The base of a prism is a right triangle with legs measuring 3 feet and 4 feet. If the height of the prism is 13 feet, determine its volume

\(\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=9\\ s=9.7 \end{cases}\implies 9.7=\cfrac{\theta \pi (9)}{180}\implies 9.7=\cfrac{\theta \pi }{20} \\\\\\ 194=\theta \pi \implies \cfrac{194}{\pi }=\theta \implies 62\approx \theta\)

The mean of the given set of data will be 8.3.

Given is the following data -

3, 5, 8, 11, 11, 12

We have -

3, 5, 8, 11, 11, 12

We can calculate the mean as -

m = (3 + 5 + 11 + 8 + 11 + 12)/6

m = 50/6

m = 8.3

Therefore, the mean of the given set of data will be 8.3.

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The number of possible combinations of 7 objects taken 4 at a time is 35. Then the correct option is D.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

The number of possible combinations of 7 objects taken 4 at a time.

so, the number of the combination is given as

\(^7C_4 = \dfrac{7!}{4!(7-4)!} \\\\\\^7C_4 = \dfrac{7!}{4!(3)!} \\\\\\^7C_4 = \dfrac{7 \times 6\times 5\times 4!}{4!(3\times 2)} \\\\\\^7C_4 = 35\)

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Answer:

D. 35

Hope this helps!

Step-by-step explanation:

Answer:

1. 3/7

2.6/10

3.17/12

4.41/42

5.4/10

6.10/7

hopefully this helped :)

pls mark me as the brainliest

Answer:

x = 35

Step-by-step explanation:

angles in a triangle add up to 180.

x + 11 + 3x + 1 + x - 7 = 180

combine like terms

5x + 5 = 180

subtract 5 from both sides of the equation

5x + 5 - 5 = 180 - 5

5x = 180 - 5

5x = 175

divide both sides of the equation by 5

5x/5 = 175/5

x = 175/5

x = 35

Answer:

C

Step-by-step explanation:

the range is all the possible numbers on the Y axis. We can see that the graphs peaks at 3 and then goes down both ways. This means that eventually the y axis will be equal to all real numbers less than 3

The range of the function looks to be all real numbers less than or equal to -1, according to the provided graph. The best choice is B.

This is due to the fact that the graph's horizontal line at y=-1, which shows that the function accepts all values less than or equal to -1, stretches eternally in both directions.

The collection of all potential output values that a function can take on is generally referred to as the function's range. You can look at the vertical spread of the graph to see what values the function can take on in order to determine the range of a function from its graph.

Observe that the accompanying graph features a horizontal line at y=-1 that spreads out infinity in both directions. This indicates that for all values of x, the function takes on the value of -1.

The graph also features a vertical line at x=2 that goes on forever in both directions, as can be seen. This shows that the function can accept any value of y for x=2.

Combining these findings, we can determine that the function has a range of all real numbers less than or equal to -1 since it takes on the value of -1 for all x and the range of potential values of y is unrestricted.

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Answer:

4500 + 150.25s = 3696 + 200.5s Solve for s 4500 - 3696 = 200.5s - 150.25s 804 = 50.25s s = 804/50.25 = 16 tons of sugar The cost is found by plugging this value into either side of the original equation; it is $6904.

Step-by-step explanation:

Answer:

a) They would cost the same with 16 tons of sugar.

b) This would cost 9 108 dollar.

Step-by-step explanation:

! This is only true if the amount of rented trucks remains the same no matter what amount of sugar ! ( Which is really weird but ok.)

a) x= tons of sugar

=>7500+100,50X=6296+175,75X

<=> 75,25x=1204

<=> x=16

b) 7500+100,50.16=9108

Answer:

Yasmin will spend $6

Nadia will spend $5.9

Step-by-step explanation:

Step one:

the cost of 5 jars at Central market is $3

the cost of 1 jar = 3/5= $0.6

60 cents per jar

we are told that Valley Market sells jars of jam at 59 cents per jar.

$0.59

Step two:

If Yasmin buys 10 jars from Central Market,

Yasmin will spend = 10*0.6= $6

If Nadia buys 10 jars from Valley Market.

