Question
A group consisting of 10 children and adults went to a movie theater. Children's tickets cost $5 each and adults' tickets cost $8 each, and the total cost for the 10 people was $62. How many children were in the group?

Answer:

[tex]Area = 1200m^2[/tex]

[tex]Perimeter = 148m[/tex]

Step-by-step explanation:

To find the area, just multiply the length by the width. In fact, we have a simple formula for this:

[tex]A(area) = lw[/tex]

[tex]l(length) = 50[/tex]

[tex]w(width)= 24[/tex]

Now, we need to plug in our values:

[tex]A(area)= 50*24[/tex]

Simplify:

[tex]A(area) = 1200[/tex]

Therfore, the area of the rectangle is:

[tex]1200m^2[/tex]

Now, lets move on to the perimeter(again, we have a simple formula!):

[tex]P(perimeter) = 2(l+w)[/tex]

Plug in our values from before:

[tex]P(perimeter)= 2(50 + 24)[/tex]

Simplify:

[tex]P(perimeter)= 2(74)[/tex]

Multiply it out:

[tex]P(perimeter) = 148[/tex]

Therfore, the perimeter of your rectangle is 148 m

Always remember to include the proper units and format your work well to minimize mistakes and leave less room for error.

~~~Harsha~~~

Answer:

A translation of (x+6, y-3)

Step-by-step explanation:

X goes left or right, while Y goes up or down. So, to move the triangle 6 units to the right, we take our current x coordinate, and add 6 to it.

The surface area of the Triangular pyramid is approximately 331.3 square millimeters.

The surface area of a triangular pyramid, we need to calculate the area of its base and the area of each triangular face, then add them together. The formula for the surface area of a triangular pyramid is:

SA = (1/2)P*l + B

where SA is the surface area, P is the perimeter of the base, l is the slant height of each triangular face, and B is the area of the base.

In this case, the base of the triangular pyramid is an equilateral triangle with legs of 13 millimeters and a height of 11.3 millimeters. To find the area of the base, we can use the formula for the area of an equilateral triangle:

B = (sqrt(3)/4)*a^2

where a is the length of a side of the equilateral triangle.

Substituting a = 13 into the formula, we get:

B = (sqrt(3)/4)*13^2

B = (sqrt(3)/4)*169

B = 43.7 square millimeters (rounded to one decimal place)

Next, we can find the perimeter of the base:

P = 3a

P = 3*13

P = 39 millimeters

Now we can use the formula for the surface area of a triangular pyramid:

SA = (1/2)P*l + B

Substituting P = 39, l = 17, and B = 43.7, we get:

SA = (1/2)*39*17 + 43.7

SA = 331.3 square millimeters (rounded to one decimal place)

Therefore, the surface area of the triangular pyramid is approximately 331.3 square millimeters.

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An exponential function would best fit the data because as x increases, the y values change multiplicatively. The rate of change of the function is of approximately 0.8275.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant, which is the rate of change of the exponential function.

The rate of change for this problem is approximated as follows:

Hence the rate can be rounded to 0.8275.

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For this reason, 968 grams of coffee are needed to make a grande cup, and 998 grams are needed to make a jumbo cup.

Let's call the amount of coffee required to make a grande cup "g" and the amount of coffee required to make a jumbo cup "j". We want to find the values of g and j.

From the first piece of information, we know that:

60g + 59j = 61,644

From the second piece of information, we know that:

60g + 74j = 71,184

We can solve this system of equations by using the method of elimination. To eliminate g, we can subtract the first equation from the second equation:

(60g + 74j) - (60g + 59j) = 71,184 - 61,644

Simplifying, we get: 15j = 9540

Dividing by 15, we get: j = 636

Now that we know j, we can substitute it into either equation to find g. Let's use the first equation:

60g + 59(636) = 61,644

Simplifying, we get: 60g = 59,880

Dividing by 60, we get: g = 998

Therefore, the amount of coffee required to make a grande cup is 968 grams, and the amount of coffee required to make a jumbo cup is 998 grams.

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Answer:

I don't understand you

The monthly payments you can withdraw from the retirement account is $1,583.4.

The monthly payments you can withdraw from the retirement account, is calculated as;

PV = Px [(1 - (1 + r)⁻ⁿ) / r]

where;

The total number of periods = 25 years x 12 months/year = 300 months

PV = P x [(1 - (1 + r)⁻ⁿ) / r]

$300,000 = P x [(1 - (1 + 0.04/12)⁻³⁰⁰) / (0.04/12)]

$300,000 = P x 189.47

P = $300,000 / 189.47

P= $1,583.4

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Answer:

Each bundle of wood weighs approximately 56.3 pounds.

Explanation:

To determine the weight of one bundle, we divide the total weight of all the bundles by the number of bundles. Thus, the weight of one bundle is equal to 3,941 pounds divided by 70 bundles, which is approximately 56.3 pounds. Therefore, each bundle of wood weighs approximately 56.3 pounds.

The Trigonometric functions sine (s) and cosine (c) c(5) ≈ -0.2837.

The trigonometric functions sine (s) and cosine (c). To determine s(5), we need to know the value of sine of 5 radians.

We can use a scientific calculator or a trigonometric table to find this value.

