2. Find the dimensions (outside parts) of the Area Model below. Then write the area as a
product and as a sum.
X²
3x
-5x
-15
Product
Sum

Answer:

a) The exponential function is \(A(t) = 10083(1.068)^t\)

b)

The balance after 1 year is of $10,768.644

The balance after 2 years is of $11,500.91

The balance after 5 years is of $14,010.25.

The balance after 10 years is of $19,467.15

c)

The doubling time is of 10.54 years.

Step-by-step explanation:

Continuously compounded interest:

The amount of money earning after t years, with interest compounded continuously, is given by:

\(A(t) = A(0)(1+r)^t\)

In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.

a) Find the exponential function that describes the amount in the account after time t, in years.

Suppose that $10,083 is invested at an interest rate of 6.8% per year

This means, respectively, that \(A(0) = 10083, r = 0.068\)

So

\(A(t) = A(0)(1+r)^t\)

\(A(t) = 10083(1+0.068)^t\)

\(A(t) = 10083(1.068)^t\)

b) What is the balance after 1 year? 2 years? 5 years? 10 years?

After 1 year:

\(A(1) = 10083(1.068)^{1} = 10,768.644\)

The balance after 1 year is of $10,768.644

After 2 years:

\(A(2) = 10083(1.068)^{2} = 11,500.91\)

The balance after 2 years is of $11,500.91.

After 5 years:

\(A(5) = 10083(1.068)^{5} = 14,010.25\)

The balance after 5 years is of $14,010.25.

After 10 years:

\(A(10) = 10083(1.068)^{10} = 19,467.15\)

The balance after 10 years is of $19,467.15.

c) What is the doubling time?

This is t for which \(A(t) = 2A(0)\). So

\(A(t) = A(0)(1.068)^t\)

\((1.068)^t = 2\)

\(\log{(1.068)^t} = \log{2}\)

\(t\log{1.068} = \log{2}\)

\(t = \frac{\log{2}}{\log{1.068}}\)

\(t = 10.54\)

The doubling time is of 10.54 years.

Answer:

No, because it fails the line test.

Step-by-step explanation:

The line test is a test to tell whether or not a graph represents a function. If the line passes through the graph at one point, it is a function. x's length is at least 8, which means the line would cut through more than one point. Therefore, it is not a function.

The answer is (2.5,7)

Answer:

this answer could help you...

Step-by-step explanation:

make me brainiest

The speed where Trish is driving is 46 miles per hour.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

Given the table where a number of hours and miles are shown,

The unit rate of first data = 69/1.5 = 46

the unit rate of second data = 161/3.5 = 46

And so on

So, 46 will be constant of the function

It means the function will be y = 46x and the rate of the function will be y/x = 46.

Hence "The speed where Trish is driving is 46 miles per hour".

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ANSWER:

u = 2

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solve for u:

The solution of the equation is 2

Answer: The distance is sqrt(40).

Step-by-step explanation:

Let's use the Pythagorean Theorem (a^2 + b^2 = c^2)

(Look at the image I attached)

Let's set a = 2 and b = 6. The mystery side is c, which is opposite to the right angle that is formed when you draw perpendicular lines from each of the points.

(2)^2 + (6)^2 = c^2 <--- First, we need to simplify

4 + 36 = c^2

40 = c^2 <--- Now, we need to take the square root of both sides.

c = sqrt(40)

So, the distance between (5, -4) and (-1, -2) is sqrt(40). I recommend looking at some videos on Khan Academy if you need more help! Let me know if you want me to attach a link that you can visit.

The inversion point of (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

To find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0, we need to follow these steps:

Step 1: Write the equation of the given circle in standard form by completing the square for x and y: (x - 2)² + (y - 3)² = 16.

Step 2: Find the radius of the circle by taking the square root of the constant term: r = √16 = 4.

Step 3: Find the distance between the given point (4, 5) and the center of the circle (2, 3) using the distance formula: d = √[(4 - 2)² + (5 - 3)²] = √8.

