A hand-made carton has the following dimensions:

length of the base-7 inches

width of the base-6 inches

height of the carton-6 inches

what change should be made to the dimensions to increase the
volume of the carton by 42 cubic inches?

a. increase the height of the carton to 7 inches

b. increase the height of the carton to 8 inches

c. increase the width of the base to 8 inches

d. increase the width of the base to 9 inches

The volume of the large box is 200 cubic inches. The volume of the small box is 150 cubic inches. The difference in the volumes of the two boxes is 50 cubic inches. The units that should be used for each of these answers is cubic inches.

To find the volume of each box, we'll use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.

For the larger box, the dimensions are:
Length = 8 inches
Width = 2.5 inches
Height = 10 inches

Volume of large box = 8 × 2.5 × 10 = 200 cubic inches

For the smaller box, its length is 75% of the larger box's length:
Length = 0.75 × 8 = 6 inches

The width and height remain the same, so the dimensions are:
Length = 6 inches
Width = 2.5 inches
Height = 10 inches

Volume of small box = 6 × 2.5 × 10 = 150 cubic inches

The difference in the volumes of the two boxes is:
200 cubic inches - 150 cubic inches = 50 cubic inches

So, the difference in the volumes of the two boxes is 50 cubic inches. The units used for these answers are cubic inches.

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The value of the arc is approximately 14.3 cm.

We are given that;

The angle = 62, 20

Now,

To find the value of arc if angle is 82 degrees

Step 1: Convert the angle from degrees to radians

Angle in radians = Angle in degrees x π/180 Angle in radians = 82 x π/180 Angle in radians ≈ 1.43

Step 2: Multiply the angle by the radius

Arc length = Angle x Radius Arc length = 1.43 x 10 Arc length ≈ 14.3 cm

Therefore, by the arc length the answer will be approximately 14.3 cm.

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Answer:

B

Step-by-step explanation:

0.4 inches = 2 miles

x    inches = 8 miles

Cross multiplication:

0.4 * 8 = 2 * x

3.2 = 2x

x = 1.6''

The length of the diagonal AC in square ABCD is approximately 9.899 units.

To find the length of the diagonal AC, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In our case, since ABCD is a square, angle ABC is a right angle. Therefore, triangle ABC is a right-angled triangle with sides AB and BC both equal to 7 units. We can apply the Pythagorean theorem to find the length of diagonal AC (the hypotenuse):

AC² = AB² + BC²

Plugging in the side lengths:

AC² = 7² + 7² = 49 + 49 = 98

Now, we take the square root of both sides to find the length of AC:

AC = √98 ≈ 9.899

So, the length of the diagonal AC in square ABCD is approximately 9.899 units.

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Answer:

48

Step-by-step explanation:

can be divided into two 4x6 rectangles. Therefore, the area is 4x6 + 4x6 = 48

Total outcomes when we spin the spinner and flip a coin = 12

In the figure

In spinner the labelled number are from 1 to 6

And for a coin there are two outcomes head and tail

Therefore,

total number of outcomes for spinner = 6

total number of outcomes for a coin   = 2

Then the number of outcomes when both are performed once

= 6x2

= 12

Hence total outcomes = 12

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Answer: B

Step-by-step explanation:

Therefore, the simplified expression is 24.

To simplify the expression (-8)(10+(-5)+(-8)), you first need to solve the parentheses, following the order of operations, which requires solving the addition and subtraction within the parentheses before multiplying.

So, you have (-8)(10-5-8), which becomes (-8)(-3) after solving the parentheses. Finally, you can solve the multiplication by multiplying -8 by -3, resulting in 24.

It's important to remember the order of operations when simplifying expressions, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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We can use the given point P(3, 4) to find the values of sin(theta) and cos(theta) as follows:

[tex]sin(theta) = opposite/hypotenuse = 4/5[/tex]

[tex]cos(theta) = adjacent/hypotenuse = 3/5[/tex]

Since theta is a first-quadrant angle, we know that tan(theta) = sin(theta)/cos(theta).

Using the half-angle formula for tangent, we have:

[tex]tan(1/2 * theta) = ±√((1 - cos(theta))/2) / (1 + √((1 - cos(theta))/2))[/tex]

We can substitute the values of sin(theta) and cos(theta) that we found earlier:

[tex]tan(1/2 * theta) = ±√((1 - 3/5)/2) / (1 + √((1 - 3/5)/2))[/tex]

[tex]tan(1/2 * theta) = ±√(1/5) / (1 + √(1/5))[/tex]

[tex]tan(1/2 * theta) = ±√5 - 1[/tex]

Since theta is in the first quadrant, tan(1/2 * theta) is positive. Therefore:

[tex]tan(1/2 * theta) = √5 - 1[/tex]

We can simplify this expression by rationalizing the denominator:

[tex]tan(1/2 * theta) = (√5 - 1) / (√5 + 1) * (√5 - 1) / (√5 - 1)[/tex]

[tex]tan(1/2 * theta) = (5 - 2√5)[/tex]

So the answer is (5 - 2√5), which is approximately 0.382. Therefore, the answer is not one of the choices given.

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Answer:

--------------------------

Let the equal sides be both marked as ?

Use the perimeter formula to determine one of the equal sides.

Substitute the expression for the perimeter and find the value of ?

Hence the length of each of equal sides is 4x² - x + 2.

The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.+

To calculate the surface area of the pool that is lined with plastic material, we need to find the area of the curved part and the area of the top and bottom circles.

First, let's find the radius of the pool, which is half of the diameter:

radius = 11 feet / 2 = 5.5 feet

The curved part of the pool is a cylinder with a height of 2 feet and a circumference of [tex]2 * π *radius:[/tex]

curved area = height * circumference

[tex]curved area = 2 feet * 2 * 3.14 * 5.5 feet[/tex]

[tex]curved area = 68.2 square feet[/tex]

The top and bottom of the pool are two circles with a radius of 5.5 feet:

circle area = π * radius²

[tex]circle area = 3.14 * 5.5 square feet[/tex]

[tex]circle area = 95.0 square feet[/tex]

To find the total surface area of the pool that is lined with plastic material, we add the area of the curved part and the area of the top and bottom circles:

Total area = curved area + 2 * circle area

Total area = 68.2 square feet + 2 * 95.0 square feet

Total area = 258.2 square feet

The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.

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The circumference of the tank is is 125.66m and the percentage of the circumference that is visible to the person is 10.24%.

a) To calculate the circumference of the cylindrical tank, using the formula C = 2πr, where C is the circumference and r is the radius of the tank. In this case, r = 20 m, so:

C = 2π(20 m) ≈ 125.66 m

b) To determine the percentage of the circumference visible to the person, we first need to calculate the angle (in degrees) that subtends the visible arc. This can be done using the inverse tangent function:

angle = atan(opposite/adjacent) = atan(20 m/60 m)

angle ≈ 18.43°

Since the visible arc is symmetrical on both sides, the total angle of the visible arc is twice the calculated angle:

total angle ≈ 36.86°

Now, calculate the percentage of the circumference that is visible by dividing the total angle by 360° and multiplying by 100%:

percentage = (36.86°/360°) × 100% ≈ 10.24%

So, the visible percentage of the circumference to the person is approximately 10.24%.

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When all 967 tickets are purchased, the probability of not winning is 0 (or 0%).

The probability of an event occurring is defined by probability. There are numerous real-life scenarios in which we must forecast the outcome of an occurrence.

To find the probability of not winning the TV with a given number of tickets, we need to calculate the ratio of the number of losing tickets to the total number of tickets. The completed table is as follows:

Number of Tickets | Number of Losing Tickets | Probability of Not Winning

-----------------|-------------------------|----------------------------

      0         |           967           |           1.000        

      1         |           966           |           0.999        

      10        |           957           |           0.990        

      50        |           917           |           0.948        

      100       |           867           |           0.897        

      200       |           767           |           0.793        

      300       |           667           |           0.690        

      400       |           567           |           0.587        

      500       |           467           |           0.483        

      600       |           367           |           0.380        

      700       |           267           |           0.277        

      800       |           167           |           0.173        

      900       |            67           |           0.069        

      967       |             0           |           0.000        

As the number of tickets purchased increases, the probability of not winning the TV decreases. When no tickets are purchased, the probability of not winning is 1 (or 100%). When all 967 tickets are purchased, the probability of not winning is 0 (or 0%).

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Answer:

1/6

Step-by-step explanation:

Answer: -403

Step-by-step explanation:

Answer:62700

Step-by-step explanation:

You take your original value and move the decimal point 4 times to the right as it is a positive power.

Answer:

Step-by-step explanation:

Let's call the total volume of the container "V".

We know that the container was originally 15% full, so the amount of water in the container was 0.15V.

When 48 litres of water was added, the new volume of water in the container became 0.15V + 48.

We also know that the container is now 75% full, so the new volume of water in the container must be 0.75V.

We can set up an equation to solve for V:

0.15V + 48 = 0.75V

Subtracting 0.15V from both sides:

48 = 0.6V

Dividing both sides by 0.6:

V = 80

So the container can hold 80 litres of water when it is full.

The two numbers are 129 and 62, which satisfy the given conditions: their sum is 191 and their difference is 67 .

You are asked to find two numbers whose sum is 191 and whose difference is 67. Let's use the variables x and y to represent these two numbers.

We can establish the following two equations under the given conditions: 1) x + y = 191 2) x - y = 67

Now we can solve this system of linear equations to find the values of x and y.

We can start by adding both equations:

(x + y) + (x - y) = 191 + 67

2x = 258

Then we'll divide by 2 to find the value of x:

x = 129

Now, we can plug x into Equation 1 to find the value of y:

129 + y = 191

y = 191 - 129

y = 62

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The overall percentage decrease in the value of Alec's house for the two-year period is 9.9%.

Let's assume the original value of Alec's house as $100. After the first year, the value of the house increased by 1%, which means the new value of the house is $101.

Now, in the second year, the value of the house decreased by 10% of its value at the end of the first year. Therefore, the new value of the house at the end of the second year can be calculated as $101 - (10/100)*$101 = $90.90.

To find the overall percentage decrease in the value of Alec's house for the two-year period, we can use the formula:

Overall percentage decrease = [(Original value - Final value)/Original value] * 100%

Substituting the values, we get,

Overall percentage decrease = [($100 - $90.90)/$100] * 100% = 9.9%

Therefore, the overall percentage decrease in the value of Alec's house for the two-year period is 9.9%.

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Answer:

g(-2) = 4.

Step-by-step explanation:

To find g(-2), we simply need to substitute -2 for x in the function g(x) and simplify:

g(-2) = -4(-2) - 4

g(-2) = 8 - 4

g(-2) = 4

Therefore, g(-2) = 4.

The area of the shaded region is 422.8 m², rounded to the nearest tenth.

To find the area of the shaded region, we first need to determine the areas of the two shapes that make up the region. The first shape is a rectangle with dimensions of 18.6 m by 30 m, which has an area of:

Area of rectangle = length x width = 18.6 m x 30 m = 558 m²

The second shape is a semi-circle with a diameter of 18.6 m, which has a radius of 9.3 m. The area of a semi-circle is half the area of a full circle, so we can use the formula for the area of a circle to find the area of the semi-circle:

Area of semi-circle = (1/2) x π x r² = (1/2) x π x 9.3² = 135.2 m²

To find the area of the shaded region, we need to subtract the area of the semi-circle from the area of the rectangle:

Area of shaded region = Area of rectangle - Area of semi-circle
Area of shaded region = 558 m² - 135.2 m²
Area of shaded region = 422.8 m²

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The circumference of a circle is the distance around the edge or perimeter of the circle.

1) Radius = 5cm/2 = 2.5 cm

2) Radius = 28 mm/2 = 14 mm

3) Radius = 3 1/2 m * 1/2 = 3/4 m

4) diameter = 2 * 6cm = 12 cm

5) diameter = 2 * 2m = 4 m

6) diameter = 2 * 0.8 ft = 1.6 ft

Circumference can be calculated using the formula:

C = 2πr

7) circumference = 2πr = 2 * 3.14 * 10/2 = 31.4 in

8) circumference = 2 * 7 * 3.14 = 43.96 in

9) Circumference = 2 * 3.14 * 18/2 = 56.52 in

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The temperature are the times  indicated are:

T( 0) =   5.800°

T( 0.22) = -4.9094 °

T (0.44) = -2.6792 °

T(0.66) = 2.3244°

T(0.88)  = 4.8184°

T(1.1) = -4.1686 °

To solve the above, we need to use the formuala that we given which is T(x) = 5.8cos(3.8πx)

Entering the various values of x, can can obtain

T(0) = 5.8 cos (3.8π  (0) )  = 5.8cos(0) = 5.800

T(0.22) = 5.8 cos (3.8  π(0.22)) ≈ -4.9094

T(0.44) = 5.8cos (3.8π (0.44) ) ≈ -  2.6792

T(0.66) = 5.8cos(3.8π (0.66)) ≈ 2.3244

T(0.88) = 5.8cos(3.8π(0.88)) ≈ 4.8184

T(1.1) = 5.8 cos(3.8π(1.1  )) ≈ -4.1686

So the above answers are correct.

