Betsy, a recent​ retiree, requires ​$5000 per year in extra income. She has ​$70000 to invest and can invest in​ B-rated bonds paying 15​% per year or in a certificate of deposit​ (CD) paying 5​% per year. How much money should be invested in each to realize exactly ​$5000 in interest per​ year?

Answer:

a: 27 apples

b: $0.40 apples

Step-by-step explanation:

a: another way of saying that the price of an apple one-third that of an orange is that you can get 3 apples for the price of 1 orange. If he bought 5 oranges, he could have gotten 15 apples, so 27 apples total.

b:  $10.80/27 = $0.40 per apple

Answer:

  √13 units

Step-by-step explanation:

Find points B and C on the figure and locate the line between those points. The number next to the line is its length. Read the length from the diagram.

In a right triangle, the hypotenuse is the side across from the 90 degree angle. Without more information, we can't determine the length of the hypotenuse (BC), but if the lengths of the other two sides or the measurements of the other angles are known, the Pythagorean theorem or trigonometry can be used.  It is expressed as BC^2 = AB^2 + AC^2.

In a right triangle, the hypotenuse is the side that is opposite to the 90 degrees angle. In your right triangle, as you mentioned the sides as BC, I assume you have a triangle ABC where B and C are the two base angles and A is the right angle (90 degrees).

Without additional information such as the lengths of the other two sides (AB, AC), or the measurements of angles B or C, it is impossible to determine the length of the hypotenuse (BC). However, if you do have this information, you can use the Pythagorean theorem or trigonometric ratios to find the length. Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides. It is expressed as BC^2 = AB^2 + AC^2.

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Answer:

  graph D

Step-by-step explanation:

You want to choose the graph with a y-intercept of 70 and an x-intercept of 140. Graph D matches that.

___

Comment on graph D

The horizontal scale is a bit weird in that the numbers don't correspond to hash marks on the horizontal axis. The hash mark between the numbers 120 and 160 will correspond to a distance of 140 ft. That is where the graph touches the horizontal axis, so that is one indication it is the graph you want.

Answer: it should be will receive a refund of $278

Step-by-step explanation:

That’s just what was on my test though

Hope that helps somebody

The amount Ms. Wilson will receive after she figures out her tax for the year is; $999.88

The tax bracket Ms. Wilson falls into demands that she pays 12% of her taxable income in tax.

Hence, the tax she's supposed to pay is;

Hence, she will receive after she figures her taxes for the year is; $5344 - $4,344.12 = $999.88

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100:40

=2.5

1200 : 2.5

=480

About 480 people out of the 1,200 customers are likely satisfied with their service.

To determine how many of the company's customers are likely satisfied with their service based on the survey results, we can use the concept of proportions. This involves simple multiplication and understanding ratios in percentages.

Find the proportion of satisfied customers in the survey:

Number of satisfied customers in the survey: 40

Total number of people surveyed: 100

Proportion of satisfied customers = (Number of satisfied customers) / (Total number of people surveyed)

Proportion of satisfied customers = 40 / 100 = 0.4 or 40%

Apply this proportion to the entire customer base:

Total number of the company's customers: 1,200

Estimate of satisfied customers = Proportion of satisfied customers × Total customers

Estimate of satisfied customers = 0.4 × 1,200 = 480

Answer:

6 to the power of 1 over 6

Answer:

The correct option is 4.

Step-by-step explanation:

The given interpretation is square root of the cube root of 6. The mathematical expression is

[tex]\sqrt{\sqrt[3]{6}}[/tex]

It can be written as

[tex]((6)^{\frac{1}{3})^{\frac{1}{2}}[/tex]

Using the property of exponent, we get

[tex](6)^{\frac{1}{3}\times \frac{1}{2}}[/tex]         [tex][\because (x^m)^n=(x)^{mn}][/tex]

Now simplify the power.

[tex](6)^{\frac{1}{6}}[/tex]

The simplified form of given expression is 6 to the power of 1 over 6. Therefore the correct option is 4.

whats the question? ill help you out i just wanna Answer the right question

Answer: c. Exponential

Answer:

5/2

Step-by-step explanation:

The multiplicative inverse is what me need to multiply by to get 1

2/5 * what = 1

Multiply by the reciprocal

5/2 *2/5 * what = 1 *5/2

what = 5/2

The multiplicative inverse is 5/2

5/2 is the multiplicative inverse

Answer:

Step-by-step explanation:

27

Answer:

option H

457.9 CM squared

Step-by-step explanation:

Given that,

base of parallelogram = 30 cm

side of parallelogram = 18 cm

one of the angle of parallelogram = 58°

Formula to calculate area of parallelogram is

To calculate height we will use trigonometry identity  

sin(58) = height / 18

height = 15.27

Area = 30 x 15.27

         = 457.9 cm²

so the area of parallelogram is 457.9 cm²

Answer:

x ≈ -0.93, x ≈ 1.06

Step-by-step explanation:

A graphing calculator can show you the approximate solutions. (It is also capable of refining those solutions to full calculator precision, if you need.)

_____

Comment on the graphical solution

I prefer to have the calculator show me the zeros of a function, where the zeros correspond to solutions of the original equation. For the purpose, it is sufficient to define the function as the difference between the sides of the original equation.

__

The definition of g(x) in the attachment corresponds to the iterator of Newton's Iteration method for finding zeros of a function. When the input and output values of that iteration function match, the value of x is a zero of the function f(x).

Answer:

x = 2

Step-by-step explanation:

The minimum occurs where the value being squared is zero. x-2 = 0 when x=2.

Answer:

C. 2

Step-by-step explanation:

Point B is 6-(-4) = 10 units up from point A. A point (F) that partitions that distance in the ratio 3:2 will be 3/(3+2) = 3/5 of the distance from A to B. That is, it will be ...

3/5 · 10 units = 6 units

above A. The y-coordinate of F will be 6 units added to the y-coordinate of point A, -4 +6 = 2.

To find out how many games Natalie and her friends played, we subtracted the total shoe rental cost for 6 people from the $21 spent and divided the remainder by the cost per game, which gave us a result of 3 games played.

The question asks us to solve a real-world math problem where Natalie and her friends go bowling and spend a total of $21. The cost to play one game is $3 and shoe rental is $2 per person.

To determine the number of games they played, we need to calculate the cost of shoe rental for all people and then figure out how much of the $21 was left for the games.

First, we calculate the shoe rental for 6 people (Natalie and her 5 friends):

Next, we subtract the shoe rental cost from the total amount spent to find the amount spent on games:

Finally, we divide the amount spent on games by the cost per game to find the number of games played:

Natalie and her friends played 3 games of bowling.

Answer:

6a. -8

8b. 1/125

Step-by-step explanation:

If you know powers of 2 and the squares and cubes of small integers, you can work these in your head. There is no "work" to show. Of course, a calculator can evaluate these easily. (see attached)

___

6a. (-128)^(3/7) = ((-2)^7)^(3/7) = (-2)^3 = -8

___

8b. (27^(2/3) +8^(4/3))^(-3/2) = ((3^3)^(2/3) +(2^3)^(4/3))^(-3/2)

= (3^2 +2^4)^(-3/2) = (9+16)^(-3/2) = 25^(-3/2)

= (5^2)^(-3/2) = 5^(-3) = 1/5^3

= 1/125

Answer:

x = 45, y = 24.

Step-by-step explanation:

If the 2 numbers are x and y:

x + y = 69...........(1)

x = 2y - 3

x - 2y = -3...........(2)

Subtract: (1) - (2):

x - x + y - (-2y) = 69 - (-3)

y + 2y = 72

3y = 72

y = 24.

From equation 1:-

x + 24 = 69

x = 45.

The numbers are x = 24 and y = 45 respectively.

An algebraic expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

Given is that the sum of two numbers is 69. The larger number is three less than twice the smaller number.

Assume that the numbers are {x} and {y}. So, we can write the equations as -

x + y = 69

y = 2x - 3

Rewriting equation {1}, we get -

x + y = 69

x + 2x - 3 = 69

3x = 72

x = 24

and

y = 2 x 24 - 3

y = 45

Therefore, the numbers are x = 24 and y = 45 respectively.

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I think the last one is maybe ten, maybe

Answer:

Step-by-step explanation:

no

Answer:

5 cm

Step-by-step explanation:

ΔABC is equilateral, so BC = AB = 5 cm.

____

AO is the perpendicular bisector of BC and the angle bisector of angle A, so ∠OAC = ∠OAB = 30°. Then vertex angle BAC of isosceles triangle ABC is 60°, which means all angles in the triangle are 60° and the triangle is equilateral.

The length of BC is 5cm

Given that line AB is tangent to circle K at point B, and line AC is tangent to circle K at point C, we know that the radius of the circle at the point of tangency is perpendicular to the tangent line. Therefore, OB is perpendicular to AB, and OC is perpendicular to AC. This forms two right triangles,[tex]$\triangle OAB$ and $\triangle OAC$.[/tex]

Let's denote OB as the side opposite the 30° angle and OA as the hypotenuse. Then we have:

[tex]OB = $\frac{1}{2}$AB = $\frac{1}{2} \times 5$ cm = 2.5 cm[/tex]

OA = AB = 5 cm (since AB is the hypotenuse of the right triangle)

Now, since the circle is the same, OA is also the radius of the circle, and thus OB = OC = 2.5 cm.

Therefore [tex], $\triangle OBC$[/tex] is an equilateral triangle because all angles are 60° and the sides opposite these angles are equal. Hence, BC = OB = OC = 2.5 cm.

Thus, BC = OB + OC' = 2.5 cm + 2.5 cm = 5 cm.

But this is not the final answer. We have to consider that the length of the chord BC is equal to the diameter of the circle because the tangents from a common external point to a circle are equal in length. Therefore, the diameter of the circle is twice the length of the radius OB (or OC').

Diameter = 2 * OB = 2 * 2.5 cm = 5 cm

BC = 5cm

Answer:

b

Step-by-step explanation:

100%

The explicit formula for the sequence -5, -3, -1, 1, 3 is a_n = -5 + (n - 1)2.

Each term of an arithmetic sequence can be found using the formula:

a_n = a + (n-1)d

The given sequence is 5, -3, -1, 1, 3.

From this, we can see that the value of:

a = -5

d = -3 - (-5) = -3 + 5 = 2

∴ The explicit formula can be written as:

a_n = -5 + (n - 1)2

Therefore we have found the explicit formula for the sequence -5, -3, -1, 1, 3 as a_n = -5 + (n - 1)2.

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Answer:

Step-by-step explanation:

a) The image A'B'C'D' is smaller than the original ABCD, so the dilation is a reduction. The image is reduced in size from the original.

__

b) Each image point is 1/2 the distance of the original point from the origin. Count the grid squares to see this, or compare coordinates:

  A'(-1, 2) = 1/2·A(-2, 4)

Thus the scale factor is 1/2.

Answer:

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex]

Step-by-step explanation:

We want to evaluate:

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x[/tex]

When x=0, we obtain the first term of the geometric series as

[tex]a_0=2(\frac{1}{3})^0[/tex]

The common ratio of this geometric series is [tex]r=\frac{1}{3}[/tex]

The sum of the first n-terms of a geometric series is

[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

From x=0 to x=15, we have 16 terms.

The sum of the first 16 terms of the geometric series is

[tex]S_{16}=\frac{a(1-(\frac{1}{3})^{16})}{1-\frac{1}{3}}=2.99999993031[/tex]

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex] to the nearest tenth.

Answer:

1282.82ft³

Step-by-step explanation:

To find the volume of the entire shape, we first need to find the volume of the cone and the cylinder separately.

Let's begin by getting the volume of the cylinder.

The formula to find the volume of a cylinder is:

[tex]V=\pi r^{2}h[/tex]

r = 7 ft

h = 6 ft

Let's plug in our values into the formula.

[tex]V=\pi (7)^{2}6[/tex]

[tex]V=\pi (49)6[/tex]

[tex]V=\pi (294)[/tex]

[tex]V=923.63[/tex]ft³

Now that we have the volume of our cylinder we need to find the volume of the cone.

The volume of the cone can be found by using the formula:

[tex]V=\dfrac{1}{3}\pi r^{2}h[/tex]

Our variables for the cone are:

r = 7 ft

h = 7 ft

[tex]V=\dfrac{1}{3}\pi (7)^{2}(7)[/tex]

[tex]V=\dfrac{1}{3}\pi (49)(7)[/tex]

[tex]V=\dfrac{1}{3}\pi (343)[/tex]

[tex]V=\dfrac{1}{3}1077.57[/tex]

[tex]V=359.19[/tex]ft³

Now that we found both of the volumes of the two shapes, we can then simply get the sum of both volumes to get the total volume of the shape.

Total Volume = 923.63ft³ + 359.19ft³

Total Volume = 1282.82ft³

The probability that a randomly chosen card from a standard 52-card deck is either an ace or a heart is approximately 31%.

In a standard deck of 52 cards, there are 4 suits and each suit has 13 cards: hearts, clubs, diamonds, spades. Therefore, the total number of heart cards in the deck is 13 and the total number of aces in the deck is 4 (one for each suit).

To compute the probability P (A or H), the probability that Anthony chooses a card which is either an ace or a heart, we first need to calculate individual probabilities. The probability of drawing a heart P(H) is 13/52 = 0.25, and the probability of drawing an ace P(A) is 4/52 = 0.077. However, as the aces also include one heart (Ace of Hearts), the probabilities overlap.

To correct this, we use the rule of sum for probabilities which says that the probability that A or B will happen is the probability that A will happen plus the probability that B will happen, minus the probability that both A and B will happen. Applying this, P ( A or H) = P(A) + P(H) - P(A and H) = 0.077 + 0.25 - 0.019 = 0.308, or approximately 31%

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Final answer:

The probability of drawing either an ace or a heart from a standard deck of cards is 11/26.

Explanation:

To find the probability of choosing either an ace or a heart card, we need to calculate the individual probabilities of each event and then subtract the probability of neither event happening.

There are 4 aces in a deck of 52 cards, so the probability of picking an ace is 4/52, which simplifies to 1/13.

Similarly, there are 13 hearts in a deck, so the probability of picking a heart is 13/52, which simplifies to 1/4.

Since the events are mutually exclusive (a card can't be both an ace and a heart), we can add the probabilities together to find the probability of either event happening: 1/13 + 1/4 = 4/52 + 13/52 = 17/52.

Finally, to find the probability of either an ace or a heart, we subtract the probability of neither event happening (the probability of picking a card that is neither an ace nor a heart):

P(A or H) = 17/52 - 39/52 = 22/52, which simplifies to 11/26.

Answer:

Since 2 inches represent 8 feet then 2.5 would represent x feet so  

2/8 = 2.5/x  

By doing cross multiplication :  

2 x = 20 --> x = 10 feet

Step-by-step explanation:

Answer:

Failing to pay debt

Step-by-step explanation:

Final answer:

Defaulting on a debt, failing to pay debt, and building a credit history are crucial aspects of managing one's financial health.

Explanation:

Defaulting on a debt occurs when a borrower fails to repay the loan according to the terms agreed upon with the lender. This can lead to serious consequences such as damage to one's credit score and possible legal actions taken by the lender.

One of the contributing factors to defaulting is failing to pay debt on time. This affects a person's credit history and the lender's trust in the borrower's ability to repay borrowed money.

It is important to build a credit history by responsibly managing credit accounts, paying bills on time, and avoiding opening too many accounts rapidly to maintain a good credit score and prevent defaulting.

Answer:

(x, y) ⇒ (-x, y)

Step-by-step explanation:

Any transformation that multiplies a variable by something other than ±1 is not a rigid transformation — it involves some sort of dilation. Constants can be added or subtracted to effect translation, but none of the transformations shown here do any translation.

The first transformation is a reflection across the y-axis, hence the rigid transformation you're looking for.

_____

Comment on rotations

A rotation about the origin can be written in the form ...

(x, y) ⇒ (ax -by, bx +ay)

where a^2 +b^2 = 1 and b/a = tan(angle of rotation)

This rigid transformation is an exception to the statement above about multiplication by something other than ±1.

Answer: function b has a greater rate of change

Answer:

1) 17p + 45.99 = 200

2) 200 > 45.99 + 17p

Step-by-step explanation:

Total Budget = $200

Cost of Party Room = $45.99

Cost of movie ticket for one person = $12.50

Cost of one small bag of popcorn = $4.50

Part 1: Possible Equation by Tomas

The possible equation that can be set up will have the total budget equal to total expenses.

So,

200 = Total Cost of party

200 = Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

If p people attend the party, the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.

So, now the equation will be:

200 = 45.99 + 12.50p + 4.50p

200 = 45.99 + 17p

or

17p + 45.99 = 200

This is a possible equation that Tomas might have used to represent the cost of the party.

Part 2: Possible Inequality by Emilio

Emilio might want to keep the cost below $200 of the entire party. So the possible inequality will be of the form:

200 > Total Cost of party

200 > Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

200 > 45.99 + 12.50p + 4.50p

200 > 45.99 + 17p

This is a possible inequality that Emilio might have used to represent the cost of the party.

Answer: OPTION D

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Convert from 48 inches to foot. You know that 12 inches=1 foot. Then you have:

 [tex](48inches)(\frac{1foot}{12inches})=4feet[/tex]

- Therefore, keeping on mind that 48 inches is 4 feet, and you must find the ratio that  correctly compares 2 feet to 48 inches, you can write:

[tex]ratio=\frac{2feet}{4feet}[/tex]

- Reduce the fraction, then:

[tex]ratio=\frac{1}{2}[/tex]

- You can rewrite it as following:

[tex]ratio=1:2[/tex]

Answer:

D

Step-by-step explanation: