Betsy, a recent​ retiree, requires ​$6,000 per year in extra income. She has ​$50,000 to invest and can invest in​ B-rated bonds paying 13​% per year or in a certificate of deposit​ (CD) paying 3​% per year. How much money should be invested in each to realize exactly ​$6,000 in interest per​ year?

The rectangular form of the polar expression \(12(cos\pi+ isin\pi)\) is -12

The given equation is:

\(12(cos\pi+ isin\pi)\)

The above equation is in polar form

Note that:

\(cos \pi = -1\\\\sin\pi = 0\)

Substituting \(cos \pi = -1\) and \(sin \pi = 0\) into the expression \(12(cos\pi+ isin\pi)\) in order to get the rectangular form of the expression

\(12(cos\pi+ isin\pi)\)

=  12(-1   +   1(0))

=  12 ( -1  +  0)

=  12(-1)

=  -12

Therefore, the rectangular form of the polar expression \(12(cos\pi+ isin\pi)\) is -12

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Answer:

FGCG

Step-by-step explanation:

Answer:   72 dollars

Step-by-step explanation:

each=1

1 record cost 9$

8 record costs (9)(8)$

I did multiplication here

(9)(8)=72 $

Answer:

0.25

Step-by-step explanation:

there is no hundredth in 0.25

Rounding 0.25 to the nearest hundredth gives us 0.26.

We must look at the digit in the thousandth place, which is the following decimal place after the hundredth place, in order to round 0.25 to the closest hundredth.

We round up the digit in the hundredth place by adding 1 since the digit in the thousandth place is 5, which is equal to or larger than 5.

Thus, 0.26 is obtained by rounding 0.25 to the next tenth.

0.25 (initial number) worked

(Number in the thousandth place) (Number in the hundredth position)

We round up the digit in the hundredth place since the digit in the thousandth place is 5, which is 5.

Hence rounding to the nearest hundredth, 0.25 equals 0.26.

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Answer:

(10x−7)^2

Step-by-step explanation:

(10x+7)(10x-7)

i stead of making it a "100" since they are both the same  but positive and negative () and bring it to the power of 2

1a) An equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper is; y = ¹/₂ + ¹/₄x

1b) Ledger paper has a thickness of 2/5 in. per `100` pages, the equation is; y = ¹/₂ + ²/₅x

2) The equation will be; y = ²/₃ +¹/₄x

1) We are told that the front cover and the back cover have a thickness of 1/4 inches and they also have a thickness of 1/4 inch. Thus;

The addition of both gives to the book thickness of;

1/4 + 1/4 = 1/2 inch, despite how many pages the book  has.

We are told that for every hundred pages, a thickness of 1/4 inch is added to the book, then the equation is:

y = ¹/₂ + ¹/₄x

where;

y is the width of the book in inches.

x is every hundred pages printed on bond paper.

1b) If ledger paper has a thickness of 2/5 in. per 100 pages, then the equation is now;

y = ¹/₂ + ²/₅x

2) If both front and back covers now, have a thickness of 1/3 inches instead of 1/4 inches each, then the equation will be;

y = 2(1/3) +¹/₄x

y = ²/₃ +¹/₄x

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Answer:

well you could do 26 groups of 6 people

Step-by-step explanation:

Answer:6

18 as a product of its prime factors is 2*3*3 while 60 is 2*2*3*5 therefore considering common factors between both numbers we can see that there's one pair of two visible in both products and one pair of three we multiply both of these common values to get the final gcf which is 3*2=6

Answer:

Step-by-step explanation:

The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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9514 1404 393

Answer:

  (c)  BK = 65

Step-by-step explanation:

Corresponding sides are proportional in similar triangles, so ...

  ZT/ZQ = KF/KB

  27/(2x +7) = 45/(4x+1)

  27(4x+1) = 45(2x +7) . . . cross-multiply

  3(4x +1) = 5(2x +7) . . . . divide by 9

  12x +3 = 10x +35 . . . . . eliminate parentheses

  2x = 32 . . . . . . . . . . . . . subtract 10x+3

  x = 16 . . . . . divide by 2

Then the length of BK is ...

  BK = 4x+1 = 4·16 +1

  BK = 65

The number of posters Jill had on Monday are 18.

The equation is p + 8 - 4 = 22.

Given that:-

Number of posters bought by Jill on Tuesday = 8

Number of posters left on Thursday = 22

We can write,

Number of posters destroyed on Wednesday = (1/2)*8 = 4

Let the number of posters Jill had on Monday be p.

Hence, the equation for the posters is given by:-

Posters on Monday + Posters bought on Tuesday - Posters destroyed on Wednesday = Total posters on Thursday

It can be written as:-

p + 8 - 4 = 22

Solving the equation, we get

p + 4 = 22

p = 22 - 4

p = 18

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Answer:

20%

Step-by-step explanation:

p(outcomes)=#of favourable outcomes/#of possible outcomes

=1/5

=0.2

=20%

Answer:

It will cost £21 ...............

Answer:

It will cost $21

Step-by-step explanation:

The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)

Divide both sides by 433.4:

\(e^{(0.032t)} = 1.836\)

Take the natural logarithm of both sides:

\(ln(e^{(0.032t)}) = ln(1.836)\)

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

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To determine the number of minutes you would have to exercise each day to have a resting heart rate of 60 beats per minute, we need to consider the relationship between exercise and heart rate.

Regular exercise can help lower resting heart rate as it strengthens the cardiovascular system. The American Heart Association recommends engaging in moderate-intensity aerobic exercise for at least 150 minutes per week to maintain cardiovascular health.

If we assume that you exercise evenly throughout the week, we can calculate the daily exercise time as follows:

150 minutes per week ÷ 7 days = approximately 21.43 minutes per day.

Therefore, if you exercise for approximately 21.43 minutes per day, it can contribute to maintaining a healthy resting heart rate. It's important to note that individual results may vary, and consulting with a healthcare professional is always recommended before starting or modifying an exercise routine.

However, it's crucial to understand that exercise alone may not be the sole factor affecting resting heart rate. Other factors, such as genetics, overall health, stress levels, and lifestyle choices, can also influence heart rate. Additionally, achieving a resting heart rate of 60 beats per minute may not be feasible or suitable for everyone, as the ideal range can vary based on individual circumstances.

Therefore, while regular exercise can be beneficial for cardiovascular health, it's essential to consider personalized factors and consult with a healthcare professional for tailored advice on achieving and maintaining a healthy resting heart rate.

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Answer:

0.1536

Step-by-step explanation:

The computation of probability that the building failure will occur over its life is shown below:-

P(building failure) is

\(P(ES \cup C)\\\\ = P(ES) + P(C) - P(ES\cap C)\\\\ = P(ES) + P(C) - P(ES) P (C | ES)\\\\ = 0.12 + 0.06 - 0.12 \times 0.22\)

now we will solve the above equation

= 0.18 - 0.0264

After solving the above equation we will get

= 0.1536

Therefore for computing the probability that the building failure will occur over its life we simply applied the above formula.    

Answer:

B. 8.6 units

Step-by-step explanation:

I've plotted both points on the picture below. The distance between the two points is 8.6023252670426 units, which is closest to B, 8.6 units. As a result, B is the answer to this question.

Answer:

which one's anwer you want

2. length= 65 ft width=24 m area=135 in2

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Ok, so

Given:

We want to find (fog)(x) and (gof)(x).

First, let's find (fog)(x).

This is:

So we're going to evaluate f in (x2 + 5).

Now, let's find (gof)(x). This is:

So we're going to evaluate g in the function f.

The expression that is equivalent to \(1/ a^2 - 2a - 8 / a - 5 / a - 4\) is:

\((-a^2 + 3a + 3) / [(a - 4)(a + 2)]\)

The given expression is:

\(1 / (a^2 - 2a - 8) - (a - 5) / (a - 4)\)

We can factor the denominator of the first fraction as \((a - 4)(a + 2)\):

\(1 / [(a - 4)(a + 2)] - (a - 5) / (a - 4)\)

To simplify this expression, we need to find a common denominator for the two fractions in the numerator.

The common denominator is\((a - 4)(a + 2):\)  so we can rewrite the expression as:

\([a - 5 - (a^2 - 2a - 8)] / [(a - 4)(a + 2)]\)

Now we can simplify by multiplying the first fraction by the reciprocal of the second fraction, and then multiplying the result by the reciprocal of the third fraction:

\([a - 5 - a^2 + 2a + 8] / [(a - 4)(a + 2)]\)

Combining like terms:

\([-a^2 + 3a + 3] / [(a - 4)(a + 2)]\)

Therefore, the expression that is equivalent to \(1/ a^2 - 2a - 8 / a - 5 / a - 4\) is:

\((-a^2 + 3a + 3) / [(a - 4)(a + 2)]\)

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The expression is equivalent to the expression (12 + 3) ÷ 5 is (3 + 12) ÷ 5

From the question, we have the following parameters that can be used in our computation:

(12 + 3) ÷ 5

The above expression is a quotient expression

However, we can apply some algebraic properties

Take for instance;

12 + 3 can be expressed as 3 + 12

So, we have

(12 + 3) ÷ 5 = (3 + 12) ÷ 5

Hence, the expression is equivalent to the expression is (3 + 12) ÷ 5

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The amount in the bank after 2.5 years will be $241.875.

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. Mathematically -

\($A = P (1 + rt)\)

{A} = final amount

{P} = initial principal balance

{r} = annual interest rate

{t} = time (in years)

Given is the amount deposited by Velvet in a bank for 2.5 years at a rate of 3%.

The amount in the bank after 2.5 years will be -

A = 225(1 + 0.03 x 2.5)

A = 225(1 + 0.075)

A = 225 x 1.075

A = 241.875

Therefore, the amount in the bank after 2.5 years will be $241.875.

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Based on the direct variation relationship between x and y, where y is 33 when x is 11, we find that y is 36 when x is 12.

If x and y vary directly, it means that they have a constant ratio between them. We can express this relationship as:

y = kx,

where k is the constant of variation.

To find the value of k, we can use the given information that when x is 11, y is 33. Substituting these values into the equation, we have:

33 = k * 11.

Dividing both sides by 11, we find:

k = 3.

Now that we have determined the constant of variation, we can find y when x is 12 by substituting this value into the equation:

y = 3 * 12.

Evaluating this expression, we get:

y = 36.

Therefore, when x is 12, y will be 36.

Based on the direct variation relationship between x and y, where y is 33 when x is 11, we find that y is 36 when x is 12.

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Answer:

can you write this on paper and send me? i have feeling ik this but i don't understand what u need

Answer:

Step-by-step explanation:

a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.

__

b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.

Answer:

Step-by-step explanation: