Simply The Problem And Express The Answer In Scientific Notation (2024)

Step-by-step explanation:

The value of 6 in the equation represents the rate of acceleration of the eagle, which denotes how quickly the eagle is moving. This rate of acceleration is calculated by subtracting the final height (3 m) from the initial height (74 m) and dividing by the total time (t). So, in this case, the eagle is accelerating at a rate of 6 m/s^2.

P(s) = 0.6 which means the probability that a randomly selected person from the two states combined supports the liberal candidate is 0.6 or 60%.

To find the probability that a randomly selected person from the two states combined supports the liberal candidate, we can use the law of total probability.

P(s) = P(s|a)P(a) + P(s|b)P(b)

P(s|a) is the probability that a person supports the liberal candidate given that they live in state a, which is 0.5. P(a) is the probability that a person is from state a, which is 0.4.

P(s|b) is the probability that a person supports the liberal candidate given that they live in state b, which is 0.6. P(b) is the probability that a person is from state b, which is 0.6.

So, P(s) = (0.5)(0.4) + (0.6)(0.6) = 0.24 + 0.36 = 0.6

Therefore, the probability that a randomly selected person from the two states combined supports the liberal candidate is 0.6 or 60%.

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Answer:

About 3 1/2 videos/mo

Step-by-step explanation:

11 2/3 months ÷ 328 videos = 0.03556910569

Equation, a formula that expresses the equality of two expressions by joining them with an equals sign. The missing operators are +, - and +.

An equation is a mathematical statement that two expressions are equal: it is an identity in which the variables can take any value, or a constraint equation in which the variables have only certain values.

In mathematics, an operator is generally an application or function that acts on elements of one space to produce elements of another space.

The following equation is given:

-1080?379?-3?15=-683 ,

so we need to add the "+" and "-" operators to the equation to get the solution.

So,

-1080+379?-3?15 = -683

-1080 + 379 -(-3) + 15 = -683

(as we know - and - becomes +)

The missing operators are +, - and +.

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sin(θ) = (√11)/5 when cot(θ)=5/6.

What is trigonometric?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It involves the study of the properties of trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant, and their applications in solving problems related to trianglesandcircles.

Given by the question.

We can start by using the fact that cotangent is the reciprocal of tangent, and using the Pythagorean identity for the tangent:

cot(θ) = 5/6

tan(θ) = 1/cot(θ) = 6/5

Then, we can use the Pythagorean identity for the sine:

[tex]sin^{2}[/tex](θ) + [tex]cos^{2}[/tex](θ) = 1

We know that tan(θ) = sin(θ)/cos(θ), so we can substitute 6/5 for tan(theta) and simplify:

[tex]sin^{2}[/tex](θ) + (1 - [tex]sin^{2}[/tex](θ)) = 1/[tex]cos^{2}[/tex](θ)

[tex]sin^{2}[/tex](θ) + [tex]cos^{2}[/tex](θ) - [tex]sin^{2}[/tex](θ)[tex]cos^{2}[/tex](θ) = 1

Now we can use the fact that cot(θ) = cos(θ)/sin(θ) and substitute 5/6 for cot(theta):

cos(θ)/sin(θ) = 5/6

cos(θ) = (5/6) sin(θ)

Substituting this into the equation above, we get:

(25/36) [tex]sin^{2}[/tex](θ) + (1 - 25/36) = 1

(25/36) [tex]sin^{2}[/tex](θ) = 11/36

sin^2(θ) = 11/25

Taking the square root of both sides and choosing the positive root, we get:

sin(θ) = √ (11/25) = (√11)/5

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The probability of the events are

Event 1 : 1/2

Event 2 : 3/5

Event 3 : 1

Event 4 : 2/5

To determine the order of the events from least likely to most likely, we can use the probabilities of each event.

Event 1: Choosing a blue marble from Bag A.

The probability of choosing a blue marble from Bag A is 5/10 or 1/2.

Event 2: Choosing a blue marble from Bag B.

The probability of choosing a blue marble from Bag B is 9/15 or 3/5.

Event 3: Choosing a blue or black marble from Bag A.

The probability of choosing a blue or black marble from Bag A is 1, as there are no other colors in the bag.

Event 4: Choosing a black marble from Bag B.

The probability of choosing a black marble from Bag B is 6/15 or 2/5.

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The car that travels 2 miles has tires with 6.84 inches of radius

What is angular velocity?

When an object is in uniform circular motion, the angle described by the radius in each unit of time is known as angular velocity. It is measured in units of (rad/s) (revolutions/s).

It is known that in 1 mile there are 63360 inches. So, in 2 miles we have:

2 miles * (63360 inches/1 mile) = 126720 inches

It is also known that in 1 revolution, the distance covered by the car is 2*π*r

Therefore, the distance covered by the car in 2950 revolutions will be equal to:

d = 2950*2*π*r

d = 5900*π*r

Now, equate 126720 inches to 5900*π*r and clearing the value of r we have:

126720 inches = 5900*π*r

r = 126720 inches / 5900*π

r = 6.84 inches

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Answer:

If the core of the sun is ~15 million kelvin why do we say the blackbody temperature of the sun is ~5800 kelvin?

Step-by-step explanation:

Answer: You do rise over run.

Step-by-step explanation:

So rise over run is how far up/down and how far right/left so it is -3 down

and 3 right so it equals -3/3 and that simplifies to -1.

Answer:

Each friend would get 1/7th of a pie.

Step-by-step explanation:

Jilly started with 4 pies, and her brother ate half of one pie, which means he ate 1/2 of a pie. So, Jilly has 3 and a half pies left, which is equal to 7/2 pies. If she wants to divide the pies equally among her 21 friends, she can divide 7/2 by 21 to find the fraction of the pie that each friend will get:

(7/2) ÷ 21 = 7/2 ÷ 21/1 = 7/2 x 1/21 = 7/42

Therefore, each friend would get 7/42 of a pie, which can be simplified to 1/6 or 1/7 (rounded to the nearest whole number). So, each friend would get 1/7th of a pie.

The function that is changing faster is g(x) = 4 ( 3 ) x - 5.

The function that has a higher y - intercept is f(x) = 3 ( 1 / 3 ) x + 2.

The function that has a lower asymptote is f(x) = 3 ( 1 / 3 ) x + 2.

How to find the function ?

The function that would be changing faster is the one that has the larger slope. The slope is the number which is multiplying the independent variable on the right side of the equation so the function which is changing faster is g(x) = 4 ( 3 ) x - 5.

The function that has a higher y - intercept is f(x) = 3 ( 1 / 3 ) x + 2 because the y - intercept here is 2 which is higher than the y - intercept of - 5 .

The function with a lower asymptote is f(x) is 3 ( 1 / 3 ) x + 2 due to the smaller slope.

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There are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

To determine the number of ways to award first, second, and third prizes in a contest with 950 contestants, we can use the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of contestants and r is the number of prizes to be awarded (in this case, 3).

Using this formula, we get:

P(950, 3) = 950! / (950 - 3)!

= 950! / 947!

= 950 × 949 × 948

= 853,818,600

Therefore, there are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

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As a result of answering the question, we may state that The fraction that represents the portion of the class that chose the least common instrument (the flute) is therefore 1/6.

what is fraction?

To represent a whole, any sequence of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of the exponent to the denominator. They can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators.

Flute is the least chosen instrument, with only three pupils choosing it.

We must divide the number of students who chose the flute by the total number of students in the class to determine the percentage of the class that chose the least popular instrument

There are a total of 18 pupils in the class (5 + 4 + 3 + 6).

3/18 or 1/6 of pupils choose to play the flute.

The proportion that represents the portion of the class that chose the least common instrument (the flute) is therefore 1/6.

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By following these instructions, you can measure 6 gallons of water accurately.

The steps below can be used to measure 6 gallons of water precisely using the 4-gallon and 9-gallon pails:

Step 1: The 9-gallon pail should be filled up to the top (9 gallons).

Step 2: Fill the 4-gallon container with the water from the 9-gallon pail.

The 9-gallon bucket will now contain 5 gallons of water (5 - 4 = 5 gallons).

Step 3: There are now 4 gallons in the 4-gallon pail and 5 gallons in the 9-gallon pail.

Step 4: Empty the 4-gallon pail completely.

Step 5: Fill the empty 4-gallon pail with the remaining 5 gallons of water from the 9-gallon pail.

Step 6: You will be left with a full 4-gallon pail and a 9-gallon pail that holds one gallon of water.

Step 7: Empty the 4-gallon pail and fill it with the 1 gallon of water from 9-gallon pail [step 6].

Step 8: Fill the 9-gallon pail again to its maximum capacity.

Step 9: Fill the 4-gallon pail with water by carefully pouring water from the 9-gallon pail into it.

The 9-gallon bucket will contain exactly 6 gallons of water (6 - 3 = 6 gallons).

The 4-gallon pail will now only contain 3 gallons of water from the 9-gallon pail because it already contained 1 gallon of water.

