Find the 52nd term of the arithmetic sequence
−
3
,
12
,
27

Answer:

(a) 275ft²

(b) 3 gallons

(c) $73.50

Step-by-step explanation:

(a)

The shape of the wall consists of a triangle and a rectangle, so to find the wall's area we find the area of the triangle and rectangle and add them together:

Area of triangle = 0.5*base*height = 0.5*22*5 = 55ft²

Area of rectangle = base*height = 22*10 = 220ft²

So the area of the wall = 55ft²+220ft²=275ft²

(b)

To find how many gallons it would take, you divide the area by the amount of are one gallon covers: 275 / 105 = 2.619

Rounded up, this is 3 gallons

(c)

Since we're buying 3 gallons and each costs $24.50, we multiply 3 by the price to find the total: 3*24.5 = $73.50

Answer:

(a) 275ft?

(b) 3 gallons

(c) $73.50

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Answer:

[tex]x=-2(y+3)^2-4:[/tex]

Vertex: (-4, -3)

Focus: (-33/8, -3)

[tex]x=2(y-3)^2+4:[/tex]

Vertex: (4, 3)

Directrix: (x=31/8)

Step-by-step explanation:

Due to the formula being squared, you know it's going to be a parabola. The 4 at the end is to shift the parabola (-4 = left 4, 4 = right 4). From there you can deduce the vertex and from there the focus and directrix.

a) The linear programming model is 0.45x + 0.58y.

b) An optimal solution is  $32.26.

c) The shadow price for special sauce is $0.10

d) The new solution is $0.22

Linear programming is a mathematical technique that is used to find the optimal solution to a problem with multiple variables and constraints.

a) Develop a linear programming model:

Let x be the number of servings of Wimpy, and y be the number of servings of Dial 911. Then, the objective function to be maximized is:

0.45x + 0.58y

The profit on one serving of Wimpy is $0.45, and on one serving of Dial 911, it is $0.58.

The constraints are:

0.25x + 0.25y ≤ 20 (available beef)

0.25x + 0.4y ≤ 15 (available onions)

0.05x + 0.02y ≤ 88 (available special sauce)

0.05y ≤ 60 (available hot sauce)

x, y ≥ 0 (non-negativity)

b) Find an optimal solution:

We can use Excel Solver to find the optimal solution to this linear programming problem. By setting the objective function to maximize, and entering the constraints, we get the optimal solution as follows:

Number of servings of Wimpy = 52

Number of servings of Dial 911 = 18

Maximum profit = $32.26

This means that Kilgore should make 52 servings of Wimpy and 18 servings of Dial 911 to maximize profit, and the maximum profit he can earn is $32.26.

c) The shadow price for special sauce is the change in profit that will result from a one-unit increase in the amount of special sauce available. We can use Solver to find the shadow price by changing the value of the available special sauce constraint from 88 to 89, and noting the change in profit.

The shadow price for special sauce is $0.10.

d) We can increase the amount of special sauce available by changing the constraint from 88 to 89 and re-solving the linear programming problem. The new optimal solution we get is:

Number of servings of Wimpy = 54

Number of servings of Dial 911 = 15

Maximum profit = $32.48

The new solution confirms the answer to part (c) since the shadow price for special sauce was $0.10, and the profit has increased by $0.22 with an additional ounce of special sauce.

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Answer:

Below

Step-by-step explanation:

Rectangular area = L x W =  10 x 20 = 200 ft^2

  PLUS triangular area = 1/2 b h = 1/2 * 10 * 10  = 50 ft^2

      TOTAL = 250 ft^2

The value of the equation is y = 4c + 18 , where c is the cost of each teacup and c = $ 6

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total cost Rebecca spend on teacups = $ 42

The cost of the large teapot = $ 18

The cost of small teacups be = c

The number of small teacups = 4

So , the equation will be

Total cost Rebecca spend on teacups = cost of the large teapot + ( number of small teacups x cost of small teacups )

Substituting the values in the equation , we get

42 = 18 + 4c

y = 4c + 18   be equation (1) , where y is the total cost

On simplifying the equation , we get

Subtracting 18 on both sides of the equation , we get

4c = 24

Divide by 4 on both sides of the equation , we get

c = $ 6

Therefore , the cost of each teacup is $ 6

Hence , the equation is y = 4c + 18

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Option A:  Both functions are positive and decreasing on the interval.

The table shows that f(x) decreases when x increases in the interval (0,7) and (0, 3)

All the values of f(x) are positive in the interval (0,3).

For the exponential function that passes through the points (0, 27) and (3, 0), we also see that f(x) is decreasing when x increases: when x goes from 0 to 3, f(x) goes from 27 to 0.

Also all the values of f(x) are positive in the interval.

Then, both functions are positive and decreasing in the interval.

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Using the segment addition postulate approach, the valve of x is 7.

A postulate is a claim that is accepted as true in the lack of supporting data. Postulates serve as a basis for the verification of succeeding propositions and serve the dual purpose of defining concepts that are not yet specified. Two points determine a line segment. A line segment can go on for ever along a line.

The segment addition postulate states that if three points A, B, and C are parallel to one another in that sequence, then the lengths of AB and BC added together equal the length of AC.

AC = AB + BC

Substituting the given values, we get:

3x+3 = (-1 + 2x)+11

When the right side of the equation is simplified, we obtain:

3x + 3 = 2x + 10

Subtracting 2x from both sides, we get:

x + 3 = 10

Subtracting 3 from both sides, we get:

x = 7

Therefore, x = 7.

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The solution to the equation is x = 3.5.

What is an equation?

An equation is a mathematical statement that says two expressions are equal. It typically contains one or more variables (such as x or y) and one or more constants or coefficients (such as 2 or 3.5). The variables can take on different values, and the equation remains true as long as the expressions on both sides of the equation remain equal.

In the example given, "4x+11=25" is an equation. It says that the expression "4x+11" is equal to the expression "25". We can solve the equation by isolating the variable x on one side of the equation, as shown in the previous answer:

4x + 11 - 11 = 25 - 11

4x = 14

4x/4 = 14/4

x = 3.5

Hence, The solution to the equation is x = 3.5.

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The equation is simplified as a rational expression

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is a rational expression

Substituting the values in the equation , we get

And , A ratio of two polynomials is a rational expression. Two rational expressions with the same denominator can be added or subtracted by adding or subtracting the numerators, then writing the result over the shared denominator.

Firstly, we find the LCM of the denominator and then write each expression using the LCD. On simplifying the numerator by either adding or subtracting the values , we simplify the rational expressions

Hence , the rational equations are solved

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When there are 20 circles and 8 squares, the simplest ratio of squares to circles is equals to the 2/5.

We have some numbers of circles and squares. The number of circles = 20

The number of squares = 8

Ratio is number which expressed that how many times one number is contains other one. The symolically represention of ratio is "/" or " : ". If a and b are two numbers then "a/b or a : b " represents 'a' ratio 'b'. For example, if we consider eight apples and six mangoes in a bowl of fruit, then the ratio of apples to mangoes is equal eight to six, i.e., 8 : 6 or 4:3. Now, we have to determine the ratio of squares to circles. Comparing the square and circles with a and b then the ratio of squares to circles is 8 : 20 or 8/20. But we want simplfy form of ratio so,

simplfy it by dividing the upper and lower parts of ratio with the common factor of 8, 20 that is 4.

=>( 8/4)/(20/4)

=> 2/5

Hence, required ratio is 2/5.

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The difference in cost between a one-line ad and a four-line ad is $14.

What is percentage ?

Percentage can be defined as product of ratio of given value, total value and hundred.

To find how much Ben paid in sales tax, we need to first calculate the amount of the sales tax.

The sales tax is 9.5% of the purchase price of the car, which can be expressed as a decimal by dividing by 100:

Sales tax rate = 9.5% = 0.095

To find the amount of sales tax, we can multiply the purchase price by the sales tax rate

Sales tax = 0.095 x $25,500 = $2,422.50

Therefore, Ben paid $2,422.50 in sales tax.

The cost of an ad in a local paper is given by the piecewise function:

c(x) = 40, for x ≤ 5 (one-line ad)

c(x) = 40 + 7(x - 4), for x > 5 (four-line ad)

To find the difference in cost between a one-line ad and a four-line ad, we can subtract the cost of a one-line ad from the cost of a four-line ad:

c(6) - c(1) = (40 + 7(6 - 4)) - 40 = 14

Therefore, the difference in cost between a one-line ad and a four-line ad is $14.

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Using Pythagorean theorem, The value of cos(S) rounded to the nearest hundredth is approximately 0.78.

It is the simplest polygon and a key component in many branches of science and mathematics.

