considering the arrhenius equation, what is the slope of a plot of ln k versus 1/t equal to? a) k b) -k c) ea d) -ea/r e) a

Yes, The quotient of two polynomial expressions is a rational expression. so the statement is true

Polynomial Expression

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

Rational expression

A rational expression is the quotient of two polynomial expressions where the denominator is not equal to zero.

Consider two polynomial p(x) & q(x)

and q(x) [tex]\neq[/tex] 0

then the quotient is a rational expression

so the statement is true.

Yes, The quotient of two polynomial expressions is a rational expression. so the statement is true

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Answer:

4

Step-by-step explanation:

Given expression:

[tex]\left(2-\log_{\sqrt{2}}10\right)\left(2-\log_{\sqrt{5}}10\right)[/tex]

[tex]\textsf{Apply the radical rule}: \quad \sqrt{a}=a^{\frac{1}{2}}[/tex]

[tex]\implies \left(2-\log_{2^{\frac{1}{2}}}10\right)\left(2-\log_{5^{\frac{1}{2}}}10\right)[/tex]

[tex]\textsf{Apply the log rule}: \quad \log _{a^n}(x)=\frac{1}{n}\log _a\left(x\right),\:\quad \:a > 0[/tex]

[tex]\implies \left(2-\dfrac{1}{\frac{1}{2}}\log_{2}10\right)\left(2-\dfrac{1}{\frac{1}{2}}\log_{5}10\right)[/tex]

[tex]\implies \left(2-2 \log_{2}10\right)\left(2-2\log_{5}10\right)[/tex]

Rewrite 10 as 2 · 5 and 10 as 5 · 2:

[tex]\implies \left(2-2 \log_{2}(2 \cdot 5)\right)\left(2-2\log_{5}(5 \cdot 2)\right)[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \left(2-(2 \log_{2}2+2\log_2 5)\right)\left(2-(2\log_{5}5 +2\log_52)\right)[/tex]

[tex]\implies \left(2-2 \log_{2}2-2\log_2 5\right)\left(2-2\log_{5}5 -2\log_52\right)[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies \left(2-2(1)-2\log_2 5\right)\left(2-2(1) -2\log_52\right)[/tex]

[tex]\implies \left(2-2-2\log_2 5\right)\left(2-2 -2\log_52\right)[/tex]

[tex]\implies \left(-2\log_2 5\right)\left(-2\log_52\right)[/tex]

Multiply:

[tex]\implies 4 \cdot \log_2 5 \cdot \log_52[/tex]

[tex]\textsf{Apply the log rule}: \quad \log _{a}(x) \cdot \log_{x}(a)=1[/tex]

[tex]\implies 4 \cdot 1[/tex]

[tex]\implies 4[/tex]

The equation of line passes through the points (14, 10) and (0, 2) will be;

⇒ y = 4/7x + 2

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (14, 10) and (0, 2)

Now,

Since, The equation of line passes through the points (14, 10) and (0, 2)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 10) / (0 - 14)

m = - 8 / - 14

m = 4/7

Thus, The equation of line with slope 4/7 is,

⇒ y - 10 = 4/7 (x - 14)

⇒ y - 10 = 4/7 (x - 14)

⇒ y = 4/7x - 8 + 10

⇒ y = 4/7x + 2

Therefore, The equation of line passes through the points (14, 10) and

(0, 2) will be;

⇒ y = 4/7x + 2

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Considering the definition of perpendicular line, the equation of the perpendicular line is y= 1/5x - 13/5.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= -5x +1.

In this case, the line has a slope of  -5. If you multiply the slopes of two perpendicular lines, you get –1, you get:

(-5)× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-5)

slope perpendicular line= 1/5

So, the perpendicular line has a form of: y= 1/5x + b

The line passes through the point (2, -1). Replacing in the expression for perpendicular line:

-1= 1/5× 2 + b

-1= 2/5 + b

-1- 2/5= b

-13/5= b

Finally, the perpendicular line is y= 1/5x - 13/5.

