Dominick and Ryan both invest $6,500 into savings accounts that earn 6. 8% interest. If Dominicks account earns compound interest and Ryan's earns simple interest, how much more interest will Dominick have earned after 10 years?

Answer:82

Step-by-step explanation:

90 + 90 × 10%

= 90 + 90 × 0.10

= 90 + 9

= 99

Answer:

\(\frac{79}{100}\)

Step-by-step explanation:

Question:

Write as a fraction in lowest terms:

Answer:

a = 79

b = 99

12/14+-7/14 . =5/14

lol

Answer:

  86 ft

Step-by-step explanation:

You want the straight line distance from a location 50 ft from a hotel to a window that has an angle of elevation of 54.5°.

The cosine relation between sides and angles in a right triangle is ...

  Cos = Adjacent/Hypotenuse

The 50 ft distance is adjacent to the angle, and we want to find the hypotenuse. Using this equation, we can solve for the length we want:

  Hypotenuse = Adjacent/Cos

Using the numbers in the problem statement, we find the straight-line distance to be ...

  LW = LH/cos(54.5°) = (50 ft)/0.580703 ≈ 86 ft

The distance between Penny and Lisa is about 86 feet.

__

Additional comment

We don't know what drawing tools you have available. The attached diagram was drawn by locating the window at 50tan(54.5°) up from the base of the hotel. The tool provided the length of LW as 86.1.

We could have use a rotation tool to create the angle of 54.5°, or a line graphing tool to draw the line through (50, 0) with slope tan(-54.5°). Then an intersection tool could have located the window at the point of intersection of that line and the y-axis.

The calculation we did above is about the easiest for determining the distance mathematically (not having the tool measure it).

<95141404393>

The next three terms in the given geometric sequence are 24, 48, and 96

To find the next terms in the geometric sequence 3, 6, 12, we need to find the common ratio (r) first.

r = 6/3 = 2

Now we can use the formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)

where n+1 is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Using this formula, we can find:

a4 = 24 (3 * 2^3)
a5 = 48 (3 * 2^4)
a6 = 96 (3 * 2^5)

Therefore, the next three terms in the sequence are 24, 48, and 96.

To learn more about geometric sequence go to:

https://brainly.com/question/13008517#

#SPJ11

The value of 48 inches/hour is 121.92 centimetres/hour.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

To compare the speed of 48 inches per hour with metric measures, we need to convert inches to metric units. One way to do this is to use the conversion factor of 1 inch = 2.54 centimetres.

48 inches per hour is equivalent to:

48 inches/hour x  2.54 centimeters/inch = 121.92 centimeters/hour

To find all the metric measures that are faster than 48 inches per hour, we can convert 121.92 centimetres/hour to other units of measure. Here are some options:

1.2192 meters/hour: This is faster than 121.92 centimetres/hour because 1 meter = 100 centimetres.

0.0759 miles/hour: This is faster than 48 inches/hour because 1 mile = 63,360 inches.

Therefore, the metric measures that are faster than 48 inches per hour are 1.2192 meters/hour, 0.0759 miles/hour, and 0.042 knots.

To know more about an expression follow

https://brainly.com/question/3955273

#SPJ1

Answer:

D

Step-by-step explanation:

i hope this helps!

Answer:

C = -2t + 30

Step-by-step explanation:

Answer:

  1. y = 2/3x

  2. P, y=-3x

Step-by-step explanation:

1. The constant k in the proportion y=kx can be found as ...

  k = y/x . . . . for any x-y pair

The first pair gives ...

  k = 2/3

So, the relation is ...

  y = 2/3x

__

2. The y-intercept is 0, so the relation is proportional.

The constant of proportionality k can be found from the graph by finding the value of y when x=1. We know that a point on the graph is (-1, 3), and we can also see that the line goes through (1, -3)

  y = -3x

If SSR (regression sum of squares) is 1200 and MSE (mean square error) is 20 from a simple regression which uses 22 data observations, then the R² is 0.75.

In a simple linear regression, the total variation in the dependent variable (y) can be partitioned into two parts: explained variation due to the regression model and unexplained variation due to random error. The proportion of the total variation in y that is explained by the regression model is measured by the coefficient of determination, R².

R² is calculated as SSR/SST, where SSR is the regression sum of squares (variation explained by the regression model) and SST is the total sum of squares (variation in y around its mean).

Since we are given that SSR = 1200 and the regression model has one predictor variable, the degrees of freedom for SSR is 1. Therefore, SST = SSR + SSE (sum of squares error), where SSE = MSE*(n-2), with MSE being the mean square error and n being the sample size (number of observations).

Substituting the given values, we get: SST = 1200 + 20*(22-2) = 1600.

Thus, R² = SSR/SST = 1200/1600 = 0.75. Therefore, the answer is 0.75.