Nadia will spend = 10*0.59= $5.9

The market difference is 6-5.9= $0.1

Answer:

1 cm : 25000 cm

Convert 25000cm to km = 1cm : 0.25 km

9cm = 9 x 0.25 km

9cm = 2.25 km

Step-by-step explanation:

The horizontal change from triangle ABC to triangle ABC include the following: A. right 5 units.

The vertical change from triangle ABC to triangle ABC include the following: C. down 2 units.

The translation rule in the standard format is: (x, y) → (x + 5, y - 2).

In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

By translating the pre-image of triangle ABC horizontally right by 5 units and vertically down 2 units, the coordinate A of triangle ABC include the following:

(x, y)                               →                  (x + 5, y - 2)

A (3, 5)                        →                  (3 + 2, 5 - 2) = A' (5, 3).

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Missing information:

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

To express 1/4 as an equivalent fraction with a different denominator, we need to find a common multiple of 4 and the desired denominator.

Let's say we want to express 1/4 as an equivalent fraction with a denominator of 12. To do this, we can multiply both the numerator and denominator of 1/4 by 3, which gives us:

1/4 x 3/3 = 3/12

So 1/4 is equivalent to 3/12 when the denominator is 12.

In general, to express a fraction a/b as an equivalent fraction with a different denominator c, we can multiply both the numerator and denominator by the same value that makes b equal to c.

This is because when we multiply both the numerator and denominator by the same value, we are essentially multiplying the fraction by 1, which does not change its value.

For example, to express 2/5 as an equivalent fraction with a denominator of 15, we can multiply both the numerator and denominator by 3, which gives us:

2/5 x 3/3 = 6/15

Therefore, 2/5 is equivalent to 6/15 when the denominator is 15.

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Answer:

composite number

Step-by-step explanation:

gssjkspfpfigogptitootjf

Hello!

0 4 5

The numbers that you can make by using these number cards will definitely be a Even number

Answer:

Option a represents a proportional relationship.

Step-by-step explanation:

A proportional relationship is a relationship where two variables are directly related to one another, meaning that their ratio is always the same. In other words, when one variable changes, the other variable also changes in the same ratio.

In the equation y = 2/3 * x, the value of y is directly proportional to the value of x, meaning that for every change in x, the corresponding change in y will always be 2/3 of that change. This is because the coefficient of x is a constant value, in this case 2/3. Therefore, as x increases or decreases, y will also increase or decrease at the same rate in proportion to x.

Option a represents a direct proportion.

Option b, c, and d are not proportional relationships because they include a constant or an operation like subtraction, addition or negative sign.

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Answer:

y=-2x+1

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of one another.  slope 1/2 perpendicular will be -2/1=-2

y-5=-2(x-(-2))

y-5=-2(x+2)

y-5=-2x-4

y=-2x-4+5

y=-2x+1

Adding a derivational suffix to a word often changes the part of speech is true.

What is derivational suffix ?

A derivational suffix is a type of affix that is added to the end of a base word to create a new word with a different meaning, often a different part of speech.

For example, adding the derivational suffix "-ness" to the base word "kind" creates the new word "kindness," which is a noun that refers to the quality or state of being kind. Similarly, adding the derivational suffix "-able" to the base word "value" creates the new word "valuable," which is an adjective that describes something that is worth a lot.

Derivational suffixes can change the meaning and function of a word, and they are often used to create new words in English. Some common derivational suffixes include "-er," "-able," "-ness," "-ful," "-ish," and "-ize."

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Complete question is: Adding a derivational suffix to a word often changes the part of speech is true.

Answer:

\({ \tt{slope = \frac{7 - 1}{0 - ( - 2)} = 3 }} \\ \\ { \tt{y = mx + c}} \\ { \boxed{ \bf{y = 3x + 7}}}\)

Answer:

No

Step-by-step explanation:

Add two sides together and see if it is greater than the third. (You have to do this with all possible combinations)

5 + 14 > 19

19 > 19

No, it isn't a triangle

14 + 19 > 5

23 > 5

19 + 5 > 14

24 > 14

The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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The derivative dy/dx or y' for the curve xy = y^3 + x^2 + 2x + 1 is given by y' = (3y^2 + 2x + 2) / (y - x).

To find the derivative using implicit differentiation, we treat y as a function of x and differentiate both sides of the equation with respect to x.