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Answer:

x = pm - pn

Step-by-step explanation:

m = n + [tex]\frac{x}{p}[/tex]  Subtract n from both sides

m - n = n - n + [tex]\frac{x}{p}[/tex]

m-n = [tex]\frac{x}{p}[/tex]   Multiply both sides by p

p(m - n) = ([tex]\frac{p}{1}[/tex]) [tex]\frac{x}{p}[/tex]          [tex]\frac{p}{1}[/tex] means the same as p

pm - pn = x             Distribute the p

x = pm - pn

The slope of line perpendicular to line 3x - 6y = 90 is -2.

Slope-Intercept form of equation => y = mx + c

Slope = m

Given equation,

3x - 6y = 90

 x - 2y = 30

      2y = x - 30

        y = x/2 - 15

        y = (1/2)x + (-15)

Here, slope = m1

                   = 1/2

For line perpendicular slope will be negative reciprocal of the slope of given line.

Therefore, slope of other line = m2

                                                 = -1/m1

                                                 = -2

Hence, slope of line perpendicular to line 3x - 6y = 90 is -2.

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Answer:

$361,660

Step-by-step explanation:

(a)

the original value represents 100%

an increase of 7% is then 100% + 7% = 107% = [tex]\frac{107}{100}[/tex] = 1.07 then

new value = 1.07 × old value

(b)

new value = 1.07 × $338,000 = $361,660

The value of the x in g(h(x)) = 4 is 4 if the g⁻¹(4) = 2 and at x = 4 h(x) = 2 option (C) is correct.

The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The relation is,

g (h (x)) = 4

Now, Substitute x = 4;

LHS;

g (h (x)) = g (h (4))

            = g (2)

           = 4

Thus, The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

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As it is given, 1% of left tree is decaying every year.

Number of tree left after 8 years.

A = P{1-R/100}^[tex]^{T}[/tex] = 10M{1-1%/100}^  [tex]^{8}[/tex]

= 10M *(0.99)[tex]^[/tex]^[tex]^{8}[/tex]

= 9227446

If round at hundredth, then,

Number of tree = 9227400.

Identify the asset's cost. Get the asset's total depreciable value by deducting the projected salvage value from the asset's purchase price. Determine the asset's useful life. The annual depreciation amount is obtained by dividing the sum of steps (2) and (3) by the figure determined in steps (3).

Depreciation is the practice of deducting the cost of a company asset over a number of years as opposed to just one. There are four primary ways to depreciate assets: linear, twofold declining, sum of the years' digits, and manufacturing units.

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2,092.1 is the population of the town after 5 years, and P(t)=2500*(1-0.035)^t is the exponential function.

In mathematics, exponential decay defines the process of diminishing an amount by a consistent percentage rate over a period of time.

It can be stated by the formula y=a(1-b)x wherein y is the total form and is the initial money, b is the decay factor, and x is the quantity of time that has passed.

So, we got:

r = 3.5%/100% = 0.035

We have our exponential function:

P(t) = 2500*(1 - 0.035)^t

The number after 5 years is provided by substituting t = 5, we will get:

P(5) =  2500*(1 - 0.035)^5 = 2,092.1

Therefore, 2,092.1 is the population of the town after 5 years, and P(t) = 2500*(1 - 0.035)^t is the exponential function.

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Correct question:
The population of the town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential decay function to find the population of the town after 5 years

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{x - y^2}\\\mathsf{= 3 - (-5)^2}\\\mathsf{= 3 + \bf 5^2}\\\mathsf{= 3 + \bf 5\times5}\\\mathsf{= 3 + \bf 25}\\\mathsf{= 28}\\\\\huge\text{Therefore, your answer should be: \boxed{\textsf{28}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

A

Step-by-step explanation:

y=-2 when x=-4 y=-4 when x=-8

what's given: 4. what's given:2

-4k=-2. -8k=-4

-4/4. -2/4. -8/8. -4/8

k=0.5. k =0.5

0.5(2) =1. 0.5(2)=1

Answer:

Step-by-step explanation:

You want to identify the proportional relations in the given tables and equations, and you want to find and use the constant of variation given that y=35 when x=7.

A proportional relation is one that has an equation of the form ...

  y = kx

One variable is a constant multiple of the other. If the relation cannot be put in this form, it is not a proportional relation.

The value of k in the above equation can be found as ...

  k = y/x . . . . . . . divide both sides by x

This is a constant if the relation is proportional.

  y/x = -8/-4 = -4/-2 ≠ 18/6 . . . . . not a proportional relation

  y/x = -4/-5 ≠ 10/2 . . . . . not a proportional relation

  y/x = -12/-3 = 24/6 = 32/8 = 4 . . . . . a proportional relation

You are looking for equations of the form y = kx. The only ones having that form are ...

The others represent inverse proportions and a linear (not proportional) relation.

As we saw above, the constant of variation is ...

  k = y/x = 35/7

  k = 5

Then the value of x can be found from ...

  49 = 5x

  49/5 = x = 9.8

The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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The probability that the resulting integer is divisible by 8 is 1/6

According to the question,

Nancy Rolled a six-sided die twice to generate two-digit integers

Total number of outcome by rolling a die = {1 , 2 , 3 , 4 ,5 ,6 }

If you roll twice then total number of outcomes becomes = 6 × 6

=> 36

We have to find  the probability that the resulting integer is divisible by 8

Number of two - digit integer divisible by 8 = 16 , 24 , 32 , 48 , 56 , 64

that is 6  

So, Probability = Number of favorable outcomes / total number of outcomes

=> 6 / 36

=> 1/6 is required probability

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In geometry, the distance formula is a formula used to calculate the distance between two points in a plane. It is derived from the Pythagorean Theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance formula is an equation used to calculate the distance between two points in a plane. It is derived from the Pythagorean Theorem which defines the relationship between the three sides of a right triangle. To calculate the distance between two points, (x1, y1) and (x2, y2), the formula is:

d = √((x2-x1)^2 + (y2-y1)^2).

This means that the distance between the two points is equal to the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates. To find the answer, you must first subtract the two x-coordinates (x2-x1) and then square the result. Then you must subtract the two y-coordinates (y2-y1) and square the result. Finally, add the two squared results together and take the square root of the sum to get the distance between the two points.

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The angle of elevation is 72.5° and the height at which the ladder will elevate on the building is 19.06 ft.

Here we have to find the angle of elevation of the ladder and the height the ladder will reach on the building if the ladder is leaned against a building.

Data given:

length of the ladder = 20 ft

the base of the ladder = 6ft

we have to find the angle of elevation.

cos Ф = base/ hypotenuse

= 6/20

Ф = [tex]cos^{-1}[/tex] ( 6/20)Ф

    = 72.5°

Now we have to find how high the ladder reaches on the building when leaned against a building.

sin(72.5°) = x/ 20

x = 0.953 ×20

x = 19.06 ft

Therefore the angle of elevation is 72.5° and the ladder will elevate to 19.06.

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I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

The value of x is x ≤ 9 for which y ≤ -5(x - 18) - 2 when y = 43.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is y ≤ -5(x - 18) - 2.

Now the values of x when y = 43 is,

43 ≤ - 5(x - 18) - 2.

43 ≤ - 5x + 90 - 2.

43 - 88 ≤ - 5x.

- 45 ≤ - 5x.

5x ≤ 45.

x ≤ 9.

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Answer:

120m/s

Step-by-step explanation:

v-? (speed)

s-5400m(travel)

t-45s(time)

v=s/t

v=5400/45

v=120m/s

The general solution of the given differential equation is y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2) and the largest interval is (-infinity, -2) U (-1, infinity).

