a tool box has the dimension of 8 in by 7 in by 4 in.

Answer:2

Step-by-step explanation:Because the 2 is closest to the middle line

Answer:

relationship describes angles 1 and 2 is supplementary angles. From the given figure

it is concluded that

the relation ship between angle 1 and 2 is supplementary angles

because its is  linear pair

and forms a line

therefore , the angles are supplementary angles

hence , relationship describes angles 1 and 2 is supplementary angle

Step-by-step explanation: Hope this helps !! Mark me brainliest!! :))

Answer:

Experimental Procedure:

Materials:

Piece of wood

Electronic balance

Bunsen burner

Heat-resistant mat

Stopwatch or timer

Safety goggles

Lab coat

Safety Precautions:

Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.

Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.

Use the Bunsen burner only under adult supervision.

Be cautious when handling hot objects, and allow them to cool before touching.

Procedure:

Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.

Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.

Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).

After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.

Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.

Calculate the difference between the initial and final mass of the wood, and record it in the table.

Repeat steps 1-6 three times to obtain three sets of data.

Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.

Conclusion:

If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.

The answer is x = 5±√61/2, I really hope this helps (:

Answer:

162, 147 etc.

Step-by-step explanation:

we have to find

[tex]N = k^2 \cdot p[/tex]

we can iterate k = 1 to 10 to check all possible solutions,

[tex]N = 9^2 \cdot 2[/tex]

[tex]N = 7^2 \cdot 3[/tex]

N = 162, 147 etc.

Hopefully this answer helped you!!

Answer: 2.5 dm

Step-by-step explanation:

Divide 25.0 by 10

= 2.5

Answer:

Step-by-step explanation:

To find the value of t, we can use the information given about the temperature at two different elevations and use the formula for a linear equation.

Let's assume that the temperature decreases by tº Fahrenheit for every additional 100 feet above sea level, where t is the constant we want to find.

Then, using the two points given:

- (8000, 65) where 65 is the temperature in Fahrenheit at 8000 feet above sea level

- (10,500, 15) where 15 is the temperature in Fahrenheit at 10,500 feet above sea level.

We can calculate the slope of the line connecting these two points:

slope = (15 - 65) / (10,500 - 8,000) = -25

The slope of the line represents the amount that the temperature decreases per unit increase in elevation. In this case, we've found that the temperature decreases by 25 Fahrenheit for each increase in elevation of 1000 feet.

To find the value of t, we need to express the slope in terms of the decrease in temperature per 100 feet of elevation. We can do this by dividing the slope by 10:

t = slope / 10 = -2.5

Therefore, the value of t is -2.5.

Answer: 3. 35x + 15 = 155

Step-by-step explanation:

35 x 4 = 140

140 + 15 = 155

The volume of the capsule is [tex]3052.08 mm^3[/tex]

What is volume of the hemisphere ?

The formula for the volume of a hemisphere is [tex]V = (2/3)\pi r^3[/tex], where r is the radius of the hemisphere.

The volume of a hemisphere is half of the volume of a full sphere with the same radius. This is because a sphere can be divided into two hemispheres of equal size. Therefore, we can use this formula to find the volume of a hemisphere:

[tex]V = (1/2) (4/3)\pi r^3[/tex]

Simplifying this expression, we get:

[tex]V = (2/3)\pi r^3[/tex]

So, the volume of a hemisphere is [tex](2/3)\pi r^3[/tex].

According to the question:
To find the volume of a capsule, we need to break it down into two parts: a cylinder and two hemispherical ends.

The formula for the volume of a cylinder is[tex]Vcylinder = \pi r^2h[/tex], where r is the radius of the cylinder and h is its height.

The formula for the volume of a sphere (or hemisphere) is[tex]Vsphere = (4/3)\pi r^3.[/tex]

Since the capsule is made up of two hemispheres and a cylinder, the total volume of the capsule is the sum of the volumes of these three parts:

[tex]Vcapsule = 2Vsphere + Vcylinder[/tex]

First, let's calculate the volume of the cylinder. We are given that the radius is 3mm and the height is 100mm, so we have:

[tex]Vcylinder = \pi r^2h = 3.14 x 3^2 x 100 = 2826 mm^3[/tex]

Next, let's calculate the volume of the hemispheres. Since the capsule has a radius of 3mm, each hemisphere has a radius of 3mm. So, we have:

[tex]Vsphere = (4/3)\pi r^3 = (4/3) ( 3.14) (3^3 )= 113.04 mm^3[/tex]

Finally, we can calculate the total volume of the capsule by adding the volume of the cylinder and the two hemispheres:

[tex]Vcapsule = 2Vsphere + Vcylinder = 2 *113.04 + 2826 = 3052.08 mm^3[/tex]

Therefore, the volume of the capsule is [tex]3052.08 mm^3[/tex].

