Average IQ scores are normally distributed
mean µ: 100
standard deviation σ: 15
(a) What percent of the data in your set is more than one
standard deviation from the mean? What percent of the data i

Answer:

180 calculators.

Step-by-step explanation:

She has 180 calculators because if you were to un - simplify 5:1 you would get 180:5 and you would use the first number. So, you have 180 calculators.

Sorry if this is wrong I tried my best.

The probability that the A1 allele will be fixed is 0.4167, or about 42%.

We are given that;

Number of head= 150

Now,

Substitute all known values into the equation from step 4, then solve for the unknown quantity. We know that N = 150, (A1A1) = 25, (A1A2) = 75, and (A2A2) = 50. Substituting these values into the equations for p and q, we get:

\($$p = \frac{2(25) + (75)}{2(150)}$$$$p = \frac{125}{300}$$$$p = 0.4167$$$$q = \frac{2(50) + (75)}{2(150)}$$$$q = \frac{175}{300}$$$$q = 0.5833$$\)

Substituting these values into the equation for Pfix, we get:

\($$Pfix = \frac{p}{p + q}$$$$Pfix = \frac{0.4167}{0.4167 + 0.5833}$$$$Pfix \approx \frac{0.4167}{1}$$$$Pfix \approx 0.4167$$\)

Therefore, by probability the answer will be 0.4167 or about 42%.

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Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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To complete the square to make a perfect square trinomial, the formula that we need to use is:b² + 2ab + a²The perfect square trinomial that we need to use as a binomial squared is:(b + a)²

To complete the square to make a perfect square trinomial, the formula that we need to use is:

\([b^2 + 2ab + a^2]\)

The perfect square trinomial that we need to use as a binomial squared is:

\([(b + a)^2]\)

So, to complete the square of \((q^2 - 20q)\) , we need to add half of -20, squared:

First, we need to find half of -20 which is -10.

Now we have to square \(-10: ((-10)^2 = 100)\)

Therefore, \((q^2 - 20q)\) can be completed as a perfect square trinomial by adding 100 in such a way that:

\((q^2 - 20q + 100 - 100 = (q - 10)^2 - 100)\)

This result can be written as a binomial squared by rearranging it as follows:

\(((q - 10)^2 = q^2 - 20q + 100)\)

Therefore, the result of completing the square of \((q^2 - 20q)\) and writing it as a binomial squared is \(((q - 10)^2).\)

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Answer

Explanation

Given:

To determine the value of g(f(x)), we substitute x with 1/3x^2+4 for g=9x-12:

Therefore, the value of g(f(x)) is C:

Academic writing is characterized by several distinct features that set it apart from other forms of writing. These features include precision, objectivity, formal tone, evidence-based arguments, clarity, and adherence to specific style guidelines.

Academic writing is known for its precision and accuracy in presenting information. It emphasizes objectivity by relying on evidence and research to support claims. The use of a formal tone is common in academic writing, maintaining a professional and authoritative voice. Academic writing also places importance on presenting arguments based on empirical evidence and logical reasoning. Clarity is essential, with clear organization and structure to convey complex ideas effectively. Additionally, academic writing follows specific style guidelines, such as APA or MLA, ensuring consistency and uniformity in citations, references, and formatting. These characteristics collectively define the nature of academic

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

The population of the world be in 2030 is 8.6 billion.

Given that,

a. = 6.9 billion

V= 1.1 % = 0. 011

a ) Let An represents The population on year after

2010 .

Population grow rate= 1.1%.

So ,

an = an-1 + an-1 ( 1.1 % )

an = an-1 + an-1 (0. 011 )

an = an- 1 ( 1.011 )

(B)

Given ,

ao = 6.9 billion

an = ( 1 .011 ) an- 1

an = (1 .011 ) an- 1 = (1 .011 ) (1 .011) an - 2 = ( 1 .011) (1 .011 ) an- 3

= ( 1.031 ) 3 ( 1 1018 ) an-4 .. . .

an = ( 1 1 012 ) " - ( 1 012 ) am-n

an = ( 1 .01 1 ) " ap

(ao = 6.9 )

an = 6 .9 ( 1 . 01 1 ) h

Now ,

an = 6 . 9 ( 1 . 0 1 1 ) 2

( means 20 year Later from 2010. )

at 2030

So , n = 20

2 20 = 6.9 ( 1 . 0 11 ) 20

a20 = 609 ( 1. 24 4 580 8428 )

a20 = 8.58 7607815 billion

or

azo = 8.6 billion

( rounded to + decimal place)

Thus, 8.6 billion people will live on Earth in 2030.

