Jason knows that the equation to calculate the period of a simple pendulum is , where T is the period, L is the length of the rod, and g is the acceleration due to gravity. He also knows that the frequency (f) of the pendulum is the reciprocal of its period. How can he express L in terms of g and f?

Answer:

the 3rd dot is correct........

Answer:

20 percent

Step-by-step explanation:

200 divided by 40 that’s five so we need a number that would times that to get 100 so five times 20 equals 100 percent the answer is 20 percent

20% of 8th graders at the school are taking art.

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, At a school, there are 200 students in the 8th grade. 40 students are taking art. We have to find what percentage of 8th graders at the school are taking art,

The required percentage = 40 / 200 × 100

= 40 / 2

= 20

Hence, 20% of 8th graders at the school are taking art.

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Answer:

To simplify the expression 5^-1/-9^0, we need to follow the order of operations, which is to evaluate exponents first, then perform any multiplication or division from left to right, and finally perform any addition or subtraction from left to right.

Since any number raised to the power of 0 is equal to 1, we have 9^0 = 1. Therefore, the expression simplifies to:

5^-1/1

Now, any number raised to the power of -1 is its reciprocal or multiplicative inverse. So, we have:

1/5 / 1

Dividing by 1 does not change the value of the expression, so we can simply write:

1/5

Therefore, 5^-1/-9^0 simplified to 1/5 in its simplest form.

It will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.

The decay rate of 137Cs is given by the formula:

A = A0 * e^(-λt)

Where A is the decay rate, A0 is the initial decay rate (10^10 decays per second), λ is the decay constant (ln(2)/30.1 years) and t is the time in years.

To calculate the time, t, required for the decay rate to decrease to 10^7 decays per second, we solve for t and substitute the given values into the equation:

\(t = (ln(A0/A))/λ\\t = (ln(10^10/10^7))/(ln(2)/30.1)\\t = 19.44 years\)

Therefore, it will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.

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Answer:

$24

Step-by-step explanation:

if you multiply 32 by .25 you get 8 which i subtracted from 32 to get the original price

Answer:$18

Step-by-step explanation:

32 * (0.75) * (0.75) = 18

Compute the cumulative incidence of stroke in persons over 75 years of age Cumulative Incidence 5 Years= 16/79 = 0.203. Cumulative incidence of stroke= 0.203.

The cumulative occurrence, occasionally termed assault fee while used throughout a sickness outbreak, is a degree of the prevalence of latest instances of contamination or disorder in a population in a given time period—for example, a month or a year—and is specially beneficial for describing acute diseases of short duration.

Cumulative occurrence is calculated as the range of latest occasions or cases of disorder divided by the total wide variety of people inside the populace at threat for a specific time c programming language.

Cumulative prevalence is the percentage of folks that broaden the final results of interest at some point of a special block of time. occurrence rate is a real price whose denominator is the overall of the organization's person times "at danger"

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The integral is equal to 1/2 [ln|1 + v| - ln|1 - v|] + C.

The integral in this exercise converges, which means that it has a finite value.

To evaluate the integral without using a table, start by breaking the fraction into partial fractions.

Use the identity 2 cot-1v = ln(v²+1) - ln(v²-1) and partial fractions to rewrite the integral as follows:

∫ dv/[(1 + v)(1 - v)]

= ∫ [1/2(1 + v) - 1/2(1 - v)] dv

= 1/2 ∫ [1/(1 + v) - 1/(1 - v)] dv

= 1/2 [ln|1 + v| - ln|1 - v|] + C, where C is the constant of integration.

Therefore, the integral is equal to 1/2 [ln|1 + v| - ln|1 - v|] + C.

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Answer:

1.6

Step-by-step explanation

2 is les than 5 so you round down

Answer:

\(-0.375\)

For more help, take a look at this chart.

In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

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Answer:

n = -96

Step-by-step explanation:

-n + 7 = 103

-n = 103 - 7

-n = 96

n = -96

Answer:

2.25

Explanation:

The expected value can be calculated as:

Where x1, x2, x3, x4, and x5 are the different values that the variable x can take and P(x1), P(x2), P(x3), P(x4), P(x5) are their respective probabilities.

Therefore, the expected value will be equal to:

So, the answer is 2.25

In a regular tetrahedron with point P equidistant from its vertices, the ratio of the distance from P to point E to the edge length is (sqrt(3) - 1) / (2sqrt(3) - 1).

