What is the value of x?

Enter your answer in the box.

x =

Answer:

x = 3 ± \(\sqrt{24}\)

or

x = 3 + \(\sqrt{24}\), x = 3 - \(\sqrt{24}\)

Step-by-step explanation:

given f(x) = 2(x - 3)^2 - 8, find when f(x) = 40

So, we plug in 40 for f(x) in the 1st equation and solve for x.  (Aim to got x on its own)

40 = 2 (x - 3)^2 - 8

+ 8          + 8

-----------------------------

48 = 2 (x - 3)^2

/2            /2

-----------------------------

24 = (x - 3)^2

square root both sides

--------------------

\(\sqrt{24}\) = x - 3

x = 3 ± \(\sqrt{24}\)

Answer:

The probability is  \(  P( X \ge 2)  =  0.986 \)  

Step-by-step explanation:

From the question we are told that

     The proportion people with  Blood type AB-negative in the world  is p = 0.006

     The sample size is  n =  30

 Generally the distribution of people with  Blood type  AB-negative  follows a binomial distribution  

i.e  

         \(X  \~ \ \ \  B(n , p)\)

and the probability distribution function for binomial  distribution is  

      \(P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}\)

Here C stands for combination hence we are going to be making use of the combination function in our calculators  

   Generally the probability that at least 2 of them have blood type AB-negative is mathematically represented as

         \( P( X \ge 2) = 1 - P( X <  2 ) \)

         \( P( X \ge 2) = 1 - [P( X = 0  ) + P( X = 1 ) ] \)

=>      \( P( X \ge 2) = 1 - [1  *  1  *  0.8348  ] + [30  *  0.006 *  0.83986 ] \)

=>     \(  P( X \ge 2)  =  0.986 \)  

Answer:

245 feet

Step-by-step explanation:

215 - (-30)

215 + 30

245

Answer:

n = 12

Step-by-step explanation:

You first write it out as in equation and get 3n-7=2n+5

You then do addition property of equality to add 7 on both sides, and gets 3n=2n+12

Then you subtract 2n from both sides to get

n=12

Hope this helps!

