Challenge. A large university accepts ​60% of the students who apply. Of the students the university​ accepts, ​50% actually enroll. If 10,000 students​ apply, how many actually​ enroll?

Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order.

We get,

a)  [tex]$\sum_{n=0}^{\infty}$[/tex]

Infinity

b)  [tex]$\sum_{n=1}^{\infty}\left(\frac{4}{2^n}\right)$[/tex]

[tex]\sum_{n=1}^{\infty} \frac{4}{2^n}[/tex]

[tex]& =4 \cdot \sum_{n=1}^{\infty} \frac{1}{2^n} \\[/tex]

[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]

[tex]& =4\left(\sum_{n=0}^{\infty} \frac{1}{2^n}-\frac{1}{2^0}\right)[/tex]

[tex]& \sum_{n=0}^{\infty} \frac{1}{2^n}=2 \\[/tex]

[tex]& =4\left(2-\frac{1}{2^0}\right)[/tex]

Then we get,

=4

c) [tex]$\sum_{n=1}^{\infty}\left(\frac{7}{10^n}\right)$[/tex]

[tex]$\sum_{n=1}^{\infty} \frac{7}{10^n}[/tex]

[tex]& =7 \cdot \sum_{n=1}^{\infty} \frac{1}{10^n} \\[/tex]

[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]

[tex]& =7\left(\sum_{n=0}^{\infty} \frac{1}{10^n}-\frac{1}{10^0}\right)[/tex]

[tex]& \sum_{n=0}^{\infty} \frac{1}{10^n}=\frac{10}{9} \\[/tex]

[tex]& =7\left(\frac{10}{9}-\frac{1}{10^0}\right)[/tex]

Simplify

[tex]$7\left(\frac{10}{9}-\frac{1}{10^0}\right): \quad \frac{7}{9}$[/tex]

= 7/9

Therefore,

a) infinity, b) =4, and c) = 7/9

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Answer:

2.83 cm

Step-by-step explanation:

The other leg is also 2cm

Pythagorean Theorem

  hypot ^2 = 2^2 + 2^2

  Hypot = sqrt 8 =~ 2.83 cm

Answer:

Step-by-step explanation:

an isosceles triangle where the two legs form a 90-degree angle is an isosceles right triangle. So, the hypotenuse of the triangle is 2√2

Answer:

Step-by-step explanation:

The value of x when y = 1000 is 8.59.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

y = 1.7952 x [tex]2.0657^x[/tex]

Substitute y = 1000

1000 = 1.7952 x [tex]2.0657^x[/tex]

10³ = 1.7952 x [tex]2.0657^x[/tex]

Taking logs on both sides.

log 10³ = log (1.7952 x [tex]2.0657^x[/tex])

3 log 10 = log 1.7952 + x log 2.0657

3 x 1 = 0.25 + 0.32x

3 = 0.25 + 0.32x

0.32x = 3 - 0.25

x = 2.75/0.32

x = 8.59

Thus,

The value of x is 8.59.

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Answer: -2, -7

Step-by-step explanation:

The equation is given by A = ∛ ( 375/345 ) and A = ( ∛375 ) / ( ∛ 345 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = (375/345) ^ 1/3   be equation (1)

On simplifying the equation , we get

The number raised to the power ( 1/3 ) means it is the cube root of the number ,

So , A = ∛ ( 375/345 )

Now , taking the cube root on both the numerator and denominator ,

A = ( ∛375 ) / ( ∛ 345 )

Hence , the value of A is  ( ∛375 ) / ( ∛ 345 )

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Answer:If you make ₱ 58,000 you will be taxed ₱ 4,711. That means that your net pay will be ₱ 53,289 per year, or ₱ 4,441 per month.

Answer:

1The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers.

2An asymptote is a line that a graph approaches but never touches. That line can be vertical, horizontal, or even slanted, and graphs can have multiple types of asymptotes.

3constant of variation (k) is a ratio that represents the relationship between the independent variable (x) and the dependent variable (y). It can be found by dividing y by x, if both of those variables have known values.

The dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.

An object's capacity is the amount of material it can hold inside, while an object's volume is the amount of space it takes up. Here, the cubic unit is used to measure either of the two.

Cubic units are used to measure volume. The quantity of cubes needed to completely fill any given figure, such as blocks in a box, is its volume.

As there is no  definite shape is given we can assume that the shape is cube.

Volume of cube = a³

given the volume 18000cm³

dimensions of the marble,

a × a × a = 18000

a³ = 18000

a = ∛18000

a = 10∛18

a = 26.21

Hence, the dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.

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So, the correct simplification for the expression (3x^3 y^4 z^4) (2x^3 y^4 z^2) is option d: 6x^6 y^8 z^6.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

The given equation is -

(3x^3 y^4 z^4) (2x^3 y^4 z^2)

On simplification -

=[3·2(x^3+3)(y^4+4)(z^4+2)]

=6x^6y^8z^6

Therefore, the value obtained is 6x^6y^8z^6.

