Simplify the expression 4x3× 2x3

Answer:

The interest amount Karen needs to pay each month is $1000 * .0025 = $2.5.

So, she needs to pay $1100 - $1000 = $100 in interest.

Therefore, Karen will have to pay for 100 / 2.5 = 40 months.

Rounding to the nearest month, Karen will have to pay for 40 months.

Answer:

12.5%

Step-by-step explanation:

Percent decrease is calculated as

\(\frac{decrease}{original}\) × 100%

Decrease = $400 - $350 = $50 , thus

percent decrease = \(\frac{50}{400}\) × 100% = \(\frac{50(100)}{400}\) = 12.5%

The percent decrease on a DVD recorder that is 12.5%. The correct option is 3

A percentage is a minimum number or ratio that is measured by a fraction of 100.

let the value of which a thing is represented in percentage is "a'

let the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), therefore we will first divide the whole part in 100 parts and then we multiply it with b so that we can get b items per 100 items(that is exactly what b per cent means).

Hence, that thing in number is

(a/100)x b

Percent decrease is calculated as;

Decreased in price/original price × 100%

Decrease = $400 - $350 = $50 , thus

Therefore, percent decrease = 50/400 × 100%  

= 12.5%

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Answer:

x=27⁰

Step-by-step explanation:

4x+7=5(x-4)

4x+7=5x-20

4x-5x=-20-7

-x=-27

x=27⁰

The probability that X is greater than 145.28 is approximately 0.0465.

Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Approximately 16.28 cm

1) We can sketch out this triangle to better figure out:

2) So now, let's resort to the Pythagorean Relation:

Note that the hypotenuse is always on the left, in the Pythagorean Theorem.

False, one of the most pieces of information with a var is whether each estimated coefficient for the lags is statistically significant (t-tests)

A statistical test called a t-test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment truly affects the population of interest or whether two groups differ from one another.

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Answer:

the answer is 15.

Answer:

it is 15

Step-by-step explanation:

74. 94×10³= 74940 because the number 10³ has zeros when it is written without an exponent.

Using scientific notation, it's found that the number in standard notation is represented by:

74. 94 × 10³= 74940

Using scientific notation, you can write extremely large or extremely small numbers. When a number between 1 and 10 is multiplied by a power of 10, the result is expressed in scientific notation as variety.

Scientific notation for the following number is:

\(a \times 10^{b}\)

In this problem, the amount is given by:

= 74. 94 × 10³

Hence, applying the multiplication, we have that:

74. 94 × 10³ = 74. 94 × 1000 = 74940

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The integral from ∫cos(3x)sin⁴(3x) dx will be (-1/18) [ (2/7)(1 - sin².

To integrate ∫cos(3x)sin⁴(3x) dx, we can use the substitution u = sin(3x) and du/dx = 3cos(3x). Then, dx = du/(3cos(3x)), and we have:

∫cos(3x)sin⁴(3x) dx = ∫u⁴ du/(3cos(3x))

Next, we need to eliminate the x dependence in the integral. Using the identity sin²(θ) + cos²(θ) = 1, we can rewrite sin⁴(3x) as (sin²(3x))² = (1 - cos²(3x))², which expands to 1 - 2cos²(3x) + cos⁴(3x). Thus, we have:

∫cos(3x)sin⁴(3x) dx = ∫u⁴ du/(3cos(3x))

= (1/3) ∫(u⁴ - 2u² + 1) du/cos(3x)

Now, u = sin(3x), so cos(3x) = √(1 - u²), and we have:

∫cos(3x)sin⁴(3x) dx = (1/3) ∫(u⁴ - 2u² + 1) du/√(1 - u²)

This integral can be evaluated using the substitution v = 1 - u² and dv/dx = -2u(du/dx) = -6cos(3x)u. Then, du = (-1/6cos(3x))dv, and we have:

∫cos(3x)sin⁴(3x) dx = (1/3) ∫(u⁴ - 2u² + 1) du/√(1 - u²)

= (1/3) ∫((1 - v)² - 2(1 - v) + 1)(-1/6cos(3x)) dv/√v

= (-1/18) ∫(v⁵/2 - 3v⁴/4 + 3v³/2 - v² + 2v - 1)/√v dv

This integral can be evaluated using the power rule and the half-angle formula for √v:

∫vⁿ/√v dv = 2∫t^(2n-1) dt, where t = √v

∫√v dv = (2/3)v^(3/2)

Using these rules, we get:

∫cos(3x)sin⁴(3x) dx = (-1/18) [ (2/7)v^(7/2) - (2/5)v^(5/2) + (3/4)v^(3/2) - (1/3)v^(3/2) + v^(3/2) - 2v ] + C

= (-1/18) [ (2/7)(1 - u²)^(7/2) - (2/5)(1 - u²)^(5/2) + (5/12)(1 - u²)^(3/2) - 2√(1 - u²) + u ] + C

Finally, substituting back u = sin(3x), we have:

∫cos(3x)sin⁴(3x) dx = (-1/18) [ (2/7)(1 - sin²

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The area of circle C, which passes though points W and Z is 324π square meters.