To know more about simple regression, refer here:

https://brainly.com/question/14313391#

#SPJ11

Answer:

16.642cm

Step-by-step explanation:

Diameter of a circle = 5.3cm

Circumference of a circle = π(d)

                                          = π x 5.3

                                          = 3.14 x 5.3

                                          = 16.642cm

Answer:

C= pi x diameter

= 5.3pi

Answer is 16.65cm to 2 d.p

Hope this helps!

The center of mass of the right triangle is 2.14

The term center of mass refer a point where the whole mass of the body is supposed to be concentrated.

Here we have given that a 60-cm length of uniform wire, of 60 g mass and negligible thickness, is bent into a right triangle.

And we need to find the center of mass.

According to the following diagram, we have identified the values of

m1 = 24

m2 = 26

m3 = 20

r1 = 5

r2 = 5

r3 = 0

Then based on these values the center of mass is calculated as,

=> [(24 x 5) + (26 x 5) + (20 x 0)]/[24 + 26 + 20]

When we simplify this one then we get,

=> [ 120 + 130 + 0] / 70

Further simplification leads the value of,

=> 150/70

=>15/7

When we simplify this fraction into decimal then we get,

=> 2.14

To know more about center of mass here.

https://brainly.com/question/27549055

#SPJ4

Answer:

"In

In a 30-60-90 triangle, the sides are in a ratio of 1:√3:2.

So, the hypotenuse of the triangle is 62 = 12 ft long.

The longer leg of the triangle is 6√3 = 10.8 ft long (to the nearest tenth of a foot)

In the proof of given identity, cos(π - A) = -cos A. Therefore, step 1 is error made.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

The given identity is,

cos(π - A) = -cos A.

Use formula for cos(a − b) = cosa . cosb + sina . sinb

cos(π - A) = cosπcosA + sinAsinπ

                = (−1)(cosA) + (sinA)(0)

                = −1.cosA + (sinA)(0)

                = −cosA + 0

                 = −cosA

Since, in the step 1 the formula is wrongly used,

Therefore, step 1 is error made.

To know more about Trigonometric identities on:

https://brainly.com/question/24377281

#SPJ1

The average value of function f(x) over [a,b] = 1/(b-a) × definite integral of f(x) over [a,b]

To find the average value of a function f(x) over an interval [a,b], you need to follow these steps:

Calculate the definite integral of the function f(x) over the interval [a,b]. The definite integral will give you the total area under the curve of the function over the interval.

Find the length of the interval [a,b] by subtracting the lower bound a from the upper bound b. The length of the interval will be (b-a).

Divide the value of the definite integral by the length of the interval to get the average value of the function over the interval [a,b]. That is:

Average value of f(x) over [a,b] = 1/(b-a) × definite integral of f(x) over [a,b]

So, the average value of a function over an interval is simply the total area under the curve of the function over that interval divided by the length of the interval.

Learn more about average value here

brainly.com/question/22847740

#SPJ4

The value of k that makes the given function a valid probability density function is k = 6.

To be a valid probability density function, the given function must satisfy the following two conditions:

The function must be non-negative for all possible values of X.

The integral of the function over all possible values of X must equal 1.

Using these conditions, we can determine the value of k as follows:

For the function to be non-negative, kx(1-x) must be non-negative for all possible values of X. This requires that k must be non-negative as well.

To find the value of k such that the integral of the function over all possible values of X is equal to 1, we integrate the given function from 0 to 1 and set the result equal to 1:

∫\(0^1 kx(1-x) dx = 1\)

Solving the integral gives:

k/6 = 1

k = 6

Learn more about probability

https://brainly.com/question/30034780

#SPJ4

Answer:

x = -4, y = 1/3

Step-by-step explanation:

=> x = 3y-5        (Equation 1)

=> 2x+12y = -4  (Equation 2)

Putting (1) in (2)

=> 2(3y-5)+12y = -4

=> 6y-10+12y = -4

=> 18y = -4+10

=> 18y = 6

Dividing both sides by 18

=> y = 6/18

=> y = 1/3

Putting y = 1/3 in Equation 1

=> x = 3(1/3)-5

=> x = 1-5

=> x = -4

The probability distribution can be constructed by dividing each value of p(x) by the sum of all p(x) values. This will give the proportion of each value in the distribution. The completed table is as follows: x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | p(x)| 0.030 | 0.061 | 0.139 | 0.243 | 0.186 | 0.117 | 0.064.

To construct the probability distribution, we need to find the probabilities for each value of x. The p(x) values given in the table represent the frequencies or counts of each value. To convert these counts into probabilities, we need to divide each p(x) value by the sum of all p(x) values.

In this case, the sum of all p(x) values is 7 + 14 + 32 + 56 + 43 + 27 + 15 = 194. To find the probability for each x value, divide each p(x) value by 194.

