find the sum of the series. [infinity] (−1)n2n 32n(2n)! n = 0

Bianca will earn interest of $382.5 for a period of 3years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same.

Simple interest is calculated with the following formula:

S.I. = P × R × T,

where P = Principal, R = Rate of Interest in % per annum, and T = Time

Given,

Principal P = $3000

Rate of interest R = 4.25% = 4.25/100 = 0.0425

Time T = 3 years

Simple interest S.I. = P × R × T

                               = 3000 × 0.0425 × 3

                               = 127.5 × 3

                       S.I.   = $382.5

Hence, Interest Bianca will earn in 3 years = $382.5

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An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = [tex]a^x[/tex]

Where a>0 and a is not equal to 1.

x is any real number.

If the variable is negative, the function is undefined for -1 < x < 1.

Here,

“x” is a variable

“a” is a constant, which is the base of the function.

The examples of exponential functions are:

f(x) = [tex]2^x[/tex]

f(x) = 1/ [tex]2^x[/tex] = [tex]2^-x[/tex]

f(x) =[tex]2^(x+3)[/tex]

f(x) = [tex]0.5^x[/tex]

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Answer:

x = 11

Step-by-step explanation:

We'll have to get X alone by doing the opposite of what the current equation is showing

67 = 7x-10. I usually turn the numbers around cause it looks better...

7x-10 = 67

We see it's subtracting 10, so we'll add 10 on both sides

7x = 67 + 10

7x = 77

Since 7x is being multiplied, we'll divide on both sides

x = 77/7

x = 11

Answer: -11

Step-by-step explanation:

rearrange it so it's -7x-10=67

add 10 to itself and 67

then you get -7x=77

then divide 77 by -7

and you get -11

i hope this was right :)

The difference's mathematical equivalent is minus (-). In the subtraction statement, minuend is the initial digit.

Mathematical difference is the outcome of one of the key operations, which is the subtraction of two numbers. It reveals the degree to which one number deviates from the other.

In math, the goal of calculating the difference is to determine how many numbers are present between the two supplied numbers. The difference's mathematical equivalent is minus (-).

In the subtraction statement, minuend is the initial digit. The second number in the subtraction sentence is called subtract, and the outcome is the difference between the two integers.

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Option b is correct monthly payment = $163.07

A loan of $7,500 with an 11% interest rate compounded monthly over a time period of 5 years.

Monthly Payment = Amount / Discount factor

Discount factor [tex]D = \frac{1-(1+i)^{n} }{i}[/tex]

where,

Amount = $7500

Rate= 11%=0.11

[tex]i = \frac{0.11}{12} = 0.0091[/tex] ( by using division)

Time = 5 years

Time (n) = 5 × 12 = 60

Now, put i and n in the Discount factor,

[tex]D = \frac{1-(1+i)^{n} }{i}[/tex]

[tex]D = \frac{1-(1+0.009)^{-60} }{0.009}[/tex]

[tex]D = \frac{1-(1.009)^{-60} }{0.009}[/tex]

[tex]D = \frac{0.421 }{0.009}[/tex]

D = 46.77

Monthly payment (M),

[tex]M = \frac{Amount}{Discout factor} = \frac{A}{D}[/tex]

[tex]M = \frac{7500}{46.77}[/tex] ( by using division)

Monthly payment = 163.07

Therefore, Option b is the correct monthly payment = $163.07.

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Answer:

656

Step-by-step explanation:

Answer:

the answer to your question is 3.

The solution of the given system of equation x + y = 5 , 3x + 5y = 15 represents it has one solution given by intersecting lines at point

(x, y ) = ( 5, 0).

As given in the question,

Given system of equation is :

x + y = 5 __(1)

3x + 5y = 15 ___(2)

The standard rule to get the solution of the system of equation is given by :

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂= 0

One solution  :

a₁ / a₂ ≠ b₁ / b₂

No solution :

a₁ / a₂ = b₁ / b₂ ≠ c₁/c₂

Infinitely many solution :

a₁ / a₂ = b₁ / b₂ = c₁/c₂

Here in the given system of equation:

1/3 ≠ 1/5

One solution exist.

Solve by elimination method.

Multiply (1) by 3 and subtract from (2) we get,

3x + 5y = 15

3x + 3y = 15

      2y = 0

⇒y =0

Substitute y =0 in (1) we get,

x = 5

It represents both the lines intersect at point ( x, y) = ( 5,0)

Therefore , the given system of equation has one solution equal to

intersecting point ( x, y) = ( 5,0).

The above question is incomplete , the complete question is :

Determine whether the system of equation has no solution, one solution, or infinitely many solution. If the system of equation has one solution, name it.

x + y = 5

3x + 5y = 15

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f(x)=mx+b. The function's value is f(x). The line's slope is m. When x is equal to 0, the function's value is equal to b.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function.  Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

iven

f(x)=mx+b. The function's value is f(x). The line's slope is m.

When x is equal to 0, the function's value is equal to b, which is also the coordinate at where the line in the coordinate plane crosses the y-axis.

The x-value coordinate's is given by x.

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Assumption 1: [tex]\triangle ABE \sim \triangle ACD/tex]

[tex]\frac{x}{10}=\frac{3}{15} \implies x=2[/tex]

Assumption 2: [tex]\triangle ABE \sim \triangle ADC[/tex]

[tex]\frac{x}{15}=\frac{3}{10} \implies x=4.5[/tex]

How many crickets did Greta feed Lizzy?

Answer:

56

Step-by-step explanation:

For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Since Gretta fed Draco 77 crickets just do:

77 ÷ 11

= 7

Then:

8 x 7

= 56

You're welcome

The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

The cost of adult ticket be x and child ticket be y respectively.

Now as per sum ,

(i) 5x + 13y = 59 and,

(ii) 5x + 9y = 47

Subtracting equation (ii) from (i) we get,

13y - 9y = 59 - 47

⇒ 4y = 12

⇒ y = 3

putting y = 3 in equation (ii) we get

5x + 9*3 = 47      ⇒ x = 20/5 = 4

The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.

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Answer: 7 and 1/2

Step-by-step explanation:

When dividing a fraction by a whole number you could turn the whole number into a fraction:

5 = 5/1

Once you turn the whole number into a fraction you then do the keep, change, flip, method

you would keep 5/1 as it is and change the divide sign to the multiplication sign the flip 2/3 to 3/2:

5/1 x 3/2

then you just multiply across

5/1 x 3/2 = 15/2

and 15/2 could be simplified to 7 and 1/2

15/12 is the right representation of  5 divided by 2/3 as a fraction.

To divide a number by a fraction, you can multiply the number by the reciprocal of the fraction. In this case, to divide 5 by 2/3, you can multiply 5 by the reciprocal of 2/3.

Reciprocal of 2/3 = 3/2

So, 5 divided by 2/3 can be written as:

5 * (3/2)

To simplify this, you multiply the numerators together and the denominators together:

(5 * 3) / (2 * 1) = 15/2

Therefore, 5 divided by 2/3 is equal to 15/2 as a fraction.

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Answer:

The mass of Jupiter is about 11.8 times the mass of Venus.

Step-by-step explanation:

When the length, breadth, and height are provided as 8 inches, 7.5 inches, and 6 inches, respectively, the rectangular prism's total surface area is 360 inches2.

Surface area is a measure of how much space an object's surface takes up overall. The total area of a three-dimensional shape's surroundings is its surface area. Surface area refers to the total surface area of a three-dimensional shape. You may compute the surface area of a cuboid with six rectangular faces by adding together their individual areas. Alternatively, you can use the following formula to name the box's dimensions: Surface (SA) = 2lh plus 2lw plus 2hw. A three-dimensional shape's surface area is calculated as the total amount of space it occupies (a three-dimensional shape is a shape that has height, width, and depth).

given

rectangle prism has a length of 8 inches and a width of 7.5 inches.

6 inches is the rectangular prism's height.

SA equals two square units of (lh + wh + lw).

A=360 inches2

When the length, breadth, and height are provided as 8 inches, 7.5 inches, and 6 inches, respectively, the rectangular prism's total surface area is 360 inches2.

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Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.

A relationship that explains how two variables relate to one another is represented by the word "functions," which is frequently used in mathematics. There are three: a variable, which can be any type of input, and predictor variables, which are the results of the function or equation.

Here,

A quadratic function's "width" can be calculated using the coefficient before the variable.

The graph will be narrower than the parent graph if the coefficient is more than one (f(x)=x2), and

wider if the coefficient is less than one. Thus, from widest to narrowest:

f(x)=0.5x²

f(x)=3x²

f(x)=-5x²

Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.

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Answer: A vertical line has an undefined slope, so we cannot use the slope-intercept form (y = mx + b) to write the equation of the line. Instead, we can use the point-slope form (y - y1 = m(x - x1)) where the slope m is undefined and we have a point (x1,y1) on the line.

Since the line goes through the point (8,4), we can use the point (8,4) in the point-slope form:

y - 4 = undefined(x - 8)

We can simplify this equation by dropping the undefined slope and replacing it with a variable:

y = kx + b

Where k is the slope and b is the y-intercept.

The equation of the vertical line that goes through the point (8,4) is x = 8

It's worth noting that the x-coordinate of a vertical line doesn't change, thus it's equal to a constant value and the equation for a vertical line is of the form x=k where k is a constant.

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

The equation of a vertical line is in the form:

x = anumber

You were given the point (8,4) which is in the form (x,y). So x is 8 and y is 4.

x is 8

x = 8

In the lens maker's formula, R1 and R2 represent the radii of curvature

The lens maker's method specifies the association among the focal length, refractive index, and curvature radii of a lens's two surfaces. It's a method that lens makers employ to make lenses with a particular power out of the glass with a particular refractive index.

R1 and R2 in the lens manufacturer's formula stand for the radii of curvature of the two surfaces of a lens. R1 and R2 are the radiuses of the surfaces that face the item being imaged and the surface that faces the image, respectively. A lens's focal length is calculated using a formula based on the lens's surface curvature and the material's refractive index.

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Answer: graph a and d

Step-by-step explanation:

Answer:

55°

Step-by-step explanation:

so the total should be 360, so if 2 angles are 125 (360-250=110) then the leftover 110 has to be split into 2 angles, which is 55

A triangle with two equal side lengths is known as an isosceles triangle. The angle of an isosceles triangle is 70 degrees.

A triangle is a three-sided geometry shape with 3 vertices. The internal angle of the triangle, which is 180 degrees, is built. It means that a triangle's internal angles sum to 180 degrees.

A triangle with two equal side lengths is known as an isosceles triangle. The vertex angle is the leftover angle that results from subtracting the two specified angles from 180 degrees. The two angles between it base and equal sides are identical in magnitude.

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The probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.

1. There are a total of 15 SweetTarts in the bag (4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTarts).

2. The probability of drawing a yellow SweetTart first is 2/15.

3. The probability of drawing a yellow SweetTart second is 1/14 (since one yellow SweetTart has already been drawn).

4. The probability of drawing a yellow SweetTart third is 2/13 (since two yellow SweetTarts have already been drawn).

5. The overall probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.

The probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.

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It is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm because the sum of two sides(2.5 cm and 4.5 cm) are smaller than three sides(8 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 2.5 and 4.5

2.5 + 4.5 < 8

7 < 8

Now we add 2.5 and 8

2.5 + 8 > 4.5

10.5 > 4.5

Now we add 4.5 and 8

4.5 + 8 > 2.5

12.5 > 2.5

It is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm because the sum of two sides(2.5 cm and 4.5 cm) are smaller than three sides(8 cm).

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Answer:

x = 3.25

Step-by-step explanation:

Answer:

Just subtract the answer to what your adding:

7.50 - 4.25 = 3.25

Step-by-step explanation:

Hope it helps! =D

The required amount of sweets Steve will get is 42.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,
Ali and Steve share some sweets in a ratio of 2:7 Steve gets 30 more sweets than Ali.

Let the amount of sweet Ali and steve be x and y,
According to the question,
x / y = 2/7

x = 2y/7 - - - - (1)

And

y = 30 + x

From equation 1
y = 30 + 2y / 7
5y = 30 × 7
y = 42

Now,
x = 2 × 42 /7
x = 12

Thus, the required amount of sweets Steve will get is 42.

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To solve the problem, we must first find the slope of the line containing (4, -2) and (x, -6). The slope of a line is calculated as the change in y-coordinates divided by the change in x-coordinates, or (y2 - y1) / (x2 - x1). In this case, the slope of the line containing (4, -2) and (x, -6) is (-6 - (-2)) / (x - 4) = -4 / (x - 4)

Since the line containing (4, -2) and (x,-6) is perpendicular to the line containing (-2,-9) and (3,-4), we know that the product of the slopes of these two lines is -1. We can use that information to find the slope of the second line: -1 = (-4 / (x - 4)) * m, where m is the slope of the second line. Solving for m, we get m = -1 / (-4 / (x - 4)) = (x - 4) / 4.

We can now use the point-slope form of a linear equation to find the equation of the line containing (-2,-9) and (3,-4). The point-slope form is y - y1 = m(x - x1). In this case, we can use (-2,-9) as (x1, y1) and (x - 4) / 4 as m:

y - (-9) = (x - 4) / 4 * (x + 2)

Simplifying we get y = (x-4)/4 + (-9) = (x-4)/4 - 9

Now we can substitute x = -2 and y = -9 to check if it belongs to this line:

-9 = (-2 - 4)/4 - 9

-9 = -2/4 - 9

-9 = -0.5 - 9

-9 = -9.5

It match so this line is the correct one.

The value of x that satisfies the given conditions is x = -2

You can graph this line on a separate sheet of paper by plotting the point (-2, -9) and using the slope (x-4)/4 to find additional points on the line.

The perimeter of the rectangle, given that the rectangle has an area of 40 ft² and a length of 8 ft is 26 ft

We'll begin by obtaining the width of the rectangle. The width of the rectangle can be obtained as follow:

Area = Length × Width

40 = 8 × Width

Divide both sides by 8

Width = 40 / 8

Width = 5 ft

Finally, we shall determine the perimeter of the rectangle. Details below:

Perimeter = 2(Lenght + Width)

Perimeter = 2(8 + 5)

Perimeter = 2(13)

Perimeter = 26 ft

Thus, we can conclude that the perimeter is 26 ft

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He must work for 10 hours a day to complete the job in 10 days. 10 hours per day is the optimal amount of time to finish the job in 10 days

1. Begin by setting up an equation. Let x be the number of hours worked.

2. 8 hours x 12 days = 96 hours

3. We want to finish the job in 10 days, so 10x = 96

4. Solve for x. 10x = 96, x = 9.6

5. Since we can't work partial hours, round up to 10 hours. Therefore, the man must work 10 hours a day to complete the job in 10 days.

To finish the job in 10 days, the man must work for a total of 100 hours. This means he must work for 10 hours a day to complete the job in the allotted time. Working 8 hours a day would take 12 days, and working 9 hours a day would take 11.11 days. Therefore, 10 hours per day is the optimal amount of time to finish the job in 10 days.

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The angle m∠7 corresponds to angle m∠3 which is vertically opposite the angle m∠1, and so the measure of the angle m∠7 = 118°

angles m∠1 and m∠3 are vertically opposite angles and are said to be equal so;

m∠1 = m∠3 = 6x - 20

angles m∠3 and m∠7 are corresponding angles and are said to be equal so;

m∠3 = m∠7 = 6x - 20

angles m∠7 and m∠8 lie on a straight line so;

6x - 20 + 4x - 30 = 180°

10x - 50° = 180°

10x = 180° + 50° {collect like terms}

10x = 230°

x = 230°/10 {divide through by 10}

x = 23

Therefore since the value of x is 23, then the measure of the angle m∠7 = 6(23) - 20, which result to 118°

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