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The function f(x) = -5x^2 is not a linear transformation.

To determine if f(x) is a linear transformation, we need to check two conditions:

f(x + y) = f(x) + f(y)

f(cx) = c(f(x))

Let's evaluate these conditions for the given function:

f(x + y) = -5(x + y)^2 = -5(x^2 + 2xy + y^2) = -5x^2 - 10xy - 5y^2

f(x) + f(y) = -5x^2 + (-5y^2) = -5x^2 - 5y^2

The two expressions -5x^2 - 10xy - 5y^2 and -5x^2 - 5y^2 are not equal, so f(x + y) is not equal to f(x) + f(y). Therefore, the condition f(x + y) = f(x) + f(y) is not satisfied, indicating that f(x) is not a linear transformation.

f(cx) = -5(cx)^2 = -5c^2x^2

c(f(x)) = c(-5x^2) = -5cx^2

The two expressions -5c^2x^2 and -5cx^2 are not equal, so f(cx) is not equal to c(f(x)). Thus, the condition f(cx) = c(f(x)) is also not satisfied.

Since both conditions for a linear transformation are not fulfilled, we can conclude that f(x) = -5x^2 is not a linear transformation.

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The area of the surface obtained by rotating the curve x = 20 cos(3θ), y = 20 sin(3θ), where 0 ≤ θ ≤ π/2, about the x-axis is calculated using the formulA for surface area of revolution

To find the area of the surface, we can use the formula for the surface area of revolution. Given a curve defined parametrically by x = f(θ) and y = g(θ), where α ≤ θ ≤ β, the surface area obtained by rotating the curve about the x-axis is given by:

A = ∫[α,β] 2πy √(1 + (f'(θ))²) dθ

In this case, we have x = 20 cos(3θ) and y = 20 sin(3θ), with 0 ≤ θ ≤ π/2. Taking the derivatives, we find f'(θ) = -60 sin(3θ) and g'(θ) = 60 cos(3θ).

Plugging these values into the surface area formula and simplifying, we get:

A = ∫[0,π/2] 2π(20 sin(3θ))(√(1 + (-60 sin(3θ))²)) dθ

Evaluating this integral will give us the exact value of the surface area of the rotated curve about the x-axis within the given range of θ.

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Answer:

show image

Step-by-step explanation:

The correlation is statistically significant, it is not a perfect relationship and there may be other factors at play that affect academic performance. Overall, the results suggest that studying for more hours per week may lead to better academic performance

Based on the given information, we can conclude that there is a positive correlation between the number of hours studied per week and academic performance of 25 UK University students. The correlation coefficient of 0.71 suggests a moderate to strong positive relationship between the two variables. This means that as the number of hours studied per week increases, the academic performance of the students also tends to increase. However, it is important to note that the "critical r" value of 0.87 with a significance level of p≤0.05 indicates that there is a chance of 5% that the observed correlation between the variables could be due to random chance. This means that while the correlation is statistically significant, it is not a perfect relationship and there may be other factors at play that affect academic performance. Overall, the results suggest that studying for more hours per week may lead to better academic performance, but it is not the only factor that contributes to success. Other variables such as natural ability, motivation, and study habits may also play a role in academic achievement.

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The flow rate of 5 MGD is equivalent to 7.73615 cfs

To convert million gallons per day (MGD) to cubic feet per second (cfs), we need to use the conversion factor between the two units. The conversion factor is 1 MGD = 1.54723 cfs.

Therefore, to convert MGD to cfs, we can multiply the given value of MGD by the conversion factor. For example, if we have a flow rate of 5 MGD, we can convert it to cfs as follows:

5 MGD x 1.54723 cfs/MGD = 7.73615 cfs

So, the flow rate of 5 MGD is equivalent to 7.73615 cfs. Similarly, we can convert any given flow rate in MGD to cfs by using the same conversion factor.

It is important to note that these units are commonly used in the context of water supply and distribution systems, where flow rates are a crucial factor in the design and operation of such systems. Therefore, knowing how to convert between different flow rate units is essential for engineers and technicians working in this field.

