Evaluate (6.1 x 10-3) (8 x 109). Write your answer in scientific notation and standard form.
Scientific Notation:
Standard Form:

\( \huge \boxed{Answer \hookleftarrow}\)

=》1² + 3²

=》1 + 9

=》10

Answer:

p = 62

Step-by-step explanation:

(x^25)^2 = x^(25*2) = x^50.  Then we have:

(x^12)(x^50) = x^(12 + 50) = x^62

Therefore, p = 62

The Standard Form of the polynomial function 3x^2 4x + 7x^3 + 1 is 7x^3 +3^2 +4x + 1

The meaning of the Standard Form of polynomial function can be explained as when the terms are in this equation or functions are be written in descending order of exponents.

This is usually done starting from the from left to right, we were given the function as :3x^2 +4x + 7x^3 + 1  , then let us arrange it as:

7x^3 +3^2 +4x + 1

Therefore, the Standard Form of polynomial function is 7x^3 +3^2 +4x + 1 .

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Answer:

it will help you

Step-by-step explanation:

thank you

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See the solution below ~

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

a.) The required expression is ~

here, k = proportionality constant ~

b.) Let's find the equation by Plugging the values as " x = 4 and y = 2 ~

now, the value of k can be determined ~

c.) find the value of x when y = 4 ~

Plugging the value of x as 4 and k as 50, we get ~

I hope it helped ~

Two rays with a common endpoint form an angle. An angle is defined as a geometric figure formed by two rays that share a common endpoint. In other words, an angle is formed when two rays emanating from a common point, and this common point is known as the vertex.

The rays are the sides of the angle, and the angle is measured in degrees. Angles have different measures, ranging from 0 degrees to 360 degrees. The two rays that make up an angle are also called the sides or arms of the angle. The angle is measured in degrees, and the size of the angle depends on the distance between the two sides of the angle that meet at the vertex.

In geometry, an angle can be named in different ways, depending on the context in which it is being used. Angles are essential in mathematics, physics, and other scientific fields, where they are used to measure the rotation of an object, determine the direction of an object, and in other applications involving rays and lines. Two rays with a common endpoint form an angle.

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Answer: Ill show you some not everything so u can try

Step-by-step explanation: for example 8+y=92

you can make a new problem...

move the 92...

92

subtract

92-

subtract the other number which isnt the variable

92-8

subtract and you get your answer!

Step-by-step explanation:

an equation means that whatever is on one side of the "=" sign is truly equal to whatever is on the other side.

it is like a balance.

you can change the content on one side of the balance, but then you have to make the same change on the other side of the balance. otherwise the balanced relation between both sides is destroyed. and it is no longer an equation.

for the same reason, you can perform any mathematical operation on an equation, as long as you do it simultaneously on both sides.

all these equations are equations with one variable.

so, if we find a way to bring all terms with the variable to one side, and everything else (typically constant numbers) to the other side, while still maintaining the equation relation, then we can solve this by saying "this is only an equation, if the variable has this is that value".

and that is the whole trick.

so, for e.g. t + 3 = 5, how can we get only the variable on one side ? well, the "+ 3" is disturbing, so we subtract 3.

and to keep the balance, we need to subtract 3 on both sides.

that gives us then

t + 3 - 3 = 5 - 3

t = 2

and boom ! the equation has solved itself right in front of our eyes.

and the same thing for all the other equations.

find what is the disturbing additional term on the side of the variable, then get rid of it (and repeat that exact action on the other side) and see what is left on the other side. and you have solved the equation.

that works in every direction like

n + 22 = 5

n + 22 - 22 = 5 - 22

n = -17

12.5 = 7.4 + z

12.5 - 7.4 = 7.4 - 7.4 + z

5.1 = z or

z = 5.1

remember, it is an equation like a balance. you can switch the balance bowls from left to right and right to left, and still they are in balance.

Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.

Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.

To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).

The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.

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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%

Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.

To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.

We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.

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There are four levels of measurement: nominal, ordinal, interval, and ratio.

The level of measurement of a variable refers to the type or scale of measurement used to quantify or categorize the data. There are four levels of measurement: nominal, ordinal, interval, and ratio.

1. Nominal level: This level of measurement involves categorical data that cannot be ranked or ordered. Examples include gender, eye color, or types of cars. The data can only be classified into different categories or groups.

