a = 4.2 × 10^-24 b = 3 × 10^145 (a) Work out the value of a × b Give your answer in standard form.​

We can see that equation (1) is quadratic in nature To find the gradient of the given curve, we need to differentiate the equation (1) with respect to x Gradient is given by

Function is \(y = (a + bx)²At x = 1, y = (a + b(1))²⇒ y = (a + b)²\)
Expanding the above equation, we get y = a² + b² + 2abx …(1)

\(dy/dx⇒ d/dx (a² + b² + 2abx)\) …(2)

Taking the derivative of the above equation, we get⇒
\(d/dx (a² + b² + 2abx) = d/dx(a²) + d/dx(b²) + d/dx(2abx)⇒ 0 + 0 + 2ab⇒ 2ab\)
Now, substituting the value of x in equation (2), we getx = 1, gradient = 2ab

We have to differentiate the given function y = (a + bx)² using the differentiation rule.

To find the gradient of the curve, we need to differentiate the above function, which is given as follows;
\(y = (a + bx)²y = (a + bx) (a + bx)\)

By using the product rule of differentiation, we have
\(dy/dx = (a + bx)d(a + bx)/dx + (a + bx)d(a + bx)/dx= (a + bx) * b + (a + bx) * b= 2b(a + bx)\)

Substituting the value of x = 1, we get the gradient of the curve;
\(y' = 2b(a + b)\)

Therefore, the gradient of the curve \(y = (a + bx)² at x = 1 is 2b(a + b)\).

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From the given information provided, the percent of apartments in the building that are small is 85%.

If the ratio of small apartments to regular apartments is 17 to 3, this means that for every 17 small apartments, there are 3 regular apartments.

We can think of the total number of apartments in the building as a multiple of the ratio 17:3. Let's call this multiple "x". Then, the total number of small apartments would be 17x, and the total number of regular apartments would be 3x.

The percentage of apartments in the building that are small can be calculated as follows:

percentage of small apartments = (total number of small apartments / total number of apartments) x 100%

= (17x / (17x + 3x)) x 100%

= (17x / 20x) x 100%

= 85%

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Answer:  12

Step-by-step explanation: Because the absolut value of something will always be positive.

Answer:

The value for |12| is D. 12

Answer:

SAS, because vertical angles are congruent.

Answer:

3rd degree binomial

-2x has a coefficient of -2

-x³  has a coefficient of -1

Step-by-step explanation:

-2x - x³ is typically written in decreasing exponent order:

-x³ - 2x  ⇒ this is a third degree binomial because of the value of the greatest exponent

there are two 'x' terms:

-2x and -x³

the coefficient of -2x is the integer which precedes the 'x', which is -2

the coefficient of -x³ is -1

based on the given information, we can definitively conclude that PV- is closer to 0 than to 1. The option (b) "PV- is closer to 0 than to 1" is the correct answer.

The present value (PV) represents the current value of a future cash flow or investment. If PV is approximately 1, it means that the value of the future cash flow or investment is close to its full value in the present.

When we subtract a value from PV to get PV-, the resulting value will be smaller than PV. Since PV is approximately 1, it implies that PV- is closer to 0 than to 1. This conclusion holds because subtracting a value from 1 will always yield a smaller value.

For example, if PV is exactly 1 and we subtract 0.5 from it, the resulting PV- will be 0.5, which is closer to 0 than to 1.

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D. None of these, as neither option B nor option C can be obtained using the Law of Detachment.

The Law of Detachment states that if a conditional statement "if p, then q" is true and p is true, then q must also be true.

Analyzing the given options:

A. The conclusion "There is no school" can be obtained by applying the Law of Detachment to the given information, as it matches the format of the law: "If today is Saturday (p), then there is no school (q)." Since today is Saturday (p), the conclusion that "There is no school" (q) can be derived using the Law of Detachment.

B. The conclusion "He is able to buy a new set of headphones" is not directly obtained by using the Law of Detachment. It involves an additional conditional statement and is not in the form of the given "if p, then q" structure.

C. The conclusion "George lives in both Brick and Ocean County" cannot be derived using the Law of Detachment. It is not in the form of a conditional statement, and there is no given information that connects George's residence to the conditional statement provided. Therefore, D is the right answer. None of them are possible utilizing the Law of Detachment, as neither option B nor option C can be obtained. Therefore, Option D is correct.

The question was incomplete. find the full content below:

Which of the following conclusions is true AND obtained by using the Law of Detachment

A. If today is Saturday, then there is no school.

Today is Saturday.

There is no school.

B. If you work 8 hours, then you'll earn $100.

If you earn $100, you'll be able to buy a new set of headphones.

Jonathan works 8 hours.

He is able to buy a new set of headphones.

C. If a person lives in Long Beach Island, then they live in Ocean County.

Brick is in Ocean County.

George lives in both Brick and Ocean County

D. None of these.

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The transformation from the graph of \(f\) to the graph of \(r\) is 4.

The given functions are f(x)=-1/4 x-2 and r(x)=4f(x).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

r(x)=4f(x)

So, r(x)=4(-1/4 x-2)

⇒ r(x)=-x-2

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Vertical: stretch

The graph of the functions is given below.

Therefore, the transformation from the graph of \(f\) to the graph of \(r\) is 4.

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Answer: Thank you for the points & B

Step-by-step explanation: Hope this help :D

Answer:

1.5

Step-by-step explanation:

3÷2= 1.5

6÷4=1.5

12÷8= 1.5

Answer:

x=11

Step-by-step explanation:

The sum of the angles of a triangle is 180

We know the angle with a box is 90

90 + 5x-2  + 3x+4 = 180

Combine like terms

8x +92 = 180

Subtract 92 from each side

8x+92-92 = 180-29

8x = 88

Divide each side by 8

8x/8 = 88/8

x = 11

Answer:

- 2/3

-2/3

2/-3

Step-by-step explanation:

The mathematically possible value of Pr(A and B) is either a) 0, b) 0.2, d) 0.8, or e) 0.5, depending on the specific probabilities of events A and B and their overlap.

For the first question, we need to find the mathematically possible value of Pr(A U B), which represents the probability of either event A or event B occurring. Since events A and B are not mutually exclusive (it is possible for a student to wear glasses and be less than 6 feet tall), we can use the formula Pr(A U B) = Pr(A) + Pr(B) - Pr(A and B) to find the desired probability.

Given that Pr(A) = 0.3 and Pr(B) = 0.8, we can substitute these values into the formula and rearrange it to solve for Pr(A and B): Pr(A U B) = Pr(A) + Pr(B) - Pr(A and B) => Pr(A and B) = Pr(A) + Pr(B) - Pr(A U B).

Now, let's analyze the options:

a) 0.4: This value is not possible since probabilities cannot exceed 1.

b) 0.2: This value is possible depending on the values of Pr(A) and Pr(B) and their overlap.

c) 0.6: This value is not possible since probabilities cannot exceed 1.

d) 0.9: This value is not possible since probabilities cannot exceed 1.

e) 0.5: This value is possible depending on the values of Pr(A) and Pr(B) and their overlap.

Therefore, the mathematically possible value of Pr(A U B) is b) 0.2.

For the second question, we need to find the mathematically possible value of Pr(A and B), which represents the probability of both event A and event B occurring.

Again, using the formula Pr(A U B) = Pr(A) + Pr(B) - Pr(A and B), we can rearrange it to solve for Pr(A and B): Pr(A and B) = Pr(A) + Pr(B) - Pr(A U B).

Analyzing the options:

a) 0: This value is possible if events A and B are mutually exclusive, meaning they cannot occur together.

b) 0.2: This value is possible depending on the values of Pr(A), Pr(B), and their overlap.

c) 0.6: This value is not possible since probabilities cannot exceed 1.

d) 0.8: This value is possible depending on the values of Pr(A), Pr(B), and their overlap.

e) 0.5: This value is possible depending on the values of Pr(A), Pr(B), and their overlap.

Therefore, the mathematically possible value of Pr(A and B) is either a) 0, b) 0.2, d) 0.8, or e) 0.5, depending on the specific probabilities of events A and B and their overlap.

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The correct statement is (a) Regression coefficients estimated using least squares are always BLUE.

Therefore, statement (a) is true. The other statements are not correct. Statement (b) is incorrect because the omitted variable bias can be positive or negative, depending on the direction of the correlation between the omitted variable and the other explanatory variables. Statement (c) is incorrect because R2 j is obtained from the regression of the jth explanatory variable on the rest of the explanatory variables, not the dependent variable. Statement (d) is incorrect because statement (a) is true.

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Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

i believe its hurricane

Step-by-step explanation:

Answer:

each smoothie costs 4 dollars disincluding the 3 dollar tip

Step-by-step explanation:

Answer:

23-3=20

Step-by-step explanation:

Answer:

-61

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write expression

-18/-6 + 8 × - 8

Step 2: Divide

3 + 8 × -8

Step 3: Multiply

3 - 64

Step 4: Subtract

-61

Answer:

If instructed to simplify the question, your answer is -5+8x.

Step-by-step explanation:

-18 divided by -6 equals positive 3.

3 + 8x -8 would become -5+8x, because 3 minus 8 is -5. Hope this helps!

Answer:

1 & 7

2 & 8

5 & 3

6 & 4

Step-by-step explanation:

Answer:

1 and 7

2 and 8

5 and 3

6 and 4

it take for all the water to drain from the tank is 1 hour 11 min 26 sec for a water tank is shaped like a vertical circular cylinder

Using the Bernoulli's laws to use the conserved energy

Solve the speed and the radio of this speed of the tank is open to the air

p₀ + ρgh₀ + ½ρv₀² = p₁ + ρgh₁ + ½ρv₁²

5000Pa + 1000kg/m³ * 9.8m/s² * 0.800m + 0 = 0 + 0 + ½ * 1000kg/m³ *

v²

v² = 25.68  m²/s²

v1 = 5.06 m/s

Because it is open the cylinder tank so P=0 pa so:

0 Pa + 1000kg/m³ * 9.8m/s² * 0.800m + 0 = 0 + 0 + ½ * 1000kg/m³ * v²

v² = 15.68  m²/s²

v2 = 3.96 m/s

The ratio on the air is solve using both velocities so:

R = v1/v2 = 5.06 m/s / 3.96 m/s

R = 1.27

Now to find the time it takes for the tank to drain if the tank is open to the air

dh/dt = -u

dh/dt = -v * A/A'

dh/dt = v*(.02m)²/(2.0m)² = -v / 10000

and we can further substitute for v:

dh/dt = -(1/1e4)*√[(p+9800h)/500]

Solve replacing

-(1000/49)*√(49000h) = t + C

-(1000/49)*√(49000*0.8) = 0 + C

C = - 4040.6

Then when h = 0,

t = 4286 s

t = 1 hr, 11 min, 26 sec  

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3/10 (option B)

fraction that chose vanilla ice cream = 2/5

fraction that chose chocolate ice cream = 3/10

let the fraction that chose strawberry ice cream = y

Total fraction = 1

fraction that chose vanilla ice cream + fraction that chose chocolate ice cream + fraction that chose strawberry ice cream = 1

2/5 + 3/10 + y = 1

Fraction of the class chose strawberry ice cream is 3/10 (option B)

Answer:

\(a:b = -17:1\)

Step-by-step explanation:

Given

\(\frac{a-3b}{a+2b} = \frac{4}{3}\)

Required

Find a:b

\(\frac{a-3b}{a+2b} = \frac{4}{3}\)

Cross Multiply

\(3(a-3b) = 4(a+2b)\)

Open brackets

\(3a - 9b = 4a + 8b\)

Collect Like Terms

\(3a - 4a = 8b+9b\)

\(-a = 17b\)

Divide through by -b

\(\frac{-a}{-b} = \frac{17b}{-b}\)

\(\frac{a}{b} = \frac{17}{-1}\)

\(\frac{a}{b} = \frac{-17}{1}\)

Represent as a ratio

\(a:b = -17:1\)

The correct answer is

H₀ : μh - μc = 0

H₀ : μh - μc ≠ 0

Given that,

Regarding the subsequent 3 inquiries: A study collected information on how much time 28 randomly chosen high school students and 31 randomly chosen college students spent each day on their cellphones. The researcher is interested in learning whether there is proof that students use their phones for varying amounts of time in high school and college.

Because the samples of college and high school students are independent, the independent samples t-test should be utilized.

The study's research (Claim) aims to ascertain whether students' cell phone usage patterns alter between high school and college.

For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,

H₀ : μh - μc = 0

H₀ : μh - μc ≠ 0

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The proper null and alternative hypotheses are

\(H_{0}\) : μh = μc

\(H_{A}\) : μh - μc

The study's research wants to ascertain whether difference between the time spent by high school students and college students.

The actual test begins by considering two hypothesis i.e. null hypothesis and alternative hypothesis.

Let, H= time spent on the phone by high school students;

C= Time spent on the phone by college students; and

d=H−C

For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,

\(H_{0} :\) μh = μc  (time spent by high school students is equal to college students)

\(H_{A} :\) μh - μc  (difference between the time spent by high school students and college students)

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Answer:

20,480

Step-by-step explanation:

For the ratio of the average flux for e > 45 degrees to the omnidirectional flux, we divide the flux per solid angle for the directional case by the flux per solid angle for the omnidirectional case.