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It becomes

\($$\begin{aligned}5: 8: & 6.5: x \\5 \times x & =8 \times 6.5 \\x & =\frac{8 \times 6.5}{5} \\x & =\frac{52}{5} \\x & =10.4\end{aligned}$$\)

Therefore,

5 machines will take $10.4$ hour to produce the same number of parts.

Equivalent interest rates are interest rates that produce the same future value after one year. For example, 10% compounded quarterly and 10.125% compounded semiannually are equivalent nominal interest rates. If you calculate the future value of $100 invested at either rate for one year, you will obtain $110.38.

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A total of 12,000 dollars is made from the sale of 300 books at a price of $40 each. 25 fewer books are sold for every $5 increase in price.      R(x)=(40+5x)(300−25x) R ( x ) = ( 40 + 5 x ) ( 300 − 25 x )

Assumed in this instance is , At a price of 40 dollars apiece, \($(300)(40 \$)=12,000 \$$\) books generate $300 in revenue. The result is that 25 fewer books are sold if we raise the price of each book by $5. That's \($(300-25 x)$\). Due to the fact that the price always rises by five times more than the number of books, the cost is \($(40+5 x)$\).

\($R=(300-25 x) \cdot(40+5 x)$\)

\($R=12000+6000 x-1000 x-125 x^2$\\$R=-125 x^2+5000 x+12000$\\$R=125 x^2-5000 x-12000$\)

The revenue R is expressed as a function of the number x as it approaches 5. R(x)=(40+5x)(30025x) is the necessary revenue function. R(x) = (40 + 5 x)(300 25 x) is the necessary revenue function.

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a = 7

b = 13

c = -10

Re-writing the expression above in the form: ax² + bx + c = 0

7x² = 10 - 13x

7x² + 13x - 10 = 0

From 7x² + 13x - 10 = 0

a = 7

b = 13

c = -10

The integer that represents the change in Park City's temperature is  -5F

A whole number that may be either positive, negative, or zero is known as an integer. They have different qualities and may be added to or removed from. The temperature in the described case is known to have declined, or plummeted. As a result, a negative number might be used to symbolise this decline.

In the example question, the temperature dropped by 5 degrees when a storm rolled through Park City. As a result, the issue informs us that the temperature decreased by 5 degrees, which equals a -5 degree difference. The number 5 denotes the percentage of the temperature fall, which is indicated by the negative sign.

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Answer:

"sixty-three hundredths of a Kilometer"

Step-by-step explanation:

Decimal measurements are read based on the place of their digits. In this case, Ajay would read this measurement as "sixty-three hundredths of a Kilometer". This is because the final digit of the decimal form measurement is in the "hundredths" position. One more to the right and it would be in the "thousandths" while one more to the left would be the "tenths"

Answer:

7, 7, 60, 60, 60

Step-by-step explanation:

When you draw the circles thhey all hhave radius AB so AB=AC=BC =7

and since all sides are congruent you have a equilateral treangle so all angles are equal to 180/3=60

If a tailor bought 5 yards of cloth he used  \(2\frac{3}{8}\) yards of cloth to make 1 pair of pants and he made 2 pairs, the length of the cloth that left is 1/4 yards

The total length of the cloth that he bought = 5 yards

The length of cloth that he used to make 1 pair of pants = \(2\frac{3}{8}\) yards

Convert the mixed fraction to the simple fraction

\(2\frac{3}{8}\) yards = 19/8 yards

The length of cloth required to make 2 pants = 2 × The length of cloth that he used to make 1 pair of pants

Substitute the values in the equation

= 2 × (19/8)

= 19/4 yards

The remaining cloth = The total length of the cloth that he bought - The length of cloth required to make 2 pants

= 5 - (19/4)

= 1/4  yards

Hence, the length of the cloth left is 1/4 yards

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Answer:

no idea my friend sorry

Step-by-step explanation:

Answer:

Estimate of 15/30

B:1/2

Answer:

_

113 -✓5

Step-by-step explanation:

_

113-(-(-✓5))

_

=113-✓5 (decimal:110.763932)

Jamal spends a total of $44 on lunch for his family, including tax and tip.

Algebraic expression can be defined as combination of variables and constants.