In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.

~~~Harsha~~~

Answer:

121 pi

Step-by-step explanation:

;)

Answer:

121π ft²

Step-by-step explanation:

area = πr²

area = π × (11 ft)²

area = 121π ft²

Answer:

Step-by-step explanation:

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

There are 20 possible routes that a man could take to go between cities and then take a different route back.

In mathematics, a permutation of a set is, broadly speaking, the rearranging of its elements if the set is already sorted, or the arrangement of its members into a sequence or linear order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context.

Let the number of roads between the cities A and B = 5.

The rules of permutation must be used in this situation.

A permutation is an arrangement of all or a portion of a collection of items that takes into account the arrangement's order.

The man uses five different routes to get from A to B because there are five different routes accessible.

He can get back by 4 (5 1) methods because he needs to take a different route.

Therefore, there are 20 possible routes that a man could take to go between cities and then take a different route back.

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The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:

Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.

Some of the common profitability ratios include:

Stockholders' equity = $442,600

Total assets = $640,000

Net sales = $480,000

Net income = $36,000

Profit margin ratio = Net income/Net Sales x 100

= $36,000/$480,000 x 100

= 7.5%

= 8%

Return on equity ratio = Net income/Shareholders' Equity x 100

= $36,000/$442,600 x 100

= 8.13%

= 8%

Asset turnover ratio = Net Sales/Total Assets

= $480,000/$640,000

= 0.75

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Answer:

x=44/43

Step-by-step explanation:

Subtract 1 from both sides

Simplify

Divide both sides by the same term

Cancel terms that are in both the numerator and the denominator

The answer is the product

Answer:

Assuming u meant 2y - 13y^(11), the degree is 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

The highest power is 11 so the degree of polynomial is 11.

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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The amount of heavy-duty fencing to be used is 2000 ft for $9000 and the amount of standard fencing to be used is 3000 ft for $9000 in order to make a total cost of $18000.

The area of the rectangular plot is denoted by the length multiplied by the width.

Let us assume that the length = x and the width = y.

Then, for two opposite with heavy fencing for $4.50 a foot and the standard fencing for $3 a foot, we have:

2x (4.50) + 2y(3) = 18000  ---- (1)

⇒ 9x + 6y = 18000

Make (y) the subject, we have:

\(\mathbf{y = \dfrac{18000-9x}{6}}\)

Replace the value of y with the area of the rectangle, and we get:

\(\mathbf{Area =x(\dfrac{18000 - 9x}{6})}\)

Area = x(3000 - 1.5x)

Area = 3000x - 1.5x²

For the area to be maximum, we take the differentiation of the Area:

dA/dx = 0

dA/dx = 3000 - 3x

x = 3000/3

x = 1000 ft

From equation (1)

2x (4.50) + 2y(3) = 18000  

x (4.50) + y(3) = 9000  

1000(4.50) + 3y = 9000

3y = 9000 -4500

y = 4500/3

y = 1500 ft

So, there are (1000× 2)ft = 2000ft heavy duty fencing for $9000, and (1500 ×2)ft = 3000ft standard fencing for $9000 to make a cost of $18000.

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The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer:

\(\frac{dv}{dt} =7239.168 cm/sec\)

Step-by-step explanation:

From the question we are told that:

Rate \(\frac{dh}{dt}=1cm\)

Height \(h=12cm\)

Radius \(r=4h\)

Generally the equation for Volume of Cone is mathematically given by

\(V=\frac{1}{3}\pi r^2h\)

\(V=\frac{1}{3}\pi (4h)^2h\)

Differentiating

\(\frac{dv}{dt} =\frac{16}{3}\pi3h^2\frac{dh}{dt}\)

\(\frac{dv}{dt} =\frac{16}{3}*3.142*3*12^2*1\)

\(\frac{dv}{dt} =7239.168 cm/sec\)

Answer:

170

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is of:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

Assume:

\(\pi = 0.06\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a pvalue of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

What is the smallest sample size required to obtain the desired margin of error?

This is n for which M = 0.03. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.645\sqrt{\frac{0.06*0.94}{n}}\)

\(0.03\sqrt{n} = 1.645\sqrt{0.06*0.94}\)

\(\sqrt{n} = \frac{1.645\sqrt{0.06*0.94}}{0.03}\)

\((\sqrt{n})^2 = (\frac{1.645\sqrt{0.06*0.94}}{0.03})^2\)

\(n = 169.6\)

Rounding up, 170.

The five-period moving average forecast for period 7 is 10.7.The five-period moving average forecast for period 7 can be calculated as:MA5,7 = 0.5*8 + 0.3*13 + 0.1*11 + 0.05*12 + 0.05*10 = 10

The five-period moving average forecast for period 7 is calculated using a weighted average of the most recent five periods. The weights represent the relative importance of each period in the calculation. The formula is: MA5,7 = 0.5*X6 + 0.3*X5 + 0.1*X4 + 0.05*X3 + 0.05*X2Where MA5,7 is the five-period moving average forecast for period 7 and X6, X5, X4, X3, and X2 are the data for periods 6, 5, 4, 3, and 2 respectively.In this example, the data for each period is as follows:

X2 = 10 X3 = 12 X4 = 11 X5 = 13 X6 = 8 .The five-period moving average forecast for period 7 can be calculated as:MA5,7 = 0.5*8 + 0.3*13 + 0.1*11 + 0.05*12 + 0.05*10 = 10.7Therefore, the five-period moving average forecast for period 7 is 10.7.

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Answer:

84.78 inches cubed  - hope this helped :)

Step-by-step explanation:

formula - πr^2\(\frac{h}{3}\)

3 x 3 x 3.14 = 28.26

28.26 x 9/3

28.26 x 3

answer = 84.78

Answer:

84.78 inches cubed

Step-by-step explanation:

You need to comprehend the volume formula for cones

Volume Formula for Cones: V=1/3hπr²

Your measurements:

9 inches for height

3 inches for radius

**Radius is half of a circle and diameter is full of the circle/base.***

Equation:V=1/3 x 9in x π x 3²

