According to cavalieri's principle, which pair of shapes would have equal volumes?

Answer:

[tex]\textsf{B)} \quad a_n=-22+7(n-1)[/tex]

Step-by-step explanation:

An explicit formula for a sequence allows you to find the nth term of the sequence.

A recursive formula for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

Given recursive rule:

[tex]\begin{cases}a_{n+1}=a_n+7\\a_1=-22\end{cases}[/tex]

From the given recursive rule, we can see that each term is 7 more than the previous term.  Therefore, the common difference between terms is d = 7.

[tex]a_n = a_1 + (n - 1)d[/tex]

Input the values of a₁ and d into the explicit formula:

[tex]\implies a_n=-22+(n-1) \cdot 7[/tex]

[tex]\implies a_n=-22+7(n-1)[/tex]

Therefore, the explicit formula for the given sequence is:

[tex]\boxed{a_n=-22+7(n-1)}[/tex]

The decay factor in the equation y=41(0.92)^t is the value of (0.92) raised to the power of t.

In this case, the base of the exponential function is 0.92, which is less than 1. This means that as t increases, the value of (0.92)^t decreases exponentially, leading to a decay in the value of y. The decay factor is the factor by which the value of y decreases each year.

In this case, the decay factor is 0.92, which means that the value of the car decreases by 8% each year. This is because (0.92) x 100% = 92%, so the value of the car decreases to 92% of its previous value each year.

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Answer:

statistical experiments performed on a well defined sample space

Step-by-step explanation:

experiments can be performed either by probability, or other repetitive actions on sample space for possible outcomes.

Answer:

392.5g

Step-by-step explanation:

Density =mass/volume

Mass = Density x volume

Mass = 7.85g/cm³ x 50 cm³

Mass = 392.5g

Answer: 5cm

Step-by-step explanation:

You divide the area of green (93.75) by pink's length (7.5)

that gives you 12.5.

12.5 is the length of green.

12.5 - 7.5 = 5

You subtract the 7.5 because to get yellow's length because Yellow's length plus pink's length is equal to green's total length.

Using matrix inversion method and perimeter of rectangle, the dimension of the rectangle are 16cm and 7cm

Let the length of the rectangle be l and the width be w. We know that l - w = 3.5 and 2l + 2w = 67. We can rewrite these equations as a system of linear equations in matrix form:

[tex]$$\begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix} \begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}3.5 \ 67/2\end{bmatrix}$$[/tex]

We can solve for [tex]$\begin{bmatrix}l \ w\end{bmatrix}$[/tex] by multiplying both sides of the equation by the inverse of the coefficient matrix:

[tex]$$\begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix}^{-1} \begin{bmatrix}3.5 \ 67/2\end{bmatrix}$$[/tex]

To find the inverse of the coefficient matrix, we can use the following formula:

[tex]$$\begin{bmatrix}a & b \ c & d\end{bmatrix}^{-1} = \frac{1}{ad-bc} \begin{bmatrix}d & -b \ -c & a\end{bmatrix}$$[/tex]

Plugging in the values for our matrix, we get:

[tex]$$\begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix}^{-1} = \frac{1}{1 \cdot 2 - (-1) \cdot 2} \begin{bmatrix}2 & 1 \ -2 & 1\end{bmatrix} = \begin{bmatrix}1/2 & 1/4 \ -1/2 & 1/4\end{bmatrix}$$[/tex]

Now we can substitute this matrix and the vector on the right-hand side of the equation into our formula to obtain the solution:

[tex]$$\begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}1/2 & 1/4 \ -1/2 & 1/4\end{bmatrix} \begin{bmatrix}3.5 \ 67/2\end{bmatrix} = \begin{bmatrix}16 \ 7\end{bmatrix}$$[/tex]

Therefore, the dimensions of the rectangle are 16 cm by 7 cm.

