What is the volume of the prism?

A prism has hexagon bases with each side 12 centimeters. From the side of the base to the center of the base is 10 centimeters. The height of the prism is 9 centimeters.

Answer:

Step-by-step explanation:

You have two problems involving quadratic sequences. For the sequence that starts 20, 18, 14, 8, ..., you want the n-th term, the 12-th term, and the term number of -36. For the sequence with terms 2, 3, and 5 having values 1, -6, and -14, you want the second difference and the first term.

The first attachment shows the first and second differences of this sequence each begin with -2. The first of differences at level n can be put into a formula for the n-th term:

  ∆0 +(n -1)(∆1 +(n -2)/2(∆2 + ...))

We have (∆0, ∆1, ∆2) = (20, -2, -2), so the expression for the n-th term is ...

  tn = 20 +(n -1)(-2 +(n -2)/2(-2))

(a) tn = -n² +n +20

Listing the first 12 terms, we find the 12th term is ...

(b) t12 = -112

Locating the term -36 in the list, we find ...

(c) -36 is term 8

For a quadratic sequence the third differences are zero. The second attachment shows us the third differences for this sequence are ...

  -3(y +11) = 0   ⇒   y = -11

  y -x +21 = 0   ⇒   x = 10

That attachment also shows us the second differences are x-8 (or y+13):

  x -8 = 10 -8 = 2

(a) The second difference is 2.

(b) The first term is 10.

__

Additional comment

The ability of this free calculator app to perform arithmetic symbolically and to find differences of successive list elements is very helpful for solving questions related to sequences. The linear and quadratic regression capabilities can also be useful for some questions. It pays to know your tools.

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Becky contributed $50 towards the building for the aged.

Let's calculate the amounts contributed by each student:

Azar contributed 50% of the total amount:

Amount contributed by Azar = 50% of $200

= (50/100) × $200

= $100

Sunil contributed 25% of the total amount:

Amount contributed by Sunil = 25% of $200

= (25/100) × $200

= $50

Now, we can calculate the amount contributed by Becky:

Total contribution by Azar and Sunil = $100 + $50 = $150

The remaining amount contributed by Becky can be found by subtracting the total contribution by Azar and Sunil from the total amount:

Amount contributed by Becky = Total amount - Total contribution by Azar and Sunil

= $200 - $150

= $50

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Beth and Kelly were on vacation for 6 days. both spent same amount of money for dog sitting while on vacation.

Let's assume the number of days Beth and Kelly were on vacation is represented by 'd.'

For Beth:

Total cost for dog sitting = (Cost per day * Number of days) + Cleaning and food fee

24.50d + 90.50

For Kelly:

Total cost for dog sitting = (Cost per day * Number of days) + Cleaning fee

32d + 45.50

Since both Beth and Kelly spent the same amount, we can set their total costs equal to each other and solve for 'd':

24.50d + 90.50 = 32d + 45.50

Rearranging the equation:

24.50d - 32d = 45.50 - 90.50

-7.50d = -45

Dividing both sides by -7.50:

d = -45 / -7.50

d = 6

Therefore, both Beth and Kelly were on vacation for 6 days.

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The length of the radius of the circle of equation (x + 3)² + (y - 7)² = 289 is given as follows:

b) 17.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation for the circle in this problem is given as follows:

(x + 3)² + (y - 7)² = 289.

Hence the center and the radius are obtained as follows:

Hence option B is the correct option for this problem.

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Answer:

A. 16.7%

B. 89.5%

Step-by-step explanation:

A) Inside the Square

length:4

The square has an area of 16 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being in the square is:

(area of square)/(area of rectangle)

= 16/96

= 0.16666666666666666

This is equal to 16.7%.

B) Outside the right angles Triangle

base:4 height 5

The triangle has an area of 10 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being outside the triangle is:

(area of rectangle - area of triangle)/(area of rectangle)

= (96 - 10)/96

= 0.8958333333

This is equal to 89.5%.

1. The total in mass of the ingredients used is 2.35kg

2. The cost of sugar needed is R25.78.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

These statements are interpreted into mathematical equation or expression.

1. The recipes are ;

0.8kg = 800g

sugar = 650g

butter = 900000 mg = 900000/1000 = 900g

Therefore the total mass of ingredients

= 800 + 650 +900

= 2350g

in kilograms, 1000g is 1kg

2350g = 2350/1000

= 2.35kg

2. If 150g = R5.95

1g = 5.95/150

650g = 5.95 × 650/150

= R25.78.

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The expression that is undefined in the set of real numbers would be = 0/-4. That is option B.

Real numbers are those numbers that can either be positive or negative and that are rational or irrational numbers which are different from complex numbers.

An expression can be said to be an undefined set of real numbers when it's numerator = 0 as seen in 0/-4.

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Answer:

The missing variable θ is equal to (11π)/8.

Step-by-step explanation:

Given:

ω = π/8 radian per min

t = 11 min

Step 1: Identify the formula and the missing variable.

The formula is ω = (θ/t), and we are trying to find the value of θ.

Step 2: Rearrange the formula to solve for the missing variable.

To isolate θ, we can multiply both sides of the equation by t:

ω * t = θ

Step 3: Substitute the given values.

Substituting the given values into the rearranged formula, we have:

θ = (π/8) * 11

Step 4: Simplify the expression.

To multiply fractions, we multiply the numerators and multiply the denominators:

θ = (π * 11) / (8 * 1)

θ = (11π) / 8

Step 5: Finalize the answer.

The value of the missing variable θ is (11π)/8. This is the exact answer unless otherwise indicated.

Therefore, the step-by-step process shows that the missing variable θ is equal to (11π)/8.

The values of the side m and n for the right triangle are 36 and 12√3 respectively using the trigonometric ratio of sine

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

recall that sin60° = √3/2 and sin30° = 1/2

sin 60° = m/(24√3) {opposite/hypotenuse}

√3/2 = m/(24√3)

m = (24√3 × √3)/2 {cross multiplication}

m = 12 × 3

m = 36

sin 30° = n/(24√3)

1/2 = n/(24√3)

n = 24√3/2 {cross multiplication}

n = 12√3

Therefore, the values of the side m and n for the right triangle are 36 and 12√3 respectively using the trigonometric ratio of sine

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Answer: 49.4 thats the answer i devided it

The height of the average fourth grader is 135 cm 21 mm

From the question, we have the following parameters that can be used in our computation:

Birth age = 45 cm 7 mm

Average fourth grader = three times as tall

using the above as a guide, we have the following:

Average fourth grader = 3 * Birth age

So, we have

Average fourth grader = 3 * 45 cm 7 mm

Evaluate

Average fourth grader = 135 cm 21 mm

Hence, the height of the average fourth grader is 135 cm 21 mm

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In the excerpt, Li's crush gave his girl   friend a rose. The text states: Li's crush gave his girl   friend a rose. She was so happy!

Li's mother was upset about the gift later because she thought it was too expensive.

The text states: Li's mother was upset when she found out how much the rose cost. She thought it was too much money to spend on a gift.

Li's mother's reaction is understandable. Roses are expensive flowers, and it is possible that Li's mother did not have the money to spend on such a gift. However, it is also important to remember that Li's crush was trying to do something nice for his girl friend, and the rose was a symbol of his love for her. In the end, it is up to Li and his girl friend to decide whether or not the rose was worth the money.

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The length of side b in triangle ABC is 18.7 units.

In Mathematics and Geometry, the law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation (ratio):

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

In this context, the value of b can be determined as follows;

sin112/37 = sin28/b

b = 37sin28/sin112

b = 17.3705/0.9272

b = 18.7 units.

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The required equation to find the distance of any star from the Sun is d = 1/ tan [tex]\theta[/tex].

Given that, the astronomer is finding the distance(d) of star to the sun in astronomical unit (AU) and tan [tex]\theta[/tex] = 0.000001389.

To find the equation by using the trigonometric function that is

tan a = perpendicular / base.

By using the data and the tangent trigonometric function, the equation is

tan [tex]\theta[/tex] = 1/d.

On simplifying gives,

Thus, d = 1/tan [tex]\theta[/tex].

Hence, the required equation to find the distance of any star from the Sun is d = 1/ tan [tex]\theta[/tex]

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The curved surface area of the cylinder is 24 cm².

We have,

To find the curved surface area of a cylinder, we need to know its height (h) and the circumference of its base (C).