Using a calculator, we can simply enter "sin(5)" and get the answer. On most calculators, the answer will be displayed as a decimal.

Using a trigonometric table, we can look up the value of sine for 5 radians. The table will list the sine of angles in degrees, so we need to convert 5 radians to degrees first. One radian is equal to 180/π degrees, so

5 radians = (5 × 180)/π degrees ≈ 286.48 degrees

Looking up the sine of 286.48 degrees in the table, we get:

sin(286.48°) ≈ -0.9589

Therefore, s(5) ≈ -0.9589.

To determine c(5), we need to know the value of cosine of 5 radians.

We can again use a calculator or a trigonometric table to find this value.

Using a calculator, we can enter "cos(5)" to get the answer.

Using a trigonometric table, we can look up the cosine of 5 radians. Since we have already converted 5 radians to degrees, we can simply look up the cosine of 286.48 degrees in the table. We get:

cos(286.48°) ≈ -0.2837

Therefore, c(5) ≈ -0.2837.

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As per the given scenario, the amplitude of the tip of King Arthur's Sword is equal to the length of the side of either the regular hexagon or the regular pentagon.

To decide the amplitude of the tip of King Arthur's Sword, we want to locate the gap from the center of the regular hexagon and pentagon to one in every of their vertices.

A regular hexagon has six identical aspects and 6 same angles. The distance from the center to one of the vertices of a everyday hexagon is identical to the length of its side.

Thus, a everyday pentagon has 5 equal facets and 5 same angles. The distance from the middle to one of the vertices of a everyday pentagon is also equal to the length of its aspect.

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If a rectangular container is 25cm by 37cm by 21cm, then it will overflow after reaching the volume of 19425 cm³.

To know the volume after which the container will overflow, first we have to calculate the volume it can contain.

As, Volume of cuboid= length × breadth × height

So, Volume of rectangular container = 25 × 37 × 21 cm³

Volume = 19425 cm³

So, volume of rectangular container whose dimensions are  25cm by 37cm by 21cm is 19425 cm³ and it will overflow after reaching this volume.

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The image of the point (-3, -7) after a reflection over the x-axis is (-3, 7)

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

Point = (-3, -7)

Transformation rule

A reflection over the x-axis

The rule of a reflection over the x-axis is

(x, y) = (x, -y)

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

Image = (-3, 7)

Hence the image of the point after a reflection over the x-axis is (-3, 7)

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The function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

The total area of the composite figure is the sum of the areas of the individual shapes

So, we have

Area = Rectangle + Triangle

Using the area formula, we have

M(x) = (x + 2)(x - 2) × 1/2 × x ×  (x + 2)

Factorize the expression to get the function

M(x) = (x + 2)(x - 2 + x/2)

So, we have

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

Hence, the function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

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The Standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.

To write an expression in standard form, we need to arrange the terms in descending order of degree and combine like terms.

The given expression is:

48 + 24x3 - x + 10x4 - 5x2

First, we arrange the terms in descending order of degree:

10x4 + 24x3 - 5x2 - x + 48

Next, we combine the like terms:

10x4 + 24x3 - 5x2 - x + 48 = 10x^4 + 24x^3 - 5x^2 - x + 48

Therefore, the standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.

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Answer:

The 13.2 meters from that point on the ocean floor to the wreck.

Step-by-step explanation:

As given

A ship's sonar finds that the angle of

depression to a ship wrack on the bottom of the ocean is 12.5°.

If a point on the ocean floor is 60

meters.

Now by using the trigonometric identity.

tano = Perpendicular /Base

As shown in the figure given below.

Perpendicular CB

Base AC = 60 meters

0 = 12.5°

Put in the identity CB

tan 12.5°

AC

tan 12.5° CB 60

tan 12.5° 0.22

tan 12.5° = 0.22

0.22 CB 60

CB = 60 × 0.22

CB= 13.2 meters

Therefore the 13.2 meters from that point on the ocean floor to the wreck.

Answer:

C. x =8; y = -4

Step-by-step explanation:

To find the x and y intercepts, substitute with zero.

8x - 16y = 64

Finding the x-intercept:

8x - 16(0) = 64

8x = 64

Divide both sides by 8.

x = 8

Finding y-intercept:

8(0) - 16y = 64

-16y = 64

Divide both sides by -16.

y = -4

a) The solution to the equation is given as follows: x = -12.

b) The solution to the inequality is given as follows: -12 ≤ x < 7.

The equation for this problem is given as follows:

f(x) = g(x).

The point of intersection of the functions f(x) and g(x) is given as follows:

(-12, -7).

Hence the solution is given as follows:

x = -12.

For the inequality, we have that:

Hence the solution to the inequality is given as follows:

-12 ≤ x < 7.

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The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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Answer:

1 - ($73,310.56/$73,608.40)^12 = .047

= 4.7%

The measure of x is 25.2 degree

Given that,

Total number of votes = 3200

Bowerman's share = 224

Now the percentage of  Bowerman's  share = (224/3200)x100

                                                                         = 7%

Now we know that.

The complete angle of circle is 360 degree.

Therefore the value of x shown in the figure is,

x = 7% 360

  = (7 x 360)/100

  = 25.2 degree

Therefore,

⇒ x  = 25.2 degree

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Answer:

To solve this problem using spherical coordinates, we need to parameterize the region E using rho, theta, and phi. The cone z = x^2 + y^2 becomes phi = arctan(sqrt(x^2+y^2)/z), and the sphere x^2 + y^2 + z^2 = 1 becomes rho = 1, while x^2 + y^2 + z^2 = 64 becomes rho = 8. Then, we can integrate over the bounds rho = 1 to rho = 8, theta = 0 to theta = 2pi, and phi = 0 to phi = arctan(sqrt(x^2+y^2)/z), using the integrand x^2 + y^2 + z^2. The final result is a numerical value that represents the volume of the region E.

Answer:

41

Step-by-step explanation:

Given

Perimeter of a square ( P ) = (x + 7) cm

Side length ( L ) = 12 cm

To find : The value of x

Formula :

Perimeter of a square = 4L

4 * 12 = x + 7

48 = x + 7

x + 7 = 48

x = 48 - 7

x = 41

Answer:

Step-by-step explanation:

ok Let me explain :

Your argument of saying that the prob is 1/2 because there are 2 colors.

Had there been red, blue and green cubes you would have ended up calculating the prob as 1/3.

But this concept is wrong.

Prob is the chance occurrence of an event given many such events.

here since we have 4 cubes , the chance to pick any one is equal and that is 1/4

chance of picking a blue cube (1/4)*1 ....since we have one blue cube

chance of picking a red cube (1/4)*3 ....since we have one red cubes

You can think in a simple manner also, when something is greater in number (3>1) , the chances to pick that would obviously be more , so the probability cannot be half.

Hello !

Answer :

Explanation :

[tex] \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } [/tex]

[tex] \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } [/tex]

[tex] ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}[/tex]

Have a nice day ;)

The linear equation that gives the graph expression is: d = 2h

The general formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

We are given the equation as: d = rh

where:

d is dollars

r is rate

h is hours,

From the graph, we can find the rate by finding the slope of the graph.

(1, 4) and (2, 8)

Thus:

Slope = (8 - 4)/(2 - 1)

Slope = 2

Thus, r = 2

Then d = 2h

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The minimum amount of wrapping paper that is needed to cover the package is 576 square inches.

In Mathematics and Geometry, the total surface area of a trapezoidal prism can be calculated and determined by using this mathematical equation or formula:

Total surface area of a trapezoidal prism, TSA = (a + b)h + (a + b + c + d)l

Where:

By substituting the given parameters into the total surface area of a trapezoidal prism, we have:

TSA = [(12 + 4) × 6/2] × 2 + [(12 × 15) + (10 × 15) + (4 × 15) + (9 × 15)]

TSA = 96 + 180 + 150 + 60 + 90

TSA = 576 square inches.

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Missing information:

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

Answer:

Easy

Step-by-step explanation:

Let the time taken by Badri to complete the work be B. Then Amit can complete the work in 2.25 days, so we can write:

A = 2.25/B

Chetan takes double that of Badri to complete the work, so we can write:

C = 2B

Das takes double that of Chetan to complete the work, so we can write:

D = 2C = 4B

Let the first group consist of Amit and Das, and the second group consist of Badri and Chetan. Then the time taken by the first group to complete the work is:

T1 = A + D = 2.25/B + 4B

The time taken by the second group to complete the work is:

T2 = B + C = B + 2B = 3B

The difference between the times taken by the two groups to complete the work is:

T2 - T1 = 3B - (2.25/B + 4B) = 3B - 2.25/B - 4B

To minimize this difference, we take the derivative with respect to B and set it equal to zero:

d/dB (3B - 2.25/B - 4B) = 0

3 + 2.25/B^2 - 4 = 0

2.25/B^2 = 1

B = sqrt(2.25) = 1.5

Therefore, the time taken by Badri to complete the work is B = 1.5 days. Amit takes 2.25/1.5 = 1.5 days, Chetan takes 2B = 3 days, and Das takes 4B = 6 days.

To minimize the difference between the times taken by the two groups, we can take the faster group to consist of Amit and Badri, and the slower group to consist of Chetan and Das. The faster group takes 1.5 + 1.5 = 3 days to complete the work, and the slower group takes 3 + 6 = 9 days to complete the work. Therefore, the composition of the faster group could be Amit and Badri.

Answer:

The answer is located inside the file sent below

The value of x that makes the equation true is 0.2.

We have the Equation,

0.17x - 0.03 = 0.03x - 0.002

Simplifying the equation by adding 0.002 to both sides, we get:

0.17x - 0.028 = 0.03x

Subtracting 0.03x from both sides, we get:

0.14x - 0.028 = 0

Adding 0.028 to both sides, we get:

0.14x = 0.028

Dividing both sides by 0.14, we get:

x = 0.2

Therefore, the value of x that makes the equation true is 0.2.

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