You successfully measured 6 gallons of water by above steps.

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The asymptotes of (2x + 1)/(x - 5) are given as follows:

Horizontal: y = 2.Vertical: x = 5.

What are the asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

For the vertical asymptote, we consider that the denominator of the function cannot be zero, hence:

x - 5 = 0

x = 5.

For the horizontal, we consider the terms with the highest degree of the numerator and of the denominator, hence:

y = 2x/x

y = 2.

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The distance along the line of sight from the helicopter to the buoy is 634.51 meters.

How to determine the distance along the line of sight

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

Angle of depression, x = 52 degrees

Altitude = 500 meters

The distance (d) along the line of sight is calculated as:

sin(x) = Altitude/d

So, we have

d = Altitude/sin(x)

Substitute the known values in the above equation, so, we have the following representation

d = 500/sin(52 degrees)

So, we have

d = 634.51

Hence, the distance is 634.51 meters.

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The linear function with the greatest rate of change is function B.

Which linear function has the greatest rate of change?

A general linear function can be written as:

y = a*x + b

Where a is the rate of change and b is the y-intercept.

The rate of change tells us how fast the variable y changes when the variable x changes.

In option A, we can see that x goes in increments of 2, while y goes in increments of 5, then the rate of change is:

5/2 = 2.5

On function C we have on increase of 1 unit in y for an increase of 3 units in x,so the rate is 1/3.

And for function B the rate is 3.

For function D the rate is -1

Then we can see that the larger rate is the one of function B, the correct option is B

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Answer:

F

Step-by-step explanation:

area of the circle=[tex]\pi r^{2}[/tex]=3.14x[tex]4^{2}[/tex]

area of the triangle=[tex]\frac{4*4}{2}[/tex]

area of sharded= 3.14x[tex]4^{2}[/tex] - [tex]\frac{4*4}{2}[/tex]

Answer:

-22

Step-by-step explanation:

Simplify the expression.

−22

The following are polynomials with their number of terms and degrees:

a). s -1 (2 terms and degree 1)

b). 9k⁸ - 8k⁷ + 10k⁵ - 10k² (5 terms and degree 8)

c). 4b⁴ - 2b³ - b² - 9b (4 terms and degree 4)

What is a polynomial

A polynomial expression is an algebraic expression made up of variables and coefficients, combined using only the operations of addition, subtraction, and multiplication. The variables are raised to a power, which is a non-negative integer, and the coefficients are real numbers. A polynomial can have any number of terms, but it always has a degree, which is the highest power of the variables in the expression.

For the polynomial expression, s -1 there are only 2 terms and it has a degree of 1

For the polynomial expression, 9k⁸ - 8k⁷ + 10k⁵ - 10k² there are only 5 terms and it has a degree of 8

For the polynomial expression, 4b⁴ - 2b³ - b² - 9b there are only 4 terms and it has a degree of

In conclusion, the polynomials have their number of terms and degrees as:

a). s -1 (2 terms and degree 1)

b). 9k⁸ - 8k⁷ + 10k⁵ - 10k² (5 terms and degree 8)

c). 4b⁴ - 2b³ - b² - 9b (4 terms and degree 4)

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The value of c that will complete the square in the expression above to make it a perfect square trinomial is 49.

What is a perfect square trinomial?

In Mathematics, a perfect square trinomial can be defined as an expression that is typically obtained from the square of a binomial equation.

Generally speaking, a quadratic function (trinomial) of the form ax² + bx + c is considered as a perfect square trinomial, if and only if, it satisfies the following condition;

b² = 4ac

From the given quadratic function (trinomial), we have:

a = 1

b = 14

Substituting, we have:

b² = 4ac

14² = 4c

196 = 4c

c = 196/4

c = 49

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Answer:

1/100, or 0.01

Step-by-step explanation:

We can start off by making an equation.

74/x = 7400, x being the variable

to begin solving, we first multiply both sides by x to begin to isolate it.

(74/x) · x = 7400· x

Simplify:

74 = 7400x

Lastly, to isolate and solve for x, we divide both sides by 7400

74/7400 = 7400/7400x

Simplify

x= 1/100

The solution of expression is,

x = 0.01

We have,

74 divided by what = 7400

Let us assume that,

Solution of given expression is, x

Hence, We get;

74 / x = 7400

74 = 7400x

x = 74 / 7400

x = 1/100

x = 0.01

Therefore, The solution of expression is,

x = 0.01

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Answer:

x² is the correct answer

Step-by-step explanation:

Hello, We are required to use the FTOC pt.1 Before we do this , know that we can break up the integral to have 0 as a limit of integrand.

[tex]int(3x,x {}^{3} )(e {}^{t} \tan(t) )dt [/tex]

Using properties of integrals, this becomes

[tex]int(0, {x}^{3} )(e {}^{t} \tan(t) )dt - int(0,3x)( {e}^{t} \tan(t) )dt[/tex]

Using the chain rule, the integral of the first one computes to

[tex]e { }^{ {x}^{3} } \tan( {x}^{3} 3 {x}^{2} ) [/tex]

The integral of the second one computes to

[tex]3e {}^{3x \tan(3x) } [/tex]

So we end up getting

[tex] \frac{dy}{dx} = {e}^{ {x}^{3} } \tan( {x}^{3} ) 3 {x}^{2} - 3e {}^{3x} \tan(3x) [/tex]

The value of x for the given triangles is 48.

What is the similarity?

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

Given that there are two triangles. The two triangles are similar to each other.

The value of x will be calculated by applying the property of similarity in the two triangles.

(18+x) / (56+21) = x / 56

(18+x) / ( 77 ) = x / 56

1008 + 56x = 77x

1008 = 21x

x = 48

Therefore, the value of x will be 48.

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The measure of the base of the pyramid is 118 meters

How to determine the value

It is important to note that the six different types of trigonometric identities are;

secantcosecanttangentcotangentcosinesine

Some properties of a pyramid are;

The base is a regular polygonLateral edges are equalLateral faces are same as an isosceles trianglesThe altitude meets the base at its center

Then, we have;

The opposite side = 221 meters

The angle of elevation = 62 degrees

The adjacent side = x

Using the tangent identity, we have

tan 62 = 221/x

find the value

x = 221/1.8807

x = 118 meters

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Answer:

235 meters.

Step-by-step explanation:

:p

Answer: $113

Step-by-step explanation:

The equation for the monthly balance of the account can be represented as:

y = 100 * (1 + 0.02)^x

where x is the number of months and y is the balance in the account.

So, when x = 6,

y = 100 * (1 + 0.02)^6

y = 100 * 1.127436

y = 112.7436

Rounding to the nearest whole number,

f(6) = 113

So, after 6 months, the balance in the account will be $113.

I'm happy to help you with Part A of your honors segment one activity of composite figure from environment.

For this assignment, you need to choose an object from your environment that is composed of multiple geometrical shapes. You cannot choose a simple shape like a triangle or a rectangle. The object you choose should be feasible for creating a 2-D diagram that represents its 3-D form.

After you have chosen your object, make a construction of it on a piece of paper using a compass and straightedge. You should create a side view, top view, and front view of your object. Consider whether your object has congruent segments, angles, parallel or perpendicular lines, or any special shapes such as equilateral triangles, squares, or regular hexagons.

Finally, use complete sentences to describe the object you chose to make a model of and why you chose this object. You should discuss any pros and cons of the object with your instructor.

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The coefficient of variation is a unit free statistic , the correct option is (B) .

The coefficient of variation (CV) is defined as a statistical measure that expresses the standard deviation as a percentage of the mean.

The coefficient of variation is calculated as ,

⇒ CV = (standard deviation/mean) × 100%

The CV is a unit-free statistic because it doesn't depend on the unit of measurement of the variables being compared. This makes it useful for comparing the variability of variables that are measured in different units.

Therefore , the correct option about the coefficient of variation is (B) .

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Answer:

less then

Step-by-step explanation:

Answer:

X≤10

Step-by-step explanation:

The equation of the line that is parallel to the line passing through the points (2,0) and (-2,8) is y = -2x + 4.

To find the equation of a line that is parallel to the line passing through the points (2,0) and (-2,8), we need to use the fact that parallel lines have the same slope.

First, we need to find the slope of the line passing through the points (2,0) and (-2,8). The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

So, for the line passing through (2,0) and (-2,8), we have:

slope = (8 - 0) / (-2 - 2) = 8 / (-4) = -2

Now we know that the slope of the line we are looking for is also -2, since it is parallel to the given line.

We also need a point on the line we are looking for to fully determine its equation. We can choose any point we want, but to keep things simple, let's use the midpoint of the two given points, which is ((2 + (-2))/2, (0 + 8)/2) = (0, 4).

Now we have the slope (-2) and a point (0,4) on the line we are looking for. We can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values we found, we get:

y - 4 = -2(x - 0)

Simplifying, we get:

y - 4 = -2x

y = -2x + 4

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