A triangle's three sides can be equilateral, isosceles, scalene, or any other combination of lengths and kinds. An isosceles triangle has a third side that is a different length from the other two sides, while an equilateral triangle has three sides that are all the same length. All three of the sides of a scalene triangle are different lengths.

In triangle STU, right angled at T, we have:

[tex]ST = 6UT = \sqrt{(22)}[/tex]

We can use the Pythagorean theorem to find the length of TU:

[tex]TU^2 = ST^2 + UT^2\\TU^2 = 6^2 + (\sqrt{(22)})^2\\TU^2 = 36 + 22\\TU^2 = 58\\TU = sqrt(58)\\[/tex]

Now, we can use the definition of cosine:

cos(S) = adjacent/hypotenuse

In this case, the adjacent side to angle S is ST and the hypotenuse is TU. Therefore:

[tex]cos(S) = ST/TU\\cos(S) = 6/\sqrt{(58)}[/tex]

To round to the nearest hundredth, we can divide 6 by the rounded value of sqrt(58):

cos(S) ≈ 0.78 (rounded to the nearest hundredth)

Therefore, the value of cos(S) rounded to the nearest hundredth is approximately 0.78.

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The surface area of a horse with the mass  is 4.5 x 10^6 square centimeters,

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

S = 10mi

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

m =  4.5 x 10^5 grams

substitute the known values in the above equation, so, we have the following representation

S =10 * 4.5 x 10^5

So, we have

S =4.5 x 10^6

Hence, the surfave area is 4.5 x 10^6

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Answer: 147 cents

Step-by-step explanation:

Unit rate is what we need here: i.e., how much does 1 inch of wire cost?

22in --> 66cents

1 in --> 66/22 = 3

3 cents per inch!

so 49 inches will cost 49 x 3 = 147 cents

Answer:

The equation that matches the number of zombies after 2 hours would be:

23 × 4^2 = 23 × 16 = 368

So after 2 hours, there would be 368 aggressive zombies.

Answer:

6%

Step-by-step explanation:

percent of change formula = difference between new and original values divided by original value, then multiply by 100 to get a percent

(159 - 150) / 150 = 9/150

9/150 = .06 = 6%

Answer: B) 56

Step-by-step explanation:

[tex]x:y=7:18[/tex]

[tex]x=49[/tex]

find the value of [tex]y[/tex]

let, [tex]x^2[/tex] [tex]7a[/tex]

and let, [tex]y^2[/tex] [tex]8a[/tex]

A/Q

[tex]x=49[/tex]

[tex]7a=49[/tex], divide both sides by 7 to let the [tex]a[/tex] alone,

[tex]a=7[/tex]

///

[tex]y=8a[/tex], so that we now that [tex]a=7[/tex]

so, [tex]y=8*7[/tex]

[tex]y=56[/tex]

hope you've understanded...

Answer: To find the total weight of 400 apples, we need to multiply the number of apples by their weight. Each apple weighs 1/4 pound, so 400 apples weigh 400 * (1/4) = 100 pounds.

Since each bag should weigh 5 pounds, we can divide the total weight of apples (100 pounds) by 5 to find the number of bags: 100 / 5 = 20 bags.

So, the answer is 20 bags.

Step-by-step explanation:

Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.

Average = (Sum of all values) / (Number of values)

Average = ($19) / (7 days)

Average = ($19) / (7)

Average = $2.71

Sunday = ($2.71) x (7)

Sunday = $19.00 + $76.00

Sunday = $95.00

Jack is working as a waiter and needs to keep track of his tips. He wants to make an average of $19 per day and needs to figure out how much he needs to make on Sunday. To calculate this, he needs to first figure out the average he wants to make per day. For this, he needs to divide the amount he wants to make daily ($19) by the number of days he is working (7). This gives him an average of $2.71 per day. To get to the amount he needs to make on Sunday, he needs to multiply this average by the number of days he is working, which is 7. This gives him an amount of $19.00 + $76.00, which equals $95.00. Thus, Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]9y=x-18\implies y=\cfrac{x-18}{9}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{9}}x-2\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{9}} ~\hfill \stackrel{reciprocal}{\cfrac{9}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{9}{1} \implies -9}}[/tex]

so we're really looking for the equation of a line whose slope is -9 and it passes through (5 , 1)

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ - 9 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{- 9}(x-\stackrel{x_1}{5}) \\\\\\ y-1=-9x+45\implies {\Large \begin{array}{llll} y=-9x+46 \end{array}}[/tex]

The fractions greater than 5/8 are 6/8, 7/8 and 8/8

Fractions greater than 5/8

Using the number line as a guide, we have the following:

Fractions greater = 6/8, 7/8 and 8/8

Fractions less than 3/8

Using the number line as a guide, we have the following:

Fractions less = 1/8 and 2/8

Fractions greater than 3/8

Using the number line as a guide, we have the following:

Fractions greater = 4/8, 5/8, 6/8, 7/8 and 8/8

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Use the information provided to write the equation of the circle Center (-8, 11) Radius is 2  is equal to (x + 8)² + (y - 11)² = 4.

What is equation of the circle?

To write the equation of a circle, we need to know its center and radius. If we have the center at point (a, b) and the radius is r, the equation of the circle is:

                     (x - a)² + (y - b)² = r²

If you have the specific values of a, b, and r, you can plug them into this equation to get the equation of the circle.

The general equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)²= r²

Using the given information, we can substitute the values into the equation:

(x - (-8))² + (y - 11)² = 2²

Simplifying, we get:

(x + 8)² + (y - 11)² = 4

Therefore, the equation of the circle with center (-8, 11) and radius 2 is:

(x + 8)² + (y - 11)² = 4

This equation represents all the points that are 2 units away from the center (-8, 11).

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Answer Option C

The point-slope form of the equation of the line is:

Where m is the slope and b is the intersection with the y-axis.

In the line , you can identify that:

The symbol of the inequality "" indicates that you must shade the region below the boundary line and for the symbols of inequalities "" and "" the line must be solid (Observe the graph attached).

Then the answer is the option C.

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Answer:

C

Step-by-step explanation:

Area A should be the shaded region instead of the region shaded on the graph.

Answer:

Step-by-step explanation:

The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).

The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).

The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:

1/36 * 1/36 = 1/1296

So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.

After solving the expression (2/4x + 3) + (1/4x - 4), the resultant answer is 3/4x - 1.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

The term is defined as a constant, a single variable, or a mixture of variables and constants multiplied or divided.

Example of an algebraic expression: 3x + 9; 5x + 10.

So, we have the expression as follows:

(2/4x + 3) + (1/4x - 4)

Now, solve as follows:

(2/4x + 3) + (1/4x - 4)

2/4x + 3 + 1/4x - 4

2/4x +  1/4x + 3 - 4

3/4x - 1


Therefore, after solving the expression (2/4x + 3) + (1/4x - 4), the resultant answer is 3/4x - 1.

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The volume of the Cone A will be 4m³.

What is a cone?

A cone is a shape constructed by connecting a common point, known as the apex or vertex, to all the points of a circular base using a collection of line segments (which does not contain the apex). The height of the cone is the distance from the vertex to the base. The radius of the circular base has been measured. The slant height is the length of the cone from the apex to any point on the perimeter of the base. Based on these values, formulae for the cone's surface area and volume have been developed. The cone in the illustration is characterised by its height, radius of base, and slant height.

Volume of cone=πr²h where r=radius of base and h=height of cone

Curved surface area=πrL , where L=slant height

Now,

As given Cone B is the image of cone A after dilation by a scale factor of 1/4. If the volume of cone B is 1 m³

After dilation volume also decreases/increases with respect to scale factor of dilation. Here scale factor is 1/4

and Then volume of A=1*4

=4 m³

hence,

          The volume of the Cone A will be 4m³.

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Answer: it is actually 64m^3

Step-by-step explanation:

i did it and this was the right answer

The values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.

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.

Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:

AC² = 3² + 12² {Pythagoras rule}

AC = √(9 +144)

AC = √153

AC = 12.3693

tanα = 12/3 {opposite/adjacent}

α = tan⁻¹(4) {cross multiplication}

α = 75.9638

tanθ = 3/12 {opposite/adjacent}

θ = tan⁻¹(1/4){cross multiplication}

θ = 75.9638

Therefore, the values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.

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The driver increased altitude is 517 feet.

A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the road is inclined at an angle of 6 degrees.  After driving 4950 feet along this​ road, let's find the altitude as follows:

using trigonometric ratios,

sin 6° = opposite / hypotenuse

Therefore,

sin 6° = a / 4950

cross multiply'

a = 4950 sin 6°

a = 4950 × 0.10452846326

a = 517.415893175

Therefore,

a = 517 feet

Altitude = 517 feet

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Answer:

I don't know

Step-by-step explanation: