A saving account that earns 3.2% interest compounded bi annually has a balance of $6049.15 after 6 years Determine the total amount of interest earned on the account
O1049.15
O1409.15
O4145.24
O5000.0

Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

Mrs. Adams commutes 17 miles each way to work, so she travels a total of 17 * 2 = <<172=34>>34 miles per day.

Since the Honda Element gets 23 miles per gallon on the highway, it uses 34 / 23 = 1.48 gallons of gas per day.

At a gas price of $3.00 per gallon, the Honda Element costs 1.48 * 3 = $<<1.483=4.44>>4.44 in gas per day.

The Toyota Prius gets 41 miles per gallon on the highway, so it uses 34 / 41 = 0.83 gallons of gas per day.

At a gas price of $3.00 per gallon, the Toyota Prius costs 0.83 * 3 = $<<0.83*3=2.49>>2.49 in gas per day.

The Toyota Prius costs $2.49 in gas per day, while the Honda Element costs $4.44 in gas per day.

The difference in gas cost between the two vehicles is $4.44 - $2.49 = $1.95 per day.

To pay for itself in gas savings, the Toyota Prius needs to save $6,500 / $1.95 = 3345.38 days of gas.

At a rate of 365 days per year, this is approximately 3345.38 / 365 = <<3345.38/365=9.14>>9.14 years.

Therefore, it will take approximately 9.14 years for the Toyota Prius to pay for itself in gas savings.

Answer: Length: 4, width: 6

Step-by-step explanation:

Let the length be x and width be y

Then x=2y-8 and xy=24

Substitute to get 2y-8 * y = 24, so 2y^2-8y=24 or y^2-4y=12, then solve to get y=6 or y=-2. Since width is positive y=6.

Substitute y=6 into xy=24 to get x=4.

Length: 4, width: 6

Hope that helped,

-sirswagger21

Answer:

11. (a) 3/4+1/2=5/4

   (b) 4/5= 8/10 , 16/20

12. 8 children don't like choc ice cream

Step-by-step explanation:

11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)

12. 3/5 of 20 = 12

     20-12=8

The correct answer is option C: \(\(k + 4 = 16\).\) This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

\(\[Tina = Kai + 4\]\)

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

\(\[16 = k + 4\]\)

This equation represents the fact that Tina has volunteered \(16\) times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

\(\[k + 4 = 16\]\)

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: \(\(k + 4 = 16\).\)

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Answer:

The length of the hypotenuse is 100.

Step-by-step explanation:

To find the length of the hypotenuse, we use the following formula:

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

c=\(\sqrt{28^2+96^2}\)

c=\(\sqrt{10,000}\)

c=100

Therefore, the length of the hypotenuse is 100.

Answer:

\(c = \dfrac{1}{4}\)

Explanation:

\(\sf 2^{-4} \ \cdot \ 2^2= a^b = c\)

----

\(\sf c = 2^{-4} \ \cdot \ 2^2\)

apply indices law : \(\sf a^m \ \cdot \ a^n = a^{m+n}\)

\(\sf c = 2^{-4+2}\)

simplify

\(\sf c = 2^{-2}\)

\(\sf c = \dfrac{1}{2^2}\)

evaluate

\(\sf c = \dfrac{1}{4}\)

The solution to the given addition problem is 150.6 ft^9.

Converting everything to the same unit is the simplest solution to this problem.

The conversions are:

1 cubic yard = (27 cubic feet)

1 cubic inch = (0.000578704 cubic feet)

The addition can be performed as,

(6 cu yd × 9 cu ft × 134 cu in) + (1 cu yd × 12 cu ft × 200 cu in)

=  [6(27 cu ft) × 9 cu ft × 134(0.000578704 cu ft)] + [1(27 cu ft) × 12 cu ft × 200(0.000578704 cu ft)]

= 150.6 ft^9

The result of the addition is 150.6 ft^9.

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Answer:

  a = 15/8

Step-by-step explanation:

You want the solution to the two-step linear equation ...