Step 4: Use the formula for inversion point to find the coordinates of the inversion point (x', y'): (x', y') = (h + r²/d² * (x - h), k + r²/d² * (y - k)), where (h, k) is the center of the circle and r is the radius.

Plugging in the values, we get: (x', y') = (2 + 4²/8 * (4 - 2), 3 + 4²/8 * (5 - 3)) = (6, 7).

Therefore, the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

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The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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Answer:

B. Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?

Step-by-step explanation:

Remember we are told there's already a question whether pediatricians should recommend early exposure or avoidance. Thus, the research question should answer these two issues (early exposure or avoidance).

Hence, the question we are asking is: Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?

The statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true.

Given, two functions  y = -2f(x) = 1/x

To determine whether the statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true or false, we need to find the value of Y for both functions when x = -2.

Substituting x = -2 in the functions we get:I would ask y = -2(-2) = 4f(-2) = 1/(-2) = -1/2Therefore, the Y value of the function I would ask is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2. Hence, the given statement is true.

Therefore, the statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true.

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Answer:

\(P(R\ or\ odd\ Numbered)=5/7\)

Step-by-step explanation:

From the question we are told that:

Number of Red Marble \(n_r=6\)

Number of Blue Marble \(n_b=8\)

Sample size \(n=n_r+n_b\)

\(n=6+8\)

\(n=14\)

And

No of red or Odd numbered \(x= 6+4 = 10\)

Generally the equation for  probability the marble is red or odd numbered. is mathematically given by

\(P(R or odd Numbered)=x/n\)

\(P(R or odd Numbered)=10/14\)

\(P(R\ or\ odd\ Numbered)=5/7\)

Answer:

Step-by-step explanation:

Surface area of cuboid A with side a is:

Same for cuboid B with side b:

Ratio of surface areas:

Volumes of A and B are:

And their ratio is:

Correct option is B

Answer:

B. 125 : 216

Step-by-step explanation:

Answer:

77°

Step-by-step explanation:

103° + ∠1° = 180°

Answer:

80⁰+ 105⁰+ 75⁰+ x = 360

260⁰+ x =360

x= 360 - 260

x= 100⁰

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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Answer:

Step-by-step explanation:

Let the number of hours driven by Maggie be x and that of Alan be y

If Maggie and Alan drive for a total of 32 hours, then;

x+y = 32 ..... 1

Also if Maggie drives three times the number of  hours that Alan drives on their vacation, then x = 3y ...... 2

Substitute eqn 2 into 1;

x+y = 32

3y+y = 32

4y = 32

y = 32/4

y = 8 hours

Since x = 3x

x = 3(8)

x = 24 hours

Hence Maggie drives for 24 hours and Alan drives for 8 hours

a. In this figure, Dev wants to add a metal trim around the perimeter of the sign. So,

7 +3.5+35+2+2+1/2*3*3= 18+ 4.71= 22.71 ft.

b. Area = L x W = 7*3.5= 24.5 ft2

c.  1 pin has 20 ft2 so 24.5 ft2 x 1 pin /20 ft2 = 1.225 pin

Answer:

680 students

Step-by-step explanation:

The 68 - 95 - 99.7  rule (empirical rule) states that 68% of the population lies within one standard deviation of the mean,  95% of the population lies within two standard deviations and 95% of the population lies within three standard deviations.

Hence since it was said that within 1 deviation (of the mean) of all people like MATH 123, therefore the number of people that like MATH 123 is:

number of people that like MATH 123 = 68% of the population

number of people that like MATH 123 = 0.68 * 1000

number of people that like MATH 123 = 680 students

Answer:

They are all almost a dollar difference.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Steps of calculation:

Answer is 5

Answer Key:

1. Since the question says Mr. Smith runs 2.7 miles every day of the week, you will need to multiply it with 365, the days of the year. The total answer you would get D. 985.5 miles.

| I just want to help you with #2 anyway