Compute the amount in an account after 8 yr if $6500 is invested at an annual interest rate of 5.25% compounded quarterly. Round to two decimal places.

Answer:

Should be 480.

Answer:

Domain: all real numbers

Range: all real numbers

Step-by-step explanation:

I'm assuming you mean the function [tex]f(x)=x^{\frac{1}{5}}[/tex].  That's usually written

f(x) = x^(1/5) with the ^ meaning "to the power of..." and the fraction exponent in parentheses so as not to be confused with x^1/5 which could mean x to the first power, divided by 5.

Fractional exponents are used to indicate roots.  In this case, x is being raised to the 1/5 power, so this is the fifth root of x, written [tex]\sqrt[5]{x}[/tex].  The 5 is called the root index.

For odd roots, like this one, the domain is all real numbers--x can be any number at all.  So the domain is all real numbers.

The range is also all real numbers.  Attached is a graph of this function. It might not look like it, but the graph rises to the right to any height.  The larger x gets, the larger the 5th root gets.  A similar thing happens on the left--the smaller x gets, the smaller the 5th root gets.

EDIT: see the comment.  For the function [tex]f(x)=(1/5)^x[/tex], the domain is all real numbers. The range is positive real numbers.  I'll attach a graph!

Answer:

71

Step-by-step explanation:

because the theorem is sum of the square

The answer is d. hypotenuse.

Here's why:

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).

So, if you have a right triangle with legs of length a and b, and hypotenuse of length c, the equation would be: a^2 + b^2 = c^2.

Therefore, the sum of the squares of the legs (a^2 + b^2) is equal to the square of the hypotenuse (c^2).

The other options are incorrect because:

a. shorter leg: The theorem doesn't differentiate between the lengths of the legs, it simply states that the sum of their squares is equal to the square of the hypotenuse.

b. longer leg: Same as above, the theorem doesn't consider the individual lengths of the legs, just their squares.

c. sum of the angles: The Pythagorean Theorem deals with the sides of a right triangle, not its angles. The sum of the angles in any triangle is always 180 degrees.

Complete Question:

In the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the

a. shorter leg

b. longer leg

c. sum of the angles

d. hypotenuse

Constructing a frequency distribution table for visitor numbers with a range of 29 to 73 and class intervals of 10 provides a clear overview, facilitating analysis and interpretation of the data.

Construct a frequency distribution table for the given data, with explanations:

1. Find the range of the data:

The lowest number of visitors is 29.

The highest number of visitors is 73.

The range is 73 - 29 = 44.

2. Determine the appropriate class intervals:

Choose a class interval width that will create a reasonable number of classes, typically between 5 and 10.

Consider the range of the data and aim for intervals that are easy to interpret.

In this case, a class interval width of 10 would be suitable, resulting in 5 classes:

29-38

39-48

49-58

59-68

69-78

3. Create the table:

Draw a table with three columns:

Class Interval

Tally (optional)

Frequency

4. Tally the data (optional):

Go through each data point and mark a tally mark in the appropriate class interval. (This is helpful for visual counting, but not strictly necessary.)

5. Count the frequencies:

Count the number of data points that fall into each class interval and record those numbers in the frequency column.

Complete question:

The number of visitors to the Railroad Museum during 24 randomly selected hours is shown here. 67 62 38 73 34 43 72 35 53 55 58 63 47 42 51 62 32 29 47 62 29 38 36 41 The error in the data is 1. a) Construct a frequency distribution table

Answer: 5409.828

Step-by-step explanation: calculator

Answer:

[tex]11\sqrt{3} + 5\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{108}+\sqrt{125} - \sqrt75}[/tex]

1. [tex]\sqrt{108} = 6\sqrt{3}[/tex]\

2. [tex]\sqrt{125} = 5\sqrt{5}[/tex]

3. [tex]\sqrt{75} = 5\sqrt{3}[/tex]

4.    Add [tex]6\sqrt{3} + 5\sqrt{3} = 11\sqrt{3}[/tex]

your left with [tex]11\sqrt{3}+5\sqrt{5}[/tex]

Answer:

12

Step-by-step explanation:

Answer:

12 (3.15 pound) containers.

Step-by-step explanation:

37.8 divided by 3.15 equals 12 (3.15 pound) containers.

Answer: -72

Step-by-step explanation:

[tex]-3(k^2+2n)\\-3((-4)^2+2(4))\\-3(16+8)\\-3(24)\\-72[/tex]

Answer:

4

Step-by-step explanation:

(x+2)^2+(y-3)^2=4

From this equation, we can find the radius of this circle.

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

radius = 2

diameter = 2*radius = 2*2 = 4

Answer:

The speed of the wind is 32 mph and the speed of the plane in still air is 351 mph.

Step-by-step explanation:

Let the speed of the plane be Vp and the speed of the wind be Vw. In the first situation, the wind is exerting force towards the same direction as the plane so we can say that Vp + Vw = 383 mph. In the second situation, the forces are opposite of each other, so the equation can be written as Vp - Vw = 319 mph.

If we solve them together, we get the result of 2Vp = 702 mph which means that the speed of the plane is Vp = 351 mph. If we put Vp into one of the equations and solve for Vw then the speed of the wind can be found as       Vw = 32 mph.

I hope this answer helps.

Answer: the height of a flower in the field is 13.6 centimeters.

Step-by-step explanation:

Since the heights of different flowers in a field are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = heights of different flowers.

µ = mean height

σ = standard deviation

From the information given,

µ = 12.7 centimeters

σ = 2.3 centimeters

The z-score is 0.4

Therefore,

0.4 = (x - 12.7)/2.3

Cross multiplying by 2.3, it becomes

0.4 × 2.3 = x - 12.7

0.92 = x - 12.7

x = 0.92 + 12.7

x = 13.6 centimeters to the nearest tenth

Answer:

Compound interest =$14.58

Simple Interest=$14.79

Step-by-step explanation:

Let's assume the interest rate charged on the loan was simple in nature.

-Simple interest is calculated using the formula:

[tex]I=PRT,\\\\=1500\times 0.04\times \frac{90}{365}\\\\=14.79[/tex]

Hence, the simple interest on the loan was $14.79

#If the interest is compound in nature with just one compounding per year:

[tex]A=P(1+i)^n\\\\I=A-P\\\\I=1500(1.04)^{90/365}-1500\\\\=14.58[/tex]

Hence, the compound interest charged on the loan is $14.58

Answer:

1250

Step-by-step explanation:

x^3*y^1

Let x = 5 and y = 10

5^3* 10^1

PEMDAS says powers first

125 * 10

Then multiply

1250

Answer:

C = 73

Step-by-step explanation:

Formula used: a²+b²=c²

A and B represent the numbers other than the hypotenuse, so C equals the hypotenuse. It doesn't matter which number you put as A or B. Here's the equation we're working with:

(55)² + (48)² = C²

That simplifies to:

3025 + 2305 =C²

5329 = C²

Now, C needs to be by itself in order for us to get the answer, so the next step is to do inverse operations. The inverse of sqauring a number (x²) is to square root it (√x). Here is the new equation we are working with:

√5329 = √C

That simplifies to:

73 = C

Hope this is correct!

Answer:

Francesca!! 13 is less than 15

Step-by-step explanation:

Final answer:

To determine who got home first, compare the times it took for Alessandro and Francesca to run home. If Francesca's time is less than Alessandro's time, then she got home first. If Alessandro's time is less than Francesca's time, then he got home first.

Explanation:

To determine who got home first, we need to compare the time it took for each person to run home. Let's assume it took Alessandro t minutes to run home. According to the information given, Francesca took 13/15 times as long as Alessandro, which means it took Francesca (13/15) * t minutes to run home. To determine who got home first, we can compare their times. If Francesca's time is less than Alessandro's time, then Francesca got home first. If Francesca's time is greater than Alessandro's time, then Alessandro got home first.