Given a regular tetrahedron with vertices A, B, C, and D and a point P equidistant from A, B, C, and D, the ratio of the distance from P to point E to the length of an edge is (sqrt(3) - 1) / (2sqrt(3) - 1).

Let A, B, C, and D be the vertices of the regular tetrahedron, and let P be the unique point equidistant from A, B, C, and D. Let E be the point where line PD intersects face ABC.

Since ABCD is a regular tetrahedron, all its edges have the same length, say s. Let h be the height of the tetrahedron, which can be found using the Pythagorean theorem as:

h = sqrt(2/3) * s

Since P is equidistant from A, B, and C, it lies on the perpendicular bisectors of the edges opposite to these vertices. Therefore, the distance from P to each of the vertices A, B, and C is h/3.

Since triangle ABE is equilateral, we have:

AB = BE = s

Therefore, triangle ABE is an isosceles triangle, and the altitude from E to AB (which is also the perpendicular bisector of BE) bisects AB at point F. Therefore, FA = FB = s/2.

Since line PD passes through P and is perpendicular to face ABC, we have:

PE = h/3

Therefore, triangle PED is a right triangle with hypotenuse PD and one leg PE. Using the Pythagorean theorem, we can find the length of the other leg DE as:

DE = sqrt(PD^2 - PE^2)

Since triangle ABE and triangle CDE are similar, we have:

AB/CD = AE/CE

Substituting AB = s and CD = DE, and using the fact that AE = FA + FE = s/2 + PE and CE = CD - DE = s - DE, we get:

s/DE = (s/2 + h/3) / (s - DE)

Simplifying and solving for DE/s, we get:

DE/s = (sqrt(3) - 1) / (2sqrt(3) - 1)

Therefore, the ratio DE to the edge length s is (sqrt(3) - 1) / (2sqrt(3) - 1).

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The volume of the parallelepiped defined by the given vectors is 20 cubic units.

To find the volume of a parallelepiped defined by three vectors, we can use the determinant of a 3x3 matrix. Let's denote the given vectors as v1, v2, and v3.

The volume can be calculated as follows:

Volume = |v1 · (v2 × v3)|,

where · denotes the dot product and × represents the cross product.

Taking the dot product of v2 and v3 gives the vector v2 × v3. Then, we take the dot product of v1 and the resulting cross product.

By performing the calculations, we find that the dot product of v1 and (v2 × v3) is -20. Taking the absolute value of -20 gives us the volume of the parallelepiped, which is 20 cubic units.

In summary, the volume of the parallelepiped defined by the given vectors [2, -4, -1], [2, -3, -5], and [-2, 4, 0] is 20 cubic units. This value is obtained by calculating the absolute value of the dot product between the first vector and the cross product of the other two vectors.

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Number of quarters is 6 and number of nickels are 42.

One eighth of Al's coins are quarters, so if we let x be the total number of coins, then x/8 is the number of quarters Al has.

We know that:

Quarters are worth $0.25 and nickels are worth $0.05 and total value of the coins is $3.60

so, x/8 * $0.25 + (x-x/8) * $0.05 = $3.60

=> x/8 * 0.25 + 7x/8 * 0.05 = 3.60

multiplying both sides by 8 to cancel out 8, we get

=> x*0.25 + 7x * 0.05 = 28.8

=> x/4 + 7x/20 = 28.8

=> (5x + 7x)/20 = 28.8

=> 12x = 576

=> x= 48

x/8 = 6 and (x-x/8) = 42

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The number of marbles in the bag for each color=56 orange, 24 purple, 40 blue.

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

Hence, The number of marbles in the bag for each color=56 orange, 24 purple, 40 blue.

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Answer:

15. x = 4

16. x = 7

Step-by-step explanation:

15.

CD/ ED = DG / DF

48 / (5x - 2) = 40 / (2x + 7)

48 (2x + 7) = 40 (5x - 2)

96x + 336 = 200x - 80

200x - 96x = 336 + 80

104x = 416

x = 4

16.

ST / PL = TU / LM

(x + 1) / 72 = (2x - 3) / 99

99 (x + 1) = 72 (2x - 3)

99x + 99 = 144x - 216

144x - 99x = 99 + 216

45x = 315

x = 7

Answer:

15.  x = 4

16.  x = 7

Step-by-step explanation:

Similar Triangles

In similar triangles, corresponding sides are always in the same ratio.

If ΔCDG ~ ΔEDF then:

From inspection of the given diagram:

Therefore:

\(\implies \sf CD : ED = DG : DF\)

\(\implies 48 : (5x-2) = 40 : (2x+7)\)

\(\implies \dfrac{48}{(5x-2)} = \dfrac{40}{(2x+7)}\)

\(\implies 48(2x+7)=40(5x-2)\)

\(\implies 96x+336=200x-80\)

\(\implies 416=104x\)

\(\implies x=\dfrac{416}{104}\)

\(\implies x=4\)

If ΔSTU ~ ΔPLM then:

From inspection of the given diagram:

Therefore:

\(\implies \sf ST : PL = TU : LM\)

\(\implies (x+1) : 72 = (2x-3) : 99\)

\(\implies \dfrac{(x+1)}{72}= \dfrac{(2x-3)}{99}\)

\(\implies 99(x+1)=72(2x-3)\)

\(\implies 99x+99=144x-216\)

\(\implies 315=45x\)

\(\implies x=\dfrac{315}{45}\)

\(\implies x=7\)

Answer:A

Step-by-step explanation: 1 Gallon is equal to 8 pints.

Answer:

A

Step-by-step explanation:

pint=1/8 of a gallon

therfor 7 pints = 7/8

7/8<1gal

Express the number of each result as a fraction of the total number of games played and multiply with 100.

Answer:

4x^2 – 25

Step-by-step explanation:

i'vegot your back :))

Answer:

2

Step-by-step explanation:

Answer:

by comparing the two triangles,

we take the ratio of each side to be equal

Step-by-step explanation:

By comparing the sides of the triangles,

we take the ratio of each sides to each other

de/cb = fe/ca

de.ca = fe.cb

fe = (de.ca)/cb

fe = (7* 18)/14

fe = 9

The measure of side FE of triangle DEF is FE = 9

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ABC

Now , let the second triangle be DEF

And triangle ABC and DEF are similar triangles

So , corresponding sides of similar triangles are in the same ratio

And , AE = EB and CF = FB

From the similar triangle theorem ,

EF / AC = DE / CB

Substituting the values in the equation , we get

EF / 18 = 7 / 14

Multiplying by 18 on both sides of the equation , we get

EF = ( 7 x 18 ) / 14

EF = 18/2

EF = 9

Therefore , the value of EF is 9

Hence , the measure of side EF is 9

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Answer:

1/3000

Step-by-step explanation:

3 meters to centimeters:

3 × 100 = 300

= 1/10 ÷ 300

= 1/10/300

= 1/(10×300)

= 1/3000

A coterminal angle is an angle that has the same initial side and terminal side as a given angle. The difference between the angle and the coterminal angle is a multiple of 360 degrees.

The following steps can be used to find a coterminal angle between 0 and 360 degrees:

Step 1: Identify the given angle. Let's assume that the given angle is 100 degrees.

Step 2: Add or subtract multiples of 360 degrees to the given angle to obtain a new angle that has the same initial and terminal sides. To obtain the angle that is between 0 and 360 degrees, add or subtract 360 degrees from the angle until the result is between 0 and 360 degrees.There are two ways to do this.

The first method is to add or subtract multiples of 360 until the result is between 0 and 360 degrees. The second method is to divide the given angle by 360 degrees and then multiply the quotient by 360 degrees.

The first method:Subtract 360 degrees from 100 degrees to get -260 degrees. Add 360 degrees to -260 degrees to get 100 degrees, which is between 0 and 360 degrees. Therefore, 100 degrees and 460 degrees are coterminal angles between 0 and 360 degrees.

The second method:Divide 100 degrees by 360 degrees to get a quotient of 0.27777777778. Multiply 0.27777777778 by 360 degrees to obtain 100 degrees, which is between 0 and 360 degrees.

Therefore, 100 degrees and 460 degrees are coterminal angles between 0 and 360 degrees.

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Identify population or sample parameter.

The question is to determine whether the given values are population parameters or sample statistics. In option (a), the value "20% of all vehicles sold" refers to the entire population of vehicles sold and hence is a population parameter. In option (b), the value "70% of 300 students" refers to a sample of students who passed statistics and hence is a sample statistic. In option (c), the value "92% of diamond princess cruise ship passengers" refers to the entire population of passengers and hence is a population parameter. In option (d), the value "25% of a recent sample of 250 people" refers to a sample of people and hence is a sample statistic.