2. Ordinal level: This level of measurement involves data that can be ranked or ordered, but the differences between the categories are not equal or measurable. Examples include rankings in a race (1st, 2nd, 3rd) or satisfaction levels (very satisfied, satisfied, dissatisfied).

3. Interval level: This level of measurement involves data that can be ranked and the differences between the categories are equal or measurable. However, there is no meaningful zero point. Examples include temperature measured in degrees Celsius or Fahrenheit.

4. Ratio level: This level of measurement involves data that can be ranked, the differences between the categories are equal, and there is a meaningful zero point. Examples include height, weight, or age.

It's important to note that the level of measurement affects the type of statistical analysis that can be performed on the data.

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The correct option for showing the interval (-∞, -7) is Option C.

What is Interval?

An interval includes all the numbers that come between two particular numbers.

The given interval is (-∞, -7).

Now, On the number line (-∞, -7) is shown as;

The interval is open interval.

Hence, At point -7 the graph is in open circle.

And, The graph is going left side.

Hence, The correct option for showing the interval (-∞, -7) is Option C.

Which is shown in figure.

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Answer:

P = 10n + 50

Step-by-step explanation:

fixed charge 50

10 / unit

for n units of water charge is n * 10

Water bill is P

P = n * 10 + 50

P = 10n + 50

Answer:

D.)

Step-by-step explanation:

Combine Like Terms:

=3x+3x+3x+2+2

=(3x+3x+3x)+(2+2)

=9x+4

have a great day (っ◔◡◔)っ ❤

Answer:

the correct answer is D

Step-by-step explanation:

Therefore, the expression 9q² - 2(3q-7) + 5q² is equivalent to 14q² - 6q + 14.

To simplify the expression 9q² - 2(3q-7) + 5q², we can apply the distributive property and combine like terms.

Expanding the expression within the parentheses:

9q² - 2 * 3q + 2 * 7 + 5q²

Simplifying further:

9q² - 6q + 14 + 5q²

Combining like terms:

(9q² + 5q²) + (-6q + 14)

Simplifying within the parentheses:

14q² - 6q + 14

Therefore, the expression 9q² - 2(3q-7) + 5q² is equivalent to 14q² - 6q + 14.

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The formula relating x, y, and c is given by: Kc = xy.

To arrive at this formula, we can start by using the fact that Julia bought x oranges at Ky each. This means that the total cost of the oranges is given by xy. Since she spent Kc, we can set up the equation:

Kc = xy

This gives us the formula relating x, y, and c.

The formula for t, the total cost of P pawpaws at K4y each, can be given by: Kt = 4Py.

Using a similar reasoning as above, we know that the total cost of the pawpaws is given by the product of the number of pawpaws (P), the cost per pawpaw (K4y), and we can write this as 4y. Therefore, the total cost of the pawpaws is Kt = 4Py. This gives us the formula for t in terms of P and y.

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The given transformation of reflection, rotation and translation are rigid transformation

The transformation that must take any point A to any point B are;

Reason:

Question: The given quadrilaterals ABCD and A'B'C'D' are congruent

Required; To select all transformation that must take a point A to point B

Solution:  

A rotation of 180° about the midpoint of segment AB will change the places of points A and B

A(x, y) → R₁₈₀ → A'(-x, -y)

Let the coordinates of the origin be the midpoint of segment AB, and let (x, y) represent the coordinate of the point B(x, 0) we have;

∴ The coordinates of point A is A(-x, 0), which gives;

A(-x, 0) → R₁₈₀ → A'(x, 0) = point B

Therefore a rotation about the midpoint of AB must take point A to point B

The reflection of a point (x, y) about y-axis gives a point (-x, y), therefore, we have;

A(-x, 0) → Reflection across the y-axis → A'(x, 0) = point B

Therefore, a reflection across the perpendicular bisector of the line AB must take the point A to point B

A translation along the directed line segment AB of point A(-x, 0) 2·x units right gives;

A'(-x + 2·x, 0) = A'(x, 0) = Point B

Therefore, the transformations that must take any point A to any point B are;

Rotation of 180° around the midpoint of segment AB

Reflection across the perpendicular bisector

Translation by the directed line segment AB

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IH + HJ = 2 (IH)

0.75 + HJ = 2(0.75)

0.75 + HJ = 1.5

HJ = 1.5 - 0.75

HJ = 0.75

Answer:

10 months

Step-by-step explanation:

30x = 22x + 80

8x = 80

x = 10

The measure of angle of ∠BAM (θ) will be 9°. Then the correct option is D.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

ABCD is a rectangle with AB = 3BC.