The total cost of the drinks is 4 x $1.75 = $7.

The total cost of the sandwiches is 4 x $7.50 = $30.

So, the subtotal before the tip is $7 + $30 = $37.

Since the prices include tax, we can directly add the tip to the subtotal to get the total amount Jamal spends:

Total cost = Subtotal + Tip = $37 + $7 = $44.

Therefore, Jamal spends a total of $44 on lunch for his family, including tax and tip.

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Answer:

Step-by-step explanation:

Slopes of parallel lines are the same. ( \(m_{1}\) = \(m_{2}\) )

Slopes of two perpendicular lines are opposite reciprocals. ( \(m_{1}\) × \(m_{2}\) = - 1 )

( \(x_{1}\) , \(y_{1}\) )

( \(x_{2}\) , \(y_{2}\) )

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

~~~~~~~~~~~~~

(9, 9)

(6, 1)

\(m_{m}\) = \(\frac{1-9}{6-9}\) = \(\frac{8}{3}\)

(10, 7)

(1, 15)

\(m_{n}\) = \(\frac{15-7}{1-10}\) = - \(\frac{8}{9}\)

Lines m and n neither parallel, nor perpendicular.

Answer:

10

Step-by-step explanation:

19-17=2

10+2=12-2 =10

Answer:

$\frac{10}{3}$ in by $\frac{14}{3}$ in by $\frac{10}{3}$ in.

Step-by-step explanation:

Let's denote the length of the box as $l$, the width as $w$, and the height as $h$. We are given that the original piece of cardboard has dimensions 10 in by 12 in, so we know that:

$$l + 2h = 10 \quad \text{and} \quad w + 2h = 12.$$

To find the dimensions of the box with the largest volume, we need to maximize the volume function, which is given by:

$$V(l,w,h) = lwh.$$

Using the equations above, we can express the volume in terms of just two variables, say $l$ and $h$:

$$V(l,h) = lwh = l(10-2h)h = 10h^2 - 2h^3.$$

Now we can use calculus techniques to find the maximum of this function. To do this, we need to find the critical points, which are the values of $h$ where the derivative of $V$ with respect to $h$ is zero or undefined.

Taking the derivative of $V$ with respect to $h$, we get:

$$V'(h) = 20h - 6h^2.$$

Setting this to zero to find the critical points, we get:

$$20h - 6h^2 = 0 \quad \Rightarrow \quad h(10 - 3h) = 0.$$

This equation has two solutions: $h = 0$ and $h = \frac{10}{3}$. We can check that $h=0$ corresponds to a minimum, and $h = \frac{10}{3}$ corresponds to a maximum by computing the second derivative of $V$ with respect to $h$:

$$V''(h) = 20 - 12h.$$

At $h=0$, we have $V''(0) = 20$, which is positive, so $h=0$ is a minimum. At $h=\frac{10}{3}$, we have $V''\left(\frac{10}{3}\right) = -8\frac{1}{3}$, which is negative, so $h=\frac{10}{3}$ is a maximum.

Therefore, the maximum volume is achieved when $h=\frac{10}{3}$. Using the equations we derived earlier, we can find the corresponding values of $l$ and $w$:

$$l = 10 - 2h = \frac{10}{3}, \quad w = 12 - 2h = \frac{14}{3}.$$

So the dimensions of the box with largest volume are $\frac{10}{3}$ in by $\frac{14}{3}$ in by $\frac{10}{3}$ in.

The gross pay for Martin is $832, calculated by multiplying his regular hourly wage by the number of regular hours worked and adding overtime pay for the additional hours worked.

To calculate Martin's gross pay, we need to consider regular pay for the first 40 hours and overtime pay for the additional hours. Martin worked 48 hours, which means he worked 8 hours of overtime (48 - 40).

For the regular pay, we multiply the regular hourly rate ($16) by the number of regular hours worked (40), which gives us $640.

For the overtime pay, we calculate time and a half of the hourly rate. The overtime rate is $16 * 1.5 = $24. We then multiply the overtime rate by the number of overtime hours (8), which gives us $192.

Adding the regular pay and overtime pay together, we have $640 + $192 = $832.

Therefore, the gross pay for Martin is $832.

Note: The given options in the question seem to be incorrect as none of them matches the correct answer.

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