Expand the given logarithm and simplify. Assume when necessary that all quantities represent positive real numbers. Be sure to factor out any common factors in your final answer.
log5(125/ x^{2}-576)

Answer:

gradient = 2

Step-by-step explanation:

calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-5)}{2-0}[/tex] = [tex]\frac{-1+5}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

If David wants to withdraw $32,635.15 every year from his account at the end if each year for 30 years, he has to have $783243.6 in the bank account .

We would use the equation for calculating present annuity.

It is written as

PV = R[1 - (1 + r)^- n]

In which.

Considering the data provided,

r = 1.5/100 = 0.015

n = 30 years

R = $32,635.15

Put the values in the formula,

PV = 32635.15[1 - (1 + 0.015)⁻³⁰]/0.015

PV = 32635.15[1 - (1.015)⁻³⁰]/0.015

PV = 32635.15(1 - 0.64)/0.015

PV = 32635.15 × 24

PV = $783243.6

Thus, amount David must have in the bank presently is  $783243.6.

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Answer:

Step-by-step explanation:

You want the domain, range, intercepts, asymptotes, and holes of the rational function f(x) = (2x³ +10x² +8x)/(x³ +7x² +12).

The given function can be simplified by cancelling common factors from numerator and denominator. These cancelled factors show where the holes are in the graph.

  [tex]f(x)=\dfrac{2x^3+10x^2+8x}{x^3+7x^2+12}=\dfrac{2x(x+4)(x+1)}{(x(x+4)(x+3)}=2\left(\dfrac{x+1}{x+3}\right)\quad x\notin\{-4,-3,0\}[/tex]

The function is defined for all real numbers except those where the denominator is zero: {-4, -3, 0}.

The function can produce every output value except the value of the horizontal asymptote: y = 2. The range is all real numbers except 2.

The x-intercept is found where the numerator of the simplified function is zero: x = -1

The y-intercept is the function value at x=0. The function is undefined there, so the y-intercept does not exist. (The limit as x approaches zero is y = 2/3.)

The function has a horizontal asymptote at the y-value corresponding to the ratio of the highest-degree terms of the numerator and denominator: y = 2.

The vertical asymptote is at the uncanceled denominator zero, x = -3.

The holes are where a numerator and denominator factor cancel. The y-value at the hole is the limit of the function value as x approaches the hole location. This is the value of the simplified function.

The holes are (-4, 6) and (0, 2/3).

Answer:

22x

Step-by-step explanation:

2x 2(6x+3)

2x 12x+6x

22x

The numerical value of the statistic ^p or sample proportion (p-hat) is 0.2.

^p = X/N where X denotes the number of successes and N denotes the size of the sample. Here, X=55 and N=11.

Sample Proportion (p-hat) of the data:

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From the given statement the mean mcr rt tomatometer score is significantly above fresh.  

What is tomatometer score?

The Tomatometer score represents the percentage of professional critic reviews that are positive for a given film or television show.

To find answer we need to perform hypothesis.

The mean MCU Rotten Tomatoes score is equal to or less than 75%, which is the null hypothesis.

The mean MCU Rotten Tomatoes score is more than 75%, which is the alternative hypothesis. To test this theory, we can use a one-tailed t-test.

The null hypothesis can be rejected if the p-value is less than the significance level, which is typically 0.05, at which point it can be determined that the mean MCU Rotten Tomatoes score significantly exceeds fresh.

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Answer:

Ok this is easy you got this!

Step-by-step explanation:

Ok so, we know their over total is 98.00, we also know that the boots cost $34 each

lets start with 34+34= 68

now we are going to take that from 98

98-68=30

now because they bought two canteens we will divide 30 by 2

30 divided by 2 is 15

the cost of each canteen is $15

The probability that the first ball drawn is a red is 8/14

the probability that the first ball drawn is a yellow is 6/13

Let A = getting a red ball

B= getting a yellow ball given that first was red ball

P( A ) = 8/14

P( B  ) = 6/ 13 (since 1 red ball is out)

A(A ∩ B)= 6/13 x 8/14 =

48/182

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

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No, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.

