Chords AB and CD intersect inside a circle at point E. AE= 2, CE =4 , and ED =3 . Find EB.

Therefοre, the sοlutiοn οf the given prοblem οf graph cοmes οut tο be  the parabοla's apex is (-2, -9).

Mathematicians use graphs tο lοgically depict οr chart assertiοns οr values in a visual way. Usually, a graph pοint shοws the cοnnectiοn between twο οr mοre οbjects. A graph is a particular kind οf nοn-linear rail delivery up οf parts knοwn as nοdes as well as lines. The bοrders, alsο referred tο as nοdes, shοuld be jοined tοgether with glue.

The rοοts and vertex οf the parabοla must be identified in οrder tο draw the equatiοn y = x² + 4x - 5.

Setting y = 0 and figuring οut x's value will allοw us tο discοver the rοοts first:

=> \(x^2 + 4x - 5 = 0\)

=> (x + 5)(x - 1) = 0

=> x = -5 or x = 1

Therefore, x = -5 and x = 1 are the equatiοn's solutions.

The vertex can then be lοcated by completing the rectangle as follows:

=> \(y = x^2 + 4x - 5\)

=> \(y = (x^2 + 4x + 4) - 9\)

=>\(y = (x + 2)^2 - 9\)

Consequently, the parabοla's apex is (-2, -9).

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Hi there!

The answer for this question is C, BD. As you can see, BC and DA are the same which means that AB and CD are also the same.

That only leads to BD which means that BD has the shortest sides.

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Southern agriculture was economically devastated by the Civil War primarily because they no longer had enslaved people to work their plantations.

With the abolition of slavery, plantation owners struggled to find laborers who would work for low wages. Additionally, the Confederate casualties outnumbered Union casualties, leaving the South with fewer able-bodied men to work the land. The North, on the other hand, had a larger population and a more diversified economy. Finally, the federal government encouraged people to move west, further reducing the labor supply in the South. As a result, Southern agriculture was left in a state of ruin, with many plantations abandoned or left fallow. This dramatically increased labor costs and reduced production capacity. Additionally, Confederate casualties further depleted the available labor force. The South's smaller population compared to the North also limited its ability to recover. Lastly, the federal government's encouragement of westward expansion attracted potential labor away from the region, further hampering the South's agricultural recovery.

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Answer:

10 km/hr

Step-by-step explanation:

The aircraft carrier and the container ship both took 30 hours to travel their respective distances. If you divide both numbers by 30, you find that their differences is 5. We can tell that the aircraft carrier traveled 450 ÷ 30 = 15 km/hr and the container ship traveled at a speed of 300 ÷ 30 = 10 km/hr. The aircraft carrier traveled 5 km/hr faster. So, we can tell the container ship traveled at 10 km/hr.

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Answer:

6 + 3\(\sqrt{2}\) + 2\(\sqrt{3}\) + \(\sqrt{6}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Given

(3 + \(\sqrt{3}\) )(2 + \(\sqrt{2}\) )

Each term in the second factor is multiplied by each term in the first factor, that is

3(2 + \(\sqrt{2}\) ) + \(\sqrt{3}\) (2 + \(\sqrt{2}\) ) ← distribute both parenthesis

= 6 + 3\(\sqrt{2}\) + 2\(\sqrt{3}\) + \(\sqrt{6}\)

Assuming that the bacteria population doubles every 15 minutes, it will take around 70.6 minutes for the population to increase from 100 to 12,800.

If the population of bacteria doubles every 15 minutes, it means that the growth rate is exponential. The initial population is 100, and we want to find the time it takes for the population to reach 12,800.