To find the ratio of the average flux for e > 45 degrees to the omnidirectional flux in a pancake distribution of sin(a) where a = 0, we need to calculate the directional flux, omnidirectional flux, directional solid angle, and omnidirectional solid angle.

Directional Flux:

The directional flux is the flux within a specific direction or range of angles. In this case, we are interested in e > 45 degrees.

Omnidirectional Flux:

The omnidirectional flux is the total flux in all directions or over the entire solid angle.

Directional Solid Angle:

The directional solid angle is the solid angle subtended by the specified direction or range of angles. In this case, it would be the solid angle corresponding to e > 45 degrees.

Omnidirectional Solid Angle:

The omnidirectional solid angle is the total solid angle subtended by all possible directions or over the entire sphere.

To find the flux per solid angle for both the directional and omnidirectional cases, we can use the formula:

Flux per Solid Angle = Total Flux / Solid Angle

Finally, to find the ratio of the average flux for e > 45 degrees to the omnidirectional flux, we divide the flux per solid angle for the directional case by the flux per solid angle for the omnidirectional case.

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a) pV_m = RT(1 + ((-RT / a) - b)V_m - (a / V_m) - b^2 / V_m)  this equation can be written in the form of a virial equation of state in powers of 1/V_m.

b) a ≈ 1.673 cm^6·atm·mol^(-2)

c) The Boyle-temperature for argon can be estimated using the calculated van der Waals constants as V_m approaches infinity.

Step by step:

(a) To show that the van der Waals equation can be written in the form of a virial equation of state, we start with the given van der Waals equation:

p = (RT / (V_m - b)) - (a / V_m^2)

We can rewrite this equation by multiplying both sides by V_m:

pV_m = RT - bV_m - (a / V_m)

Now, let's substitute B and C in terms of a and b:

B = b - (RT / a)

C = b^2

Substituting these values into the equation, we have:

pV_m = RT - (RT / a)V_m - (a / V_m) - bV_m - b^2 / V_m

Rearranging terms, we get:

pV_m = RT(1 + ((-RT / a) - b)V_m - (a / V_m) - b^2 / V_m)

This equation can be written in the form of a virial equation of state in powers of 1/V_m.

(b) Given that B = -21.7 cm^3·mol^(-1) and C = 1.200×10^3 cm^6·mol^(-2), and using R = 8.2057×10^(-2) dm^3·atm·K^(-1)·mol^(-1), we can substitute these values into the equations for B and C:

-21.7 = b - (8.2057×10^(-2) / a) (Equation 1)

1.200×10^3 = b^2 (Equation 2)

From Equation 2, we can solve for b:

b = ±√(1.200×10^3)

Since b cannot be negative according to the van der Waals equation, we take the positive square root:

b = √(1.200×10^3) = 34.64 cm^3·mol^(-1)

Now, substituting this value of b into Equation 1, we can solve for a:

-21.7 = 34.64 - (8.2057×10^(-2) / a)

Solving for a, we find:

a = (8.2057×10^(-2)) / (34.64 + 21.7)

a ≈ 1.673 cm^6·atm·mol^(-2)

(c) To estimate the Boyle temperature, we use the condition:

d(1/V_m) / dZ = 0

At Boyle temperature, V_m approaches infinity. Taking the derivative, we have:

d(1/V_m) / dZ = (2a / V_m^3) - b = 0

Solving for V_m, we get:

V_m = (2a / b)^(1/3)

Substituting the values of a and b that we calculated earlier, we can find V_m:

V_m = (2(1.673) / (34.64))^(1/3)

V_m ≈ 2.519 dm^3·mol^(-1)

Therefore, the Boyle temperature for argon can be estimated using the calculated van der Waals constants as V_m approaches infinity.

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Answer:

Step-by-step explanation:

Given,

One side of an equilateral triangle

\( = (4mn^3 - 5)yds\)

Therefore,

Perimeter of the equilateral triangle

\( = 3 \times side\)

\( = 3 \times (4mn^3 - 5)yds\)

\( = 12m {n}^{3} - 15yds(ans)\)

The possible formula for P(x) would be \(P(x)=x^5+x^4-5x^3+3x^2\).

What is a polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The polynomial of degree 5.

Each root corresponds to a linear factor, so we can write:

        \(P(x) = x^2(x-1)^2(x+3)\\\\P(x)=x^2(x^2-2x+1)(x+2)\\\\P(x)=x^5+x^4-5x^3+3x^2\)

Hence, the possible formula for P(x) would be \(P(x)=x^5+x^4-5x^3+3x^2\).

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