A smooth-drawn figure or line with a bend or turn is referred to as a curve.

A circle is an illustration of a curved shape.

The path, also known as the topological arc, is the name of the curve (or just arc).

If a curve is the continuous injective image of an interval or a circle, it is considered simple.

If a curve is determined by a continuous function, in other words.

So, it possible for the curve to have a horizontal tangent:

On the curve, horizontal tangents appear where:

x = -1 and y ≠ -1

y = 0 where the curve crosses the x-axis.

-1² + 2(-1) + 0⁴ + 4.0 ≠ 5

No, the point where the curve crosses the x-axis cannot have a horizontal tangent.

Therefore, no, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.

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Complete question:

Consider the closed curve in the xy-plane given by : x²+2x+y⁴=4y = 5

Is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? explain your reasoning.

Answer: There are not any roots for that equation.

Outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 65 degrees at midnight and the high and low temperature during the day are 76 and 54 degrees, respectively. assuming t is the number of hours since midnight, the temperature, d, in terms of t. The Equation is :

                                    D = - 11 sin(π/12) + 65

The range is 76 - 54 = 22

so, a = 11

we know that the period is 24 hours

So, 2π/k=24

  ⇒ 24k = 2π

⇒ k = π/12

So far we have:

D = 11 sin(π/12)(t) + 65

Giving us a range from 76 to 54

But obviously the temp after midnight would decrease, whereas our function has it increasing to 76 when t = 6 (6:00 am)

We could do a phase shift, or more simply, just flip the function to

D = -11sin(π/12)t + 76

Checking some values

t = 0 , D = -11sin0 + 65 = 65

t=6 , (6:00 am) D = -11 sin (π/2) + 65 = 54

t = 12 (noon), D = -11 sin π + 65 = 65

t = 18 , (6:00 pm) , D = -11sin 3π/2 + 65 = 76

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Short Answer:

The given equation has one solution; [tex]n=0[/tex].

______________________________________________________

"How Can You Determine Whether An Equation Has One Solution, Infinite Solutions, or No Solution?"

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

This being said, lets now go back to the given scenario and determine the amount of solutions it has, if any.

1. We are given the following to solve:

2. First, subtract 1 from both sides.

3. Simplify.

4. Move 4n to the left side, leaving us with our final solution.

____________________________________________________

Hope this helps!

The general antiderivative is; (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C

Given,

f (x) = x/8 + 1/8x + (1/8)ˣ

We have to find the antiderivative;

Antiderivative;-

In calculus, a differentiable perform F whose spinoff is sufficient to the initial perform f could be an antiderivative, inverse derivative, primitive perform, primitive integral, or integral of a perform f. Symbolically, this could be expressed as F' = f.

Here,

To find antiderivative, we have to integrate the function first;

Then,

∫ f(x) + g(x) dx = ∫ f(x) dx + g(x) dx

∫ f(x/8) dx = x² / 16

∫ f(1/8 x) dx = 1/8 ln |x|

∫ f(1/8ˣ) dx = -1/ (3 ln × 2 × 8ˣ)

That is,

∫ x/8 + 1/8x + 1/8ˣ dx = (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C

Therefore,

(x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C will  be the antiderivative.

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Answer:

the first one at the top . but can you put up a better picture ?

Step-by-step explanation:

The variance of the number of occasions a 6 appears when a fair die is thrown 12 times is 0.156.

It determines the likelihood of achieving a specific number of successes over a specific number of trials with a consistent success rate using the binomial distribution.

With a 1/6 likelihood of success for each trial, the number of successes in this example is equal to the number of 6s that occur.

The probability of each conceivable value of the quantity of 6s that appear may be calculated using the binomial formula. The likelihood of receiving exactly 0 number of 6s is (12 choose 0) ×[tex](\frac{1}{6})^0[/tex] × [tex](\frac{5}{6}) ^{12}[/tex] = 0.1680. The probability of getting exactly 1 number of 6 is (12 choose 1) × [tex](\frac{1}{6})^1[/tex] × [tex](\frac{5}{6})^{11}[/tex] = 0.4401. The probability of getting exactly 2 numbers of 6s is (12 choose 2) × [tex](\frac{1}{6})^2[/tex] × [tex](\frac{5}{6})^{10}[/tex] = 0.3744. And so on.

