The number e is the base of the ____________?

natural logarithm

decimal system

irrational number system

rational functions

You would receive $13.50 if you cashed in 135 dimes. That's the equivalent of 1,350 pennies.
If you cashed in 135 dimes, you would receive 1,350 pennies.

This is because each dime is worth 0.1 dollars, or 10 pennies. So, to find the total number of pennies you would receive, you can simply multiply the number of dimes by the number of pennies in each dime:
135 dimes * 10 pennies/dime = 1,350 pennies
So, you would receive 1,350 pennies if you cashed in 135 dimes.

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Answer:

The y-intercept is 1

at the point (0,1)

Step-by-step explanation:

The y-intercept is the point at which a graph crosses the y-axis.

The area of the given isosceles trapezoid is 120 square units.

An isosceles trapezoid is a quadrilateral formed by a trapezium whose base angles are equal due to which the left and right sides are also equal in length.

In the given question,

Length of left/right side = 10

Length of bigger base = 21

Length of smaller base = 9

If we join the edges of the smaller base to the bigger base in such a way that we get 2 right-angled triangles formed by the legs of the trapezoid and the base,

we can say that the length of the base would be

=(bigger base-smaller base)/2

=(21-9)/2

=6

and we know that the length of the legs is 10

So to the Pythagorean theorem,

the height of the trapezoid would be

h=√(10² - 6²) = √64 = 8

Now that we know all the variables, we can easily calculate the area of the trapezoid by the formula

= height × (bigger base+smaller base)/2

= 8 ×(21+9)/2

= 4 × (30)

= 120 square units

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793 people in the country said that they like country music if 23% of the people surveyed prefer country music.

The given data is as follows:

percentage of people prefer music = 23%

People did not like country music = 2653

Let us assume make this equation has equal properties,

0.23x = people who like country music

We know that 2,653 people did not like music. We can write this equation as:

x - 0.23x = 2653

0.77x = 2653

x = 2565 / 0.77

x = 3446.75

Taking the x value approximately, we get the x value as,

x = 3447

Now we can substitute the x value in the above equation, we get,

0.23x = 0.23(3447)

= 792.81

Therefore we can conclude that 793 people in the country said that they like country music.

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The total charges for both auto repair shops will be the same when 3 hours of labor have been performed.

Let's call the number of hours worked "h". The total charges for the first auto repair shop will be $30 (for the diagnosis) plus $25 per hour, or $30 + $25h. The total charges for the second auto repair shop will be $35 per hour, or $35h. We want to know when the total charges for both shops will be the same, so we can set the two equations equal to each other and solve for h:
$30 + $25h = $35h
$10h = $30
h = 3

So the total charges for both auto repair shops will be the same when 3 hours of labor have been performed.

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→ the lenght = 13 square units

→ the width = 2 square units

→ the area of the rectangle = 13×2 = 26 square units

→ the area of the triangle = 26 : 2 = 13 square units

Answer:

Step-by-step explanation:

you would copy and paste another triangle on top to form a rectangle. That would make the rectangle's length 13 units and its width 2 units. the area of a rectangle is found by A=length x width which in this case is 26 units^2. A single triangle's area is 1/2 the area of the rectangle making it 26/2 which is 13.

So the area of the triangle is 13 units^2.

Answer:

33 degrees

Step-by-step explanation:

Angles BFG + GFC = 90

5r +68 + 8r +113 =90

1

Collect like terms

13r + 181 = 90

Subract 181 from both sides

13r = 90-181

13r = - 91

r = - 7

Now insert the value of r into BFG (5r +68)

5r + 68 = 5(-7) +68

= -35 + 68

=33

Check your answer by inserting the value of r into 8r +113

8r + 113 =8(-7) +113

-56+113= 57

The two angles 33 and 57 must add up to 90, a rt angle

you multiply x by y and then multiply 5 to the power of 67 to then come to an answer of 500000000000x

Answer:

60

Step-by-step explanation:

850-250=600

600/10=60

60

Answer:

she must save $60 each week to have enought money to purchase the iPhone 10

Step-by-step explanation:

Because 850-250=600

                 600/10=60                

The expression written using each base only once is 4¹¹ , the correct option is (a).

The expression 4⁸×4³ can be simplified using the rule of exponents,

The rule of exponents states that when we multiplying two exponential expressions with the same base, the exponents gets added.

which means that, nᵃ×nᵇ = nᵃ⁺ᵇ;

In this case the expression is: 4⁸×4³ , it has common base as "4",

So, by the rule of exponents, the power(exponents) gets added up ;

The expression "4⁸×4³" can be rewritten as 4⁸⁺³, which is equal to 4¹¹,

Therefore, Option(a)4¹¹, is the expression written using each base only once.