Let's compare the times:

Based on the comparison, we can conclude that:

Answer:

81 inches squared

Step-by-step explanation:

You just multiply the area by the hight and get your answer

Answer:

Answer:y = 1/4x -8Step-by-step explanation:First find the slope of the linex-4y =3Subtract x from each sidex-4y -x = -x+3-4y = -x+3Divide each side by -4-4y/-4 = -x/-4 +3/-4y = 1/4 x -3/4This is in the form y= mx+b where the slope is m and the y intercept is bThe slope is 1/4We want the same slopey = 1/4x +bwe know the y intercept is -8y = 1/4x -8.

Step-by-step explanation:

Answer:

There are 127 Possible ways/combinations for this

Step-by-step explanation:

149 : 1 is the odds against your winning the boat.

Step-by-step explanation:

It is given that,

The winner of a raffle will receive a​ 21-foot outboard boat.

The odds against any event is the ratio of the unfavorable outcomes to the favorable outcomes.

The number of possible outcome that you will win ⇒ 20

The number of possible outcomes that others wins ⇒ 3000-20 = 2980

To find the odds against your winning the​ boat :

Number of possible outcomes that one of the others wins : Number of possible outcome that you will win.

⇒ 2980 : 20

⇒ 149 : 1

Therefore, the odds against your winning the boat is 149 : 1

Answer:

[tex]A'(3,6)[/tex]

Step-by-step explanation:

The given coordinate is [tex]A(2,4)[/tex].

It's important to know that a dilation implies a bigger figure than the original. In this case, we have a factor of dilation of 1.5, which means each coordinate must be multiplied by it.

So, using the factor of dilation, we have

[tex]A(2,4) \implies A'(3,6)[/tex]

Because [tex]2 \times 1.5 = 3[/tex] and [tex]4 \times 1.5 = 6[/tex]

Therefore, the right answer is [tex]A'(3,6)[/tex]

The coordinates of [tex]\( A' \)[/tex] after dilating point [tex]\( A(2, 4) \)[/tex] by a factor of [tex]\( 1.5 \)[/tex] are [tex]\( {(3, 6)} \)[/tex].

To find the coordinates of [tex]\( A' \)[/tex] after dilating point [tex]\( A(2, 4) \)[/tex] by a scale factor of [tex]\( 1.5 \)[/tex], we use the formula for dilation:

If [tex]\( A'(x', y') \)[/tex] is the image of [tex]\( A(x, y) \)[/tex] under dilation with scale factor [tex]\( k \)[/tex], then:

[tex]\[ x' = k \times x \][/tex]

[tex]\[ y' = k \times y \][/tex]

Given:

[tex]\( A(2, 4) \)[/tex]

Scale factor [tex]\( k = 1.5 \)[/tex]

Now, calculate the coordinates of [tex]\( A' \)[/tex]:

[tex]\[ x' = 1.5 \times 2 = 3 \][/tex]

[tex]\[ y' = 1.5 \times 4 = 6 \][/tex]

Answer: Jumoke is currently 16 and Aminata is currently 8

Step-by-step explanation:

Could I get brainiest please? its free :D

Jumoke is 27 and Aminata is 11.

11 + 5 = 16

16 x 2 = 32

32 - 5 = 27

27 - 11 = 16

I tried. Correct me if I'm wrong.

Answer:

2520°

Step-by-step explanation:

The sum of the angles in any triangle is 180°

shape. sides. triangles. sum int angles.

triangle. 180×1=180°

quad. 180×2=360°

pentagon. 180×3=540°

n-sides. n( n−2) 180(n−2)

16-sides. 180×14=2520°

Answer:

52 quarters

Step-by-step explanation:

-We know that a quarter dollar is equivalent to $0.25

[tex]\$1=4 \ Quarters[/tex]

-Given that Haley has $13, we multiply this amount by 4 since $1 has 4 quarters to obtain the number of quarters:

[tex]Q=13\times 4\\\\=52[/tex]

Hence, Hayley will get 52 quarters.