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a) Population parameter

b) Sample statistic

c) Population parameter

d) Sample statistic

A population parameter is a value that describes a characteristic of an entire population, while a sample statistic is a value that describes a characteristic of a sample drawn from the population. In the given examples, "20% of all vehicles sold" refers to the entire population of vehicles sold, making it a population parameter.

"In a sample of 300 students" refers to a subset of the population, making it a sample statistic. "Approximately 92% of Diamond Princess cruise ship passengers" refers to the entire population of passengers, making it a population parameter.

"In a recent sample of 250 people" refers to a subset of the population, making it a sample statistic.

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Theoretically, the number of the vertex comes at the top must be equal for infinitely many numbers of trials, but it's a tedious job to roll the dice for a large number of times. Rolling the tetrahedron only 10 times will not predict the correct result.

Han suspects that this tetrahedron is weighted in some way to make 1 appear more often than the other numbers.

So, check his suspect experimentally with the help of the concept of center of mass. A fair tetrahedron must have the center of mass at the center of the body.

The given tetrahedron has 4 equilateral triangular faces, so at first, measure all the sides of triangular faces and make sure that all are having the same length.

Then, conduct an experiment to check the location of the center of mass.

Hang the tetrahedron by attaching a thin string at the vertex 1 as shown in the figure and observe the base surface ( triangle 234) whether it is parallel to the ground or not.

Now, repeat the same by hanging it with vertices 2, 3, and 4 and observe the base surface.

For the center of mass to be located at the center of the tetrahedron, the base must be parallel to the ground (flat ground).i.e the hanging string must be perpendicular to the base for all the four cases.

If this is so, then the tetrahedron is a fair tetrahedron otherwise not.

Answer:

w = 35/4

im not exactly sure why the options are whole numbers.

Step-by-step explanation:

8 = w-3/4

-w + 8 = -3/4

-w = -3/4 - 8

-w = -3/4 - 32/4

-w = -35/4

w = 35/4

By answering the above question, we may infer that The rocket will thus equation touch down 2.5 seconds after it was fired (to the nearest tenth of a second).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Hence, we may solve for t by setting the equation for h equal to 0:

\(-16t^2 + 120t + 200 = 0\\2t^2 - 15t - 25 = 0\\(-b \sqrt(b2 - 4ac)) / 2a\)

where a=2, b=15, and c=25

\(t = (15 \sqrt(625)) / 2(2) (-(-15) \sqrt((-15)2 - 4(2)(-25))) / 4\st = (15 + 25) / 4\)

T thus equals 10/2 or -5/2. Time cannot be negative, thus we may ignore the negative number.

The rocket will thus touch down 2.5 seconds after it was fired (to the nearest tenth of a second).

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Answer:48.6805998746%, you can round this.

Step-by-step explanation:

In order to solve this, you need to divide the smaller number by the larger number, creating a fraction. This will give you a decimal number. In order to get the percent, you need to take the decimal, and move the decimal point 2 digits TO THE RIGHT. This will give you 48.6805998746%.

To check this, you can use the answer, and use a calculator such as desmos to calculate 48.6805998746% of 659470.53

This provides you with 321034.21, which means that this is the correct percent. You can round this to get something like 48.7%

Ans-The sum of the series is 35.

Solution;

To find the number of terms, we subtract the starting value from the ending value and add 1.
Number of terms = (10 - 2) + 1
= 9 + 1
= 10

So, there are 10 terms in the series.

we substitute n = 2 into the given formula:
First term = (1/2 * 2) + 3
= 1 + 3
= 4
The first term is 4.

To find the last term, we substitute n = 10 into the given formula:
Last term = (1/2 * 10) + 3
= 5 + 3
= 8
The last term is 8.

Now, let's evaluate the sum of the series.
Σ¹°n=2 (1/2 n+3) can be written as Σ¹°n=2 (1/2n + 3) = (1/2 * 2) + 3 + (1/2 * 3) + 3 + ... + (1/2 * 10) + 3.

We can simplify this expression by separating the constant term and the variable term:
Σ¹°n=2 (1/2n + 3) = (1/2 + 1/2 + ... + 1/2) + (3 + 3 + ... + 3)

Σ¹°n=2 (1/2n + 3) = (10 * 1/2) + (10 * 3)
= 5 + 30
= 35

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