  -1/2 +1/3a = 1/8

When an equation involves fractions, it is often useful to clear fractions by multiplying the equation by their least common denominator. Here, that means we want to multiply the equation by 24.

  -12 +8a = 3 . . . . . . multiply the given equation by 24

  8a = 15 . . . . . . . . add 12

  a = 15/8 . . . . . . divide by the coefficient of the variable

The solution is a=15/8 or 1 7/8.

Answer:

Step-by-step explanation:

a = 10/2 = 5

b = \(5\sqrt{3}\)

For the Special Triangles

Answer:

The total area of the flag was 394 square inches.

Step-by-step explanation:

Given that Rainey's group designed a flag, and they used 234 square inches of green fabric, twice as much green fabric as orange fabric, and 3 times as much green fabric as yellow fabric and they had 35 sq inches of yellow fabric left, to determine the total area of the flag the following calculation must be performed:

234 + 234/2 + (234/3 - 35) = X

234 + 117 + (78 - 35) = X

234 + 117 + 43 = X

234 + 160 = X

394 = X

Thus, the total area of the flag was 394 square inches.

Answer:

Step-by-step explanation:

Rainey’s group designed a flag shown for the class project. The flag was made up of Green, Orange and Yellow fabrics.

Green fabric = 234 square inches

( given in the description)

Green fabric = 2 x Orange fabric

(Twice as much Green as Orange)

So Orange fabric = 1/2 X Green fabric (half of green fabric)

Green fabric = 3 x Yellow fabric

( 3 times as much green as yellow)

So Yellow fabric = 1/3 X Green fabric ( one third of Green fabric)

After making one flag Rainey’s group has 35 square inches of yellow fabric left. To determine the total area of the flag that left over 35 square inches have to subtract.

Now add up all the fabrics and then subtract the left over yellow fabric to get the total area of the flag.

Total area of the flag = Green fabric + Orange fabric + Yellow fabric - left over fabric

So Total area of flag = 234 square inches + 234/2 square inches + 234/3 square inches - 35 square inches

= 234 + 117 + 78 - 35 square inches

= 234 + 117 + 43 square inches

= 394 square inches.

So the total are of the flag is 394 square inches.

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

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This question is incomplete, the complete question is;

Condé Nast Traveler conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service.

A sample of 37 ships that carry fewer than 500 passengers resulted in an average rating of 85.36, and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.40.

Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that carry 500 or more passengers. What is the value of the test statistic? Round your all answers to two decimal places.

Answer:

value of the test statistic is 4.13

Step-by-step explanation:

Given the data in the question;

fewer than 500 passengers                           more than 500 passengers

n₁ = 37                                                               n₂ = 44

x'₁ = 85.36                                                         x'₂ = 81.40

s₁ = 4.55                                                            s₂ = 3.97

Now, to get the test statistics, we use the following formula;

z = (x'₁ - x'₂) / √( \(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\) )

we substitute

z = ( 85.36 - 81.40 ) / √( \(\frac{(4.55)^2}{37} + \frac{(3.97)^2}{44}\) )

z = 3.96 / √( \(\frac{20.7025}{37} + \frac{15.7609}{44}\) )

z = 3.96 / √( 0.5595 + 0.3582 )

z = 3.96 / √0.9177

z = 3.96 / 0.957966596

z = 4.1337 ≈ 4.13

Therefore, value of the test statistic is 4.13

Answer:

J(-5,2), A(-5,4), and N(-1,1)

Step-by-step explanation:

It's 65. Because you add the other angles and get 90+25 and get 115. 180 -115 = 65.

Answer:

c=65°

Step-by-step explanation:

180-90=90

90-25=65

hopefully this helps :)

Answer:

A≈149.57

Step-by-step explanation:

Answer:

log(3x⁹y⁴) = log 3 + 9 log x + 4 log y

Answer:

\(\log 3+ 9\log x +4 \log y\)

Step-by-step explanation:

Given logarithmic expression:

\(\log 3x^9y^4\)

\(\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay\)

\(\log 3+\log x^9 +\log y^4\)

\(\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax\)

\(\log 3+ 9\log x +4 \log y\)

The distance between each pair of points is 2.8 units

What is Distance Between two points formula

The length of the line segment connecting two locations in a plane is known as the distance between the points.. The formula to find the distance between the two points is usually given by d=\(\sqrt{((x_{2}-x_{1} )^{2} -(y_{2}-y_{1} )^{2} ) }\) In an x-y plane or coordinate plane, this formula is used to determine the separation between any two locations.

From the fig, the end coordinate of line segments are (3,3) and (5,1).

\(x_{1}\)=3

\(x_{2}\)=5

\(y_{1}\)=3

\(y_{2}\)=1

If we the coordinate values in the distance formula, we get

d=\(\sqrt{((x_{2}-x_{1} )^{2} -(y_{2}-y_{1} )^{2} ) }\)

d=\(\sqrt{((5-3)^{2} -(1-3)^{2} )}\)

d=\(\sqrt{4+4}\)

d=\(\sqrt{8}\)

d=2.8units

Hence, the distance between each pair of points is 2.8units

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Answer:

125

Step-by-step explanation:

sum of 60 and 65 will give you x

Answer:

125

Step-by-step explanation:

65+60=125

Twelve people join hands for a circle dance.In how many ways can they do this? Suppose six of these people are men, and the other six are women. In how many ways can they join hands for a circle dance, assuming they alternate in gender around the circle

Answer:

86400 ways

Step-by-step explanation:

Since the circle can be rotated, the number of ways to arrange a distinct number of n objects in a circle will be (n−1)!.

Now, if we rotate the circle with the six women, we will see that there are 5! ways with which they can be placed in the circle.

After picking the places for the women, we will now fill each gap between two women with a man.

We have 6 men. Thus, number of ways to arrange the men is 6!

Thus,number of ways they can join hands for a circle dance, assuming they alternate in gender around the circle = 5! × 6! = 86400 ways

There are 15 cats in the animal shelter.

An equation in which is  the highest power of to the  variables 1 is knowns as the  linear equation. Mathematically: it is an  algebraic equations that can be also  written in the form of  ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.
In order to solve this problem, we must set up a proportion. Proportions are an equation that states that two ratios are equal. In this case, we are looking for the number of cats (c) in the animal shelter.

Let's set up the proportion.

5/3 = 25/c

We can then solve for c by multiplying both sides by c.

5c/3 = 25

c = 15

Therefore, there are 15 cats in the animal shelter.

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By answering the presented question, we may conclude that In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is often referred to as a rectangle with two nearby sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Also, the diagonals of the square are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

To determine the answer, multiply the areas of the shaded squares by the overall area of the figure.

Assuming that both squares are the same size, we may combine the fractions using a common denominator:

2/12 + 2/15 = 5/60 + 4/60 = 9/60 = 3/20

As a result, the entire shaded area is 3/20 of the total area of the diagram.

We can't discover the exact area of the graphic because it's not presented. As a result, we can only represent the answer in fractions or decimals.

In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

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Answer:

Each pup got \(\frac{1}{8}\) of the bone.

Step-by-step explanation:

1 bone divided by 8 puppies, so they each get one-eighth of the bone.

#teamtrees #WAP (Water And Plant)

Therefore, the measure of the intercepted arc by the inscribed angle of 61 degrees is 122 degrees.

A circle is a closed shape in geometry that is defined as the set of all points in a plane that are at a fixed distance from a given point, called the center of the circle. The distance between any point on the circle and the center is called the radius of the circle.

Given by the question.

In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of its intercepted arc.

Let's call the intercepted arc by the inscribed angle "x". Then, the measure of the inscribed angle is 61 degrees, and we can use the formula mentioned above to find the measure of the intercepted arc:

61 = x/2

To solve for x, we can multiply both sides of the equation by 2:

122 = x

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