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Answer:

Sin= 35/37

cos= 13/37

tan= 35/13

Step-by-step explanation:

Answer:

[tex]112cm^2[/tex]

Step-by-step explanation:

Volume of a rectangluar prism = Length x Width x Height

Volume, Length, and Width is given now we can solve for Height, c

[tex]V = l * w * h[/tex]

[tex]80m^3 = 4m * 4m * h[/tex]

[tex]h = 80m^3 / 16m^2[/tex]

[tex]h = 5m[/tex]

Surface area of a rectangular prism is A = 2(wl +hl +hw)

[tex]A = 2(4m * 4m + 5m * 4m + 5m * 4m)[/tex]

[tex]= 2(16m^2 + 20m^2 + 20m^2)[/tex]

[tex]= 2(56cm^2)\\A= 112cm^2[/tex]

Hope this helps!
Brainliest is much appreciated!

supongo q es es 8 cm pero no creo q sería 2 o l

Answer:

Line A has a slope of -4

Line A and line B have the same slope

Step-by-step explanation:

Line A is in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.  As we can see, -4 is m in line A so -4 is the slope of line A.

If we have two points on a line, we can find the slope using the slope formula

[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one of the points and x2 and y2 come from the other point.

Thus, if we allow (-2, 1) to be x1 and y1 and (1, -11) to be x2 and y2,

[tex]m=\frac{-11-1}{1-(-2)}\\ m=-4[/tex]

Since the slope of Line B is -4, it has the same slope as line A

Therefore, the values of a that make the expression true are approximately 0.378 and 14.121.

In mathematics, an expression is a combination of numbers, variables, and operations that represents a quantity or a mathematical relationship. Expressions can be simple or complex, and can involve arithmetic, algebraic, trigonometric, or other mathematical operations. Expressions can also include constants, which are fixed values that do not change. Expressions can be evaluated by substituting numerical values for the variables and performing the indicated operations.

Here,

To solve for the values of a that make the given expressions true, we need to isolate the variable a on one side of the equation. We can start by simplifying the left side of the equation:

1/2a - 5 1/2 = 5 - a

Multiplying both sides by 2a gives:

1 - 10a* 1/2 = 10a - 2a²

Simplifying the left side by multiplying both terms by 2:

2 - 20a = 10a - 2a²

Rearranging the terms gives a quadratic equation:

2a² - 30a + 2 = 0

We can solve for a by using the quadratic formula:

a = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = -30, and c = 2.

Plugging in these values gives:

a = (30 ± √((-30)² - 4(2)(2))) / 4

a = (30 ± √(892)) / 4

a ≈ 0.378 or a ≈ 14.121

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The use of consonance in "Thundered the battery's double brass" best conveys the violent sounds of the battle.

Consonance is a literary device where consonant sounds are repeated in close proximity, often at the ends of words, to create a musical or rhythmic effect in a text.

The passage uses consonance, which is the repetition of consonant sounds within or at the end of words, to convey the violent sounds of the battle.

In particular, the repeated "t" and "d" sounds in "Thundered the battery's double brass" and "Difficult music for men to face" create a harsh, jarring effect that emphasizes the chaos and danger of the fighting.

Similarly, the repeated "v" and "l" sounds in "Undulate like the living waves" create a sense of movement and fluidity, conveying the unrelenting and overwhelming force of the rebel advance.


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The thermometer reads -10 degrees Celsius, and the temperature drops by 10 degrees Celsius. As a result, the new thermometer reading will be -20 degrees Celsius.

If the temperature drops by 10 degrees Celsius and the initial reading on the thermometer is -10 degrees Celsius, we can calculate the new reading as follows:

New reading = Initial reading - Temperature drop

New reading = (-10) - 10

New reading = -20

Therefore, the new reading on the thermometer will be -20 degrees Celsius.

When we say the temperature drops by 10 degrees Celsius, we mean that the temperature decreases by 10 degrees Celsius from its initial value. In this case, the initial value is -10 degrees Celsius.

So, if the temperature drops by 10 degrees Celsius, we need to subtract 10 from the initial value to get the new temperature reading. This is because a decrease in temperature means the temperature value becomes lower.

The resulting new reading of -20 degrees Celsius is 10 degrees Celsius lower than the initial reading of -10 degrees Celsius. It indicates that the temperature has decreased further, and it is now even colder than before.

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[tex]\stackrel{ \textit{multiplying the 1st equation by 9} }{\begin{array}{lllllll} 9(~x&+y&=& ~~ 0)\\\\ -9x&-5y&=&-24 \end{array}}\hspace{5em} \begin{array}{llll} ~~ 9x&+9y&=&0\\\\ -9x&-5y&=&-24\\\cline{1-4} ~~0&-4y&=&-24 \end{array} \\\\[-0.35em] ~\dotfill\\\\ -4y=-24\implies y=\cfrac{-24}{-4}\implies \boxed{y=6} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{x+(6)=0\implies \boxed{x=-6}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-6~~,~~6)~\hfill[/tex]

The volume is increasing at a rate of 16755.21 mm³/s when the diameter is 100 mm.