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The given question is incomplete, the complete question is

What is the expression written using each base only once? 4⁸×4³

(a) 4¹¹

(b) 12¹¹

(c) 4²⁴

(d) 64¹¹.

(a) The distribution of Y is P(Y = y) = (12^y * e^-12)/y!

(b) E(Y) = 12.

The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0.

(a) The distribution of Y ~ Poisson(12) is given by:
P(Y = y) = (12^y * e^-12)/y!

(b) The expected value of a Poisson distribution is simply the mean, which in this case is 12. Therefore, E(Y) = 12.

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The final simplified expression is (3x+1)(5x+2)/(3x-2).

The given expression is (15x^(2)+13x+2)/(3x-2). We can try to simplify this expression by factoring the numerator and denominator, and then canceling out any common factors.

First, let's factor the numerator:

15x^(2)+13x+2 = (3x+1)(5x+2)

Now, let's factor the denominator:

3x-2 = (3x-2)

There are no common factors between the numerator and denominator, so we cannot simplify the expression any further.

Therefore, the simplified expression is:

(15x^(2)+13x+2)/(3x-2) = (3x+1)(5x+2)/(3x-2)

Since x!=(2)/(3), we do not need to worry about any undefined values.

So, the final simplified expression is:

(3x+1)(5x+2)/(3x-2)

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The system of equations according to the given instructions are x + (1/2)y = -5; 2y - 12 = x

The sum of one number and half another is negative five. Twelve less than twice the second number yields the first number.

Let x represent the first number and y represent the second number.

System:

x + (1/2)y = -5
2y - 12 = x

The system of equations that represents this situation is:
x + (1/2)y = -5
2y - 12 = x

Where x represents the first number and y represents the second number.

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Answer:

She earns $2,560

Step-by-step explanation:

She earns 2,560 because this is 8% of 32000. How do we know?
Multiply 32000 by 0.088, which is 8% of 100.

Answer:

1. around 4.86 or 4.9 for the nearest tenth

2. 17 months

Step-by-step explanation:

1. (1.7×10^6)/(3.5×10^5) = (1.7/3.5)×(10^6/10^5) = 0.4857×10 = 4.857

Therefore, 1.7×10^6 is about 4.857 times as great as 3.5×10^5.

2.  start by finding out how much Erica still owes after the down payment:

Total cost - Down payment = $1,867 - $320 = $1,547

divide the amount still owed by the monthly payment to find out how many months Erica will be paying:

$1,547 ÷ $91 per month = 17 months (rounded up)

Therefore, Erica will be paying for the bike for 17 months

The value of the scale factor is 3. And the value of the variables 'v' and 'w' will be 36 and 96, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The scale factor is given as,

SF = 162 / 54

SF = 3

Then the equation is given as,

v / (72 + v) = 1/3

Simplify the equation, then we have

3v = 72 + v

2v = 72

v = 36

Then the other equation is given as,

48 / (48 + w) = 1/3

144 = 48 + w

w = 96

The value of the scale factor is 3. And the value of the variables 'v' and 'w' will be 36 and 96, respectively.

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The correct answer is option d) \( 1+\tan x \), since \( \sec x=1+\tan x \).

The correct answer for the given expression \( \tan x \cdot \sin x+\cos x=? \) is option d) \( 1+\tan x \).

Step-by-step explanation:

We can start by using the identity \( \tan x = \frac{\sin x}{\cos x} \) to rewrite the expression:
\( \frac{\sin x}{\cos x} \cdot \sin x+\cos x=? \)

Next, we can simplify the expression by multiplying the numerator and denominator by \( \cos x \):
\( \frac{\sin^2 x+\cos^2 x}{\cos x}=? \)

Now, we can use the identity \( \sin^2 x+\cos^2 x=1 \) to further simplify the expression:
\( \frac{1}{\cos x}=? \)

Finally, we can use the identity \( \frac{1}{\cos x}=\sec x \) to rewrite the expression in terms of \( \sec x \):
\( \sec x=? \)

Therefore, the correct answer is option d) \( 1+\tan x \), since \( \sec x=1+\tan x \).

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By answering the above question, we may infer that Ling will thus require equation 42 feet of wallpaper border to install at the top of the three walls.

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.

Three walls, each 14 feet long and 12 feet tall, are being wallpapered by Ling. Just the top of the wall will be covered by the border. As a result, each wall requires a 14-foot-long wallpaper border.

