Determine the volume of the "leaning" regular hexagonal prism.
It has a base perimeter of 36 inches, a slanted height of 11 inches, and is leaning at
70°. The base is a regular hexagon with a perimeter of 36 inches.
6.70%
11"

The complete equation for the cosine rule is c² = 3² + 10² - 2(3)(10) × cos(34).

The cosine rule, also known as the law of cosines, is a formula used to find the lengths of sides or measures of angles in a triangle. It relates the lengths of the sides of a triangle to the cosine of one of its angles. The cosine rule is typically used when you have a triangle with at least one known side length and its opposite angle, and you want to find either another side length or another angle in the triangle.

The cosine rule is given by the following formula:

c² = a² + b² - 2ab × cos(C)

where:

For the given side c;

c² = 3² + 10² - 2(3)(10) × cos(34)

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Check the picture below.

Answer:

∠ BAC = 66°

Step-by-step explanation:

the inscribed angle BAC is half the angle at the centre, subtended on the same arc BC , then

∠ BAC = [tex]\frac{1}{2}[/tex] × 132° = 66°

On the basis of this information, the ratio of married male non-members to the married female non-members is (b) 3 : 1

Total married male employees = 80% × 50% = 40%

Total male Trade Union members = 91.67%

Total male non-Trade Union members = 100% - 91.67% = 8.33%

Married male Trade Union members = 40% × 91.67% = 36.67%

Married male non-Trade Union members = 40% - 36.67% = 3.33%

Now, let's find the number of married female non-members:

The ratio based on the information is 3 to 1.

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Expanding the left-hand side of the equation, we get:

(x+6)2 = (x+6)(x+6) = x(x+6) + 6(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36

So now we have the equation:

x^2 + 12x + 36 = 8

Subtracting 8 from both sides, we get:

x^2 + 12x + 28 = 0

We can factor this quadratic equation as:

(x+2)(x+14) = 0

This gives us two possible solutions:

x+2 = 0, so x = -2

x+14 = 0, so x = -14

Therefore, the solutions to the equation (x+6)2 = 8 are x = -2 and x = -14.

Step-by-step explanation:

Here is one way :

(x+6)^2 = 8        Take the square root of both sides

x+6 =   +- sqrt 8

x = -6 +- sqrt8     = -6 + 2 sqrt 2   or   -6 - 2 sqrt 2  =   -  3.17   or - 8.83

Answer:

Valid

Step-by-step explanation:

The volume of the batter in the pan can be found by multiplying the length, width, and height of the right rectangular prism-shaped pan. In this case, the length is 9 inches, the width is 5 inches, and the height is 3 inches.

Using the formula for the volume of a rectangular prism, V = lwh, we can substitute the given values to find:

V = (9 in.)(5 in.)(3 in.)

V = 135 cubic inches

Therefore, the volume of the batter in the pan is 135 cubic inches. This argument is valid because it follows the basic formula for calculating the volume of a rectangular prism and uses the specific measurements provided for the length, width, and height of the pan.

Answer:

1.5=slope

Step-by-step explanation:

To do this, we need to solve the slope.

We will use rise/run

0-3=-3

0-2=-2

-3/-2=1.5

(a) G'(a) = 2x - 3

(passing through (0, 3)) y1(x) = -3

(passing through (4, 7)) y2(x) = 5

b) The illustration of the graph is defined below.

In calculus, finding the derivative of a function is an important tool to understand the behavior of a curve at a specific point. One application of this concept is determining the equation of the tangent line to a curve at a given point. In this problem, we will use the derivative of a quadratic function to find the equations of tangent lines to the curve y = x² − 3x + 3 at the points (0, 3) and (4, 7).

To begin, we need to find the derivative of G(x) = x² − 3x + 3. Using the power rule, we have:

G'(x) = 2x - 3

Next, we can use this derivative to find the slope of the tangent line to the curve y = x² − 3x + 3 at any given point (a, G(a)). At the point (0, 3), we have a = 0, so the slope of the tangent line is:

G'(0) = 2(0) - 3 = -3

Using the point-slope equation of a line, we can find the equation of the tangent line passing through (0, 3). The equation of the tangent line is:

y - 3 = -3(x - 0)

Simplifying, we get:

y = -3x + 3

Similarly, at the point (4, 7), we have a = 4, so the slope of the tangent line is:

G'(4) = 2(4) - 3 = 5

Using the point-slope equation again, we can find the equation of the tangent line passing through (4, 7). The equation of the tangent line is:

y - 7 = 5(x - 4)

Simplifying, we get:

y = 5x - 13

To graph these tangent lines on the same screen as the curve y = x² − 3x + 3, we can plot the curve and the two tangent lines using a graphing calculator or software. The graph should show the curve as a parabola and the tangent lines as straight lines intersecting the curve at the points (0, 3) and (4, 7), respectively.

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The surface area of the rectangular prism is 502 mm²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The surface area of the prism = 2(8 mm * 13 mm) + 2(8 mm * 7 mm) + 2(7 mm * 13 mm) = 502 mm²

The surface area is 502 mm²

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The total weight of the contents is 141.33 pounds.

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Given: A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. The container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot.

The volume of the container is calculated as:

5 ft× 14.5 ft× 6.5 ft= 471.125 ft³

Then, the total weight of the contents is calculated as:

471.125 ft³×  0.3 pounds per cubic foot= 141.3375 pounds≅ 141.33 pounds

Hence, the total weight of the contents is 141.33 pounds.

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Answer:

55.5

Step-by-step explanation:

Using the Tangent and Intersected Chord Theorem we know that since the line is tangent to the circle, it will be half of the arc that surrounds the angle. Becuase the arc is 111, dividing it by 2 will give us 55.5

The functions which have a y-intercept which is greater than the y-intercept of the function g(x) = |x + 3| + 4 are :

h(x) = -5 |x| + 10

k(x) = 1/4 (x - 4)² + 4

m(x) = 1/4 |x - 8| + 6

Given function is,

g(x) = |x + 3| + 4

y intercept of a function is the value of the function when the input value is 0.

g(0) = |0 + 3| + 4 = 7

f(x) = -2 (x - 8)²

f(0) = -2 (0 - 8)² = -128

h(x) = -5 |x| + 10

h(0) = 10

j(x) = -4(x + 2)² + 8

j(0) = -4 (0 + 2)² + 8 = -8

k(x) = 1/4 (x - 4)² + 4

k(0) = 1/4 (0 - 4)² + 4 = 8

m(x) = 1/4 |x - 8| + 6

m(0) = 1/4 |0 - 8| + 6 = 8

Hence the functions h(x) = -5 |x| + 10, k(x) = 1/4 (x - 4)² + 4 and m(x) = 1/4 |x - 8| + 6 have the y intercept greater than that of g(x) = |x + 3| + 4.

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The slope of the line that is parallel to the line that contains side WV is 1.

What about slope of line?

The slope of a line is a measure of its steepness or inclination, defined as the ratio of the change in the vertical direction (y-axis) to the change in the horizontal direction (x-axis) between any two points on the line.

In other words, the slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is commonly denoted by the letter "m" and is calculated as:

m = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope can be positive, negative, zero, or undefined. A positive slope indicates that the line rises as we move from left to right, while a negative slope indicates that the line falls as we move from left to right. A slope of zero indicates that the line is horizontal, and an undefined slope indicates that the line is vertical.

According to the given information:

W(a+3, b-3) and V(a+5, b-1)

So, the slope WV,

[tex]\frac{b-3-(b-1)}{a+3 - (a+5)} \\\\\frac{-2}{-2} = 1[/tex]

So, the slope of the given condition is 1.

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The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)

When you Check the inequality by (-2,-1) then Put x=-2 and y=-1 in the given inequality.

1 < (-2)² - 2(-2) - 8

-1 < 4 + 4 - 8

-1 < 0

Hence:

(-2,-1) can be in the solution

( 0,-2) Cannot

(4,0) will not.

Therefore, The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)

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See full question below

Which of the following points is in the solution set of y < x2 - 2x - 8?

(-2, -1)(0, -2)(4, 0)

The current yield of a 4.95% coupon at a price of $102.53 is [tex]4.82%[/tex]%.

The current yield of bond means return on an investment based on its current market price.

To calculate the current yield, we will use (annual interest payment/current market price * 100).

Annual interest payment = $1,000 face value x 4.95% coupon

Annual interest payment = $49.50

Current market price = 102.53% of the face value

Current market price = $1,025.30

Current yield = $49.50 / $1,025.30 x 100

Current yield = 4.82%

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By subtraction between two points P₁(x, y) = (- 5, 3) and P₂(x, y) = (- 2, - 7), the vector V is 3 i - 10 j.

According to linear algebra, a vector can be formed by subtracting the initial point (P₁) from the final point (P₂). The equation is introduced below:

V = P₂(x, y) - P₁(x, y)

V = (- 2, - 7) - (- 5, 3)

V = (3, - 10)

V = 3 i - 10 j

The vector V = 3 i - 10 j is the result of subtracting the two points P₁(x, y) = (- 5, 3) and P₂(x, y) = (- 2, - 7).

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The dimensions that can create more than one triangle are given as follows:

three angles measuring 25°, 65°, and 90°.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the measures of the internal angles of a triangle is of:

180º.

Meaning that the first option is correct and the second is not.

Considering the law of sines, an infinite number of triangles can be formed, as long as:

sin(25º)/a = sin(65º)/b = sin(90º)/c.

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The maximum height attained by the arrow is 2128 feet

What is kinematic equation for vertical motion?

The kinematic equation for vertical motion is [tex]h = h_0 + v_0 \times (\frac{1}{2} )t - gt^2[/tex]

where:

h = height attained by the arrow (maximum height)

[tex]h_0 = [/tex]initial height (80 feet)

[tex]v_0 = [/tex]initial velocity (256 feet per second)

g = acceleration due to gravity (-32 feet per second squared)

t = time taken to reach maximum height

At the maximum height, the velocity of the arrow is zero. So we can use the fact that the final velocity is zero to find the time taken to reach the maximum height,

[tex]0 = v_0 - g \times t \\ t = \frac{ v_0}{g}[/tex]

Substituting this value of t into the first equation, we get:

[tex]h = h_0 + v_0 \times ( \frac{v_0}{g}) - ( \frac{1}{2} )g( \frac{v_0}{g})^2 \\ h = 80 + (256) \frac{256}{(-32)} - ( \frac{1}{2} )(-32)\frac{256^2}{(-32)^2} \\ h = 80 + 4096 - ( \frac{1}{2} ) \frac{(256)^2}{(32)} \\ h = 80 + 4096 - 2048 \\ h = 2128 \: feet[/tex]

Therefore, the maximum height attained by the arrow is 2128 feet.

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Answer:

Class Rank | Frequency

--- | ---

Fr | 7

So | 3

Jr | 4

Se | 6

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$879\\ r=rate\to 19.5\%\to \frac{19.5}{100}\dotfill &0.195\\ t=years\dotfill &1.5 \end{cases} \\\\\\ A = 879[1+(0.195)(1.5)] \implies A=879(1.2925)\implies A \approx 1136.11[/tex]

The mean and the median of the following gasoline prices that are listed above would be =3.29 and 4.85 respectively.

The formula that is used to calculate the mean of a data set is given as follows;

mean = sum of data set/number of data set

= 3.14+3.21+3.28+3.53/4

= 13.16/4 = 3.29

The median = 3.21+3.28/2 = 4.85

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Log3(14)

= log(14) / log(3) (Change of base formula)

= 4 / 1.965 (log(3) = 1.965)

= 2.041 (rounded to 3 decimal places)

2.041

Answer:

Step-by-step explanation:

To emulate the logarithm using the change of base formula, we need to use a base that is more convenient to evaluate. Let's use base 10:

log3(14) = log10(14) / log10(3)

Using a calculator, we can evaluate the numerator and denominator:

log10(14) ≈ 1.146

log10(3) ≈ 0.477

Dividing the numerator by the denominator gives:

log3(14) ≈ 2.402

Rounding to three decimal places, the final result is:

log3(14) ≈ 2.402

Triangles RLG and PCN are similar. The similarity is by SSS criteria and the scale factor is 2/3.

Two triangles that are similar in shape but not necessarily in size are called similar triangles. To put it another way, the two triangles' angles are similar and their corresponding sides are proportional.

If two triangles are comparable, then all pairs of related sides have the same length-to-length ratio. The scale factor of similar triangles is the name given to this ratio. The scale factor between two triangles is 2:1, for instance, if one side of a triangle is twice as long as its counterpart side in another triangle.

In the given figure we have triangle RLG and triangle PCN.

Here, the ratio of the sides of the triangle are given as:

RG / PN = 32 / 48 = 2/3

Also we have:

LG / PC = 18/27 = 2/3

LR / CN = 30 / 45 = 2/3

RG / PN = LG / PC = LR / CN = 2/3

Hence, triangles RLG and PCN are similar. The similarity is by SSS criteria and the scale factor is 2/3.

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The complete question is:

Answer:

Karl has 2.67 pounds of flour left.

Step-by-step explanation:

First, let us dissect the given.

Second, let us identify the correct solution for this problem.

Answer:

8.5 yrs

Step-by-step explanation:

parent: 41 yrs

eldest son: x

Firstly, we will need to subtract 24 from 41 to get 2x the eldest son's age.

By doing that, we will have an equation that looks like this:

41-24=2x

This equation would basically get us through the whole problem.

Simplify the equation:

17=2x

x=8.5

The eldest son's age is 8.5.

Let's check our work!

8.5 x 2 = 17

17+24=41 (parent's age.)

Hope this helps :)

So the area of the triangle is 216 square inches.

To find the area of a triangle, you can use the formula A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle. In this case, we have a height of 12 inches and a base of 36 inches.

To find the length of the missing side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, we have:

c² = a² + b²

c² = 12² + 34²

c² = 144 + 1156

c² = 1300

c = √(1300)

c = 36.06 (rounded to two decimal places)

Now that we know all three sides of the triangle, we can plug them into the formula for the area:

A = 1/2 * b * h

A = 1/2 * 36 * 12

A = 216

So the area of the triangle is 216 square inches.

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Check the picture below, so the angle looks more or less like so.

now, let's recall that the value pair in a terminal point is the adjacent and opposite sides

[tex]\cot(\theta )=\cfrac{\stackrel{adjacent}{0}}{\underset{opposite}{5}}\implies \cot(\theta )=0[/tex]

* Mary's solar panels cost $2,000.

* The panels will reduce her monthly electricity bill by $40.

* She can earn 12% interest compounded monthly.

* So her monthly savings is $40

* And her 12% monthly interest rate is 12% / 12 = 1% per month.

* So each month her balance grows by 1% of the current balance.

* Let's think through this step-by-step:

* Initial balance = $2,000 (from paying for the solar panels)

* Month 1:

** Savings = $40 (from lower electric bill)

** Interest = 1% of $2,000 = $20

** Balance after Month 1 = $2,000 + $40 + $20 = $2,060

* Month 2:

** Savings = $40

** Interest = 1% of $2,060 = $20

** Balance after Month 2 = $2,060 + $40 + $20 = $2,120

* Month 3: (continue the calculations for Months 3 through 24)

** Savings = $40

** Interest = 1% of $2,121 = $21

** Balance after Month 3 = $2,121 + $40 + $21 = $2,182

* After 24 months, the balance is $3,149 (calculated step-by-step as shown above)

* The initial investment was $2,000

* So it took about 24 months to recoup her investment.

Does this help explain the steps? Let me know if you have any other questions!

A recursive definition for the set S can be given as follows:

What is recursion?

Recursion is a programming technique where a function calls itself to solve a problem.

Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.

Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.

In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.

The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.

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