The likelihood of receiving 0 6s, for instance, multiplied by the square of the 0's divergence from 2 is 0.1680 × (0 - 2)² = 0.7056. The likelihood of receiving 1 6 when multiplied by the square of the difference between 1 and 2 is 0.4401 × (1 - 2)² = 0.4401. And so on.

To get the anticipated value of the squared departure of the number of 6s that occur from 2, we may finally total up all of these probabilities.

This predicted value is equal to 1.8801 by adding 0.7056, 0.4401, 0.3744, 0.1596, 0.0368, and 0.0036.

The range in the number of 6s that appear after tossing a fair die 12 times is thus 1.8801.

To express the variation in decimal notation, divide the difference by the total number of rolls (12), then round the output to the closest three decimals.

As a consequence, we obtain a variance of 0.1567. The variance in the number of occasions a 6 appears when a fair dice is rolled 12 times is thus 0.1567.

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The frequentist probability is objective, based on observed data, need large sample or long term frequency, and doesn't have prior knowledge.

Frequentist probability is a definition of probability that defines the probability of an event as the probability of an event being observed in a long-term or infinite experiment.

Frequentist probability is different from Bayesian probability in following points,

Thus, the statement are true for frequentist definition for the probability is doesn't have prior knowledge, need large sample, based on observed data, and objective.

Your question is incomplete, but it is general information about the frequentist definition of probability.

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The value of the expression, 13(a • b + a²) + 4, when a = 5 and b = -3 is: B. 134.

To find the value of an expression, we have to plug in the respective values for each of the variables given in the expression, then simplify.

Given the expression, 13(a • b + a²) + 4, where:

a = 5

b = -3

To find the value, substitute a = 5 and b = -3 into the expression:

13(5 • -3 + 5²) + 4

13(-15 + 25) + 4

13(10) + 4

= 130 + 4

= 134

The value is: B. 134.

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the rate at which water is being pumped into the tank in cubic centimeters per minute. is 1508527.582 cm³/min

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 8900 cm³/min,

dV/dt = k - 8900

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 11 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

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As per the question the required hypothesis are

Null Hypothesis, H0: p=0.72

Alternate Hypothesis, H1 : p ≠ 0.72

The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H0.

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample.

Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.

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Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

What is the average?

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Henry scored 85, 76, 84, and 69, and let's suppose he scored 'x' marks in the fifth exam.

Average = sum of all marks/total number of exams

  80 =(85 + 76 + 84 + 69 + x)/5

 80 = 314 + x/5

 80 * 5 = 314 + x

 400 = 314 + x

  x = 400 - 314

  x = 86

Hence, Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

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98% of the quarters can be expected to see a profit of at least $0.5 million.

What is a standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Z score = 0.7-0.5 = 0.2

σ = 0.1

P-value from Z-Table:

P(x<0.5) = 0.97725

             ≈ 98%

Hence, 98% of the quarters can be expected to see a profit of at least $0.5 million.

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The value of the decimal equivalent for 120 will be;

⇒ 0.05

What is Decimal number?

A decimal number is a number that consists of a whole and a fractional part.

Given that;

Jacob knows that 120 means “1 divided by 20.”

Now,

Since, Jacob knows that 120 means “1 divided by 20.”

Hence, The value of 120 by using this will be;

⇒ 1/20 = 0.05

Thus, The value of the decimal equivalent for 120 will be;

⇒ 0.05

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To divide complex numbers, you multiply by the conjugate of the denominator:

    [tex]\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i}[/tex]

We do this to turn the denominator into a real number.

[tex]\begin{aligned}\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i} &= \dfrac{-9+6i-18i+12i^2}{9-4i^2}\\[0.5em] &= \dfrac{-9-12i-12}{9+4}\\[0.5em] &= \dfrac{-21-12i}{13}\\[0.5em] &= -\dfrac{21}{13}-\dfrac{12}{13}i\end{aligned}[/tex]

Answer:

[tex]-\dfrac{21}{13}-\dfrac{12}{13}i[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{-3-6i}{3+2i}[/tex]

Multiply the numerator and denominator by the complex conjugate of the denominator:

[tex]\implies \dfrac{-3-6i}{3+2i} \cdot \dfrac{3-2i}{3-2i}[/tex]

Simplify:

[tex]\implies \dfrac{(-3-6i)(3-2i)}{(3+2i)(3-2i)}[/tex]

[tex]\implies \dfrac{-9+6i-18i+12i^2}{9-4i^2}[/tex]

[tex]\implies \dfrac{-9-12i+12i^2}{9-4i^2}[/tex]

Apply the imaginary number rule [tex]i^2=-1[/tex] :

[tex]\implies \dfrac{-9-12i+12(-1)}{9-4(-1)}[/tex]

[tex]\implies \dfrac{-9-12i-12}{9+4}[/tex]

[tex]\implies \dfrac{-21-12i}{13}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a-b}{c}=\dfrac{a}{c}-\dfrac{b}{c}:[/tex]

[tex]\implies -\dfrac{21}{13}-\dfrac{12}{13}i[/tex]

The calculated value |Z| = |-2.00722 | = 2.00722 > 2.054 at 0.02 level of significance. So their claim is wrong.

Given that the mean age of retirement for women, executives is 63.2

Given that the size of the sample 'n' = 78

Given that the mean of sample x⁻ = 64.2

Given that the standard deviation  'σ' = 4.4 years

Null hypothesis: H₀: μ ≠ 63.2

Alternative Hypothesis: H₁: μ = 63.2

Test statistic

Z =  -2.00722

|Z| =  2.00722 > 2.054 at 0.02 level of significance

The calculated value |Z| = 2.00722 > 2.054 at 0.02 level of significance

Therefore, we reject the hypothesis.

Statistics is the study of research and surveys on numerical data in mathematics. In order to conduct surveys, the hypothesis must be established. There are typically two different kinds of hypotheses. A null hypothesis is one that holds true, whereas an alternate hypothesis is another.

The null hypothesis is a broad assertion or default stance that there is zero happening or nothing happening in probability and statistics. For instance, there is no association between two measured events or a connection between groups.

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Answer:

Step-by-step explanation:

A health researcher conducted a survey and recorded the percentage of body fat of 20 randomly selected men from two different towns.

Answer: 7 hrs and 15 minutes

Step-by-step explanation: because 15 - 8 = 7 45 - 30 = 15

The values of x and y are x = 80° and y = 130°.

What is conservative interior angles?

When a line, referred to as the transversal line, crosses two other lines, two angles are created that are known as consecutive interior angles. Consecutive interior angles, or co-interior angles for short, are the angles formed on the inside of the two lines and on the same side of the transversal line.

Consecutive interior angle CONVERSE is another name for the same side interior angle CONVERSE.

Line line n || m

if (x - 30) + (x + 50) = 180.

x -  30 + x + 50 = 180

2x + 20 = 180

subtract 20 from both sides

2x = 160

divide both sides by 2

x = 80

IF (x - 30) + y = 180, then k || j.

(80 - 30) + y = 180

50 + y = 180

subtract 50 from both sides

y = 130

Hence, the values of x and y are x = 80° and y = 130°.

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Complete question:

Complete question is attached below,

Answer:

Step-by-step explanation:

The price decreases by $288,000*(0.19)=$54,720

The current value is then $233,280.

Answer:

There are 80 coins in her collection.

Step-by-step explanation:

We can find out how many coins are in her coin collection by first converting 5% into a fraction by moving the decimal place to the left twice. Which then we get 0.05. Then, we can set up this equation:

4 ÷ 0.05 = 80

Now, let's check our answer:

0.05 x 80 = 4.

Yep! It checks out!

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The experimental probability of an odd number other than 9 being generated is 38%.

For the stated question-

Other odd numbers outside nine are as follows: 72 - 15 = 57

Probability =  (number of odd numbers except nine)]/(total number)

Probability = 57/150

Probability = 0.38.

Thus, the experimental probability of an odd number other than 9 being generated is 38%.

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Answer:

i found something that might help you

Step-by-step explanation: