Jada deposited an amount of money in a bank 5 years ago. If the bank had been paying interest at the rate of 6%/year compounded daily (assume a 365-day year) and she has $21,000 on deposit today, what was her initial deposit?

If the triangles ABC and DEF are similar, then the measurement of line segment DE = 108.72 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

It is given that triangle ABC is similar to triangle DEF.

It can be seen in the image that ΔDEF is a dilated version of ΔABC.

In ΔABC the measurement of side AB = 23 units

In ΔABC the measurement of side BC = 11 units

In ΔDEF the measurement of side EF = 52 units

In ΔDEF the measurement of side DE = x units

Apply the formula for indirect measurement to find the measurement of side DE.

AB/DE = BC/EF

Substitute the values in the equation -

23/x = 11/52

23 × 52 = 11x

x = (23 × 52)/11

x = 1196/11

x = 108.72

Therefore, the measurement of DE is 108.72 units.

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The function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r+3 inches is f(r) = 12π(r² + 3r + 3).

In this question, we are asked to determine a function for a spherical balloon that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r+3 inches.

Volume of spherical balloon = V(r) = 4/3 π r³

If the radius of balloon is r+3 inches = V(r+3) = 4/3 π (r+3)³

The amount of air required is the difference between V(r) and V(r+3):

So, f(r) = V(r+3) - V(r) = 4/3 π (r+3)³ - 4/3 π (r)³

                                  = 4/3 π ((r+3)³ -r³)

                                  = 4/3 π (r+3 -r)((r+3)² + r(r+3) + r²)

                                  = 4π(r² + 9 + 6r + r²+3r + r²)

                                  = 4π(3r² + 9r + 9)

                             f(r) = 12π(r² + 3r + 3)

Hence, the function representing is f(r) = 12π(r² + 3r + 3).

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Answer:

yes as x increases by 10, y increased by 2

The probability that a New Yorker who possesses a cat also owns a dog is 0.103. if a new yorker is chosen at random.

New Yorkers own a dog (D) = 30%

New Yorkers own a cat (C) =  25%

New Yorkers own a cat and dog = 15%

This problem can be calculated using Bayes' theorem, which notes that the possibility of an event A given event B is equal to the possibility of event B given A times the probability of A, divided by the probability of event B.

P(D) = 0.30

P(C) = 0.25

P(C|D) = 0.15

Using Bayes' theorem:

P(D|C) = P(C|D) * P(D) / P(C)

P(C) = \(P(C|D) * P(D) + P(C|not D) * P(not D)\)

P(C) = \(P(C|D) * P(D) + P(C) * P(not D)\)

P(C) =\(P(C|D) * P(D) / (1 - P(D) * P(C|not D))\)

Now we can substitute these values into the Bayes' theorem formula:

P(D|C) = P(C|D) * P(D) / P(C)

P(D|C) = \(0.15 * 0.3 / (P(C|D) * P(D) + P(C) * P(not D))\)

P(D|C) = \(0.15 * 0.3 / (0.15 * 0.3 + P(C) * 0.7)\)

P(C) = \(0.15 * 0.3 / (1 - 0.3 * 0.25)\)

P(C) = 0.16

P(D|C) = \(0.15 * 0.3 / (0.15 * 0.3 + 0.16 * 0.7)\)

P(D|C) = 0.103

Therefore, we can conclude that the probability that a New Yorker who owns a cat also owns a dog is 0.103.

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Answer:

x < 4

Step-by-step explanation:

Solving with steps below:

x < 4 (x=3,2,1,0,-1...)

You must write x = ... at the end.

Step-by-step explanation:

5x-2 < 2x+10

or,5x -2x < 10+12

or, 3x < 12

or 3x/3 < 12/3

Therefore x < 4

so x= 3,2,1,0,-1.....

Answer:

20 percent

Step-by-step explanation:

There are 20 percent of the trees in the forest are the Oak trees.

The percentage of oak trees,  p , in the forest can be calculated using the following formula:

p = Number of oak  trees/ Total number of trees x  100

Given that there are 300 oak trees out of a total of 1,500 trees in the forest.

Plugging these values into the formula:

p = (300)/ (1500) x 100

   = 1/5 x 100

   = 100/5

   = 20

So, 20% of the trees in the forest are oak trees.

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Answer:

f(x) = x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = \(\frac{5-0}{0-(-5)}\) = \(\frac{5}{0+5}\) = \(\frac{5}{5}\) = 1

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = x + 5 , or

f(x) = x + 5

Answer:

x+5

Step-by-step explanation:

Because I said so

Answer:

$84

Step-by-step explanation:

First, let's set up an equation to solve:

each visit is $3, so we can use v to stand for the number of visits:

3v

The center charges a $30 fee so we need to add that to the previous term:

3v+30

This will altogether cost c, or the amount of money:

3v + 30 = c

How we can use substitution to solve:

3v + 30 = c

3 ( 18 ) + 30 = c

54 + 30 = c

84 = c

Answer: you total is 84$

Step-by-step explanation:

Samuel needs a total of 6 containers for his plan

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

1 cup of rubbing alcohol = 1/(1/2) = 2 shares

Also, we have

1 cup of rubbing alcohol contains = 1 + 1/2 + 16 = 17.5

For the 2 shares calculated above, we have

2 shares = 17.5 * 2

Evaluate

2 shares = 35

Given that each can hold a maximum of 6 cups, the number of containers needed is

Container = 35/6

This gives

Container = 5.83

Round up

Container = 6

Hence, he needs 6 containers

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Answer:

78.5

Step-by-step explanation:

Answer:

¾

Step-by-step explanation:

\(\boxed{slope = \frac{y1 - y2}{x1 - x2} }\)

☆ (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate

Slope of line

\( = \frac{6 - 3}{0 - ( - 4)} \)

\( =\frac{3}{4} \)

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently.