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Answer:

Step-by-step explanation:

what 1\3 of a full rotation?

so

360° x 1/3 =

360° : 3 =

120°

The equation and diameter CD of the parabola are x=1/10 y^2and 2√110

In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:

a(x – h)2 + k

Where:(h, k) - The vertex of the parabola.

a - Least distance between the vertex and the focus of the parabola.

Please notice that p < 0 when the directrix is above the focus, otherwise p < 0. The vertex is the midpoint of line segment between the directrix and the focus.

Given;

Vertex is at origins (0,0) and latus rectum = 10 and the graph open right so a is positive and the equation is:

x=a (y-k)^2+h.

To write the equation we need to find a using the latus rectum equation.

We substitute the values.Then inverse place of a with 10

Latus rectum=|1/a|                

10=|1/a|                              

a=1/10

The equation:

x=a (y-k)^2+h                      

x=1/10(y-0)^2+0

x=1/10 y^2

-Assume the distance between C and the center is EC. If E is (11,0) and C is (11, y).

-EC=y

-The equation of the parabola is x=1/10 y^2

Now, Substitute the value of C coordinate, which

x=1/10 y^2                          

Substitute the value of C coordinate, which is (11, y).

11×10=1/(10×10) y^2    

√(y^2 )=√110                

y=EC=√110

Because the distance of EC = ED

CD=EC×2                                  

CD=√110×2

CD=2√110

Therefore, the equation of parabola and CD will be x=1/10 y^2 and 2√110

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The interval over which f(x) = x² - x - 1 has an average rate of change of zero is (1/2, 1/2) as it is the only point at which the average rate of change is zero.

An average rate of change of zero means that the function is not increasing or decreasing over the interval in question. To find the interval over which f(x) has an average rate of change of zero, we need to find the critical points of the function. A critical point is a point at which the function's derivative is equal to zero or is undefined.

The derivative of f(x) = x² - x - 1 is:

f'(x) = 2x - 1

Setting f'(x) = 0, we get:

2x - 1 = 0

Solving for x, we get:

x = 1/2

Since this is the only critical point of the function, it is the point where the function has an average rate of change of zero. To determine the interval, we need to check the sign of the function's derivative on either side of the critical point.

f''(x) = 2 > 0

So x = 1/2 is the minima of the function

f'(x) = 2(1/2) - 1 = 0, at x = 1/2

so f'(x) > 0 for x < 1/2 and f'(x) < 0 for x > 1/2

Therefore the interval over which f(x) has an average rate of change of zero is (1/2, 1/2) or {1/2}.

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The given sequence is 13, 19, 25, ...

What comprises an arithmetic series?

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

This sequence appears to be increasing by 6 each time, so it is an arithmetic sequence. The common difference is 6. The nth term of an arithmetic sequence is given by the formula:

an = a1 + (n-1)d

where a1 is the first term, d is the common difference and n is the position of the term in the sequence.

We can use this formula to find the 48th term of the sequence:

a48 = a1 + (48-1)d

a48 = 13 + (48-1)6

a48 = 13 + 47*6

a48 = 13 + 282

a48 = 295

So, the 48th term of the sequence is 295.

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Answer: 256

Step-by-step explanation:

Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.

Answer: 343

Step-by-step explanation:

7 to the 3rd power

⇒7³

⇒7 × 7 × 7

⇒343 ... answer

hope that helps...

Step-by-step explanation:

Two interior opposite angles of a triangle are equal to the exterior angel

[tex]60 + 60 = 2x - 80 \\ 120 = 2x - 80 \\ 2x = 120 + 80 \\ 2x = 200 \\ x = \frac{200}{2} \\ x = 100[/tex]

Residual is the difference between the expected and actual y values, so r I = y I y i. A negative residual indicates that the anticipated value is excessively high, whereas a positive residual indicates that the projected value was excessively low. The goal of a regression line is to reduce the total amount of residuals.

What is Mcq, or salvage value?

When an item reaches the end of its useful life, its salvage value—or potential market value—is estimated. It can also be described as the asset's book value after depreciation has been taken into account.

What does the depreciation formula's residual value mean?

The asset's final worth is its residual value. To obtain the entire amount, it is therefore deducted from the starting value. Consequently, we are given the depreciation figure. This sum is divided by the usable years of the asset using the straight-line depreciation technique.

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Answer: B, $16.26 per 6 yards

Step-by-step explanation:

$11.04/ 4 yd is $2.76 a yd

$16.26/ 6 yd is $2.71 a yd

$19.11/ 7 yd is $2.73 a yd

$13.85/ 5 yd is $2.77 a yd

The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.

A ray is a segment of a line with one endpoint and an endlessly extending end. Two rays can be linked at their starting points to create an angle, and their other ends can stretch indefinitely.

According to the question,

the proportion of an angle's measurement to the width of its sides.

Therefore, an angle's measure is constant regardless of how far it is from its vertex.

Due to the fact that adjacent angles are two angles with a shared vertex, and side, but not interior points.

Therefore,

The combination of two rays with the same terminal is called an angle.

The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.

Hence the measure of an angle is the same at all distances from its vertex.

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Answer:

Step-by-step explanation:

Answer:

For the first one, the answer would be:

2/3 * 3/8 = 6/24 because,  all you have to do is multiply straight across.

2 * 3 = 6 and 3 * 8 = 24

6/24 can be simplified to 1/4 because 6 with go into the denominator 4 times, so the simplified fraction will be 1/4.

(Im not so sure what to do about the second one, so I would need to see what the options look like)

For the third:

The answer would be 3/3, because:

2 * 3 = 6

5 * 3 = 15

And the result fraction is 6/15, which matches what the image shows!

Step-by-step explanation:

Hope it helps! =D

The percentage by which Ezra should multiply the dimension of the stage so that the dimensions of the image are 1/2 the size of the original blueprint is of:

50%.

The perimeter of the updated blueprint will be 50% of the perimeter of the original blueprint.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For this problem, we want for the dimensions of the updated stage to be half the dimensions of the original stage, hence the scale factor of the dilation is given as follows:

k = 1/2.

The percentage equivalent to a fraction of 1/2 is of 50%, and the perimeter of the updated stage will be 1/2 the perimeter of the original stage, as both the perimeter and the side lengths have the same unit.

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Method of factorization in method of substitution is a technique used to solve systems of linear equations. In this method, one of the equations is multiplied by a factor to make the coefficient of one of the variables the same. This allows the equations to be combined and solved for the remaining variables.

Method of factorization in method of substitution is a useful technique for solving systems of linear equations. It allows one to isolate a single variable and make use of substitution to solve the system. The first step is to multiply one of the equations by a factor to make the coefficient of one of the variables the same in both equations. This allows the equations to be combined and solved for the remaining variables. Once the values of the variables have been found, they can be substituted into the other equation to find the solution of the system. This technique is beneficial because it allows one to avoid tedious calculations that are often required when solving linear equations.

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It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.

Now, According to the question:

We know that:

What is triangle inequality rule?

The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the  third side. The Triangle is a polygon with three line segments as its boundaries.

Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.

We have the sides:

7, 10 and 20

7 + 10 > 20

It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.

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Answer:

$37.50

Step-by-step explanation:

[tex]P+Prt=39.75 \\ \\ P+P(2)(0.03)=39.75 \\ \\ 1.06P=39.75 \\ \\ P=\$37.50[/tex]

Steps To Convert From Base 10 to Base 2

The number system is a way of representing the quantity of a physical item.

For example, the number system that is widely used by humans is the decimal number system, which is a number system that uses 10 kinds of symbols. In everyday life, the number system that is widely used by humans is the decimal number system, which is a number system that uses 10 kinds of symbols. if it is associated with Computer Logic it is represented by two-state elements, namely off and on which is the concept used in the binary number system which only uses 2 kinds of values to represent value quantities.

In addition, the Number System uses a certain number of bases or bases (base / radix). There are 4 types of number systems that have to do with computers, which include:

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The solution of the given equation 3x²+ 5x +2= 0 is given by :

option c. x = -2 / 3 or x = -1.

As given in the question,

Given equation is equal to :

3x²+ 5x +2= 0

Solve the given equation by splitting the middle term of the quadratic equation we have,

3x²+ 5x +2= 0

⇒ 3x²+ 3x + 2x + 2 = 0

⇒ 3x ( x + 1 ) + 2 ( x + 1 ) = 0

⇒ ( 3x + 2 ) ( x + 1 ) = 0

⇒ ( 3x + 2 ) = 0 or ( x + 1 ) = 0

⇒ x = -2 / 3 or x = -1

From the given options :

option c. x = -2 / 3 or x = -1 is the solution.

Therefore, the solution of the given equation 3x²+ 5x +2= 0 is equal to :

option c. x = -2 / 3 or x = -1 .

The above question is incomplete, the complete question is:

Which of the following is a solution of the equation 3x²+ 5x +2= 0?

a. x = 2/3 or x = 1

b. x = -2/3 or x = 1

c. x = -2/3 or x = -1

d. x = 2/3 or x = -1

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Answer:5.3%

Step-by-step explanation:

we say 150/1 multiplied by 0.74/1=$111

then when we convert it back to pounds, we say 111/1 multiplied by 1.28/1 =142.08

150.00-142.08=7.92

7.92/150.00 multiplied by 100=5.28 to 1 decimal place is 5.3%

hope you understand

One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. Both sides of an equation will remain equal if we add the same amount to each side.

Addition:

Subtraction:

Multiplication:

Division:

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Mike's car will be worth £4116 at the start of 2017 as the car decreases in value by 30% every year

At the start of 2014, Mike's car is worth £12000,

we shall calculate the decreased worth of the same car to the start of 2017 as follows:

At the end of 2014, 30% of £12000 is calculated as;

£12000 × 30/100 = £3600

At the start of 2015, the car will be worth

£12000 - £3600 = £8400

At the end of 2015, 30% of £8400 is calculated as;

£8400 × 30/100 = £25200

At the start of 2016, the car will be worth

£8400 - £2520 = £5880

At the end of 2016, 30% of £5880 is calculated as;

£5880 × 30/100 = £1764

At the start of 2017, the car will be worth

£5880 - £1764 = £4116

Therefore, Mike's car will decrease in value to worth £4116 at the start of 2017.

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