We are given that the radius of a sphere is increasing at a rate of 4 mm/s.

Let's first write the formula of the volume of a sphere;

[tex]V=43πr3V  =\frac{4}{3}\pi r^3V  =34πr3[/tex]

Now we can differentiate it by using the chain rule;

[tex]V'=43π3r2drdt+4πr3(4)orV'   =4πr2drdt[/tex]

The problem asks for how fast the volume is increasing, so we need to find V' when the diameter is 100 mm, or r=50 mm.

Thus;

[tex]V'=4π(50²)(4)   =40,000πV'   =125663.71 mm³/s[/tex]

Therefore, the volume is increasing at a rate of 125663.71 mm³/s when the diameter is 100 mm. Now we round to two decimal places to get;V'=16755.21 mm³/s.

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The process of counting from 0 to 10 using 4 fours and the four basic operations can be explained mathematically by the following equation: 4 + 4 - 4 x 4 / 4 + 4 + 4 - 4 = 12

The result when using 4 fours and the four basic operations (addition, subtraction, multiplication, division) to count from 0 to 10 is as follows:

0 = 4 ,1 = 4 + 4 = 8 ,2 = 8 - 4 = 4 ,3 = 4 x 4 = 16 ,4 = 16 / 4 = 4 ,5 = 4 + 4 + 4 = 12 ,6 = 12 - 4 = 8 ,7 = 8 x 4 = 32, 8 = 32 / 4 = 8 ,9 = 8 + 4 + 4 = 16 ,10 = 16 - 4 = 12 .The process of counting from 0 to 10 using 4 fours and the four basic operations can be explained mathematically by the following equation: 4 + 4 - 4 x 4 / 4 + 4 + 4 - 4 = 12. This equation is made up of four parts, each representing an operation in the correct order. The first part of the equation is 4 + 4 = 8, which adds the two fours together to get 8. The second part of the equation is 8 - 4 = 4, which subtracts the four from the 8 to get 4. The third part of the equation is 4 x 4 = 16, which multiplies the two fours together to get 16. The fourth part of the equation is 16 / 4 = 4, which divides the 16 by 4 to get 4. The fifth part of the equation is 4 + 4 + 4 = 12, which adds the three fours together to get 12. The sixth part of the equation is 12 - 4 = 8, which subtracts the four from the 12 to get 8. Finally, the last part of the equation is 8 + 4 + 4 = 16, which adds the three fours together to get 16.

By combining these six operations together, we can count from 0 to 10 using 4 fours and the four basic operations.

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What is the result when using 4 fours and the four basic operations (addition, subtraction, multiplication, division) to count from 0 to 10?

The required answers are a) 17.1 km b) 7.1 km, c) 18.6 km away from town A on a bearing of 293°.

To solve this problem, we can use vector addition to find the displacement vector from town A to the cyclist's destination.

a) To find how far east the cyclist's destination is from town A, we need to find the east component of the displacement vector. We can break down the displacement vector into its north and east components using trigonometry:

[tex]$$\text{East displacement} = 5\text{ km} + 10\text{ km}\cos(45^\circ) = 5\text{ km} + 10\text{ km}\frac{\sqrt{2}}{2} = 10\text{ km} + 5\sqrt{2}\text{ km} \approx 17.1\text{ km}$$[/tex]

So the cyclist's destination is approximately 17.1 km east of town A.

b) Similarly, to find how far north the cyclist's destination is from town A, we need to find the north component of the displacement vector:

[tex]$$\text{North displacement} = 10\text{ km}\sin(45^\circ) = 10\text{ km}\frac{\sqrt{2}}{2} = 5\sqrt{2}\text{ km} \approx 7.1\text{ km}$$[/tex]

So the cyclist's destination is approximately 7.1 km north of town A.

c) To find the distance and bearing of the cyclist's destination from town A, we can use the Pythagorean theorem and trigonometry. The displacement vector is the hypotenuse of a right triangle with legs of length 17.1 km and 7.1 km, so its length is:

[tex]$$\text{Displacement} = \sqrt{(17.1\text{ km})^2 + (7.1\text{ km})^2} \approx 18.6\text{ km}$$[/tex]

To find the bearing of the displacement vector, we can use the inverse tangent function:

[tex]$$\text{Bearing} = \tan^{-1}\left(\frac{\text{East displacement}}{\text{North displacement}}\right) \approx 67^\circ$$[/tex]

However, this angle is measured clockwise from north, so we need to subtract it from 360° to get the bearing measured counterclockwise from north:

[tex]$$\text{Bearing} = 360^\circ - 67^\circ = 293^\circ$$[/tex]

So the cyclist's destination is approximately 18.6 km away from town A on a bearing of 293°.