The length of the border on each of the three walls must be added together to determine the overall length of wallpaper border required. So:

Whole wallpaper border length is one wall's border length times the number of walls.

Overall wallpaper border length is 14 feet multiplied by 3 walls.

42 feet is the total length of the wallpaper border.

Ling will thus require 42 feet of wallpaper border to install at the top of the three walls.

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The coordinates of the point that partitions the segment BA into a ratio of 3 to 2 is (-1, 0).

Directed line segments are line segments which has an initial point and the terminal point along with the direction.

Given a directed line segment BA.

The coordinates of A are (-5, -2) and the coordinates of B are (5, 3).

Let P be the required point which partitions the segment BA in to 3 : 2.

P would be at a 3/5 along the line from B to A.

Write the components of the segment using the end points.

Components = < (x₂ − x₁),(y₂ − y₁) >

                      = < (-5 - 5) , (-2 - 3) >

                      = < -10, -5 >

Components of BP = < 3/5 (-10, -5) >

                                = < -6, -3 >

Coordinates of P = Coordinates of initial point + component of BP.

                             = (5 + -6, 3 + -3)

                             = (-1, 0)

Hence the required coordinates is (-1, 0).

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No, the point (1,4) is not a solution of the set of linear inequalities y > 5x + 1 and y ≥ (1/2)x - 1 since the point does not satisfy both inequalities.

To determine if a point is a solution, we can substitute the x and y values of the point into the inequalities and see if they are true.

For the first inequality, y > 5x + 1:
4 > 5(1) + 1
4 > 6
This is not true, since 4 is not greater than 6. So the point (1,4) is not a solution for the first inequality.

For the second inequality, y ≥ (1/2)x - 1:
4 ≥ (1/2)(1) - 1
4 ≥ 0.5 - 1

4 ≥ -0.5

This is true, since 4 is greater than -0.5.

But since the point does not satisfy both inequalities, it is not a solution for the set of linear inequalities.

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For the given function f(x) = (x - 4)² - 3, the following statements are correct -

B: relative minimum at (4,-3).

C: decreasing interval from (-∞, 4).

E: increasing interval is (4, ∞).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the relative maximum and minimum of the function, we need to find its critical points by setting the derivative of the function equal to zero -

f(x) = (x - 4)² - 3

f'(x) = 2(x - 4)

2(x - 4) = 0

x = 4

So, the only critical point of the function is x = 4.

Plug in the value of x = 4 in the equation -

(4 - 4)² - 3

0 - 3

-3

Since f''(4) is positive, the critical point at x = 4 is a relative minimum.

Therefore, the function has a relative minimum at (4, -3).

To find the increasing and decreasing intervals, we can look at the sign of the first derivative -

f'(x) = 2(x - 4)

For x < 4, f'(x) is negative, meaning that f(x) is decreasing on the interval (-∞, 4).

For x > 4, f'(x) is positive, meaning that f(x) is increasing on the interval (4, ∞).

Therefore, the decreasing interval is (-∞, 4), and the increasing interval is (4, ∞).

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f(x)=3x+5

g(x)=1/(x-3)

Q1 The point-slope equation of the line passing through the points (5,10) and (-3,12) is y-10=2(x-5) and the slope-intercept equation of the same line is y=2x-9.
Q2 a) The equation of the line which passes through (8,0) and is parallel to the line with equation y=2x-6 is y=2x.
b) The equation of the line which passes through (12,3) and is perpendicular to the line with equation y=2x-6 is y=-1/2x+9.
c) The equation of the line which passes through the points (1,2) and (5,6) is y=2x-1.
Q3 a) (f+g)(x) = 3x+5 + 1/(x-3)
b) (f⋅g)(x) = 3x+5 * 1/(x-3)
c) (2f+3g)(x) = 6x+10 + 3/(x-3)
d) (3g-4)(x) = 3/(x-3) - 4
Q4 a) (f2g)(x) = (x2)2/(x+1)
b) (∘f min g)(x) = x/(x+1)
Q5 The domain of the function f(x)=3x+5 and g(x)=1/(x-3) is all real numbers except 3 and the range of both the functions is all real numbers.

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We have the following response after answering the given question: To interest the nearest penny, the balance in the account after 12 years is thus $17,821.76.

