given:

We have vertex (0, 0).

As, from the Graph the parabola is open up.

So, it is of the form y= ax², a>0.

Thus, the Equation of parabola is y=2x².

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The equation of line with slope as "-7" and passes through point (5,9) in function notation is f(x) = -7x - 26 .

We know that the equation of the line with slope "m = -7" passing through the point (-5, 9) can be found using the point-slope form of the equation of a line : which is ⇒ y - y₁ = m(x - x₁)

where (x₁, y₁) = (-5, 9) is the point and m = -7 is the slope.

On Substituting the values of point and slope , in the equation ,

⇒ y - 9 = -7(x - (-5)) ;

Simplifying the expression further ;

⇒ y - 9 = -7(x + 5)  ;

⇒ y - 9 = -7x - 35  ;

Adding 9 to both sides,

⇒ y = -7x - 26

In function notation is f(x) = -7x - 26  .

Therefore, the required equation of the line  is  f(x) = -7x - 26  .

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A graph that shows a slow and steady increase at first, followed by a steeper increase as the bottle approaches full capacity, would be the most accurate representation. Without seeing the available graphs, it's difficult to say which one is the best representation.

The best graph to represent the height of water in a spherical bottle as a function of the amount of water in the bottle is a non-linear graph that has a curved shape.

As the volume of water in the bottle increases, the height of the water will also increase, but not at a constant rate. The curve will become steeper as the bottle fills up, because the same amount of water will fill less and less of the remaining space in the bottle. Therefore, a graph that shows a slow and steady increase at first, followed by a steeper increase as the bottle approaches full capacity, would be the most accurate representation.

The height of water in a spherical bottle as a function of the amount of water in the bottle would be represented by a non-linear graph that has a curved shape. As the volume of water in the bottle increases, the height of the water will also increase, but not at a constant rate. The curve will become steeper as the bottle fills up, because the same amount of water will fill less and less of the remaining space in the bottle.

The most correct illustration would be a graph showing a gradual increase at initially, followed by a sharper increase as the bottle nears capacity. It's challenging to determine which graph is the best depiction without seeing the available graphs.

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The number of different combinations that are possible for Nick, given his baseball hats are A. 4 combinations.

Nick has two options for hats, and two options for sweatshirts/sweaters. To find the number of combinations, we can multiply the number of options for each item.

There are two baseball hats and two clothes - sweatshirt and sweater.

The number of combinations is:

= 2 (hats) x 2 (sweatshirts/sweaters)

= 4 combinations

In conclusion, as regards the number of combinations that Nick can make, there are four.

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Answer:

Tamika has painted 1/3 of the mural, and Li has painted 1/6 of it. To find the total part of the mural that they have painted together, we need to add these fractions:

1/3 + 1/6

We need to find a common denominator to add these fractions. The smallest common multiple of 3 and 6 is 6. We can convert 1/3 to 2/6 by multiplying the numerator and denominator by 2:

2/6 + 1/6 = 3/6

So, Tamika and Li have painted 3/6 of the mural in all. We can simplify this fraction by dividing both the numerator and denominator by 3:

3/6 ÷ 3/3 = 1/2

Therefore, Tamika and Li have painted 1/2 of the mural in all

The requried a measure of the exterior angle ∠4 = 63°.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,

As we know that for a triangle, the sum of the remote interior angle is equal to the measure of the exterior angle.

So, from the figure.

31 + 32 = ∠4

∠4 = 63°

Thus, the requried measure of the exterior angle ∠4 = 63°.

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Mean of this random variable is 3.14 and standard deviation is 1.82. The mean is calculated by multiplying each value of x by its corresponding probability and then summing the result.