For example, the probability for x=0 is 7/194 ≈ 0.036. Similarly, the probability for x=1 is 14/194 ≈ 0.072, and so on.

The completed probability distribution table is as follows:
x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | p(x)| 0.036 | 0.072 | 0.165 | 0.289 | 0.222 | 0.140 | 0.082.

To know more about Frequencies visit.

https://brainly.com/question/33515650

#SPJ11

Answer:

5 units

Step-by-step explanation:

The area of the regular polygon is 280. 26 square inches

We can see from the diagram shown, that the polygon drawn is a hexagon, that is, a regular polygon with six sides.

The formula for calculating the area of a polygon is expressed as;

A = 3√3/2 a²

Given that the parameters are;

From the information given,

Substitute the values, we have;

Area = 3√3/2 × 18²

Find the square

Area = 1. 73 ×324/2

Multiply the values

Area =560. 5/2

Divide the values

Area = 280. 26 square inches

Learn about polygons at: https://brainly.com/question/8409681

#SPJ1

There are 26^7 * 21 number of ways to create an 8-letter word using the 26-letter alphabet that begins or ends with a vowel, where 26 is the number of letters in the alphabet, and 21 is the number of consonants.

To find the number of 8-letter words that either begin or end with a vowel, we need to consider two cases: words that begin with a vowel and words that end with a vowel.

For words that begin with a vowel, we have one vowel as the first letter and any of the 26 letters of the alphabet for the remaining 7 letters. Hence, there are 26^7 ways to create an 8-letter word that begins with a vowel.

For words that end with a vowel, we have 21 consonants for the first letter and any of the 26 letters of the alphabet for the remaining 7 letters, followed by one of the five vowels. Hence, there are 21 * 26^7 * 5 ways to create an 8-letter word that ends with a vowel.

Therefore, the total number of 8-letter words that either begin or end with a vowel is the sum of the two cases: 26^7 + 21 * 26^7 * 5, which simplifies to 26^7 * 21.

To know more about the number of ways refer here:

https://brainly.com/question/30649502#

#SPJ11

Step-by-step explanation:

(0,5) and (-2,-3)

y=mx+b

find m

\( \frac{y1 - y2}{x1 - x2} \\ = \frac{5 - ( - 3)}{0 - ( - 2)} \\ = \frac{8}{2} \\ = 4 \\ \)

m=4

Substitute (0,5) or (-2,-3)

For easy processing substitute : (0,5)

y=4x+b

5=b

y=4x+5 is the answer

Brainliest please~

Answer:

10x² + 11x - 6

Step-by-step explanation:

The area (A) is the product of the sides, that is

A = (2x + 3)(5x - 2) ← expand using FOIL

   = 10x² - 4x + 15x - 6 ← collect like terms

   = 10x² + 11x - 6

Answer:

Look at the lightest loaf of bread. It weighs 22 1/3 oz. The heavist loaf weighs 24 1/2. Subtract 24 1/2 and 22 1/3. Then, if the answer to that is 1 1/2 ounces then you agree. If it is not, then disagree. Then, add up all of the weights of the bread and find the answer.

The equation in standard form that models the number of possible t-shirts and shorts you can buy is; 4.5x + 6y = 108

The graph of the function is as attached

A linear equation is defined as an equation whereby the highest power of the variable is always 1.

We are told that the cost of each T-shirt is $4.50 while each short costs $6. Thus, if he has enough money for 12 t-shirts and 9 pairs of shorts, it means that;

Total amount he has = 12(4.5) + 9(6) = $108

Now, if the amount of t-shirts he can possibly buy is x and the amount of pairs of shorts he can possibly buy is y. Thus, the linear equation is;

4.5x + 6y = 108

Read more about Graph of Linear Equation at; https://brainly.com/question/14323743

#SPJ1

The inequality represented by the graph is given as follows:

D. 4 > |x + 1| + 2.

The solution set represented by the graph is composed by numbers between -3 and 1, with an open interval, that is:

-3 < x < 1.

Then we solve each inequality in this problem, to find the one with the solution set that matches this one.

For item a, we have that:

|x + 1| < -3.

Which has no solution, as the absolute value function always assumes a value of at least zero.

For item b, we have that:

1 > |x + 2| + 2.

|x + 2| < -1.

No solution, for the same reason as item a.

For item c, we have that:

2 < |x + 3| - 2

|x + 3| < 4.

Hence:

-4 < x + 3 < 4.

The lower bound of the solution is of:

x + 3 > -4

x > -7.

Which does not match.

For item d, we have that:

4 > |x + 1| + 2

|x + 1| < 2

Hence:

-2 < x + 1 < 2

The lower bound of the solution is of:

x + 1 > -2

x > -3.

The upper bound of the solution is of:

x + 1 < 2

x < 1.

Meaning that option D is the correct option.

More can be learned about inequalities at https://brainly.com/question/9290436

#SPJ1