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Answer:

Step-by-step explanation:

Geographers use satellites primarily to capture detailed images of a location from space (option A). These images can provide valuable information about the landscape, climate, and natural resources of an area, among other things. Additionally, satellites can be used in combination with other technologies to collect and store digital information about a location (option B), such as mapping the distribution of vegetation or tracking changes in land use over time. While satellites can be used to track the location of moving objects on Earth (option C), this is not typically their primary function. Finally, organizing and representing data for a location (option D) is more closely associated with Geographic Information Systems (GIS) than with satellite technology specifically.

Answer:

A. Capture detailed images of a location from space.

Step-by-step explanation:

Geographers use satellites to capture high-resolution images of the Earth's surface from space. This enables them to study and analyze different aspects of the Earth, such as its topography, land use patterns, and weather systems. These images are also used in cartography, the science of map-making, to create accurate and up-to-date maps of the Earth's surface.

Step-by-step explanation:

sqrt (5/3)  = sqrt 5 / sqrt 3    

  multiply by ONE in the form   sqrt (3) / sqrt 3

      sqrt 5 / sqrt 3    *    sqrt 3 / sqrt 3

             = sqrt 15 / 3    

Or maybe you meant  

  sqrt (5) / 3  =  .745

Answer:

Billy can buy 19 or less than 19 stickers.

Step-by-step explanation:

  Let the unknown variable - number of stickers be 'x'.

   Cost of one sticker = $1.34

   Cost of 'x' stickers = 1.34 * x = 1.34x

   Maximum amount that can be spent for buying stickers = 80 - 54.50

                                                                                                 = $25.50

   Inequality:

          1.34x ≤ 25.50

 Solving:

         Divide both sides by 1.34,

            [tex]\sf x \leq \dfrac{25.50}{1.34}[/tex]

            x ≤ 19.03

            x ≤ 19

Billy can buy 19 or less than 19 stickers.

Here are 98,280 ways to lay off 12 employees from the company.

What is combination?

In mathematics, a combination is a way of selecting objects from a set, where the order in which the objects are selected does not matter. Combinations are used in various areas of mathematics and statistics, as well as in real-world applications such as probability theory, genetics, and computer science.

We can solve this problem using combinations. We need to choose 12 employees out of a total of 14+8+6=28 employees. The number of ways to do this is:

[tex]{28 \choose 12} \\= \frac{28!}{12!16!} = 98,!280[/tex]

Therefore, there are 98,280 ways to lay off 12 employees from the company.

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The expression a⁻¹³/a⁻⁶ can be written as a⁻⁷ in aⁿ form.

We have been given the expression

a⁻¹³/a⁻⁶

We know that whenever there is a minus sign in the power, we need to consider a reciprocal of the number

Hence,

a⁻¹³ will become 1/a¹ and a⁻⁶ will become 1/a⁶

Hence the numerator and denominator will interchange to get

a⁶/a¹³

Now, we know that when a number is broght from denominator to the numerator, there is a minus sign added to the power. Hence we will get

a⁶ X a⁻¹³

Since the two numbers have the same base- a, we can add the powers up as there is multiplication sign in between to get

a⁶ ⁺ ⁽⁻¹³⁾

= a⁶ ⁻ ¹³

= a⁻⁷

Hence, the expression a⁻¹³/a⁻⁶ can be written as a⁻⁷ in aⁿ form.

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OD. M = log(I/10,000)

How can the magnitude of an earthquake be calculated when its intensity is 10,000 times that of the reference earthquake?

The correct equation that calculates the magnitude, M, of an earthquake with an intensity 10,000 times that of the reference earthquake is option B: M = log(10,000/Io).

In the given equation M = log(I/IO), I represents the intensity of the earthquake being measured, and IO represents the intensity of the reference earthquake. Since the intensity of the earthquake in question is 10,000 times that of the reference earthquake, we substitute I with 10,000 times IO.

Therefore, the equation becomes M = log(10,000/Io), which is option B. This equation allows us to calculate the magnitude of the earthquake based on the relative intensity compared to the reference earthquake.

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