Mean = (-2 * 0.12) + (0 * 0.26) + (3 * 0.28) + (4 * 0.14) + (7 * 0.22)

= 3.14

standard Deviation = [tex]\sqrt{[( (-2)2 * 0.12 ) + (02 * 0.26) + (32 * 0.28) + (42 * 0.14) + (72 * 0.22) - (3.142) ] }[/tex]= 1.82

The mean and standard deviation of a random variable with a given discrete probability distribution can be calculated using the following steps. First, each value of x is multiplied by its corresponding probability and then the results are summed to calculate the mean. For example, for the given discrete probability distribution, the mean is calculated by multiplying -2 by 0.12, 0 by 0.26, 3 by 0.28, 4 by 0.14 and 7 by 0.22 and then summing the results which is 3.14.To calculate the standard deviation, the square of each value of x multiplied by its corresponding probability is summed. Then the square of the mean is subtracted from this result and the square root of the remainder is taken to calculate the standard deviation. For the given probability distribution, the standard deviation is calculated by summing the square of -2 multiplied by 0.12, 0 multiplied by 0.26, 3 multiplied by 0.28, 4 multiplied by 0.14 and 7 multiplied by 0.22. Then the square of the mean which is 3.142 is subtracted from this result and the square root of the remainder is taken which is 1.82.

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They wanted to produce 50 more racing bikes per week (point B), what would be there opportunity cost There is no opportunity cost.

What is meant by speed?

The opportunity cost of producing 50 more racing bikes per week (moving from point A to point B) would be the amount of mountain bikes that the factory would have to give up producing in order to allocate resources to producing more racing bikes.

From the PPF, we can see that in order to produce an additional 50 racing bikes per week, the factory would have to decrease its production of mountain bikes by 50 (moving from 250 to 200). Therefore, the opportunity cost of producing 50 more racing bikes per week is 50 mountain bikes (option C).

So the answer is C. 50 mountain bikes.

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Answer: Solution set of the quadratic equation is, Empty set

Step-by-step explanation:

Given the quadratic equation:  

Subtraction property of equality states that you subtract the same number to both sides of an equation.

Subtract both sides by 1 we get;

Simplify:

Division property of equality states that you divide the same number to both sides of an equation.

Divide both sides by 6 we get;

Simplify:

For any x in real number there does not exist any number x which satisfy

, therefore, there is no solution for this set of the quadratic inequality or in other word we can say that set of the solution is Empty set.

The domain of the function g(x) is given as follows:

x ≥ -1.

The domain of a function is composed by the set that contains all possible input values for the function.

The square root function is defined only for non-negative values, hence the domain is obtained as follows:

6x + 6 ≥ 0

6x ≥ -6

x ≥ -6/6

x ≥ -1.

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The adage "You should wait until after paying all of your bills and discretionary expenses before budgeting for savings" is accurate.

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The size of a balloon increases as it is blown up because of the pressure of the air inside the balloon is greater than the atmospheric pressure outside.

The change in size of the balloon is determined by the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume (PV = nRT). Therefore, when air is added to the balloon and the pressure inside the balloon increases, its volume decreases. We can calculate the final diameter of the balloon, given the initial diameter and the change in pressure. For example, if the initial diameter of the balloon is 10 cm and the change in pressure is 0.5 atmospheres, then the final diameter of the balloon is[tex](10 cm) x [(1 + 0.5)⁰’⁵] = 10.63 cm.[/tex]

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Given that the area of the region bounded by the curve f(x) and x-axis from x=4 to x=10 is 13/5, the average value of the negative-valued function y=f(x) over the interval [4,10] is -13/30.

The average value of a function f(x) over an interval [a,b] is given by:

average value = (1/(b-a)) * integral from a to b of f(x) dx

In this case, we are given that the function y=f(x) is negative-valued, and the area of the region bounded by the curve and x-axis from x=4 to x=10 is 13/5. This means that the integral of f(x) over the interval [4,10] is equal to -13/5:

[tex]\int\limits^{10}_4 \, f(x) dx[/tex] = -13/5

To find the average value of f(x) over this interval, we divide this integral by the length of the interval:

average value = (1/(10-4)) * [tex]\int\limits^{10}_4 \, f(x) dx[/tex]

             = (1/6) * (-13/5)

             = -13/30

Therefore, the average value of the negative-valued function y=f(x) over the interval [4,10] is -13/30. This means that if we were to draw a horizontal line at the height of -13/30 over the interval [4,10], the area between this line and the x-axis would be equal to the area of the region bounded by the curve f(x) and x-axis over the same interval.

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The correct statements regarding the linear functions are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For Company P, the function is given as follows:

y = 30x + 50.

Meaning that:

From the table, for company R, the function is given as follows:

y = 25x + 75.

Meaning that:

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The average water level at the dock between 4 and 19 is 17.5 feet, calculated by taking the average of the water level at 4 and 19.

H(4) = 5 sin (pi/6 (4 - 6)) + 19 = 17

H(19) = 5 sin (pi/6 (19 - 6)) + 19 = 18

Average water level = (17 + 18)/2 = 17.5

The given equation is H(t) = 5 sin (pi/6 (t - 6)) + 19. This equation represents the water level at a dock over a 24 hour period, where t represents the time in hours. To calculate the average water level at the dock at 4 and 19, we need to first calculate the water level at 4 and 19. To do this, we substitute 4 and 19 in the equation in place of t. This gives us H(4) = 5 sin (pi/6 (4 - 6)) + 19 = 17 and H(19) = 5 sin (pi/6 (19 - 6)) + 19 = 18. The average water level is then calculated by taking the average of these two values, which is (17 + 18)/2 = 17.5. This is the average water level at the dock between 4 and 19.

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Answer:

1. 26*

2. 17*

3. 23*

The statement that " Homogeneous equation Ax = 0 has trivial solution if it has at least 1 free variable"  is FALSE .

For a system of Linear Equations, a free variable is a variable which can take any value, whereas

the Leading Variable is a variable which is determined by the values of the free variables.  

The presence of a free variable means that existence of a non trivial solution to Ax = 0  because a free variable corresponds to a column of A that does not contain a pivot position in the corresponding row of [A|0].

So , the corresponding variable can be set to any non zero value, which gives a non trivial solution to Ax = 0.

Therefore, we can conclude that the homogeneous equation Ax = 0 has the trivial solution if and only if the equation has no free variables.

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The given question is incomplete , the complete question is

The homogeneous equation Ax = 0 has the trivial solution if and only if the equation has at least one free variable. True or False ?

Answer: 12.2

Step-by-step explanation:=  

61/5=12.2

This means that out of every 100 US adults, 23 of them have not read a book in the past year. This rate is quite high, considering the vast number of books available to read.

To calculate the number of US adults who have not read a book in the past year, we can use the following equation:

Number of US Adults Who Have Not Read a Book in the Past Year = Total Number of US Adults x Proportion of US Adults Who Have Not Read a Book in the Past Year

First, determine the total number of US adults. For example, let's say that there are 80 million US adults.

Next, multiply the total number of US adults by the proportion of US adults who have not read a book in the past year (0.23). Therefore, 80 million x 0.23 = 18.4 million US adults who have not read a book in the past year.

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Answer:15

Step-by-step explanation:

We know this figure's all angles sum is equal to 180*(n-2)=180*3=540

so,

112+7x+5+6x+2+10x-8+4x+24=540

27x+135=540

27x=405

x=15

Answer: [tex]6a-2[/tex]

Step-by-step explanation:

[tex](4a-5)-(-2a-3)\\=4a-5+2a+3\\=6a-2[/tex]

The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5

Apply the product rule to 4a^5:

⇒ 4^3(a^5)^3

Raise 4 to the power of 3:

⇒ 64(a^5)^3

Apply the power rule and multiply exponents, (a^m)^n = a^mn:

⇒ 64a^5*3

Multiply 5 by 3:

64a^15

Therefore, The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5

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Answer:[tex]34\pi[/tex]

Step-by-step explanation:

c=[tex]2\pi R=2*17\pi =34\pi[/tex]

Answer:

43.98 meters

Step-by-step explanation:

Since the ratio of consecutive outputs is not constant, the function is not an exponential function. Hence the function is neither linear nor exponential.