Differentiating xy with respect to x gives us x(dy/dx) + y.

Differentiating y^3 with respect to x gives us 3y^2(dy/dx).

Differentiating x^2 with respect to x gives us 2x.

Differentiating 2x with respect to x gives us 2.

Differentiating 1 with respect to x gives us 0.

Now we can rewrite the equation as x(dy/dx) + y = 3y^2(dy/dx) + x^2 + 2x + 1.

Next, we isolate dy/dx terms on one side and collect all other terms on the other side of the equation.

Rearranging the equation, we get (x - 3y^2)dy/dx = x^2 + 2x + 1 - y.

Finally, dividing both sides by (x - 3y^2), we obtain y' = (3y^2 + 2x + 2) / (y - x).

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Ratio of rise to run between the points (-2, 8) and (4, -3) = -11/6

To find the ratio of rise to run between two points, we need to calculate the difference in the y-coordinates (rise) and the difference in the x-coordinates (run) between the two points.

Given points:

Point 1: (-2, 8)

Point 2: (4, -3)

Rise = difference in y-coordinates = y2 - y1 = -3 - 8 = -11

Run = difference in x-coordinates = x2 - x1 = 4 - (-2) = 6

Therefore, the ratio of rise to run can be calculated as:

Ratio of rise to run = Rise / Run = -11 / 6

Thus, the ratio of rise to run between the points (-2, 8) and (4, -3) is -11/6.

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Perimeter of the polygon with given vertices is 22.43

Given:

Point 1 : (-2,4) ,

Point 2 : (3,4),

Point 3 :(3,-4)  

Perimeter of a polygon  = Sum of all the sides length of polygon  

1. Length of Point 1 and point 2 = √[(x₂-x₁)²+(y₂-y₁)² ]                

= √[(3+2)²+(4-4)² ]                  

= 5  

2.Length of Point 1 and point 3 = √[(x₂-x₁)²+(y₂-y₁)² ]

           =  √[(3+2)²+(-4-4)² ]                    

= 9.43  

3. Length of Point 2 and point 3  =√[(x₂-x₁)²+(y₂-y₁)² ]            

= √[ (3-3)²+(-4-4)² ]                      

= 8

So, Perimeter of the polygon = 5+9.43+8

Perimeter of the polygon  = 22.43

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The correct symbol used for a column alias containing spaces is C. " " (quotation marks).

In SQL, when we want to assign a column alias containing spaces, we enclose the alias within double quotation marks. This is done to differentiate the alias from other SQL keywords or to handle cases where the alias includes special characters, spaces, or is case-sensitive.

For example, consider the following SQL query:

SELECT column_name AS "Column Alias"

FROM table_name;

In this query, we are selecting a column named "column_name" from the table "table_name" and assigning it the alias "Column Alias" containing spaces. By enclosing the alias within double quotation marks, we indicate to the database that it should treat the entire string as a single identifier or alias.

Using other symbols such as '', ||, or // will not achieve the desired result of creating an alias with spaces. These symbols have different meanings in SQL.

'' (two single quotation marks) typically represents an empty string or a string literal in SQL.

|| (double vertical bars) is the concatenation operator in some SQL dialects, used to combine strings or values.

// (double forward slashes) is commonly used for comments in various programming languages and does not have any special meaning for column aliases in SQL.

Therefore, the correct symbol to use for a column alias containing spaces is C. " " (quotation marks).

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Approximately 1068 randomly selected air passengers must be surveyed to achieve a 98% confidence level with a 3 percentage point margin of error.

To determine the sample size required for surveying air passengers, you need to consider the desired confidence level and the desired margin of error. In this case, you want to be 98% confident that the sample percentage is within 3 percentage points of the true population percentage.

To calculate the required sample size, you can use the formula:

n = (Z² * p * (1 - p)) / (E²)

where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, 98% confidence)

p = estimated proportion or expected proportion (use 0.5 for maximum variability)

E = desired margin of error (in this case, 3 percentage points, so E = 0.03)

Plugging in the values:

n = (Z² * p * (1 - p)) / (E²)

n = (2.33² * 0.5 * (1 - 0.5)) / (0.03²)

n ≈ 1068

Therefore, you would need to survey approximately 1068 randomly selected air passengers to achieve a 98% confidence level with a margin of error of 3 percentage points.