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Answer:

1300

Step-by-step explanation:

1864-564= 1300 students

(total - no. graduated)

Hope this helps! :)

The probability that the pitcher gave up at most 2 base hits in the game is approximately 0.53.

What is probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated.

Let X be the number of base hits given up in 120 pitches. Then X follows a binomial distribution with parameters n = 120 (number of trials) and p = 1/15 (probability of success in each trial).

The probability of giving up at most 2 base hits can be calculated as follows:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Using the binomial probability formula, we have:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k successes from n trials.

Plugging in the values, we get:

P(X = 0) = (120 choose 0) * (1/15)^0 * (14/15)^120 ≈ 0.028

P(X = 1) = (120 choose 1) * (1/15)^1 * (14/15)^119 ≈ 0.17

P(X = 2) = (120 choose 2) * (1/15)^2 * (14/15)^118 ≈ 0.33

Therefore,

P(X ≤ 2) = 0.028 + 0.17 + 0.33 ≈ 0.53

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Answer:

-5.255

Step-by-step explanation:

If Mr Corazon produces the model that would give the most profit only, this idea would be incorrect. The reason is that that poor people would not be able to buy the product.

Profit maximization is the process by which a business or a firm determines the optimal level of output or production that leads to the highest possible profit. It is an important goal for most firms, as it helps to ensure their long-term sustainability and competitiveness in the market.

Based on the question, at the profit of $375 a piece, it would mean that the price has become too high. Less people would but the product. This makes his idea a bad one.

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If the rate of the current was 3 kilometers per hour, Christine's speed in still water is 5 kilometers per hour.

Let's start by assuming that Christine's speed in still water is x kilometers per hour. We know that the current is flowing at a rate of 3 kilometers per hour.

When Christine is swimming against the current, her effective speed is reduced by the speed of the current, so her speed is (x-3) kilometers per hour. If it takes her the same amount of time to swim 2 kilometers against the current as it does to swim 8 kilometers with the current, we can set up an equation:

time to swim 2 km against current = time to swim 8 km with current

We can use the formula distance = speed x time to express the distance that Christine covers in each scenario. The distance she covers against the current is 2 kilometers, and the distance she covers with the current is 8 kilometers. So our equation becomes:

2 / (x - 3) = 8 / (x + 3)

To solve for x, we can cross-multiply and simplify:

2(x + 3) = 8(x - 3)

2x + 6 = 8x - 24

6x = 30

x = 5

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Answer:

The length of the shortest side is 3 units.

Step-by-step explanation:

Let's assume that the shortest side has a length of 3x, where x is a constant.

Then, the other sides would have lengths of 10x and 7x, respectively.

To check if this is a valid triangle, we need to make sure that the sum of the lengths of any two sides is greater than the length of the third side:

3x + 10x > 7x (sum of shortest and middle side is greater than longest side)

3x + 7x > 10x (sum of shortest and longest side is greater than middle side)

10x + 7x > 3x (sum of middle and longest side is greater than shortest side)

Simplifying these inequalities, we get:

13x > 7x

10x > 3x

17x > 0

All of these inequalities are true if x > 0, so our assumption is valid.

Therefore, the length of the shortest side is 3x. To find the value of x, we can set up the following equation based on the given ratio:

3x : 10x : 7x = 3 : 10 : 7

Simplifying this equation by dividing all sides by x, we get:

3 : 10 : 7 = 3 : 10 : 7

This is true, so any value of x will satisfy the given ratio.

However, to find the length of the shortest side, we can simply substitute x = 1 into our assumption:

Shortest side = 3x = 3(1) = 3

Therefore, the length of the shortest side is 3 units.

Hope this helps! Sorry if this is wrong. :]

The length of the opposite side (y) is equal to 3.2 centimeters.

In order to determine the length of the opposite side (y), we would apply the sine trigonometry ratio because the given side lengths represent the opposite side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

Based on the information provided in the image, we can logically deduce the following parameters:

By substituting the parameters into the sine trigonometry ratio formula, we have the following;

sin(θ) = Opp/Hyp

sin(39) = y/5

y = 5sin(39)

y = 3.2 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The investigation of a possible health concern in an office building due to an environmental toxin involves following the health status of all employees for a period of time, identifying potential sources of toxins, and taking steps to remove the toxins and protect the health of the employees.

The possible health concern in an office building that may be due to an environmental toxin can be investigated by following all 300 of their office employees for 30 days and observing their health status. On day 10, 35 employees report respiratory distress and on day 20, 70 employees report respiratory distress.

The remaining employees do not report any respiratory distress over the 30-day period. This suggests that there may be an environmental toxin in the office building that is causing respiratory distress in the employees.

It is important to further investigate the source of the toxin and take steps to remove it in order to protect the health of the employees. This may include conducting air quality tests, examining the building for potential sources of toxins, and implementing measures to improve ventilation and air quality.

It is also important to continue monitoring the health of the employees and providing them with appropriate medical care if needed.

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Answer:

Use the slope formula and slope-intercept form

y=mx+b to find the equation.

the steps and answers are in the photos

{I hope this helps you :)

The values would be

[tex]15. = \frac{1}{1000y^3}\\\\16. =-\dfrac{1024}{n^5}\\\\17. =\dfrac{1}{32k^{10}}\\\\18. =$\dfrac{49}{36c^2}$\\\\\\19. = $64^t$\\\\20. = $5 \cdot 5^t$\\\\21. = $81 \cdot 3^{4t}$\\\\22. = $\dfrac{2^{2t}}{2}$ or $2^{2t-1}$[/tex]

What is an expression?

In mathematics, an expression is a combination of symbols and/or numbers that represents a value or a relationship between values. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple operations and functions. Expressions can be used to describe relationships between variables, to represent mathematical formulas or equations, and to perform calculations.

[tex]15. = \frac{1}{1000y^3}\\\\16. =-\dfrac{1024}{n^5}\\\\17. =\dfrac{1}{32k^{10}}\\\\18. =$\dfrac{49}{36c^2}$\\\\\\19. = $64^t$\\\\20. = $5 \cdot 5^t$\\\\21. = $81 \cdot 3^{4t}$\\\\22. = $\dfrac{2^{2t}}{2}$ or $2^{2t-1}$[/tex]

Hence, the values would be

[tex]15. = \frac{1}{1000y^3}\\\\16. =-\dfrac{1024}{n^5}\\\\17. =\dfrac{1}{32k^{10}}\\\\18. =$\dfrac{49}{36c^2}$\\\\\\19. = $64^t$\\\\20. = $5 \cdot 5^t$\\\\21. = $81 \cdot 3^{4t}$\\\\22. = $\dfrac{2^{2t}}{2}$ or $2^{2t-1}$[/tex]

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The trend line equation y = 0.05x + 0.25 can be used to accurately predict the cost of gas per gallon for any year since 1970.

The equation of the trend line in the scatter plot is given by y = 0.05x + 0.25, where x is the number of years since 1970 and y is the price of gas per gallon in dollars. This equation can be used to calculate the price of gas in a given year since 1970. For example, if we want to calculate the price of gas in 2017, we can plug in x = 47 (the number of years since 1970) into the equation to get y = 0.05(47) + 0.25 = 2.85. This means that in 2017, the price of gas per gallon was approximately 2.85 dollars. This equation can be used to accurately predict the cost of gas for any given year since 1970.

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The coordinate pair for A' is as a result (4, -2) in coordinated square.

After reflecting the square ABCD over the y-axis and translating it five units down and one unit to the left, we may use the following transformations in order to get the coordinate pair of A':

Across the y-axis, reflect the square: This modifies the x-sign coordinate's while maintaining the y-original coordinate's value. Hence, A's new coordinates would be (5, 3).

Five units down and one unit to the left, translate the square as follows: The y-coordinate is moved five units down and the x-coordinate one unit to the right as a result. A's new system coordinates are calculated to be (4, -2).

the coordinate pair for A' is as a result (4, -2).

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