And M is the mid-point of BC.

2BM = BC

Then the tangent of angle of ∠BAM (θ) will be

tan θ = (BM) / (AB)

tan θ = (BM) / (3BC)

tan θ = (BM) / (3 × 2BC)

tan θ = 1/6

     θ = tan⁻¹ (1/6)

     θ = 9.46°

     θ ≅ 9°

Then the correct option is D.

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As per the following graph, if y = 0,then it makes the horizontal line on graph.

The term graph in math is defined as the visual representation of data or equation.

Here we have given that the value of y = 0.

Here we know that the slope of a horizontal line is zero while the slope of a vertical line is undefined.

Here the following Slopes represent a line's ratio of vertical change to horizontal change.

Whereas horizontal and vertical lines remain constant and never increase or decrease, they're merely straight lines.

Here we have also know that the Horizontal lines have no steepness at all.

Therefore if y=0 is the linear equation to denote the x - axis, then all the points on the x- axis, have their y co-ordinate as 0.

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The average value of the function f(x) = 4x sec^2 x on the interval [0,π/4] is equal to tan (π/4) - ln |sec (π/4) + tan (π/4)| + C/π.

The average value of the function f(x) = 4x sec^2 x on the interval [0,π/4] can be calculated using the formula for the average value of a function on an interval:

A = (1/b-a) * ∫a^b f(x) dx

Where a = 0 and b = π/4 in this case.

This can be broken down into two parts. First, the integral is equal to the antiderivative of f(x) from 0 to π/4, which is:

∫a^b f(x) dx = 2x tan x - ln |sec x + tan x| + C

Evaluating this from 0 to π/4 gives us:

∫a^b f(x) dx = 2(π/4) tan (π/4) - ln |sec (π/4) + tan (π/4)| + C

The second part of the average value equation is the difference between b and a, which in this case is b - a = π/4 - 0 = π/4.

Therefore, the average value of the function f(x) = 4x sec^2 x on the interval [0,π/4] is equal to:

A = (1/π/4) * (2(π/4) tan (π/4) - ln |sec (π/4) + tan (π/4)| + C)

A = 1/π * (π tan (π/4) - ln |sec (π/4) + tan (π/4)| + C)

A = tan (π/4) - ln |sec (π/4) + tan (π/4)| + C/π

A = tan (π/4) - ln |sec (π/4) + tan (π/4)| + C/π

The average value of the function f(x) = 4x sec^2 x on the interval [0,π/4] is therefore equal to tan (π/4) - ln |sec (π/4) + tan (π/4)| + C/π.

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The required probability of occupying seats at the end of the row by April and Bobby is equals to 0.0333.

We have,

Number of chairs in a row =  5

April and Bobby need to occupy the two end chairs.

The other two people, Bill and Candace, can sit in any of the 3 remaining chairs.

The total number of ways to seat the 4 people in the 5 chairs is

= 5!/(5-4)!

= 5x4x3x2

= 120.

April can sit in either of the two end chairs, and then Bobby can sit in the other end chair.

Bill and Candace can then sit in either of the two remaining chairs, in either order.

The number of ways to seat April and Bobby at the ends of the row is,

=  2x1x2x1

= 4.

Probability that April and Bobby will occupy the seats at the end of the row is,

4/120

= 1/30

= 0.0333

Therefore, the probability of April and Bobby occupy seats at the end of the row is 1/30 or approximately 0.0333.

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The hypotenuse measures 10 centimeters long. If one limb of a right triangle is 8 cm long and the other is 6 cm long, the triangle is right.

The Pythagorean Theorem, also known as Mathematics, is the fundamental Euclidean geometry equation between the 3 sides of a right triangle. Its area of a cube with the integrand side is the sum of the areas of circles with the other two sides, according to this formula. The Pythagorean Theorem asserts that the square that spans a right triangle's hypotenuse opposite the right angle represents the total of all the squares that span its sides. It is frequently written as the abstract numerical notation a2 + b2 = c2.

given

by pythagoras theorem

a² + b² = c²

64 + 36 = c²

100 = c²

c = 10 cm

The hypotenuse measures 10 centimeters long. If one limb of a right triangle is 8 cm long and the other is 6 cm long, the triangle is right.