The center of the outer circle, Point D, is where we want to calculate the area of the circle has a WZ diameter and WC and CZ radii.

That YZ = YD = 10 cm is known.

Let DC = x and CY = 10 - x

The outer circle's radius can be expressed as 8 + 8 + x or 10 + 10 - x, which we can equate to determine its value of x

8 + 8 + x = 10 + 10 - x

Simplify

16 + x = 20 - x

Subtract 16 on both side, we get

x = 4 - x

Add x on both side, we get

2x = 4

Divide by 2 on both side, we get

x = 2

As a result, the circle's radius is

= 8 + 8 + x

= 16 + x

= 16 + 2

= 18 cm

The area of circle = πr²

The area of circle = π(18)²

The area of circle = 324π

Thus, the circle's area is 324π square meters.

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The complete question is:

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ.

What is the area of circle C, which passes though points W and Z?

A. 81

B. 164

C. 324

D. 1296

Answer:

horizontal translation    ( this would require an  x - k   or x+k   type of a factor)

Step-by-step explanation:

It DOES have :

    vertical    due to the -9

    horizontal compression due to the  3x

    reflection due to the   -4

Answer:

The formula for relative change is x = 100 * (final - initial) / initial  Using this concept, we can plug in our values. x = (3.95 - 3.45) / 3.45 = 0.5. 0.5 * 100 = 14.49%. Rounded to the nearest tenth would give us the value 14.5%.

Step-by-step explanation:

The time taken to travel the distance 70 Km/h is 11 hours.

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

The formula can be rearranged in three ways:

Given:

time = 9 hours

speed = 85 Km/h

Now, distance

=speed * time

=85 * 9

= 765 km

As, the speed is 70 km/h

time = distance/ speed

time = 765 / 70

time = 10.92

time= 11 hours

Hence, the time taken to travel the distance 70 Km/h is 11 hours.

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The translation of the question is:

A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?

The data given has: a) A strong correlation, b) A positive correlation

Correlation is a statistical measure that expresses the extent to which two variables are linearly related, meaning they change together at a constant rate.

We have ordered pairs in the data as:

x             y

1             2

2            3

3            8

4            10

5            26

6            38

7            46

8            50

9            68

Plotting the graph (attached)

Clearly, on plotting the scatter plot on the basis of table of values, we see that the relation is a strong correlation since we can find a relationship between variable x and y.

i.e. the points will lie above or below the curve  which is formed by connecting some points of the scatter plot and are not scattered away.

Hence, the data above has: A strong correlation.

Also, the graph is a positive correlation since with the increasing value of x the y-value also increases.

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Answer:

4/1 +2

Step-by-step explanation:

2 is where you start

4 how high/low

1- how far to right

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

third graph

.............

The drama club ordered 150 short-sleeved shirts and 100 long-sleeved shirts.

Let S represent the number of short-sleeved shirts and L represent the number of long-sleeved shirts the drama club ordered.

Given that the price of each short-sleeved shirt is $5, so the revenue from selling all the short-sleeved shirts is 5S.

Similarly, the price of each long-sleeved shirt is $10, so the revenue from selling all the long-sleeved shirts is 10L.

The total revenue from selling all the shirts should be $1,750.

Therefore, we can write the equation:

5S + 10L = 1750

Now, let's use the information from the first week of the fundraiser:

They sold one-third of the short-sleeved shirts, which is (1/3)S.

They sold one-half of the long-sleeved shirts, which is (1/2)L.

The total number of shirts they sold is 100.

So, we can write another equation based on the number of shirts sold:

(1/3)S + (1/2)L = 100

Now, you have a system of two equations with two variables:

5S + 10L = 1750

(1/3)S + (1/2)L = 100

You can solve this system of equations to find the values of S and L. Let's first simplify the second equation by multiplying both sides by 6 to get rid of the fractions:

2S + 3L = 600

Now you have the system:

5S + 10L = 1750

2S + 3L = 600

Using the elimination method here.

Multiply the second equation by 5 to make the coefficients of S in both equations equal:

5(2S + 3L) = 5(600)

10S + 15L = 3000

Now, subtract the first equation from this modified second equation to eliminate S:

(10S + 15L) - (5S + 10L) = 3000 - 1750

This simplifies to:

5S + 5L = 1250

Now, divide both sides by 5:

5S/5 + 5L/5 = 1250/5

S + L = 250

Now you have a system of two simpler equations:

S + L = 250

5S + 10L = 1750

From equation 1, you can express S in terms of L:

S = 250 - L

Now, substitute this expression for S into equation 2:

5(250 - L) + 10L = 1750

Now, solve for L:

1250 - 5L + 10L = 1750

Combine like terms:

5L = 1750 - 1250

5L = 500

Now, divide by 5:

L = 500 / 5

L = 100

So, the drama club ordered 100 long-sleeved shirts. Now, use this value to find the number of short-sleeved shirts using equation 1:

S + 100 = 250

S = 250 - 100

S = 150

So, the drama club ordered 150 short-sleeved shirts and 100 long-sleeved shirts.