To calculate simple interest, divide the principal by the interest rate, the duration, and other variables. The marketing formula is simple return = capital + interest + hours. The easiest way to calculate interest is with this approach. The most popular method for calculating interest is as a percentage of the principal amount. For instance, if he borrows $100 from a friend and agrees to pay it back at 5% interest, he will only pay his portion of the 100% interest. $100 (0.05) = $5. Interest must be paid when you borrow money and must be added to any loans you make. The yearly percentage of the loan amount is frequently used to calculate interest. This percentage represents the loan's interest rate.

Continuously compounded interest is calculated as follows:

[tex]V = Pe^(rt) (rt)[/tex]

where: V = the investment's final value

P is the original investment's principle.

r equals the yearly interest rate (as a decimal)

t is the duration of the investment, in years.

P = $8290, r = 0.06 (6% as a decimal), and t = 12 years in this example.

So, [tex]V = 8290e^(0.06*12) = $17,821.76[/tex]

To the nearest penny, the balance in the account after 12 years is thus $17,821.76.

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By applying Two-Variable Linear Equation it can be concluded that the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.

Two-Variable Linear Equation is a form of relation equal to the algebraic form which has two variables and both are raised to the power of one.

We will use this concept to calculate the amount of each type of investment.

The total amount invested is $10,000, with some going to bonds and some going to certificates of deposit (CDs). According to the question, the amount invested in bonds is to exceed that in CDs by $3,000. We can write this as an equation:

$10,000 = x + y  , where:

x = the amount invested in bonds

y = the amount invested in CDs

We are also told that x = y + $3,000. We can substitute this into the first equation:

$10,000 = x + y

              = y + $3,000 + y

              = 2y + $3,000

         2y = $7,000

           y = $3,500

Now we can substitute this back into the equation for x:

x = y + $3,000

  = $3,500 + $3,000

  = $6,500

So the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.

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Fluff-ball can run at a speed of 4 meters per second.

Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit time, such as meters per second (m/s) or miles per hour (mph). Speed is a scalar quantity, meaning it has magnitude but no direction.

Fluff-ball can run at a speed of 4 meters per second.

This is because speed is equal to distance divided by time, and in this case the distance is 20 meters and the time is 5 seconds:

Speed = distance/time = 20 meters/5 seconds = 4 meters per second.

Therefore, Fluff-ball can run at a speed of 4 meters per second.

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Answer:

The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle. The area of the inner circle is pi multiplied by the square of the radius, or 3.14 * (125.6/2)^2, which equals 19644.8. The area of the outer circle is pi multiplied by the square of the radius, or 3.14 * (125.6)^2, which equals 49766.56. Subtracting the inner circle’s area from the outer circle's area, the area of the shaded region is 30121.76, rounded to the nearest hundredth

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 hour = 60 minutes, so ratio is

20:60 = 1:3

∴ n = 1

Answer:

See the attached worksheet.

Step-by-step explanation:

This assumes that the second "Beans" entry was supposed to be "Carrots, instead.

Note how the equations match the describtion in the paragraph.  The multiply the only portion of the equation not explained is the (3y+5) expression in both equations.  By process of elimination (marked), this must be the area of the garden.

Since we are not given an actual numeric value for the area, the only thing we can write in Part B is to duplicate the simplified equations from Part A.

Answer:

$211 if rounding to nearest whole number (this may be what looking for)

$211.20 if rounding to nearest tenth

Step-by-step explanation:

The answer depends on what precision of rounding is done so i am providing 2 answers

Rounding to the nearest whole number:
14,49 rounded = 14
68.64 rounded = 69
128.05 rounded = 128

$14.49 + $68.64 + $128.05 =  14 + 69 + 128

= $211

Rounding to the tenths:

14,49 rounded = 14.5

68.64 rounded = 68.6

128.05 rounded = 128.1

$14.49 + $68.64 + $128.05= 14.5 + 68.6 + 128.1 = $211.20

To restrict the domain of the function f so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. This means that for every value of x in the restricted domain, there is exactly one value of f(x).

Once we have restricted the domain, we can find the inverse function f-1 by switching the x and y values in the original function and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.

For example, consider the function f(x) = x^2. This function is not one-to-one because for every value of x, there are two values of f(x) (one positive and one negative). However, if we restrict the domain to x ≥ 0, the function becomes one-to-one and we can find the inverse function.

The restricted function is f(x) = x^2 for x ≥ 0. The inverse function is f-1(x) = √x for x ≥ 0. The domain of f is x ≥ 0 and the range is f(x) ≥ 0. The domain of f-1 is x ≥ 0 and the range is f-1(x) ≥ 0.

In general, to restrict the domain of a function so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. Once we have restricted the domain, we can find the inverse function by switching the x and y values and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.

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