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Answer:

10 cm

Step-by-step explanation:

Keep it simple, but correct :)

The player's average profit per game in the long run will be -$0.25.

To calculate the average profit per game, we need to determine the probabilities of each outcome and multiply them by the corresponding profit or loss.

When flipping a fair coin twice, there are four possible outcomes: no heads (Tails-Tails), one head (Tails-Heads or Heads-Tails), or two heads (Heads-Heads). Each outcome has a 1/4 probability of occurring because the coin is fair.

For no heads, the player loses $1 because they are charged to play the game. So the profit is -$1.

For one head, the player receives $1. Since there are two ways to get one head, the total profit for this outcome is 2 * $1 = $2.

For two heads, the player receives $5. So the profit for this outcome is $5.

Now, we calculate the average profit per game by multiplying each profit by its corresponding probability and summing them up:

(-$1 * 1/4) + ($2 * 1/4) + ($5 * 1/4) = -$0.25

Therefore, the average profit per game in the long run is -$0.25.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

3 meters per second.

Step-by-step explanation:

The formula for finding speed is: \(s = \frac{d}{t}\). D is distance. T is time. So in your case, you would divide 6.0 (distance) by 2.0 (time). Your answer is 3. Add meters per second because you divided meters/seconds.

Hope it helps!

Answer:

7.6 cm

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(a^{2}\) + \(6.5^{2}\) = \(10^{2}\)

\(a^{2}\) + 42.25 = 100 Subtract 42.25 from both sides

\(a^{2}\) = 57.57

\(\sqrt{\a^{a} }\) = \(\sqrt{57.57}\)

a ≈ 7.6

Helping in the name of Jesus.

Answer:

7.6 cm

Step-by-step explanation:

a^2+ b^2=c^2

a^2+6.5^2=10^2

a^2+42.25=100 subtract 42.25 from both sides

a^2=57.57

a=√57.57

a=7.6 cm

To find the constant of proportionality, divide the total amount of basketballs that have been used by the total number of games. This will give you the rate of new basketballs per game:

Fill the column of "Number of NBA games" with the numbers from 1 to 9. Using the constant of proportionality, multiply each number in the first column by 3 to find how many basketballs are used depending on the number of games.

Remember: the proportional relationship being represented is the number of new basketbals that are used per game. The constant of proportionality is 27/9 = 3, and that's the value that belongs next to the 1 in the table.

Answer:

The volume of a cylinder:

\(V \approx 2035.75\) \(ft^3\)

Step-by-step explanation:

-To find the volume of a cylinder, you first need the formula:

\(V = \pi (\frac{d}{2})^2 h\)

\(d =\) diameter

\(h =\) height

-Use the following diameter and height for the formula:

\(V = \pi (\frac{18}{2})^2 8\)

-Then, you solve:

\(V = \pi (\frac{18}{2})^2 8\)

\(V = \pi \times (\frac{18}{2})^2 \times 8\)

\(V = \pi \times (9)^2 \times 8\)

\(V = \pi \times 81 \times 8\)

\(V = \pi \times 648\)

\(V = 648\pi \approx 2035.752\)

-Since the hundredth place is 2, It cannot be rounded to the nearest hundredths place, so it would be:

\(V \approx 2035.75\) \(ft^3\)

The expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).

The value of an electronic book device before a holiday is represented by the variable t. After the holiday, the value of the device decreased by 15%. To find the value of the device after the holiday, we need to multiply the original value by the percentage decrease, which is 0.85 (or 1-0.15). Therefore, the expressions that correctly show the value of the electronic book device after the holiday are B and D.

Option A (1.15) represents the percentage increase and not the decrease, so it is incorrect. Option C (-0.15) represents the percentage decrease, but it cannot be used alone to find the new value. Option E (-0.85) is the negative of the percentage decrease, so it is also incorrect. Finally, option F is equivalent to option D, so it is also correct.

In summary, the expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).

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Answer:

Part A. 4x

Part B. Mr. Jefferson could ride 3 miles in 12 minutes

Step-by-step explanation:

Part A. 4 being the time it takes him to travel 1 mile and x being the number of miles rode.

Part B. To find the time it took him to travel each mile I divided 20 by 5 which gave me four. Then to find the miles he could ride in 12 minutes I divided 12 from 4 which gave me three, stating that he could travel 3 miles in 12 minutes.

__________________________________________________________

Hope this helps!!!

If I am incorrect, please tell me; I enjoy learning form my mistakes:)