Danica and Irma are flying kites. Danica's kite is 7 times as high as Irma's kite. Danica's kite is 273 feet high. How high is Irma's kite?

A .280 feet


B. 39 feet


C. 1,911 feet


D. 40 feet​

Answer:

x = 16

y = 10

Step-by-step explanation:

See attached worksheet.

(2x)^4 = 16x^4 is the continued product

The value of g(x) + j(x) is 2x³ + 3x² + 2x -6.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's basic components are a number or variable, a math operator, and another number or variable. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. 2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient, or a value multiplied by the variable. The number 2, which denotes 2 times plus x, is the coefficient of x in the formula 2x + 3.

Given,

Expression

g(x) = 2x² - 1

j(x) = 2x³ + x² + 2x - 5

g(x) + j(x).

Equating,

2x² - 1 + 2x³ + x² + 2x - 5

2x³ + 3x² + 2x -6

The value of g(x) + j(x) is 2x³ + 3x² + 2x -6.

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b) It will take approximately 24.6 years to save $3,000 for your vacation by saving $100 each month with a 3% nominal interest rate compounded monthly.

c) equivalent effective interest rates are:

i. Semi-annually: 5.06%

ii. Quarterly: 5.11%

iii. Daily: 5.13%

iv. Continuously: 5.13%

EXPLANATION:

To calculate the time it will take for you to save $3,000 for your vacation, we can use the future value formula for monthly compounding:

\(Future Value = Principal * (1 + rate/n)^(n*time)\)

Where:

- Principal is the amount you save each month ($100)

- Rate is the nominal interest rate (3% or 0.03)

- n is the number of compounding periods per year (12 for monthly compounding)

- Time is the number of years we want to calculate

We need to solve for time. Let's substitute the given values into the formula:

\($3,000 = $100 * (1 + 0.03/12)^(12*time)Dividing both sides of the equation by $100:30 = (1.0025)^(12*time)\)

Taking the natural logarithm (ln) of both sides:

\(ln(30) = ln((1.0025)^(12*time))Using logarithmic properties (ln(a^b) = b * ln(a)):ln(30) = 12*time * ln(1.0025)\)

Solving for time:

\(time = ln(30) / (12 * ln(1.0025))\)

Using a calculator:

time ≈ 24.6

c)To calculate the equivalent effective interest rate for a nominal rate of 5% compounded at different intervals:

i. Semi-annually:

The effective interest rate for semi-annual compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

For semi-annual compounding:

\(Effective Interest Rate = (1 + (0.05 / 2))^2 - 1\)

Calculating:

Effective Interest Rate ≈ 0.050625 or 5.06%

ii. Quarterly:

The effective interest rate for quarterly compounding is calculated similarly:

\(Effective Interest Rate = (1 + (0.05 / 4))^4 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051136 or 5.11%

iii. Daily:

The effective interest rate for daily compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

Since there are approximately 365 days in a year:

\(Effective Interest Rate = (1 + (0.05 / 365))^365 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051267 or 5.13%

iv. Continuously:

The effective interest rate for continuous compounding is calculated using the formula:

\(Effective Interest Rate = e^(nominal rate) - 1\)

For a nominal rate of 5%:

\(Effective Interest Rate = e^(0.05) - 1\)

Calculating:

Effective Interest Rate ≈ 0.05127 or 5.13%

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Answer:

the answer is a

Step-by-step explanation:

A function assigns values. The function that represents the graph is (1/4)^(x+2).

A function assigns the value of each element of one set to the other specific element of another set.

The function of the graph that will represent the graph given below is

\(y = (\dfrac{1}{4})^{(x+2)}\)

Thus, the function that represents the graph is (1/4)^(x+2).

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True. Statisticians can never be 100% sure that statistical outcomes in a sample perfectly match the actual parameters in the population.

This is because statistical inference is based on sampling, which involves drawing conclusions about a population based on a subset of data. There is always a degree of uncertainty or sampling error associated with estimating population parameters from a sample.

Statistical inference relies on making probabilistic statements and constructing confidence intervals or hypothesis tests to quantify the level of uncertainty. While statisticians strive to minimize bias and variability in their estimates, there is always a margin of error involved. Factors such as sampling variability, measurement errors, and the inherent randomness of data contribute to this uncertainty.

Therefore, statisticians acknowledge that their conclusions are based on probability and inference rather than absolute certainty. They provide measures of confidence or significance to communicate the level of uncertainty associated with their findings.

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Answer:

  15.30

Step-by-step explanation:

You want f(2) if f(x) is an exponential function such that f(-3) = 9 and f(7) = 26.

Using the given points, we can write the function as ...