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently, it is recommended to consider creating a new dependent entity to represent the values. This can help to simplify the design and make it easier to manage and maintain. The new entity can be linked to the original entity through a relationship, allowing each value to be processed independently while still maintaining the integrity of the data. Overall, this approach can improve the efficiency and effectiveness of the system, making it easier to work with and providing better results for the end user.

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Answer:

2^3*5^2*3

Step-by-step explanation:

600=2*2*2*5*5*3=2^3*5^2*3

The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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Answer:

4 yards

Step-by-step explanation:

11 1/2 feet is equal to 3.833333 and 4 yards is more than that.

Answer:

11 1/2 ft. < 4 yd

Step-by-step explanation:

I'm not sure if thats what your asking.

But 1 yard is 3 ft, so 4 yards is equal to 12 ft. Therfore 11 1/2 ft. < 4 yd.

Answer:

β = 110

Step-by-step explanation:

Here, we want to find the value of beta

From the diagram;

70 + β = 180

The reason for this is that the sum of angles on a straight line is 180

Thus, we have that

β = 180-70

β = 110

When we carry out a chi-square goodness-of-fit test for a normal distribution, the null hypothesis states that the population does have a normal distribution.

The null hypothesis states that the population has a normal distribution The chi-square goodness-of-fit test is not specifically used for testing the normal distribution. It is typically used to test whether observed data follows an expected theoretical distribution In the case of a chi-square goodness-of-fit test for a normal distribution, the null hypothesis would state that the observed data follows a normal distribution.

The chi-square goodness-of-fit test is a statistical test used to determine if there is a significant difference between the observed frequencies in a sample and the expected frequencies based on a theoretical distribution or model The null hypothesis in a chi-square goodness-of-fit test states that the observed data follows the expected distribution or model. The alternative hypothesis suggests that there is a significant difference between the observed and expected frequencies.

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Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

========================================================

Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

========================================================

Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\\)

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

Answer:

Find half the area of the rectangle

Step-by-step explanation:

Given

See attachment for the Serek's steps

Required

Which can be used to determine the area of the original triangle

To do this, we simply analyze each step.

At step 2, where he joined two congruent triangles to form a parallelogram.

Half the area of the parallelogram will give the area of the original triangle (since both triangles are equal)

At step 3, where he decomposed the parallelogram to a trapezoid and a right triangle.

Half the sum of the areas of the resulting shapes (trapezoid and right triangle) will equal to the area of the original triangle but half the area of each shape will not amount to the area of the original triangle

At step 4, where the right triangle and the trapezoid are merged to form a rectangle.

The area of the rectangle will equal to the area of the parallelogram in step (2).

So, half the area of the rectangle will equal to the area of the triangle.

Hence, (b) is correct

The correct option is option (A) . Using Scatter plots,

Visulazation by scatter plots show the association and the distribution of Y changes as X changes.

Scatter plots:

A scatterplot plots pairs of numeric data using one variable on each axis to explore the relationship between them. If the variables are correlated, the points are along a straight line or curve.

A correlation exists between two variables if one of them is related to the other in some way. A scatterplot is a great place to start. A scatterplot (or scatterplot) is a graph of paired (x,y) sample data with a horizontal x-axis and a vertical y-axis. Each unique (x,y) pair is represented as one point.

Thus, the Visual examination of a scattergram indicates the existence of an association between variables and change in Y with change in X .

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(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

Answer:

-15p+20

Step-by-step explanation:

The domain of the function represented by the graph is x ≥ 0

The function is represented by the graph of the function

From the given graph, we have the following observations

This means that the function has a domain of all set of real values greater than or equal to 0

This is represented as

x ≥ 0

So, the domain is x ≥ 0

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Answer:

Additive property

Step-by-step explanation:

Given

\(x - 5 = -14\)

Required

The property used

In the 2nd step, 5 was added to both sides, i.e.

\(x - 5+5 = -14 + 5\)

The above is an illustration of additive property of equality, i.e. Adding or subtracting the same variable or constant to both sides of an equation

The correct option is C. find the real range, find the interval width, and construct the frequency distribution.

To make the information easier to understand, frequency distributions are textured look which organise and present frequency counts. Absolute frequencies as well as frequency distributions, such as percentages or ratios, can be displayed in frequency distributions.

The real range is find by the following method-

The interval width is find by the following method-

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The correct question is-

The three steps for constructing a simple frequency distribution are -

Group of answer choices

A. find the observed range, find the interval width, and construct the frequency distribution

B. find the real range, count the scores, and construct the frequency distribution

C. find the real range, find the interval width, and construct the frequency distribution

D. all of the above

Answer:

-12-6p-(-2)= 6p-14

Step-by-step explanation:

If need help remember this song: Same signs add and keep, different sign subtract, take the sign of the higher number than you´ll be exact

-12-6p-(-6p)

-12--2 =-14

leave 6p alone