Note: The Z-score of 2.33 corresponds to a 98% confidence level, assuming a normal distribution.

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\(\displaystyle \large \boldsymbol{} (7 \sqrt[5]{6x-10}) ^2 +\backslash\!\!\!8=\frac{49}{x^{-\tfrac{2}{5} }} +\backslash\!\!\!8 \\\\\\ 49\!\!\!\! \diagup \sqrt[5]{(6x-10)^2} = 49\!\!\!\! \diagup \cdot \sqrt[5]{x^2} \ \ ; \\\\\\ (6x-10)^2=x^2 \\\\ (6x-x-10)(6x+x-10) =0 \Rightarrow x_1=2 \ ; \ x_2=\frac{10}{7 }\)

Answer

Area = 21 Sq units

Step-by-step explanation:

Area= 1/2[(x1y2 + x2y3 + x3y1) - (x2y1 + x3y2 + x1y3)]

Area = 1/2[(-5×5 +-3×-2+1×-2) - (-3×-2+1×5+-5×-2)]

Area = 1/2(-42)

Area = -21 sq units

Area = 21 sq units (The area is negative because it is below the x-axis.)

The homogeneous equation and a particular solution of the given nonhomogeneous equation is \(& y=c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}\).

The given nonhomogeneous equation is y" - 4y = 2

We are given \($y_1=e^{-2 x}$\)

Let \($y_2=u y_1$\)

Non-homogeneous differential equations are simply differential equations that do not satisfy the conditions for homogeneous equations. In the past, we’ve learned that homogeneous equations are equations that have zero on the right-hand side of the equation.

The two most common methods when finding the particular solution of a non-homogeneous differential equation are:

\($$\begin{aligned}& y_2=u e^{-2 x} \\& y_2^{\prime}=u^{\prime} e^{-2 x}-2 u e^{-2 x} \\& y_2^{\prime \prime}=u^{\prime \prime} e^{-2 x}-2 u^{\prime} e^{-2 x}-2 u^{\prime} e^{-2 x}+4 u e^{-2 x} \\& y_2^{\prime \prime}=u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}+4 u e^{-2 x}\end{aligned}$$\)

Substitute in \($y^{\prime \prime}-4 y=0$\), we get

\($$\begin{aligned}& u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}+4 u e^{-2 x}-4 u e^{-2 x}=0 \\& u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}=0 \\& e^{-2 x}\left(u^{\prime \prime}-4 u^{\prime}\right)=0 \\& u^{\prime \prime}-4 u^{\prime}=0 \\& u^{\prime \prime}=4 u^{\prime}\end{aligned}$$\)

Substitute \($$u^{\prime}=v$ and $u^{\prime \prime}=v^{\prime}$\), we get

\($$\begin{aligned}& v^{\prime}=4 v \\& \frac{d v}{d x}=4 v \\& \frac{1}{v} d v=4 d x\end{aligned}$$\)

Integrate both sides, we get

\($u=\frac{1}{4} C_1 e^{4 x}+C_2$$\)

put in \($y_2=u y_1$\)

\($$y_2=\left(\frac{1}{4} C_1 e^{4 x}+C_2\right) e^{-2 x}$$\)

Choose \($$C_1=4$ and $C_2=0$\), we get

\($$y_2=e^{2 x}$$\)

\($$\begin{aligned}& y_c=c_1 y_1+c_2 y_2 \\& y_c=c_1 e^{-2 x}+c_2 e^{2 x}\end{aligned}$$\)

Particular Solution

\($$\begin{aligned}& y_y=A \\& y_y{ }^{\prime}=0 \\& y_y{ }^{\prime \prime}=0\end{aligned}$$\)

Substitute in \($y^{\prime \prime}-4 y=2$\), we get

\($$\begin{aligned}& 0-4 A=2 \\& -4 A=2 \\& A=-\frac{1}{2} \\& \therefore y_y=-\frac{1}{2}\end{aligned}$$\)

General Solution

\($$\begin{aligned}& y=y_6+y_y \\& y=c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}\end{aligned}$$\)

Therefore, the second equation is \(& y_{2} =c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}\).

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Answer:

3 log(2)

Therefore:

log(2)³ = log8

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.