Given:

Circumference (C) = 4 cm

Height (h) = 6 cm

The formula to calculate the curved surface area of a cylinder is A =  Ch, where A is the curved surface area, C is the circumference, and h is the height.

Substituting the given values:

A = 4 cm x 6 cm

A = 24 cm²

Therefore,

The curved surface area of the cylinder is 24 cm².

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Answer:

2 * A^(3/2).

Step-by-step explanation:

Given that planet y is twice the mean distance from the sun as planet x, we can denote the mean distance of planet x as "A" and the mean distance of planet y as "2A".

The equation T^2 = A^3 represents the relationship between the orbital period (T) and the mean distance from the sun (A) for a planet.

Let's compare the orbital periods of planet x and planet y using the equation:

For planet x:

T_x^2 = A^3

For planet y:

T_y^2 = (2A)^3 = 8A^3

To find the factor by which the orbital period is increased from planet x to planet y, we can take the square root of both sides of the equation for planet y:

T_y = √(8A^3)

Simplifying the square root:

T_y = √(2^3 * A^3)

= √(2^3) * √(A^3)

= 2 * A^(3/2)

Now, we can express the ratio of the orbital periods as:

T_y / T_x = (2 * A^(3/2)) / T_x

As we can see, the orbital period of planet y is increased by a factor of 2 * A^(3/2) compared to the orbital period of planet x.

Therefore, the factor by which the orbital period is increased from planet x to planet y depends on the value of A (the mean distance from the sun of planet x), specifically, it is 2 * A^(3/2).

The reflections are described below.

We know that,

There are two types of reflection:

Reflection with respect to X-axis:

The x-coordinates of a point stay constant when it is mirrored across the X-axis. However, the Y-coordinates are changed into their inverse signs.

As a result, the X-axis reflection of the point (x, y) is (x, -y).

Reflection with respect to Y- axis:

The Y-coordinates of a point stay constant when it is mirrored across the Y-axis. However, the X-coordinates are changed into their inverse signs.

As a result, the Y-axis reflection of the point (x, y) is (-x, y).

Now the reflection is as following:

The point (x, y) when reflected across the x-axis becomes (x', y') = (x, -y)

The point (x, y) when reflected across the y-axis becomes (x', y') = (-x, y)

The point (x, y) when reflected across the line y = x becomes (x', y') = (y, x)

The point (x, y) when reflected across the line y = -x becomes (x', y') = (-y, x)

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The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.

To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.

For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.

If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.

However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.

To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.

If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.

the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.

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Note the full question may be :

To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.

Answer:

solution:  (0,3)

Step-by-step explanation:

You can find the solution when the two lines intersect.

The phrase "it will be tacitly understood that each such formula can be written in a form that only involves ∈ and = as nonlogical symbols" implies that although we may use certain symbols such as defined predicates, operations, and constants in our formulas, the underlying assumption is that these symbols can ultimately be expressed or defined using the fundamental symbols of set membership (∈) and equality (=).

Symbols can always be represented using set membership and equality symbols. We simplify formulas by eliminating unnecessary symbols through this convention.

If we define predicate "P," any formula with "P" can be expressed using set membership and equality. We can translate any formula with "P" into one using only ∈ and =. By adopting this convention, we ensure clear and precise communication, with a well-defined language and logical structure for formulas.

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See text below

In practice, we shall use in formulas other symbols, namely defined pred- icates, operations, and constants, and even use formulas informally; but it will be tacitly understood that each such formula can be written in a form that only involves and as nonlogical symbols.

Concerning formulas with free variables, we adopt the notational convention that all free variables of a formula

(u1,..., Un)

are among u1, ..., un (possibly some u are not free, or even do not occur, in ). A formula without free variables is called a sentence.

What is the meaning of "it will be tacitly understood that each such formula can be written in a form that only involves ∈ and = as nonlogical symbols"?

Answer:

16.829 minutes

Step-by-step explanation:

To solve this problem, we need to set up a system of equations based on the given information. Let's define the variables:

Let x be the number of minutes.

Let y be the price in cents.

For calling card A, the price can be calculated using the formula: y = 69 + 1.9x

For calling card B, the price can be calculated using the formula: y = 6x

We want to find the number of minutes (x) where the price (y) is the same for both cards. To set up the system of equations, we equate the two expressions for y:

69 + 1.9x = 6x

Now, we can solve this equation to find the value of x, which represents the number of minutes where the prices are equal.

69 + 1.9x = 6x

To simplify the equation, we can subtract 1.9x from both sides:

69 = 6x - 1.9x

Combining like terms, we have:

69 = 4.1x

To isolate x, we divide both sides of the equation by 4.1:

69 / 4.1 = x

Simplifying the division gives us:

16.829 = x

Therefore, the number of minutes (x) where the price (y) is the same for both calling cards A and B is approximately 16.829 minutes.

Hope this helps!

Answer:

For calling card A: y = 0.019x + 0.69

For calling card B: y = 0.06x

Step-by-step explanation:

For calling card A: y = 0.019x + 0.69

For calling card B: y = 0.06x

Set the prices equal to each other to find when they are the same:

0.019x + 0.69 = 0.06x

Simplify and solve for x:

0.041x = 0.69

x = 16.83 (rounded to two decimal places)

Therefore, if a person expects to talk for 16.83 minutes or more, calling card A will be cheaper. If they expect to talk for less than 16.83 minutes, calling card B will be cheaper.

To find the derivative matrix of the composition of functions f∘g, we need to compute the partial derivatives of f with respect to u and v, and then evaluate them at the point (u(x, y), v(x, y)). Let's calculate the partial derivatives first:

∂f/∂u = cos(u)cos(v)

∂f/∂v = -sin(u)sin(v)

Now, let's substitute u = 4x^2 - 5y and v = 3x - 5y into the partial derivatives:

∂f/∂u = cos((4x^2 - 5y))cos((3x - 5y))

∂f/∂v = -sin((4x^2 - 5y))sin((3x - 5y))

The derivative matrix D(f∘g)(x, y) is a 1x2 matrix (a row vector) where each entry represents the partial derivative of f∘g with respect to x and y, respectively.

D(f∘g)(x, y) = (∂f/∂u ∂f/∂v) evaluated at (u(x, y), v(x, y))

D(f∘g)(x, y) = (cos((4x^2 - 5y))cos((3x - 5y)), -sin((4x^2 - 5y))sin((3x - 5y)))

Step-by-step explanation:

Cylinder LATERAL  S.A. = circ   X   Height = 132 cm  X  30 cm  = 3960 cm^2

   PLUS the two ends  =  two  X  pi r^2

  the circumference = pi * d = 132 cm

                   then  diameter = 132 / pi   then radius =  1/2  132 / pi = 66/ pi

     so end areas :  two *    pi (66/ pi)^2   = 2773.1

TOTAL = 3960  +  2773.1 =  6733.1 cm^2

The values of the variables are y = 102° and z = 23°.

Given that are two parallel lines j and m we need to find the measures of the variables y and z,

So,

Since, j║m, therefore, y and 78° are supplementary because they are exterior consecutive angles between two parallel lines,

So,

y + 78° = 180°

y = 180° - 78°

y = 102°

Now,

y and (4z-14) are linear pair angles, which means they are also supplementary.

Therefore,

y + (4z-14) = 180°

102° + 4z - 14 = 180°

4z + 88 = 180°

4z = 92°

z = 23°

Hence the values of the variables are y = 102° and z = 23°.

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Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

[tex]a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c[/tex]

[tex]\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ[/tex]<-- You can also use other trig ratios

[tex]B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ[/tex]

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

Answer: 17 months

Step-by-step explanation:

Total cost of the bike = $1,867

Down payment = $320

so $1,867 - $320 = $1,547

$91 * 17 = 1,547

(17 = months) so $91 * 17 months = 1,547

Answer: C

Step-by-step explanation:

|-8| = 8

The image of point A after the reflection is A'(3, -4).

The image of point B after the reflection is B'(2, -3).

To reflect a point in the x-axis, we keep the y-coordinate the same and change the sign of the x-coordinate.

For point A(3, 4):

After reflecting point A in the x-axis, the y-coordinate remains the same (4), and the sign of the x-coordinate changes.

Therefore, the image of point A after the reflection is A'(3, -4).

To reflect a point in the y-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.

For point B(-2, -3):

After reflecting point B in the y-axis, the x-coordinate remains the same (-2), and the sign of the y-coordinate changes.

Therefore, the image of point B after the reflection is B'(2, -3).

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