To solve this problem, we can use the exponential growth formula:

N(t) = N0 * 2⁽ᵗ/ᵀ⁾

where:

N0 = initial population (100 bacteria)

N(t) = population at time t

t = time elapsed

T = time it takes for the population to double (15 minutes)

We want to find the time it takes for the population to reach 12,800 bacteria, so we can set N(t) to 12,800:

12,800 = 100 * 2⁽ᵗ/¹⁵⁾

Dividing both sides by 100:

128 = 2⁽ᵗ/¹⁵⁾

Taking the logarithm (base 2) of both sides:

log2(128) = t/15

t = 15 * log2(128)

Using a calculator, we can solve for t:

t ≈ 70.6 minutes

Therefore, it will take approximately 70.6 minutes for the population of bacteria to reach 12,800, if the population doubles every 15 minutes.

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The unit rate, which is a constant between the ratio of two numbers that vary concurrently, can also be used to refer to the slope. Slope follows the same rule.

As long as the rise/run along the line remains constant, the slope between any two places on a straight line will always be the same.

A linear relationship grows or shrinks at a constant rate of change, similar to a proportional relationship. This is known as the constant of proportionality in a relationship. It can also be referred to as the slope or unit rate in a linear connection. The slope of a line said to be its steepness.

Like the proportionality constant, the slope shows how quickly an amount is rising or falling. The only difference between the slope and the constant of proportionality is that the relationship need not begin at 0. Mathematicians frequently substitute the term slope or unit rate for the proportionality constant.

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To determine how long it will take Janet and Gerry to finish the job together, we need to calculate their combined work rate.

Let's first find the individual work rates:

Janet's work rate: 1 job / 3 hours = 1/3 job per hour

Gerry's work rate: 1 job / 2 hours = 1/2 job per hour

If Janet works alone for 1 hour, she completes 1/3 of the job.

When they work together, their combined work rate is the sum of their individual work rates:

Combined work rate = Janet's work rate + Gerry's work rate

= 1/3 job per hour + 1/2 job per hour

= 2/6 job per hour + 3/6 job per hour

= 5/6 job per hour

Now, since Janet has already completed 1/3 of the job, the remaining fraction of the job to be completed is 1 - 1/3 = 2/3.

To find the time it takes for Janet and Gerry to finish the remaining 2/3 of the job together, we can use the formula:

Time = Amount of work / Combined work rate

Time = (2/3 job) / (5/6 job per hour)

Simplifying, we get:

Time = (2/3) / (5/6) Time = (2/3) * (6/5) Time = 4/5 hour

Therefore, it will take Janet and Gerry approximately 4/5 hour (or 48 minutes) to finish the remaining 2/3 of the job together.

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9514 1404 393

Answer:

  $2038.85

Step-by-step explanation:

The value of the loan at that point is given by ...

  A = P(1 +rt) . . . . . Principal P, rate r, time t (years)

  A = $1850(1 + 0.1225·(10/12)) = $2038.85

Ricardo will have paid back $2038.85 at the end of the loan period.

_____

Additional comment

We assume that the loan accrues simple interest and that the amount due is the sum of principal and interest at the end of the loan period.

The question is not specific as to whether interest compounds, or whether intermediate (monthly) payments are made. There are many possible ways the loan could be repaid, generally involving different amounts for the different terms.

Answer:

y = 17

Step-by-step explanation:

the initial value of the function is obtained when x = 0

• note that \(a^{0}\) = 1

then

y = 17\((1.24)^{x}\) ← substitute x = 0

y = 17\((1.24)^{0}\) = 17 × 1 = 17

initial value of the function is y = 17

a) The type(s) of bias that might result from the random poll that asks the question as "The proposed casino will produce a number of jobs and economic activity in and around your city, and it will also generate revenue for the provincial government.

Are you in favour of this forward-thinking initiative?" can be termed as leading questions. Leading questions are a kind of biased question that persuades the respondent to answer the question in a particular manner. Since the question contains a positive view of the casino's impact,

respondents will be more inclined to favour the proposal. b) The type(s) of bias that might result from the survey that uses a cluster sample of Toronto residents to determine public opinion on whether the provincial government should increase funding for public transit is probability bias. Probability bias arises when the selection method does not offer everyone an equal opportunity of being chosen, resulting in a bias towards a particular group. Since the sample selected is cluster sampling, it may be biased toward the residents of that area, which might not reflect the views of the whole Toronto population. c)

The type(s) of bias that might result from the group of city councillors being asked whether they have ever taken part in an illegal protest is social desirability bias. Social desirability bias happens when a respondent's reaction is biased by their need to give a socially appropriate answer. The councillors may feel compelled to downplay their involvement in illegal protests to avoid political or social harm.

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Ratio analysis can be made more meaningful in all the following ways except by focusing more on long-term solvency than on short-term solvency.

Ratio analysis is a mathematical technique for analyzing a company's financial documents, such as the balance sheet and income statement, to gather knowledge about its liquidity, operational effectiveness, and profitability. Fundamental equity research is built on ratio analysis.

In order to get insights into profitability, liquidity, operational effectiveness, and solvency, ratio analysis examines line-item data from a company's financial statements.

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The full question:

ratio analysis can be made more meaningful in all the following ways except by?

Answer:

Below

Step-by-step explanation:

TANGENT is defined as the opposite leg / adjacent leg   of the right triangle formed by the angle in the unit circle

  this is   y / x  in the image below :

To find the rate at which the temperature is rising on the bug's path after 2 seconds, we need to use the chain rule of differentiation.

Let T denote the temperature function. Then, the rate of change of temperature with respect to time t is given by dT/dt = (dT/dx)(dx/dt) + (dT/dy)(dy/dt). Substituting the given values, we have dT/dt = (2/sqrt(2+t)) + 9/2. Evaluating this expression at t = 2, we get dT/dt ≈ 6.72 degrees Celsius per second.

To find the equation of the tangent plane to the given surface z = 4(x -1)^2 + 3(y + 3)^2 + 6 at the point (2, -2, 13), we need to find the partial derivatives of the surface with respect to x and y. These are given by ∂z/∂x = 8(x-1) and ∂z/∂y = 6(y+3).

Evaluating these at the given point, we get ∂z/∂x = 8 and ∂z/∂y = 0. Thus, the normal vector to the tangent plane is given by (8, 0, -1). Using the point-normal form of the equation of a plane, we get the equation of the tangent plane as 8(x-2) - z + 13 = 0.

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Answer:

So the value is 18 dollars off which is $42

Step-by-step explanation:

Well we know 50% of 60 is 30 so we want to multiply 60 x 30 = 180 and the denominator would be 100 so 180/100 now we make 180, 18! which makes 18 dollars off so 60 - 18 = 42

Answer:

5/2

Step-by-step explanation:

25 and 10 so 25/10 or 5/2 or 2 1/2

has the form: H(x) = b^x, which corresponds to an exponential function

The mode is the value that appears most frequently in a dataset. In this case, the mode is 4, as it has the highest frequency of occurrence.

The median is the middle value when the data is arranged in ascending or descending order. Since there are an odd number of families (21 in total), the median will be the value of the 11th observation when the data is sorted. Arranging the data in ascending order, we find that the median is also 4, as it is the middle value.

The mean is the average value and is calculated by summing up all the values and dividing by the total number of observations. In this case, we can calculate the mean by multiplying each number of pets by its corresponding frequency, summing up these products, and dividing by the total number of families (21). Using this approach, the mean can be calculated as:

Mean = (0*2 + 1*1 + 2*8 + 3*1 + 4*9 + 5*0) / 21 ≈ 2.76

Therefore, based on the provided data, the mode, median, and mean number of pets owned by the families are all approximately 4.

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Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

\(\frac{-36}{-216} \\=\frac{36}{216} \\=\frac{1}{6}\)

To find the velocity function, we need to integrate the acceleration function. Given that the acceleration vector is a\((t) = (3t, -4e^(-t), 12t^2)\), we integrate each component to obtain the velocity vector function v(t):the velocity function is \(v(t) = (3/2) t^2 i + (4e^(-t) - 3) j + 4t^3 k\).

\(∫ (3t) dt = (3/2) t^2 + C₁\)

\(∫ (-4e^(-t)) dt = 4e^(-t) + C₂\)

\(∫ (12t^2) dt = 4t^3 + C₃\)

Here, C₁, C₂, and C₃ are constants of integration.

Next, we apply the initial velocity U(0) = (0, 1, -3) to determine the values of the constants. At t = 0, the velocity function should be equal to the initial velocity U(0).

From the x-component: \((3/2) (0)^2 + C₁ = 0\), we find that C₁ = 0.

From the y-component:\(4e^(-0) + C₂ = 1\), we find that C₂ = 1 - 4 = -3.

From the z-component: \(4(0)^3 + C₃ = -3\), we find that C₃ = -3.

Plugging these values back into the velocity vector function, we get:

\(v(t) = (3/2) t^2 i + (4e^(-t) - 3) j + 4t^3 k.\)

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Answer:

\(\displaystyle m=0\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-3, 2)

Point (4, 2)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

x=1

Step-by-step explanation:

Answer: x=49

Step-by-step explanation:

equations

\(3\sqrt[]{153x} = 21\sqrt[]{153}\)

To remove the radical on the left side of the equation, square both sides.

\((3\sqrt{153x})^{2}= (21\sqrt{153})^{2}\)

1377x=67473

Divide each term in

1377x=67473 by 1377and simplify

x=49

THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c

TO FIND c I WILL SUBSTITUTE THE GIVEN KNOWN POINTS.

\( - 5= \frac{1}{2} (2) + c \\ - 5= 1 + c \\ c = - 5 - 1 \\ c = - 6\)

THEREFORE WE NOW HAVE

\( y= \frac{1}{2} x - 6\)

ATTACHED IS THE SOLUTION

The fact that the sample means follow an approximately normal distribution is crucial in constructing a confidence interval for a population mean with a known standard deviation.

This is because we can use the properties of the normal distribution to calculate the probability that the true population mean falls within a certain range of values. In this case, we have a sample mean of x¯=10 and a 90% confidence interval of (5, 15) with an estimated bound on the error margin (EBM) of 5. This means that we can be 90% confident that the true population mean lies within the interval (5, 15), with a margin of error of 5 units.

This result is based on the assumption that the sample means follow an approximately normal distribution.

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Probability of paYing in credit card

P(Not paying in credit card)

The probability that the next customer will pay with something other than a credit card is 0.87.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Layla owns a small business selling clothing. She knows that in the last week, 52 customers paid cash, 20 customers used a debit card, and 11 customers used a credit card.

Based on these results we have;

Total cards=52+20+11=83

Probability of paying in credit card;

11/83

0.13

Now, P(Not paying in credit card)

1-0.13

0.87

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This question is dealing with classification of triangles based on angles or on number of equal sides.

the triangle is called an Obtuse Scalene Triangle

- Acute angle is when the angle measures between 0 and 90 degrees.

- Obtuse angle is when the angle is greater than 90 but less than 180 degrees.

- right angle is when the angle is exactly 90 degrees.

- Reflex angle is when the angle is greater than 180 but less than 360 degrees.

- Isosceles triangle is one that has  2 equal sides.

- Equilateral triangle is one that has 3 equal sides.

- Scalene triangle is one that has no equal sides.

The lengths of the three sides of the triangle given are;

5 cm, 9 cm, and 12.7 cm

The three sides are not equal and from definition above it is called scalene triangle.

The angle given is 128° and from definition earlier, it is an obtuse angle.

In conclusion, the triangle is called an Obtuse Scalene Triangle

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Answer:

1,000 pencils  

Step-by-step explanation:  

First, there are 10,000 cents in $100.  

So divide 10,000 by 10.  

1,000.

I hope this helps!  

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