Use the distributive property to solve 4 2/5 x 10. Where 4 2/5 is a fraction. Please show work so I can explain. Thank you.

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.

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

The volume of the cone is  2119. 5 cubic centimeters

The formula used for calculating the volume of a cone is expressed as;

V = πr² h/3

Given that the parameters are namely;

Now, substitute the values, we have;

Volume , V = 3.14 × 15² × 9/3

Divide the values, we have;

Volume = 3.14 × 225 × 3

Multiply the values, we get;

Volume, V = 2119. 5 cubic centimeters

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All three data points are compatible with this set of equations, leading us to the conclusion that C = -195h + 550 is the function that best describes the scenario.

A function connects an input with an output. It works like a machine that has an input and an output. The traditional manner of writing a function is "f(x) = 5".

The following function represents this circumstance:

C = -195h + 550

The first two data points can be used to create two equations:

355 = -195(1) + C

1120 = -195(3) + C

When we solve for C in each equation, we obtain:

C = 550

C = 550 + 585 = 1135

We can try utilising the first and third data points as the second equation doesn't quite match the third data point:

355 = -195(1) + C

1885 = -195(4) + C

Solving for C in each equation, we get:

C = 550

C = 550 + 975

= 1525

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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:

Answer:4? Think

Step-by-step explanation:

The 3rd graph is the correct one representing the open sentence.

Inequalities is defined as the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values or data. The equal sign in between can be replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

-5≤n-2≤2

First you need to get n by itself, so add 2 to all 3 terms:

-5 +2 ≤ n-2+2 ≤ 2+2

Simplify:

-3 ≤ n ≤ 4

The less than or equal to signs (≤) mean the dots on the line graph are solid.

And n is between -3 and positive 4, the 3rd graph is the correct one.

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Answer:

1st one.-sin(X)+5e^5x

Answer:

18

Step-by-step explanation:

siz times three is eighteen

Answer: Reflection in the y -axis:

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

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: 49,000

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

Answer:

I will not show you the process it is easy the answer is 4.5 or 6 ≈

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!! :))

The probability that a randomly selected student's age is more than 18 years old but no more than 21 years old is 0.57.

What is a continuous random variable's probability?

Continuous random variables are defined as having an infinite number of possible values. A continuous random variable hence has no probability of having an accurate value.

a) In order to create a probability distribution, all potential values of the random variable must be listed along with the related probabilities. We may get the relative frequency (or probability) for each value of the random variable from the above frequency distribution:

Age Frequency Probability

16         3              0.03

17         5              0.05

18        10              0.10

19        15              0.15

20       20             0.20

21        22             0.22

22       17               0.17

Total   92              1.00

b) We can use a histogram to see the probability distribution. The likelihood is represented by the vertical axis, while the age is represented by the horizontal axis. The height of each bar in the histogram should represent the likelihood for that age, with bars for each age value.

With a peak at age 20, the distribution's shape looks to be roughly symmetrical.

c) To get the likelihood that a student chosen at random is under 20 years old, we must add the probabilities for the ages 16, 17, 18, and 19:

P(age < 20) = P(age = 16) + P(age = 17) + P(age = 18) + P(age = 19)

= 0.03+0.05+0.10+0.15

= 0.33

Consequently, there is a 0.33 percent chance that a randomly chosen student is under 20 years old.

d) To determine the likelihood that a randomly chosen student is older than 18 but not older than 21, we must add the probabilities for the ages 19, 20, and 21:

P(18 < age ≤ 21) = P(age = 19) + P(age = 20) + P(age = 21)

= 0.15 + 0.20 + 0.22

= 0.57

As a result, there is a 0.57 percent chance that a randomly chosen student will be older than 18 but not older than 21.

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

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.

Answer: click thanks if you like my answer. have a good day <:

The best way to assign values for a simulation using a random digits table is to first identify the possible outcomes and assign a number or range of numbers to each outcome. Then, using the random digits table, randomly select digits and match them to the assigned outcomes.

For example, in the given scenarios for blood types in different countries, each blood type is assigned a specific number or range of numbers. Using the random digits table, the assigned numbers can be matched to the digits in the table to simulate the occurrence of each blood type in the population.

To answer the questions:

1.What is the purpose of assigning values for a simulation using a random digits table?

The purpose of assigning values for a simulation using a random digits table is to create a simulated scenario that reflects the likelihood of different outcomes based on assigned probabilities. This can help in making predictions and decisions in various fields such as medicine, finance, and social sciences.

2.In which scenario are blood types represented with the fewest number of digits?

Blood types are represented with the fewest number of digits in the third scenario for both Country X and Country Y. Blood type O is represented with 0, blood type A with 1, blood type B with 3, and blood type AB with 4, while all other digits are ignored.

3.In which scenario are blood types represented with the most number of digits?

Blood types are represented with the most number of digits in the first scenario for Country X, where blood type O is represented with 0, 1, 2, 3, 4, and 5, blood type A with 6 and 7, blood type B with 8, and blood type AB with 9. The same applies to Country Y in the first scenario.

Step-by-step explanation:

hope its help <:

Answer:

1.986 x 10 to the tenth power

Step-by-step explanation:

Answer: 2.5 dm

Step-by-step explanation:

Divide 25.0 by 10

= 2.5

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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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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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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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 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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Answer: 3. 35x + 15 = 155

Step-by-step explanation:

35 x 4 = 140

140 + 15 = 155

To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.

Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure

Area of rectangle = length x width

= 20 ft x 8 ft

= 160 sq. ft

Area of triangle = 1/2 xbase xheight

= 1/2 x 8 ft x 10 ft

= 40 sq. ft

To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).

Using the Pythagorean theorem, we have:

12² = 10² + b²

144 = 100 + b²

44 = b²

b = √44

b ≈ 6.63 ft

Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:

Area of total figure = area of rectangle + area of triangle

= 160 sq. ft + 40 sq. ft

= 200 sq. ft

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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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According to the question the percent abundance of the medium nails in the sample is approximately 18.95%.

Whenever the set of data is presented from least to largest, the median is indeed the number in the middle. For instance, since 8 is in the middle, this would represent the median value here.

To find the percent abundance of the medium nails in the sample, we first need to calculate the total number of nails in the sample:

Total number of nails = 67 + 18 + 10 = 95

Next, we can calculate the percent abundance of the medium nails using the formula:

Percent abundance = (number of medium nails / total number of nails) x 100%

Using the values from of the table as inputs, we obtain:

Percent abundance of medium nails = (18 / 95) x 100% ≈ 18.95%

As a result, the sample's average percentage of medium nails is roughly 18.95%.

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