4-58. Lisa plans to retire on her 61st birthday. On her
22nd birthday, Lisa will start saving SA per year for
40 years. Starting on her 62nd birthday, Lisa plans on
withdrawing $10,000 and will continue these annual
withdrawals until the account is exhausted on her 85th
birthday. If Lisa's bank account pays 3% per year, what
annual amount of SA will Lisa need to invest in her bank
account to achieve her retirement goal? (4.10)​

Answer:

Answer:

cot α = 1/tan α = 1/2.4 = 0.42

Step-by-step explanation:

cot α=0.42

sin α = 0.92

we know that cot α = 1/tan α

thus,

cot α = 1/tan α = 1/2.4 = 0.42

we know that

sin(x)=tan(x)1+tan2(x)√

\begin{gathered}\ sin(\alpha )=tan(\alpha )/\sqrt{ 1+tan^2(\alpha )} \\sin(\alpha )= 2.4/\sqrt{1+2.4^2} = 2.4/\sqrt{1+5.76}\\sin(\alpha )= 2.4/\sqrt{6.76} = 2.4/2.6 = 12/13 = 0.92\end{gathered}

sin(α)=tan(α)/

1+tan

2

(α)

sin(α)=2.4/

1+2.4

2

=2.4/

1+5.76

sin(α)=2.4/

6.76

=2.4/2.6=12/13=0.92

sin α = 0.92

Therefore , the solution to the given problem of expression comes out to be  -27 + 5i.

Multiplication, division, addition, and subtraction are all possible in math. The expression structure is as follows: Expression, calculator, and a number or variable Numbers, variables, and procedures (such as subtraction, multiplication, addition, or division, etc.) are all parts of a mathematical expression. You can compare two expressions or sentences.

Here,

Given : (2 + 5i)(−1 + 5i)

To find a + bi form

we get,

=>  (2 + 5i)(−1 + 5i)

=> -2 + 10i -5i +25i²

=> -27 + 5i

Thus ,-27 + 5i forms same expression as the a+bi form so, it is the solution for this problem.

Therefore , the solution to the given problem of expression comes out to be  -27 + 5i.

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Answer:

B. 18

Step-by-step explanation:

Given that f = 2.5,

8 + 4f

=8 + 4(2.5)

8 + 10 = 18

The number of meters that the truck could go given the energy provided by the students combined, would be 800, 000 meters

To find the distance the truck would go, first find the number of meters the truck would go with the energy your heart provides :

= 32 x 1, 000 meters per kilometer

= 32, 000 meters

There are 25 people in the math class so the distance the truck would go is:

= Number of students x Distance per person

= 25 x 32, 000

= 800, 000 meters

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300,000 km/s × Distance traval by light in one year

300,000 × 365days

300,000 × 365 × 24

300,000 × 365× 24 × 60

300,000 × 365× 24 × 60 × 60

9.46 × 10¹²

A point-to-point graph, also called a line graph

To establish if a graph reflects a function, use the vertical line test. If a vertical line is dragged across the graph and only touches the graph at one location at any time, the graph is a function. If the vertical line intersects the graph more than once, the graph is not a function.

A line graph, also known as a point-to-point graph, is a visual representation of data in which precise values of a function are represented as dots on a coordinate plane. Straight lines link adjacent pairs of dots.

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The domain of the function x - 3 + 5 is  x ∈ R(real number)

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

The function is

f(x) = x - 3 + 5 = x + 2

for all value of x ∈ real number the function is define

So , the domain of the function x - 3 + 5 is  x ∈ R(real number)

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Roscoe is faster.

Speed is a scalar quantity that refers to "how fast an object is moving."

Given that, Emmy and Roscoe both run every day. Yesterday Emmy ran 8 mile in 2 hours. Roscoe ran 6 ½ miles in 1 ½ hours.

Speed = distance / time

Emily's Speed = 8 / 2 = 4 mph

Roscoe's speed = 6 ½ / 1 ½ = 6.5 / 1.5 = 4.33 mph

Since, Roscoe's speed is greater than Emily's speed.

Hence, Roscoe is faster.

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Answer:

Question 2: No Solution

Question 4: (2,-3)

Step-by-step explanation:

Question 2: {x-y=7} {x-y=-4}

Question 4: {5x+2y=4} {9x+2y=12}

There is two ways of solving this;

Elimination method and Substitution method.

I will be using the Substitution method for Question 2 and Elimination method for Question 4.

Substitution method is basically substituting in the equation like this;

Question 2:

x - y = 7 and x - y = -4

x - y = 7 into x = 7 + y

Substitute:

7 + y - y = - 4

7 = - 4

7 ≠ - 4

Therefore, there no solution to this equations.

Question 2: No Solution

Question 4:

Elimination Method is basically eliminates one of the variables, so we can solve a more simplified equation.

5x + 2y = 4 and 9x + 2y =12

5x + 2y = 4

-(9x + 2y = 12) - Multiply this equation by -1.

Now we have;

5x + 2y = 4

-9x -2y = -12

-4x = -8

x = 2

We can substitute x  to find y.

5(2) + 2y = 4

10 + 2y = 4

2y = -6    

y = -3

(2,-3)

Question 4 Solution: (2,-3)

RevyBreeze

Answer:

B) 8x + 350 ≥ 800

Step-by-step explanation:

A dance squad needs at least $800, this means the inequality sign will be greater than or equal to.

They already have $350, and each ticket is $8.

So,

8x + 350 ≥ 800

The left page number is 180 and the right page number is 181.

What is consecutive integers?

Consecutive integers or consecutive numbers are the terms used to describe the sequence of numbers. In this case, the integers are arranged in ascending order from smallest to highest. The following are a few examples: -4, -3, 2, 1, 0, 1, 2, 3, 4.

Given:

The left and right page numbers of an open book are two consecutive interfere whos sum is 361.

We have to find the page numbers.

Let

The left page number is n.

The right page number is n + 1.

As the sum of numbers is 361.

⇒ n + (n + 1) = 361

         2n + 1 = 361

              2n = 360

                n = 180

Hence, the left page number is 180 and the right page number is 181.

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Answer: 144 economy seats and 16 first class seats

Step-by-step explanation:

1 : 9 first class seats to economy seats

1 : 9 x 16 = 16 : 144

160x9=1440

Step-by-step explanation:

your welcome no explanation just get the answer

Answer:

a.y=-1/2×X + 4 is the req eqn for st.line.

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The correct value for z that makes the algebraic expression true is equal to 12

In mathematics, an algebraic expression is an expression which is made up of variables and constants, along with algebraic basic operations such as addition, subtraction, multiplication and division.

we first open the bracket

10 + z - 4 = 18

z + 10 - 4 = 18

z + 6 = 18

subtract 6 from both sides of the equation

z + 6 - 6 = 18 - 6

z = 12

Therefore, 12 is the value of z that makes the algebraic expression true.

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The final solution is -sin(1).

To evaluate the iterated integral, we need to integrate with respect to the outer variable first, then integrate with respect to the inner variable.

The given iterated integral is:

[tex]∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds[/tex]

To evaluate this, we need to integrate with respect to t first, and then integrate with respect to s.

[tex]∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds = ∫(1 to 0) [∫(s^4 to 0) cos(s^5) dt] ds= ∫(1 to 0) (-1/s^5 * sin(s^5)) \\ds= [-1/s^5 * sin(s^5)] \\evaluated at s = 1,0= (-1/1^5 * sin(1^5)) - (-1/0^5 * sin(0^5))= (-1/1 * sin(1)) - (0)= -sin(1)[/tex]

So the final solution is -sin(1)

Note that the integral is not defined for s=0, [tex]s^5=0[/tex] , as the function is not defined there.

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On solving the provided question, we can say that By addition we have the following data , Total y Stockholder's Equity is = $367,000.00 and $367,000.00 and $367,000.00      

The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers.

By addition we have the following data ,

Total y Stockholder's Equity is = $367,000.00 and $367,000.00 and $367,000.00      

                                                 Case 1                             Case 2                          

                     Before stock             After 100%                     After Stock

                    transactions         stock dividend                   Split          

Nos of             105000                210000                      210000

shares

outstanding

Par per share      $1.00                              $1.00                   $0.50

Common Stock    $105,000.00              $210,000.00      $105,000.00

Account

Additional Paid  $91,000.00            $91,000.00            $91,000.00

in capital

Retained Earnings $171,000.00             $66,000.0         $171,000.00

Total y                    $367,000.00 $367,000.00         $367,000.00

Stockholder's Equity

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The probability that all 4 computers with the critical file fail in this incident is given as follows:

0.0046 = 0.46%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of these parameters for this problem are given as follows:

N = 30, k = 4, n = 9.

The probability that all fail is P(X = 4), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,30,9,4) = \frac{C_{4,4}C_{26,5}}{C_{30,9}} = 0.0046[/tex]

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The length of the guy wire is equal to 48 ft.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: Distance of stake to the pole=14 feet and Distance from the pole to the tower as =25 ft. And height of the pole=10 feet.

Now let the angle that the guy wire makes with the stake is θ

Then we have Tanθ= 10/14

                                 =5/7

Again we also have Tan θ= height of the tower /base of the tower

Thus h/39=5/7 ( where h is the height of the tower).

    or, h=27.85

 Therefore using pythagoraes theorem we get the length of the wire as

=[tex]\sqrt{27.85^2+39^2}[/tex]

=47.92 feet or 48 ft. (Approx)

Hence, The length of the guy wire is equal to 48 ft.

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The equation of the perpendicular line is y = -5

We have to recall that the general form of the equation of a line can be given by the expression that is written as y = mx + c. m is the slope of the graph while c is the intercept of the graph.

We would then have;

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

We can see that m = 0 from the first line that has been given the we have;

y - (-5) = 0(x - 4)

y + 5 = 0

y = -5

This is the equation that has been required in the problem above.

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Answer:

2x² + 7x + 2

Step-by-step explanation:

f(x) = 3x² + 5

g(x) = 4x - 2

h(x) = x² - 3x + 1

f(x) + g(x) — h(x) =

(3x² + 5) + (4x - 2) - (x² - 3x + 1) = ==> plugin the values of f(x), g(x), and h(x)

3x² + 5 + 4x - 2 - (x² - 3x + 1) =

3x² + 5 + 4x - 2 - x² + 3x - 1 =  ==> distribute the negative sign to x², -3x, 1

                                                     x² ==> -x², -3x ==> 3x, 1 ==> -1

3x² - x² + 4x + 3x + 5 - 2 - 1 =  ==> combine like terms

2x² + 7x + 2 = ==> simplify

The completed statement would be

12ft/sec = 7.2 yd/min.

What is the unit conversion?

Unit conversion is the process of changing a measurement from one unit to another, while maintaining the same numerical value. It is used to convert measurements from one system of units to another, such as from metric units to imperial units, or from feet to meters.

To convert feet per second to yards per minute, we need to multiply the value in feet per second by the conversion factor of 1 yard/3 feet and then divide the result by the conversion factor of 1 minute/60 seconds.

12 ft/sec = (12 ft/sec) * (1 yard/3 feet) * (1 min/60 sec) = (12*1/3) * (1/60) = 4/5 = 0.8.

So, 12 ft/sec is equal to 0.8 yards per minute. Rounded to the nearest hundredth, this is 7.2 yards per minute

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While calculating the measurements given.The correct answer is 384 ft.

Given,

Inches when drawing =1/4

Actual feet according to the drawing =12 ft

To calculate the The mesurement of 8 inch

8 ÷ 1/4 = 8/1 x 4/1 = 32

32 x 12 = 384

Sometimes we find the value in feet and inches rather than converting the amount to decimals. For instance, 71 inches is equivalent to 5 feet, 11 inches. It's because we get 5 as the quotient and 11 as the remainder when we divide 71 by 12. The residual value will be expressed as the number of inches it is. This is known as converting inches to feet and feet to inches. Let's examine a few of the instances below.

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It would depend on how accurate the calculation was in this scenario.

In general, it is preferable to round each step to the correct number of significant figures, but in some circumstances, carrying one or two insignificant figures can assist prevent round-off errors.

All zeros that are to the right of the decimal point but to the left of a non-zero number in a decimal number that ranges between 0 and 1 are not significant.

If there are zeros in a whole number to the right of a non-zero digit but to the left of a recognised decimal point, the situation becomes questionable.

All of the last zeros of a decimal number are significant when it is rounded off to a specific number of decimal places.

Complete Question:

It is sometimes suggested that one or two extra decimal places be carried along in each step when rounding values to the proper number of significant figures.

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It would depend on how accurate the calculation was in this scenario.

In general, rounding each step to the right number of significant numbers is ideal, but in rare cases, carrying one or two insignificant digits can help prevent round-off mistakes.

All zeros to the right of the decimal point but to the left of a non-zero integer in a decimal number between 0 and 1 are ignored.

The issue becomes dubious if there are zeros in a whole integer to the right of a non-zero digit but to the left of a recognised decimal point.

When a decimal value is rounded to a specified number of decimal places, all of the final zeros are important.

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To find the coordinates of the point that partitions the directed line segment from ( − 5 , 4 ) to ( 1 , 8 ) into a ratio of 3 to 1, we can use the following formula:

(x,y) = (1- t) * (x1, y1) + t * (x2, y2)

Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the directed line segment, t is a value between 0 and 1 that represents the ratio of the partition, and (x, y) are the coordinates of the point that partitions the segment.

In this case, we want the ratio of the partition to be 3 to 1, so t = 3 / (3 + 1) = 3/4

So we can substitute the values into the formula:

(x,y) = (1- 3/4) * (-5, 4) + (3/4) * (1, 8)

(x,y) = (-5/4, 4/4) + (3/4, 6/4)

(x,y) = (-5/4+3/4, 4/4+6/4)

(x,y) = (-2/4, 10/4)

(x,y) = (-0.5, 2.5)

So the point that partitions the directed line segment from ( − 5 , 4 ) to ( 1 , 8 ) into a ratio of 3 to 1 has coordinates (-0.5, 2.5)

Part a: Area of habitat - Area of field = Area of mowed portion.

Part b: Area of mowed portion: 4x(b - x)

For the stated question:

Part a:

The complete area is given as: Area of habitat.

The area kept for birds: Area of mowed portion

Central unmowed portion: area of field

Thus,

Area of habitat - Area of field = Area of mowed portion

Part b: Area of mowed portion: 4x(b - x)

Proof:

b² - (b - 2x)² = [b - (b - 2x)] [b + (b - 2x)]

                    =  [b - b + 2x] [b + b - 2x]

                    = (2x)(2b - 2x)

                    = 4x(b - x)

Thus, the Area of mowed portion: 4x(b - x).

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Answer: 22[tex]\sqrt{5}[/tex]

Step-by-step explanation:

[tex]5\sqrt{5)[/tex] X 2 =10[tex]\sqrt{5}[/tex]

3[tex]\sqrt{20\\[/tex] X 2= 12[tex]\sqrt{5}[/tex]

10[tex]\sqrt{5}[/tex] + 12[tex]\sqrt{5}[/tex] = 22[tex]\sqrt{5\\[/tex]

Therefore  , solution of ratio problem is 5760 m & 5.76 km, respectively, are the distances covered per hour for the two halves.

As a/b, a ratio shows the  variable relationship between two numbers. When two ratios are equal, as when a/b = c/d, we get a proportion. Mathematical issues involving the unit numbers of the quantities can be resolved using ratio and proportion.

Here,

The ratio approach can be used to solve the above problem as follows:

(A) A 1.6 m/s walking speed is typical.

The calculation for the speed in meters per hour is

1/3600 of an hour is equal to one second.

Take the following 1.6:3600 ratio as an example:

1.6 ÷ 1/3600

= 3600 × 1.6

= 5760

The typical walking speed is 1.6 m/s.

It implies a speed of 1.6 meters per second.

Now, 1 m equals 1/1000 km.

=> 1.6 m = 1.6/1000 km

Moreover, one second is equal to three thousand six hundredths of an hour.

As a result, the distance traveled in kilometers per hour can be calculated by using the following ratio:

1.6/1000 ÷ 1/3600

= (3600 × 1.6)/1000

= 5.76

Therefore, 5760 m and 5.76 km, respectively, are the distances covered per hour in meters and kilometers.

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After using Pythagorean theorem the rectangular floor is 4m long.

What is Pythagorean theorem ?

 A right angled triangle's missing length can be discovered using Pythagoras' Theorem.

The triangle has three sides: the adjacent, which doesn't touch the hypotenuse, the opposite, which is always the longest, and the hypotenuse (which is between the opposite and the hypotenuse).

Here in the given rectangular floor,

Width = 3m and Altitude which is hypotenuse = 5 m.

Now using Pythagorean theorem,

=> [tex]length^2+width^2=hypotenuse^2[/tex]

=> [tex]length^2+3^2=5^2[/tex]

=> [tex]length^2=5^2-3^2[/tex]

=> [tex]length^2=25-9=16=4^2[/tex]

=> length = 4m

Hence the rectangular storage unit is 4m long.

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Answer: Y = x −3

Step-by-step explanation: If the inequality just has a > or < sign the line will be a broken or dotted line and its points are not included in the solution. In this case the equation of the boundary line is y = x −3 This line has a slope of 1 and a y-intercept = -3.

The answer is D. y = 3. That is because the sign shown in the question means greater than or equal to 3, meaning it can't get any greater than three, but it can equal it.