The general solution of the mentioned differential equation will be calculated as follows -

Firstly rewriting the differential equation in standard form:

(x+1) dy/dx + (x+2)y = 2x[tex] {e}^{(xy)} [/tex]

Calculating the integrating factor to make the LHS as a total derivative:

As known, formula for integrating factor is:

mu = [tex] {e}^{(integral of (x+2)/(x+1) dx)} [/tex]

= [tex] {e}^{(ln(x+1) + ln(x+2))} [/tex]

= (x+1)(x+2)

Now multiplying both sides of the equation by the integrating factor:

(x+1)(x+2) × (x+1) dy/dx + (x+1)(x+2) × (x+2)y = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)

LHS will be a total derivative. Rearrange the equation for the same -

d/dx((x+1)(x+2)y) = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)

Integrating both sides of the equation:

(x+1)(x+2)y = integral of 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2) dx

= 2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C

Now find the equation for y:

y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2)

Equation for y is the general solution of the differential equation where constant C is the arbitrary constant of integration.

The general solution is not defined at the position x=-1 and x=-2. Hence, the largest interval over which the general solution is defined is (-infinity, -2) U (-1, infinity).

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17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0)

What is slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be shown as

tan θ = Δy/Δx

So, the slope of a line is tan.

When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.

To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.

To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).

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The logarithmic form of e^a = 95/73 is  [tex]loge_{\frac{95}{73} }[/tex] = a

natural logarithm can be referred to as the power to which the base ‘e’ that has to be raised to obtain a number called its log number. Here e is the exponential function. It was initially discovered in the 17th century by John Napier, who discovered and conceptualized the theory of logarithms. Before looking into the key difference between ln and log, let’s understand the definition of log and ln.

if e^a = 95/73

means that the natural logarithm of 95/73 is the number a

so that we have

a =  [tex]loge_{\frac{95}{73} }[/tex]

In conclusion the logarithmic form of the expression is a =  [tex]loge_{\frac{95}{73} }[/tex]

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Answer:

a = [tex]\frac{b-4}{-2y}[/tex]

Step-by-step explanation:

ay + 4 = 3ay - b  Subtract 4 from both sides

ay = 3ay -b - 4  Subtract 3ay from both sides

ay - 3ay = b - 4  Factor out the a

a (y -3y)  = b =4  Combine like terms

a(-2y) = b - 4  Divide both sides by -2y

a = [tex]\frac{b-4}{-2y}[/tex]

Answer: 24 cups of sugar

Step-by-step explanation: you multiple the orginal amount neede for one batch by 8

8*3=24

The total number of fishes present in the lake on my 1 is 840.

The given data for the question-

September is equivalent to a percentage of tagged fish in May.

3/42 = 60/x

x = 60 *42 / 3

x = 840

Thus, the total number of fishes present in the lake on my 1 is 840.

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the first statement is false, and the 2nd statement is true.

the sign > indicates it is greater than the next value and the sign < indicates it is less than the next value.

In mathematics the above signs are used to compare two mathematical expressions.

7<5 cannot be possible as positive 7 is always greater than positive 5

in the next positive 3 is greater than positive 1 so it is true.

hence, 7<5 is false and 3>1 is true.

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Answer:

1.1 hectares

Step-by-step explanation:

6.93/6.3 = 1.1

He can plant 1.1 hectares of land.

No, The side lengths does not make a right triangle.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sides of the triangle are;

⇒ 20, 20 and √800

Now,

Since, The sides of the triangle are;

⇒ 20, 20 and √800

Hence, We can apply the Pythagoras theorem as;

⇒ (√800) ² = √ 20² + 20²

⇒ 800 ≠ √800

Thus, The side lengths does not make a right triangle.

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In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. the expression.343 ^ { 4 / 3 } is 7,625

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 = 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.The expression 343^ {4/3} can be broken down into 343 to the power of 4 divided by 3. Before we evaluate the expression, we must understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 can be calculated using the formula 343 x 343 x 343 x 343. This results in 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.

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