To determine whether the given function is linear, exponential, or neither, first compute the average rate of change of with respect to and then compute the ratio of the consecutive outputs.

If the average rate of change is constant, then the function is linear.

If the ratio of consecutive outputs is constant, then the function is exponential.

x    y       Average rate of change        ratio of consecutive outputs

-1    3         [tex]\frac{\delta y}{\delta x}=[/tex](6-3)/0-(-1)=3                     6/3=2

0    6        (12-6)/(1-0)=6                           12/6=2

1     12       (18-12)(2-1)=6                          3/2

2    18       (30-18)/(3-2)=12                      5/3

3    30          -                                        -

Observe the above table, for the given function, the average rate of change from  to  is , and from  to  is .

Since the average rate of change is not constant, the function is not a linear function.

Observe the above table, for the given function, the ratio of consecutive outputs from -1  to 0 is 2  from  0 to  1 is 2, and from 2 to 1  is3/2

Since the ratio of consecutive outputs is not constant, the function is not an exponential function.

Hence the function is neither linear nor exponential.

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The expected value of an unbiased estimator is equal to the parameter whose value is being estimated. A) True B) False . the answer is false

Verifiability is the ability to demonstrate that a measure is in agreement with a real-world phenomenon. It is an important qualitative characteristic of financial reporting.

Verifiability is a qualitative characteristic of financial reporting that refers to the ability to demonstrate that a measure is in agreement with a real-world phenomenon. This means that the financial information presented is accurate and reliable, and that it faithfully reflects the underlying transactions or events that it is supposed to represent. Verifiability is important because it ensures that users of financial statements, such as investors and creditors, are able to make informed and accurate decisions based on the information contained in the statements. This is achieved through the use of external auditors to objectively verify the integrity of financial statements and disclosures. If a measure is not verifiable, it is not considered to be a reliable source of information and should not be used for decision-making. Verifiability is essential for reliable financial reporting.

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The percentages of returns are given as follows:

a. Greater than 33%: 2.28%.

b. Below -37%: 0.13%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 5, \sigma = 14[/tex]

The proportion above 33% is the one subtracted by the p-value of Z when X = 33, hence:

Z = (33 - 5)/14

Z = 2.

Z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228 = 2.28%.

The proportion below -37% is the p-value of Z when X = -37, hence:

Z = (-37 - 5)/14

Z = -3.

Z = -3 has a p-value of 0.0013.

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(i) A basis for the set is {(2, 3, 4), (3, -2, 1)} and the dimension is 2.

(ii) A basis for the set is {(1, 1, 1, 1), (2, 0, 0, -1)} and the dimension is 2.

(i) {(2, 3, 4), (3, -2, 1)}

(i) The set contains the zero vector (0, 0, 0). It is closed under addition because for any two vectors in the set, the sum of the two vectors is also in the set. It is closed under scalar multiplication because for any vector in the set and any scalar, the scalar multiplied by the vector is also in the set.

A basis for the set is {(2, 3, 4), (3, -2, 1)} and the dimension is 2.

(ii) {(1, 1, 1, 1), (2, 0, 0, -1)}

(ii) The set contains the zero vector (0, 0, 0, 0). It is closed under addition because for any two vectors in the set, the sum of the two vectors is also in the set. It is closed under scalar multiplication because for any vector in the set and any scalar, the scalar multiplied by the vector is also in the set.

A basis for the set is {(1, 1, 1, 1), (2, 0, 0, -1)} and the dimension is 2.

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The complete question is:

Consider the following sets of vectors. show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. then find a basis for each set and give the dimension.

(i) {(2, 3, 4), (3, -2, 1)}

(ii) {(1, 1, 1, 1), (2, 0, 0, -1)}