  \(f(x)=9\left(\dfrac{26}{9}\right)^{\dfrac{x-(-3)}{7-(-3)}}=9\left(\dfrac{26}{9}\right)^{\dfrac{x+3}{10}}\)

Then the value of f(2) is ...

  \(f(2)=9\left(\dfrac{26}{9}\right)^{\dfrac{2+3}{10}}=9\sqrt{\dfrac{26}{9}}=3\sqrt{26}\approx 15.29706\\\\\boxed{f(2)\approx15.30}\)

__

Additional comment

The form of the function is ...

  f(x) = a·b^((x-x₀)/i)

where a=value at the beginning of the interval, b is the ratio of ending to beginning values, and i=interval width: x₁ -x₀. This can be written as an exponential function of e, but this is the simplest way to use given values.

Here, the "interval" is -3 to +7, and the corresponding beginning and ending values are 9 and 26, respectively.

Answer:

7x - 4 + 35 = 72

7x + 31 = 72

7x = 41

x = 41/7 *you cant simplify*

x = 5 6/7 as a mixed number

Step-by-step explanation:

hope this helps

Answer:

\(\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0\)

General Formulas and Concepts:

Pre-Algebra

Evaluations

Order of Operations: BPEMDAS

Algebra I

Distributive Property

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

\(\displaystyle \frac{4(3x)^2}{(2x)^2}\)

Step 2: Simplify:

\(\\ \sf\longmapsto \dfrac{4(3x)^2}{(2x)^2}\)

\(\\ \sf\longmapsto\dfrac{ 4(9x^2)}{4x^2}\)

\(\\ \sf\longmapsto \dfrac{36x^2}{4x^2}\)

\(\\ \sf\longmapsto \dfrac{x^2}{x^2}\left(\dfrac{36}{4}\right)\)

\(\\ \sf\longmapsto \dfrac{36}{4}\)

\(\\ \sf\longmapsto 9\)

Answer:

1/2

Explanation:

Let's remember how to sum 2 fractions:

So, 1/3 + (-5/6)​ is equal to:

Then, the addition of 1 and -9/18 is equal to:

Now, we can divide the numerator and the denominator by 9 to get an equivalent fraction, so:

Therefore, the answer is 1/2

Answer:

y = 4x – 3

Step-by-step explanation:

Answer:

X=-6

Step-by-step explanation:

The 2 angles add up to 180 degrees. You need to set up the equation as so

126+x+60=180, combine like terms

186+x=180, isolate x by itself, subtract 186 from 180.

X=-6

Answer:

1.dd

2.Dd

3.dd

4.Dd

5.dd

Explanation:

It's genetics

   D     d

d   D     d

d   D     d

Using compound interest, it is found that:

a) He will have paid $18,774 in total.

b) He paid $4,774 more than the price of the car.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

In this problem, the parameters are:

\(P = 14000, r = 0.049, n = 12, t = \frac{72}{12} = 6\).

Item a:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(6) = 14000\left(1 + \frac{0.049}{12}\right)^{12 \times 6}\)

\(A(6) = 18774\)

He will have paid $18,774 in total.

Item b:

18774 - 14000 = $4,774.

He paid $4,774 more than the price of the car.

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Answer:

The answer is A

Step-by-step explanation:

Answer:

Brainlist pls?

Step-by-step explanation:

The Answer is B

Answer:

the answer is c

Step-by-step explanation:

took the assignment

A deck has a total of 52 cards.

The probability of getting a black 4 is then:

Answer: The answer is where the n is the number of people in the club

Step-by-step explanation:

A)Write down an expression, in terms of n, for the number of people in the club.

B) Two of the people in the club are chosen at random. The probability that both these people are men is one tenth. Calculate the number of people in the club.

Answer:

B

Step-by-step explanation:

To find the number of extra flowers ordered, we can start by forming an equation based on the total amount paid by the customer.

Let the number of extra flowers be n.

Total paid

= cost of standard arrangement +(number of extra flowers)(cost per additional flower)

= $25 +n($1.25)

Given that the customer paid $45,

25 +1.25n= 45

Now that we have formed the equation, let's solve for n.

Subtract both sides by 25:

1.25n= 45 -25

1.25n= 20

Divide both sides by 1.25:

n= 20 ÷1.25

n= 16

To find the surface area generated by rotating the given curve about the y-axis, we can use the formula for the surface area of a surface of revolution.

The formula is given by S = 2π∫[a,b] x(y)√[1 + (dy/dx)²] dy, where a and b are the limits of integration and x(y) is the equation of the curve.

(a) For the curve x = √(16 - y²), 0 ≤ y ≤ 2, we can find the surface area by using the formula S = 2π∫[0,2] x(y)√[1 + (dy/dx)²] dy.

First, we need to find dy/dx by taking the derivative of x with respect to y. Since x = √(16 - y²), we have dx/dy = (-y)/(√(16 - y²)).

To simplify the expression inside the square root, we can rewrite it as 16 - y² = 4² - y², which is a difference of squares.

Therefore, the expression becomes dx/dy = (-y)/(√((4 + y)(4 - y))). Next, we substitute the values into the surface area formula and integrate.

The integral becomes S = 2π∫[0,2] √(16 - y²)√[1 + ((-y)/(√((4 + y)(4 - y))))²] dy. Evaluating this integral will give us the surface area.

(b) For the curve x = y³, 0 ≤ y ≤ 1.1, we can follow the same steps as in part (a). We find dy/dx by taking the derivative of x with respect to y, which gives dx/dy = 3y².

Then we substitute the values into the surface area formula, which becomes S = 2π∫[0,1.1] (y³)√[1 + (3y²)²] dy. Evaluating this integral will give us the surface area.

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b) Solving the matrix equation, we find r = 8, l = 4, and i = 3. The florist can use 8 roses, 4 lilies, and 3 irises for each centerpiece.

a) The system of linear equations representing the situation is:

r + l + i = 15 (total flowers in one centerpiece)

r = 2(l + i) (twice as many roses as irises and lilies combined)

10(2.50r + 4l + 2i) = 370 (total budget)'

Matrix equation: AX = B, where

A = [[1, 1, 1], [2, -1, -1], [25, 40, 20]],

X = [[r], [l], [i]], and

B = [[15], [0], [370]]

b) Solving the matrix equation, we find r = 8, l = 4, and i = 3. The florist can use 8 roses, 4 lilies, and 3 irises for each centerpiece.

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The Complete Question:

A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $370 allocated for the centerpieces and wants each centerpiece to contain 15 flowers, with twice as many roses as the number of irises and lilies combined. (Let r represent the number of roses, l represent the number of lilies, and i represent the number of irises.)

a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.

b) Find the number of flowers of each type that the florist can use to create the 10 centerpieces.

The student(s) that successfully outlined a series of steps to complete the construction is both Elias and Greyson

Both Elias and Greyson have presented techniques for generating a line that passes through point C in a perpendicular manner to line AB.

Although their processes differ slightly, they both necessitate the utilization of intersecting arcs prior to forming a connection between a point of intersection and point C by laying down a line.

In conclusion, choosing either Elias or Greyson as the correct answer would be accurate as shows that they both delivered relevant methods that could work.

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The value of m in the diagram is 18°

What is a right-angle?

A right angle is an angle of 90°. When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle.

A right angle is an angle that measures 90 degrees. It is the most commonly seen angle in our day-to-day life.

From the diagram, the two angles sum up to 90°

∠WZX + ∠XZY = ∠WZY

3m + 3 + 33 = 90

3m + 36 = 90

3m = 90 - 36

3m = 54

m = 54/3

m = 18°

In conclusion the value of m is 18°

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The growth rate of the bacterial colony after 3 hours is 32%, the population of a slowly growing bacterial colony after t hours is given by the function p(t) = 100 + 24t + 2t²

The growth rate of the colony is the rate of change of the population, which is given by the derivative of the function. The derivative of p(t) is p'(t) = 24 + 4t

The growth rate after 3 hours is p'(3) = 24 + 4 * 3 = 32. This means that the population of the colony is increasing by 32% after 3 hours.

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Answer:

56.25

Step-by-step explanation:

A set of points which extend infinitely in both directions is called A.) Line.

The line is a collection of points that are regular and continuous and extends in two directions. The model or representation of a line, for example, is like a thread or a straight rope that can be extended in both opposite directions to infinity.

A line has only one dimension, namely length. There are several terms for a line, including: a ray, which is a line that originates at a point and the other end can be extended in an infinite direction, the second is a line segment or line segment, which is part of a line that is bounded by two endpoints, the third is a vertical line, namely upright line, and the fourth horizontal line, which is a horizontal line.

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The correct function that gives the right syntax for the given data analysis is; =RIGHT(B3,5)

Data cleaning is defined as the process of fixing or removing data that are incorrect,  incorrectly formatted, duplicate, corrupted, or even incomplete data that exists within a dataset.

Now, when we combine multiple data sources, what it means is that there could be many opportunities for the data to be duplicated or mislabeled.

Now, from the question, we can see the given data of the spreadsheet with customer names and address and as such, we can easily say that the correct syntax is =RIGHT(B3,5). This is because the RIGHT Function usually returns a set number of characters from the right side of a text string.

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Answer:

4 dozen.

Step-by-step explanation:

Total number of eggs required =2*24 = 48

One dozen = 12 so the answer is 4 dozen eggs.