Find a quadratic function that models the


number of cases of flu each year, where y is years since 2012. What is the coefficient of x? Round your answer to the nearest hundredth

Answer:

\(x = 2\) ± \(\sqrt{7}\)

Step-by-step explanation:

Lets see the quadratic equation :

x = -b ± \(\sqrt{b^2 - 4ac}\) / 2a

So now we have our quadratic :

\(x^2 - 4x - 3 =0\)

a = ?^2 (Exponent)

b = ?x   (Variable)

c = ?     (Constant)

So replace every variable in the quadratic equation with the ones in the quadratic formula.

x = -(-4) ± (-4)^2 - 4(1)(-3) / 2(1)

(Imagine (-4)^2 - 4(1)(-3) in a square root)

x = 4 ± \(\sqrt{16 - - 12}\) / 2

x = 4 ± \(\sqrt{28}\) / 2

Of course 28 isn't available for a square root property, so lets break it up :

x = 4 ± \(2\sqrt{7}\) / 2

Simplify the radical :

\(x = 2\) ± \(\sqrt{7}\)

^^^

3x+50

6x-10

6x-10=3x+50

6x-3x=10+50

=3x. 60

(Divide both by 3)

x = 20

Answer:

X= 20 degrees

Step-by-step explanation:

i^2 = -1

So 5i^2 = 5·i^2 = 5(-1) = -5

Answer: -5

a. Phoebe's car has the greater acceleration at first.

b. The maximum distance by which the other car was ahead was approximately 0.69 feet

c. The maximum difference in velocities does not occur at the same time as the maximum distance the two cars are apart.

d. The car that was ahead at first (Calvin's car) does not regain the lead.

Acceleration is the rate at which an object changes its velocity. In other words, it's the amount of change in velocity per unit of time. The standard unit of acceleration is meters per second squared (m/s²).

a Since \(e^{t}\) is always positive and increasing, while 3\(t^{2}\) is positive but increasing at a slower rate, we can conclude that Phoebe's car has the greater acceleration at first.

b We can do this by taking the derivative of the difference and setting it equal to zero:

(su(t) - sp(t))' = 3\(t^{2}\) - \(e^{t}\) = 0

Solving for t, we get t ≈ 0.85 seconds. Plugging this value back into the distance functions, we find that at this time Phoebe was ahead of Calvin by approximately 0.69 feet.

c. The maximum difference in velocities does not occur at the same time as the maximum distance the two cars are apart.

d. Yes, the car that was ahead at first does eventually regain the lead, since both cars have unbounded distance functions.

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Answer:

its C

Step-by-step explanation:

Answer:

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Step-by-step explanation:

The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The given figure can be decomposed into the following figure.

- Semicircle

- Trapezoid

- Two rectangles

Thus,

A semicircle, a trapezoid, and two rectangles.

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Answer:

-0.725x (3.25) x (-4.4)

Since there are 2 negative numbers in the equation, the outcome will be positive.

When the number of negative numbers are even, the outcome will be positive.

When the number of negative numbers are odd, the outcome will be negative.

Answer:

18.5

Step-by-step explanation:

The length of fringe Sharon needs to purchase is: 16 feet

If Sharon gets a new bedsheet of 1.25 feet longer, she will need a new length of fringe of: 18.5 feet

Recall:

Perimeter of a rectangular = 2(length + width)

Given the following:

The length of fringe Sharon will need to purchase = perimeter of Sharon's rectangular bedspread

Perimeter = 2(3 + 5) = 16 feet

For a new bedspread that is 1.25 feet longer, she would get the following length of fringe:

Length = 3 + 1.25 = 4.25 feet

Width = 5 feet

New Perimeter = 2(4.25 + 5) = 18.5 feet

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All of these fractions are equivalent to a number greater than 26, none of them is not equivalent to 26

To determine which fraction is not equivalent to 26, convert each fraction to a decimal or mixed number and compare it to 26.

131/3 = 43.666

123612/36 = 3433

4124/12 = 343.666

696/9 = 77.333

Since all of these fractions are equivalent to a number greater than or equal to 26, none of them is not equivalent to 26. Therefore, the answer is "none of the above".

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By taking the help of the standard deviation, the answer obtained is

n = 719

What is Standard Deviation?

At first it is important to know about Variance.

Variance is the sum of the square of deviation from the mean of the data.

On taking the square root of variance, Standard deviation is obtained.

The formula used for calculating the number of samples required is

\(n=\frac{Z^{2}_{\alpha /2}\times \sigma ^{2}}{e^{2}}\), \(\sigma\) is the standard deviation , e is the error,

Here,

\(\alpha\) = 1 - \(\frac{95}{100}\)

  = 1 - 0.95

  = 0.05

Critical values of Z = \(\pm\)1.96 [ From the table]

Standard deviation (\(\sigma\)) = 9.3

error (e) = $0.68

On putting  the value,

n = \(\frac{1.96^2 \times 9.3^2}{0.68^2}\)

n = 718.5

n = 719

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A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.

Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.

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Answer:

x=3!

Step-by-step explanation:

To do this, you would have to divide by 2 on both sides.

2x/2=x

6/2=3

x=3

There are infinite combinations for the number of patients served by the nurses in both cases, considering the variability of the number of patients served by each nurse.

To calculate the different combinations for the number of patients served by the nurses, we need to consider the possible scenarios of the nurse who may or may not take a break during the time slot.

Case 1: The nurse who may take a break serves patients
In this scenario, all 4 nurses are administering shots and the nurse who may take a break is also serving patients. Let's say the nurses are able to serve x, y, z, and w patients respectively, where x, y, z, and w are arbitrary numbers. Then the total number of patients served is x + y + z + w. Since the nurses are able to serve an arbitrary number of patients, there are infinite combinations of x, y, z, and w that can add up to the total number of patients served. Therefore, there are infinite combinations for the number of patients served by the nurses in this case.

Case 2: The nurse who may take a break does not serve patients
In this scenario, only 3 nurses are administering shots and the nurse who may take a break is not serving patients. Let's say the 3 nurses are able to serve x, y, and z patients respectively. Then the total number of patients served is x + y + z. Again, since the nurses are able to serve an arbitrary number of patients, there are infinite combinations of x, y, and z that can add up to the total number of patients served. Therefore, there are infinite combinations for the number of patients served by the nurses in this case as well.

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There is a total of \($84+112 = 196$\) different combinations for the number of patients served by the nurses.

The possible scenarios for the number of patients served by the nurses:

If all four nurses are available and each serves one patient, then the remaining six patients can be distributed among the four nurses in any way.

This can be done in \(${{6+4-1}\choose{4-1}} = {{9}\choose{3}} = 84$\) ways using stars and bars.

If one nurse is on a break, then three nurses serve one patient each and the remaining six patients can be distributed among the three nurses in any way. Let's examine the following situations to see how many patients the nurses may serve:

The remaining six patients can be divided whichever you choose among the four nurses if all four are available and each treat one patient.

A nurse is taking a break, the other three nurses take turns caring for one patient apiece while dividing the remaining six patients anyway they see fit.

The four nurses may be taking a break, we increase this by 4, giving us \($4\) times 28 to equal 112 possible combinations.

This can be done in \(${{6+3-1}\choose{3-1}} = {{8}\choose{2}} = 28$\) ways using stars and bars.

The four nurses could be on a break, we multiply this by 4 to get\($4 \times 28 = 112$\)ways.

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Answer:

50 inches

Step-by-step explanation:

Given: S and E are the midpoints of BA and AM. and EM = 9

Therefore, then the length of AB = 18 and AM = 18

Use the similar triangle properties.

7/BM = 9/18

BM = (7*18)/9

BM = 7*2 = 14 inches.

Therefore, the perimeter of BAM is = AB + BM + AM

= 18 + 14 + 18

= 50 inches

Answer:

50 in

Step-by-step explanation:

Answer:

It would take him 12 hours to drive 696 miles

Step-by-step explanation:

hope this helps!!

Answer:

Option C, \(12\frac{1}{2}\)

Step-by-step explanation:

Step 1:  Multiply both sides by 5/2

\(5 = \frac{2}{5}a\)

\(5 * \frac{5}{2} = \frac{2}{5}a * \frac{5}{2}\)

\(\frac{25}{2}=a\)

\(12\frac{1}{2}=a\)

Answer: Option C, \(12\frac{1}{2}\)

Hope this helps!  Let me know if you have any questions

Answer: 72cm³

Step-by-step explanation:

lengh x width x base with means 6 x 4 x 3

Hello User,

Answer: 2.76 lb/ft

Steps:

This is a simple matter of multiplying and dividing by the appropriate conversion factors. You're highly unlikely to find a table of conversion factors for exactly this conversion so I'll demonstrate the conversion using 2 simple conversion factors. The conversion from meters to feet, and kilograms to pounds x = 4.10 kg/m * 2.20462 lb/kg / 3.28084 ft/m x = 9.038942 lb/m / 3.28084 ft/m x = 2.755069 lb/ft Since we have only 3 significant digits, round to 3 digits. x = 2.755069 lb/ft x = 2.76 lb/ft

Answer: A. (0, -1)

Step-by-step explanation: Check on a graphing calculator. The only time the 2 lines intersect is at (0, 1). So there's only one solution.

Answer:

 C

Step-by-step explanation:

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.

Random sampling, or probability sampling, is a sampling method that allows for the randomization of sample selection, i.e., each sample has the same probability as other samples to be selected to serve as a representation of an entire population.

Simple random sampling is the randomized selection of a small segment of individuals or members of a whole population. It provides each individual or member of a population with an equal and fair probability of being chosen. The simple random sampling method is one of the most convenient and simple sample selection techniques.

Simple random samples are determined by assigning sequential values to each item within a population, then randomly selecting those values.

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Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

From the question the original line is

y = 2/3x - 7

Comparing with the general equation above

Slope = 2/3

Since the lines are parallel their slope are also the same

Slope of parallel line = 2/3

So the equation of the line using point

(12 , 2 ) and slope 2/3 is

\(y - 2 = \frac{2}{3} (x - 12) \\ y - 2 = \frac{2}{3} x - 8 \\ y = \frac{2}{3} x - 8 + 2\)

We have the final answer as

\(y = \frac{2}{3} x - 6 \\ \)

Hope this helps you

First, subtract 4 from both sides:

\(5t\geq 15\)

Now, divide both sides of the equation by 5 to isolate variable t:

\(t\geq 3\)

Therefore, we know that t must be greater than or equal to 3 for this inequality to be true!

The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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Answer:

720,000,000,000,000 or 720 trillion picoseconds.

Step-by-step explanation:

1 picosecond = 1 trillionth of a second. Therefore 1 second has 1 trillion picoseconds:

0.000 000 000 001 seconds = 1 picosecond

0.000 000 000 001 * 1,000,000,000,000 seconds = 1 * 1,000,000,000,000 picosecond

1 second = 1,000,000,000,000 picoseconds

Now, one minute is the same as 60 seconds so we multiply the equation by 60:

1 minute = 60 seconds = 60,000,000,000,000 picoseconds

Finally, we need 12 minutes to be converted to picoseconds.

12 minutes = 720 seconds = 720,000,000,000,000 picoseconds.

So therefore, 12 minutes is equal to 720,000,000,000,000 picoseconds or 720 trillion picoseconds.

Hope this helps!!!

2/3  is the probability that the product of the two spinners' numbers is even.

How does probability explain work?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                       Statistics is the study of events that follow a probability distribution. There are four primary categories of probability: axiomatic, classical, empirical, and subjective.

An even number comes from multiplying an even and even, even and odd, or odd and even. Since an odd number only comes from multiplying an odd and odd, there are less cases and it would be easier to find the probability of spinning two odd numbers from 1.

            =  1 - 2/4 . 2/3

             =  1 - 1/3

            =  2/3

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Answer:

In solid matter the particles jiggle but generally do not move from place to place

Answer:

A. Supplier X offers the better deal by $3.93.

Explanation:

Supplier X offers a mechanic a part at 35% off the retail price of $65.40.

Supplier X's price is $42.51.

Supplier Y offers him the same part at 20% over the wholesale cost of $38.70.

We calculate the difference in the prices below:

Supplier X offers the better deal by $3.93.

Answer:

70.3km

Step-by-step explanation:

When the bearings are visualized and the points connected as a triangle, The angle x would be the difference of the both bearings from x

i.e 117-41 = 76

Using cosine rule,

YZ²= 43² + 67² - 2 x 43 x 67

cos76

YZ= √4944

= 70.3

The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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Answer: B

Step-by-step explanation:

Answer is B

The required method that is popular with the boys is going to school by walking.

A dual bar chart has been given, describing the method of going to school for boys and girls.

A bar chart displays the frequency counts of values for each level of a categorical or nominal variable.

Here,
According to the question,
Number of boys walk = 8,
Number of boys taking the bus = 2
Number of boys with car = 3
number of boys with cycle = 3
So the most popular method among the boys is given as by walk.

Thus, the required method that is popular with the boys is going to school by walking.

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