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Answer:

To calculate the speed of the athlete in meters per second (m/s), we can use the formula:

Speed = Distance / Time

Here, the distance is 200 meters and the time is 25 seconds. Substituting these values into the formula, we get:

Speed = 200 meters / 25 seconds

Simplifying, we get:

Speed = 8 meters/second

Therefore, the athlete ran at a speed of 8 meters per second.

Answer:

To find the total surface area of the square pyramid, we need to find the area of each of its faces and add them up.

The pyramid has a square base with sides of 8 inches and each triangular face has an isosceles right triangle shape with two sides of 8 inches and a hypotenuse of 2 x 8 = 16 inches (using the Pythagorean theorem).

The total surface area is then:

Area of the square base: 8 x 8 = 64 square inches

Area of each triangular face: 1/2 x 8 x 8 = 32 square inches (since each triangle is isosceles with base and height of 8 inches)

Total surface area: 4 x 32 + 64 = 192 + 64 = 256 square inches

Therefore, the total surface area of the square pyramid is 256 in². So, the closest answer option is 256 in, 2.

Answer:

The answer is 40% :) Hope this helps!

Answer:

1.986 x 10 to the tenth power

Step-by-step explanation:

Answer:

$27

Step-by-step explanation:

$400 earns $6

$6÷$400= 0.015% interest

$1800 * 0.015% = $27

The correct answer is A) test statistic T equals -1.952; P value, 0.0414.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true. In the scientific process, the hypothesis is developed before any pertinent research—aside from a basic background review—has been conducted.

The null hypothesis that there is no difference between the triglyceride test levels is sufficiently refuted by the available data.

With 9 degrees of freedom and a significance threshold of 0.05, this can be ascertained by comparing the derived test statistic (T) with the critical value of t from the t-distribution table. We reject the null hypothesis if the estimated T value is in the rejection zone (i.e., T value is smaller than the critical value of t).

The computed T value in this instance is -1.952, which is in the rejection region (i.e., less than the critical value of t of -1.833). Hence, we get to the conclusion that there is enough data to imply that the new diet has an effect on lowering triglyceride levels and reject the null hypothesis that there is no difference between the triglyceride test levels.

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The ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:

1/3.

The perimeter of a triangle is the total length of its three sides. To find the perimeter of a triangle, you need to add up the lengths of all three sides.

The ratio between the side lengths of triangle ABC and triangle XYZ is given as follows:

5/15 = 1/3.

The perimeter of a triangle is measured in units, as area the side lengths, hence they have the same ratio, and thus the ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:

1/3.

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Answer: Reflection in the y -axis:

Explanation: The rule for a reflection over the y -axis is (x,y)→(−x,y) .\

Answer:

A.=False

B.=True

C.=False

D.=True

Step-by-step explanation:

The original ration is 2 gallons of water for 4 players.

Each player requires 1/2 gallon of water.

To get the amount of water needed multiply 1/2 by the amount of players.

1*(1/2) does not equal 1

2*(1/2) equals 1

10*(1/2) does not equal 4

30*(1/2) equals 15

The vector equations of L₂ when expressed as Cartesian equations are

y = 0

x = (z ± √(z² - 4(z-2))) / 2

z = [(4 - ((x-1)/(-z))²) ± √((4 - ((x-1)/(-z))²)² + 64)] / 8

To find the vector equation of the line L₂, we need to find a vector that is perpendicular to L₁ and passes through the point (1,0,2). Let's start by finding the vector equation of L₁.

Let P(x,y,z) be a point on L₁. Then the vector equation of L₁ is given by:

r₁ = P + t * d₁

where d₁ is the direction vector of L₁ and t is a scalar parameter.

Since L₂ is perpendicular to L₁, its direction vector must be perpendicular to d₁. Thus, we can find a vector that is perpendicular to d₁ by taking the cross product of d₁ with any non-zero vector that is not parallel to d₁. Let's choose the vector (0,1,0):

v = d₁ x (0,1,0) = (-z,0,x)

Note that we can choose any non-zero vector that is not parallel to d₁, and we will still get a vector that is perpendicular to d₁.

Now we have a point on L₂ (1,0,2) and a direction vector (v), so we can write the vector equation of L₂:

r₂ = (1,0,2) + s * v

where s is a scalar parameter.

To express the Cartesian equations of L₂, we can write the vector equation as a set of three parametric equations:

x = 1 - sz

y = 0

z = 2 + sx

We can eliminate the parameter s by solving for it in two of the equations and substituting into the third equation:

s = (x - 1) / (-z)

s = (z - 2) / x

Setting these two expressions equal to each other and solving for x, we get:

[tex]x^2 - zx + z - 2 = 0[/tex]

This is a quadratic equation in x, so we can solve for x using the quadratic formula:

[tex]x = (z \± \sqrt{(z^2 - 4(z-2)})) / 2[/tex]

Substituting this expression for x into one of the parametric equations, we get:

y = 0

And substituting the expressions for x and s into the other parametric equation, we get:

[tex]z = 2 + [(z \± \sqrt{(z^2 - 4(z-2)})) / 2] * [(1 - sz) / (-z)][/tex]

Simplifying this equation, we get:

[tex]4z^2 - (4 - s^2)z - 4 = 0[/tex]

Again, this is a quadratic equation in z, so we can solve for z using the quadratic formula:

[tex]z = [(4 - s^2) \± \sqrt((4 - s^2)^2 + 64)] / 8[/tex]

z = [(4 - s²) ± √((4 - s²)² + 64)] / 8

Finally, we can substitute these expressions for x and z into one of the parametric equations to get:

[tex]y = 0\\x = (z \± \sqrt{(z^2 - 4(z-2)})) / 2\\z = [(4 - ((x-1)/(-z))^2) \± \sqrt{((4 - ((x-1)/(-z))^2)^2} + 64)] / 8[/tex]

These are the Cartesian equations of L₂.

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The height of the pole to the nearest foot, given the angle of elevation and the surveyor distance, is C. 135 ft

To find the height of the pole, we can use the tangent function from trigonometry. The tangent of the angle of elevation (44°) is equal to the ratio of the height of the pole (h) minus the transit height (4 feet) to the distance between the transit and the pole (140 feet).

So, we have:

tan(44°) = (h - 4) / 140

h - 4 = 140 × tan(44°)

h = 140 × tan(44°) + 4

h = 140 × 0.965 + 4

h = 135.1

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Therefore , the solution of the given problem of unitary method comes out to be the pantry has 16 quarts of ice cream.

The goal can be achieved by making use of what has expression learned to date, utilizing this global access, and incorporating all crucial elements from previous changeable study that employed a specific technique. It is going to be equation possible to get in touch with the entity again if the expected claim result actually happens, or both crucial processes will surely miss the statement. A Rs ($1.21) redeemable fee may be needed for fifty pens.

Here,

Finding the overall quantity of cake in the kitchen is a good place to start. If there are 10 pastries, each measuring 1/4 inch, then there will be:

=> 10 desserts divided by 1/4 each equals the total cake.

=> Cake total equals 10/4 cakes.

=>  2.5 pastries altogether

=>  1 3/5 pints of ice cream for every 1/4 cake.

=>  8 and a half pints of ice cream per 1/4 cake

To determine the total amount of ice cream, we can multiply the ice cream per cake by the total number of cakes:

=>  Total ice cream equals the sum of the cakes' ice cream.

=>  Total ice cream =  (8/5 quarts per 1/4 cake) * (10/4 cakes)

=> Total ice cream = 16 quarts

Consequently, the pantry has 16 quarts of ice cream.

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To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:

9/4 - 24/28

= 63/28 - 24/28

= 39/28

Therefore, 2 1/4 - 6/7 = 39/28.

To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:

2 5/12 = (2*12 + 5)/12 = 29/12

Then we can subtract 2/3 from both sides:

2 5/12 - 2/3 = blank

To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:

29/12 - 8/12

= 21/12

= 7/4

Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.

To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:

7 1/12 = (712 + 1)/12 = 85/12

5 3/8 = (58 + 3)/8 = 43/8

Then we can subtract:

85/12 - 43/8

= 85/12 - (433)/(83)

= 85/12 - 129/24

= 5/24

Therefore, 7 1/12 - 5 3/8 = 5/24.

To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:

2 9/20 = (2*20 + 9)/20 = 49/20

Then we can subtract 7/10 from both sides:

blank + 7/10 - 7/10 = 49/20 - 7/10

Simplifying the right side:

49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4

Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:

blank = 7/4

Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.

The nearest ten thousand of the digits  14509 is 14, 000.

The rule for rounding to the nearest ten thousand is to look at the last four digits.

If the last four digits of the number is greater than 5000, we have to round the value up but if the number is below 5000 we have to round below.

For example let's round up 27567 to the nearest ten thousands.

Therefore, 7567 is above 5000, Hence, we have to round up. The nearest ten thousand of 27567 is 30000.

Let's round 14509 to the nearest ten thousand.

The nearest ten thousand of 14509 is 14, 000

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Answer:

[tex]\frac{2}{3} ^{7}[/tex]

Step-by-step explanation:

1) Count how many  [tex]\frac{2}{3}[/tex] there are.

[tex]\frac{2}{3} ^{7}[/tex]

Thus,  the area of cross section perpendicular to the base area will be in form of rectangle : Area =  130.32 cm².

The area of a sliced piece of a 3D object, such a pipe, is known as the cross sectional area. The cross sectional area of a pipe when cut perpendicular to it's own longest axis is determined for the circle-shaped top portion of the sliced component.

Given data:

Base area of cylinder = 12.96 π cm²

height of cylinder = 18.1 cm.

Let the radius of the  cylinder be 'r'.

Base area of cylinder = π*r².

π*r² =  12.96 π

r² =  12.96

r = 3.6 cm

now, the area of cross section perpendicular to the base area will be in form of rectangle with.;

Base = 2*r = 2*3.6 = 7.2 cm

height =  18.1 cm.

Area = base * height

Area = 7.2 * 18.1

Area =  130.32 cm²

Thus,  the area of cross section perpendicular to the base area will be in form of rectangle : Area =  130.32 cm².

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Answer:

The excluded value in the domain is x = 2 because the denominator of the rational function becomes zero at this value of x, which results in division by zero.

At x = 2, there is a vertical asymptote, which means that the graph of the function approaches positive or negative infinity as x approaches 2 from either side.

Therefore, the measure of the intercepted arc by the inscribed angle of 61 degrees is 122 degrees.

A circle is a closed shape in geometry that is defined as the set of all points in a plane that are at a fixed distance from a given point, called the center of the circle. The distance between any point on the circle and the center is called the radius of the circle.

Given by the question.

In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of its intercepted arc.

Let's call the intercepted arc by the inscribed angle "x". Then, the measure of the inscribed angle is 61 degrees, and we can use the formula mentioned above to find the measure of the intercepted arc:

61 = x/2

To solve for x, we can multiply both sides of the equation by 2:

122 = x

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Answer: To solve the third-order differential equation y''' + y' = cot(x) by variation of parameters, we first need to find the solution to the associated homogeneous equation, which is:

y''' + y' = 0

The characteristic equation is r^3 + r = 0, which can be factored as r(r^2 + 1) = 0. This gives us the roots r = 0, r = i, and r = -i. Therefore, the general solution to the homogeneous equation is:

y_h = c1 + c2 cos(x) + c3 sin(x)

To find a particular solution to the non-homogeneous equation using variation of parameters, we assume that the solution has the form:

y_p = u1(x) + u2(x) cos(x) + u3(x) sin(x)

where u1, u2, and u3 are functions to be determined.

We can find the derivatives of y_p:

y'_p = u1'(x) + u2'(x) cos(x) - u2(x) sin(x) + u3'(x) sin(x) + u3(x) cos(x)

y''_p = u1''(x) + u2''(x) cos(x) - 2u2'(x) sin(x) - u2(x) cos(x) + u3''(x) sin(x) + 2u3'(x) cos(x) - u3(x) sin(x)

y'''_p = u1'''(x) + u2'''(x) cos(x) - 3u2''(x) sin(x) - 3u2'(x) cos(x) - u2(x) sin(x) + u3'''(x) sin(x) + 3u3''(x) cos(x) - 3u3'(x) sin(x)

Substituting these derivatives into the non-homogeneous equation, we get:

u1'''(x) + u2'''(x) cos(x) - 3u2''(x) sin(x) - 3u2'(x) cos(x) - u2(x) sin(x) + u3'''(x) sin(x) + 3u3''(x) cos(x) - 3u3'(x) sin(x) + u1'(x) + u2'(x) cos(x) - u2(x) sin(x) + u3'(x) sin(x) + u3(x) cos(x) = cot(x)

Grouping the terms with the same functions together, we get:

u1'''(x) + u1'(x) = 0

u2'''(x) cos(x) - 3u2''(x) sin(x) - u2(x) sin(x) + u2'(x) cos(x) + u2'(x) cos(x) = cot(x) cos(x)

u3'''(x) sin(x) + 3u3''(x) cos(x) - 3u3'(x) sin(x) + u3'(x) sin(x) + u3(x) cos(x) = cot(x) sin(x)

The first equation is a first-order differential equation, which can be solved by integrating both sides:

u1'(x) + u1(x) = c1

where c1 is a constant of integration. The solution to this equation is:

u1(x) = c1 + c2 e^(-x)

where c2 is another constant of integration.

Step-by-step explanation:

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

in our case

length = width + 3

and

2×length + 2×width = 30

using the first equation in the second :

2×(width + 3) + 2×width = 30

width + 3 + width = 15

2×width + 3 = 15

2×width = 12

width = 12/2 = 6 ft

length = width + 3 = 6 + 3 = 9 ft

Answer: 49,000

48805 is greater than 48500, so it rounds to 49,000