You should do 3 squared first so that you can input it into your calculator easily.

V=1/3 x 9in x π x 9

Now on a calculator do 1 divided by 3 which is the "1/3" in the formula.

Then multiply 9, 3.14 for pi, and 9 for radius.

Note: You should do 3.14 for pi not the whole pi symbol on the calculator.

Your answer: 84.78 in cubed

Answer:

D The null hypothesis is not rejected because 0.25 > 0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.

Step-by-step explanation:

Given the hypothesis :

H0 : β1 = 0

Ha : β1 ≠ 0

The Pvalue = 0.25 ; α = 0.05

Decision region :

Reject H0 ; if Pvalue < α

Comparing the Pvalue and α - value

0.25 > 0.05

Here, the Pvalue is > α ; hence, we fail to reject the Null, H0

Hence, there is no significant evidence to suggest that there is a linear relationship between what's stalk height and its yield.

Given that,

Length of the ladder = 20 ft

It casts a 12 ft shadow

To find,

If the statue casts a shadow that is 9 ft long then how tall is it?

Solution,

Let the ladder be x ft tall.

20 ft tall ladder = 12 ft shadow

9 ft tall ladder =

\(\dfrac{20}{12}\times 9\\\\=15\ ft\)

Hence, the required length is 15 ft.

Answer:

PRQ/3

Step-by-step explanation:

it is done by adding the first two

The ratio of the new volume to the old volume will be 3:1, the correct option is D.

We are given that;

The measurements= 9 cm*5 cm*3 cm

Now,

To find the volume of a rectangular prism, we can use the formula V = lwh, where l is the length, w is the width, and h is the height. Using the given dimensions, we get:

V = lwh V = 9 * 5 * 3 V = 135 cm^3

To find the new volume after tripling the width, we can use the same formula but replace w with 3w. We get:

V’ = l * 3w * h V’ = 9 * 3 * 5 * 3 V’ = 405 cm^3

To find the ratio of the new volume to the old volume, we can divide V’ by V and simplify. We get:

V’ / V = (405 cm^3) / (135 cm^3) V’ / V = 3

To write the ratio in the form of a fraction, we can use 1 as the denominator of V. We get:

V’ / V = 3 / 1

Using these steps, I found that the ratio of the new volume to the old volume will be 3:1.

Therefore, by the given rectangular prism the answer will be 3:1.

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This is likely what Jeremy did

\(\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2+15}{\text{x}-5}\\\\\frac{\text{x}^2+5}{\text{x}-5}\\\\\)

The error happens in line 2

This is what his steps should be

\(\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-(\text{x}^2+15)}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2-15}{\text{x}-5}\\\\\frac{\text{x}^2-25}{\text{x}-5}\\\\\frac{(\text{x}-5)(\text{x}+5)}{\text{x}-5}\\\\\text{x}+5\)

On the 2nd step, we subtract all of (x^2+15) and not just the x^2 part. The negative distributes to each term in step 3. Then we combine like terms, factor and cancel out the (x-5) terms.

Therefore, \(\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}=\text{x}+5\) is an identity as long as \(\text{x} \ne 5\) to avoid a division by zero error.

The end behavior of \(g(x) = -3e^x\) is As x approaches positive infinity, g(x) approaches negative infinity, As x approaches negative infinity, g(x) approaches 0.

To determine the end behavior of the function g(x) = -3e^x, we need to consider what happens to the output of the function as x gets very large (approaches positive infinity) or very small (approaches negative infinity).

As x approaches positive infinity, e^x also approaches positive infinity, since e is a positive number greater than 1. Therefore, -3e^x approaches negative infinity as x approaches positive infinity. We can write this as:

lim x → ∞ (-3\(e^x\)) = -∞

This means that the function g(x) approaches negative infinity as x approaches positive infinity.

Similarly, as x approaches negative infinity, e^x approaches 0, since e to a negative power is equal to 1 divided by e raised to the absolute value of that power. Therefore, -3e^x approaches 0 as x approaches negative infinity. We can write this as:

lim x → -∞ (-3\(e^x\)) = 0

This means that the function g(x) approaches 0 as x approaches negative infinity.

So, in summary, the end behavior of g(x) = -3\(e^x\) is:

As x approaches positive infinity, g(x) approaches negative infinity.

As x approaches negative infinity, g(x) approaches 0.

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The total medical expenses for the five people in the car are $3,000 + $3*$500 + $62,000 = $3,000 + $1,500 + $62,000 = $66,500

What does a math word problem entail?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Since Allen's personal injury protection policy covers each person up to $50,000, the insurance company must pay out $50,000*5 = $250,000 for the five people in the car.

Since the total medical expenses for the five people are $66,500, the insurance company will pay out the total medical expenses for the five people, which is $66,500.

Therefore, the insurance company must pay out $66,500 for these five people.

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Answer

$50

Step-by-step explanation:

Answer:   \(\;\;\frac{1}{6} , \;\; 0.16667,\;\; \text{or about}\;\;17\%\)

Step-by-step explanation:

   A regular dice has 6 sides, and only one of those sides side has a six.

        We write probability as;

   \(\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} = \frac{\text{number of times six is on the dice}}{\text{number of numberss on the dice}} =\frac{1}{6}\)

Hi, there!

 _______

\(\boxed{\boxed{\sf{Probability=\dfrac{Favorable \ Outcomes}{Total \ Outcomes}}}}\)

Here,

» Favourable Outcome(s) -> getting a 6 on a die (1 outcome),  because only one side of a die has a six on it

» Total Outcomes -> 6 (you can only get 1, 2, 3, 4, 5, 6 if you roll one die)

So,

\(\sf{Probability_{(6)}=\dfrac{1}{6}}\)

Hope the answer - and explanation - made sense to you,

happy studying!!

                                                                                                        \(\tiny\textit{frozen \ melody}\)