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Complete question:

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold StartFraction one-third EndFraction of the short-sleeved shirts and StartFraction one-half EndFraction of the long-sleeved shirts, for a total of 100 shirts.

The correct logic translation of "some people are afraid of some animals" is:

∃x∃y, Person(x) ∧ Animal(y) ∧ Afraid(x, y)

This translates to "There exist some person x and some animal y such that x is afraid of y, and x is a person, and y is an animal." This statement asserts the existence of at least one person who is afraid of at least one animal.

To break down the statement, the quantifier ∃x asserts that there is at least one person x who is afraid of some animal, and the quantifier ∃y asserts that there is at least one animal y that some person is afraid of. The predicates Person(x), Animal(y), and Afraid(x, y) specify the properties of x and y, where Person(x) means x is a person, Animal(y) means y is an animal, and Afraid(x, y) means x is afraid of y. The ∧ symbol represents the logical operator "and," which combines the predicates to form a single statement.

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Answer:

The slope is 1/3 and the y intercept is 6

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

3y -x =18

Add x to each side

3y = x+18

Divide each side by 3

3y/3 = x/3 +18/3

y = 1/3x +6

The slope is 1/3 and the y intercept is 6

We need to solve for y (y = mx + b):

3y - x = 18

~Add x to both sides

3y = 18 + x

~Divide 3 to everything

y = 6 + x/3 or y = 6 + 1/3/x

So... 1/3 is the slope and 6 is the y-intercept.

Best of Luck!

Using the vertical line rule, the given relation is not a function.

According to the definition of a function, each element in the domain is connected to just one element in the range. This means that each vertical line through the x-axis can only intersect the function at one specific point. The same is true for equations of higher powers in which only the x term is exponentiated as well as all linear equations.

It occasionally fails to function for equations with both the x and y terms raised to a power. For instance, the circle is described by the equation x² + y² = a². Given that a vertical line can cross a circle more than once, this equation is not a function.

If you draw a vertical line through any point and the given relation intersects it multiple times, we can confirm that the relation is not a function.

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We then applied the formula for factoring perfect square trinomials to obtain the fully factored form, which is 4(2x - 3)2.

To factor 16x2 - 48x + 36 completely, we can first factor out the greatest common factor of 4:

16x2 - 48x + 36 = 4(4x2 - 12x + 9)

Now,

we can see that the expression inside the parentheses is a perfect square trinomial, which can be factored as:

4x2 - 12x + 9 = (2x - 3)2

Therefore, putting the pieces together, we have:

16x2 - 48x + 36 = 4(4x2 - 12x + 9) = 4(2x - 3)2

Hence, the fully factored form of the given expression is 4(2x - 3)2, which is option D).

The reason why we can recognize 4x2 - 12x + 9 as a perfect square trinomial is because it has the form a2 - 2ab + b2, where a = 2x and b = 3. This form can always be factored as (a - b)2, which in this case gives (2x - 3)2. The factor of 4 in the final answer comes from the fact that we initially factored out a 4 from the given expression.

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Answer:

30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,8,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100

Step-by-step explanation:

100!

Answer:

24

Step-by-step explanation:

20+20% is equal to 24.

Answer:

i dont know im not very sure with value

Step-by-step explanation:

number of pens charles bought: 40×16=640

40 packs cost: 40×4.30=172

640pens: 172

1 pen: 172÷640= 43/160

The sum of the measures of the angle of a triangle is 180 degrees.

The given triangle is a type of triangle and the type of triangle a scalene triangle.

For a scalene triangle, the measure of the three sides are unequal and the sum of the interior angle of a triangle is 180 degrees.

Hence the measure of the angles <A, <B and <C are all less than 90 degrees since they are all acute angles.

We can therefore conclude that:

m<A + m<B + m<C = 180 degrees

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Answer:

x = 27

Step-by-step explanation:

11x - 45 = 36 + 8x

Subtract 8x from both sides.

3x - 45 = 36

Add 45 to both sides.

3x = 81

Divide both sides by 3.

x = 27

The first five terms would be -4, -20, -100, -500, and -2500 respectively.

A series is an ordered list of numbers that follow a certain pattern when appearing one after the other in the list. Series and sequences are often used in our day-to-day lives. Series are of various types - arithmetic Progression, Geometric Progression, and Hypergeometric series. \(n^{th}\) term of the series is calculated by substituting n for the term to be calculated in the formula -4.\(5^{n-1}\)

Calculation of the first five terms of the given series -

\(a_{1}\)= -4.\(5^{1-1}\)= -4(1) = -4

\(a_{2}\)= -4.\(5^{2-1}\)= -4(5) = -20

\(a_{3}\)= -4.\(5^{3-1}\)= -4(25) = -100

\(a_{4}\)= -4. \(5^{4-1}\)= -4(125) = -500

\(a_{5}\)= -4.\(5^{5-1}\)= -4(625) = -2500

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Answer:

x = 1°

Step-by-step explanation:

Bisection means splitting the angle in to 2

So that means 4x-1 = 2x+1

4x-1 = 2x +1

4x = 2x + 2

2x = 2

x = 1°

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