Answer: this answer is 130

Step-by-step explanation:

Answer:

2) y = x + 2

3) slope: height increases by 1 unit per unit increase in x

Intercept: initial height (at birth) was 2 units

Step-by-step explanation:

Using (38,40) and (48,50)

Slope: (50-40)/(48-38)

= 10/10

= 1

y = mx + b

y = x + b

40 = 38 + b

b = 2

y = x + 2

Answer:

see below

Step-by-step explanation:

There are (60,61) and (20,23) are the points that I used to find the slope for the line of best fit

m= (y2-y1)/(x2-x1)

m = (23-61)/(20-60)

   = -38/-40

   = .95

We use the slope intercept form of the equation

y= mx+b

y = .95x+b

Substituting in the point (20,23)

23 = .95(20) +b

23 = 19+b

Subtracting 19 from each side

23-19 = 19+b-19

4 =b

The equation is

y =.95x+4

The slope is how much y changes for each change in x.  You did not tell us what the units of x and y are.

The y intercept is what the y value is when x is zero.  The y value  is 4 when x is zero

By multiplying the individual probabilities of being a music student and being on the honor roll and then multiplying by the total on the honor roll, we find the expected number of music students on the honor roll to be 16.

To determine the expected number of music students who are also on the honor roll, we can use the concept of expected value in probability.

Assuming that being a music student and being on the honor roll are independent events, we can multiply the probability of a student being a music student by the probability of a student being on the honor roll.

The probability of randomly selecting a music student from the 300 students is the number of music students divided by the total number of students, P(Music) = 50/300.

The probability of a student being on the honor roll is P(Honor Roll) = 97/300. So, the expected number of music students on the honor roll would be the product of these two probabilities times the total number of students on the honor roll, which the school estimates to be 360.

The calculation: Expected number = [tex]P(Music) \(\times\) P(Honor Roll) \(\times\) Total Honor Roll = (50/300) \(\times\) (97/300) \(\times\)[/tex]

Answer: Game land sells 20 crayons for 5 cents less.

Step-by-step explanation:

Hi, to answer this question we have to calculate the price per crayon in each store, by dividing the amount paid in each case by the number of crayons that each store offers.

Toy world (T): 25/4 = 6.25 cents per crayon

Game land (G): 30/5 = 6 cents per crayon

Now, we have to multiply the cost per crayon by 20.

T=6.25 x 20 = 125 cents  

G=6 x 20 =120 cents

So, comparing both costs, Game land sells 20 crayons for 5 cents less.

125-120 = 5 cents

Final answer:

GameLand sells 20 crayons for $1.20, which is 5 cents cheaper than ToyWorld's price of $1.25 for the same quantity. Linda saves money by purchasing from GameLand.

Explanation:

To determine which store sells 20 crayons for less, we need to calculate the total cost of 20 crayons at each store. At ToyWorld, crayons are sold at 4 for 25 cents. To buy 20 crayons, Linda would need 5 sets of 4 crayons, since 20 divided by 4 equals 5. Each set costs 25 cents, so the total cost at ToyWorld would be 5 sets times 25 cents, which equals $1.25.

At GameLand, crayons are sold at 5 for 30 cents. To get 20 crayons, Linda would need 4 sets of 5 crayons. The total cost at GameLand would be 4 sets times 30 cents, which equals $1.20.

Comparing the two totals, Linda would spend $1.25 at ToyWorld and $1.20 at GameLand, so GameLand sells 20 crayons for 5 cents less than ToyWorld.

The equation of function which have vertical translation by 4 unit will be

             f(x)= 2x - 4

To understand more, check below explanation.

The equation of function is given as,

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

If we have to shift graph of function a unit down. then required equation will be,   [tex]f(x)=2x-a[/tex]

If we have to shift graph of function b unit up. then required equation will be,   [tex]f(x)=2x+b[/tex]

We have to do vertical translation by 4 units down of the function f(x)=2x.

Hence, required equator will be [tex]f(x)=2x-4[/tex]

Learn more about the graph of function here:

https://brainly.com/question/24748644