Find the inverse of y = 5x² - 6.

[tex]3x-8=14[/tex]

Add 8 to both sides:

[tex]3x-8+8=14+8[/tex]

[tex]3x=22[/tex]

Divide both sides by 3:

[tex]\dfrac{3x}{3} =\dfrac{22}{3}[/tex]

[tex]\fbox{x = $\dfrac{22}{3} $ or 7.333333}[/tex]

Answer:

approx 17 ft

Step-by-step explanation:

You need to find the 'zeroes' of this equation......where the depth is zero

x^2 - 16x - 8 = 0        You will need to use the Quadratic Formula

                                     with a = 1      b= -16     c = -8

 to find x = 8 +- 6 sqrt 2

     the distance between these zeroes is  12 sqrt2 = 16.97 = ~ 17 feet

By the slope formula, it is proved that the slope of AC is the same as the slope of DE thus option (D) is correct.

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

As per the given,

D(4,5) and E(5,3)

Slope = (3 - 5)/(5 - 4) = -2

A(6,8) and C(8,4)

Slope = (4 - 8)/(8 - 6) = -4/2 = -2

Since the slope of DE = slope of AC

Therefore, both lines will be parallel by the slope formula.

Hence "It is established using the slope formula that the slopes of AC and DE are the same".

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The complete diagram is below,

The expected value of the number of tosses is given by:E(X) = E(X) = 1/pq.PMF is (1 - p)(1 - q)^(n-1) for n ≥ 1

We can calculate the expected value of the number of tosses by taking the summation of the PMF from k=1 to k=∞ multiplied by k. The PMF for the number of tosses is given by P(X=k)=(1−p(1−q)−q(1−p))k−1(p(1−q)+q(1−p)). We can then use this to calculate the  expected value as (1-p(1-q)-q(1-p))/[p(1-q)+q(1-p)]. For the variance, we can use the formula Var(X) = E(X2) - E(X)2. We can calculate the E(X2) part using the same PMF multiplied by k2 and then subtract the expected value squared from it. The final result is (1-p(1-q)-q(1-p))/[(p(1-q)+q(1-p))^2].

PMF:

Let X be the number of tosses

P(X = n) = (1 - p)(1 - q)^(n-1) for n ≥ 1

Expected Value:

E(X) = 1/pq

Variance:

Var(X) = (1 - pq)/(pq)^2

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Answer:

Step-by-step explanation:

To compare the two options, we need to determine how much the salesperson would earn under each option. Under Option A, the salesperson would earn [tex]40 hours * $27/hour = $ < < 40*27=1080 > > 1080.[/tex]

Under Option B, the salesperson would earn a commission of 10% on her weekly sales. Let S be the amount of sales needed for the two options to be equal. We can set up the following equation:

[tex]0.1S = $1080[/tex]

Solving for S, we get:

[tex]S = $1080 / 0.1= $ < < 1080/0.1=10800 > > 10,800[/tex]

Therefore, the salesperson would need to sell $10,800 worth of products in order to earn the same amount under Option B as she would under Option A.

the probability of y1 being less than 1 is 1, regardless of the actual value of y1. P(y1 < 1) = 1

Since y1 and y2 are both uniformly distributed on the interval (0,1), this means that all possible values of y1 and y2 are equally likely. Therefore, the probability of y1 being less than 1 is 1, since any value of y1 between 0 and 1 has the same probability of occurring. This means that the probability of y1 being less than 1 is 1.

Since y1 and y2 are both uniformly distributed on the interval (0,1), this means that all possible values of y1 and y2 between 0 and 1 are equally likely to occur. This means that the probability of y1 being less than 1 is the same as the probability of y1 being equal to any value between 0 and 1. Since this probability is the same for all possible values of y1, the probability of y1 being less than 1 is 1, regardless of the actual value of y1. This is because any value of y1 between 0 and 1 has the same probability of occurring, meaning that the probability of y1 being less than 1 is 1.

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The value of x is 17.8.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Right-angled triangle.

Cos 27° = x / 20

x = 20 x Cos 27°

x = 20 x 0.89

x = 17.8

Thus,

x is 17.8.

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As per the concept of covariance, the correlation between the scores of students from the two parts of the quiz is 9.6

What is meant by covariance and correlation?

In math, the covariance is a measure of the linear relationship between two random variables where as the correlation is used to measure the linear relationship between two random variables if it is zero then variables are said to be uncorrelated and if one then perfectly correlated.

Here we have given that, instructor has given a short quiz consisting of two parts and the  accompanying table shows the number of students who obtained the indicated points for X (rows) and Y (column).

And we need to find the the correlation between the scores of students from the two parts of the quiz.

Let us consider X refers the number of points earned on the first part and Y refers the number of points earned on the second part.

=> E(max(a, x)) = ∑ₐ∑ₓ y max(x, y)p(x, y)

And then when we apply the values on it, then we get,

=> max(0, 0)p(0, 0)+max(0, 5)p(0, 5)+· · ·+max(10, 10)p(10, 10)+max(10, 15)p(10, 15)

When we simplify this one, then we get,

=> 0 ∗ 0.02 + 5 ∗ 0.06 + · · · + 10 ∗ 0.14 + 15 ∗ 0.01 = 9.6.

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Answer: 5(7+6s-9t)

Step-by-step explanation:

(note, this isn't the only expression that is equivalent but it's one of them)

You can notice that 35, 30, and 45 share a common factor of 5, and 5x7=35, 5x6=30, and 5x(-9)=-45, so:

5(7+6s-9t), which when you expand, it's equal to= 35+30s-45t

Answer:

n = the quantity 4 times c minus 3 all over negative p

Explanation:

Interpretation of answers to equation

n = the quantity 4 times c minus 3 all over negative p = [tex]\frac{4c-3}{-p}[/tex]

n = the quantity 4 times c minus 13 all over negative p = [tex]\frac{4c-13}{-p}[/tex]

n = the quantity 4 times c plus 3 all over p = [tex]\frac{4c+3}{p}[/tex]

n = the quantity 4 times c plus 13 all over p = [tex]\frac{4c+13}{p}[/tex]

Step-by-step:

[tex]-np-5=4(c-2)[/tex]

[tex]-np-5=4c-4(2)[/tex]

[tex]-np-5=4c-8[/tex]

[tex]-np-5+5=4c-8+5[/tex]

[tex]-np=4c-3[/tex]

Divide both side by -p

[tex]n=\frac{4c-3}{-p}[/tex]

n = the quantity 4 times c minus 3 all over negative p

Answer:

The answer is the option A, which is: A.) n ≥ − the quantity 4 times c minus 3 all over p.

Step-by-step explanation:

You have −np − 5 ≤ 4(c − 2)

When you solve for n, you obtain:

-np-5 ≤ 4(c-2)

-np≤4c-8+5

Therefore, you have:

n≤-(4c-3/p)

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A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck is a geometric distribution.

Given that,

A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck.

We have to find count how many times a card is drawn in this way until a jack is seen.

We know that,

A discrete probability distribution known as a geometric distribution can be used to describe the likelihood of experiencing success for the first time following a string of failures. Up until the first success, a geometric distribution can undergo an infinite number of trials.

So,

P(X=x)=qˣp.

Therefore, A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck is a geometric distribution.

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Answer:

[tex]f'(x)=7ex^{e-1}-5e^x[/tex]

Step-by-step explanation:

Differentiation rules

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $e^{x}$}\\\\If $y=e^{x}$, then $\dfrac{\text{d}y}{\text{d}x}=e^x$\\\end{minipage}}[/tex]

Given function:

[tex]f(x)=7x^e-5e^x[/tex]

Differentiate with respect to x using the differentiation rules:

[tex]\implies f'(x)=e \cdot 7x^{e-1}-5e^x[/tex]

[tex]\implies f'(x)=7ex^{e-1}-5e^x[/tex]

Answer:

a) c[tex]\int\limits gradf.dr[/tex] = 1

b) c[tex]\int\limits gradf.dr[/tex] = 0

   (the limit symbol has a circle in the center for part b)

Step-by-step explanation:

c[tex]\int\limits gradf.dr[/tex] = f(q) - f(p)

a) c[tex]\int\limits gradf.dr[/tex] = f(1, 2) - f(0, 1)

                      =  61 - 60

                      = 1

b) If C is the circle of radius 1 centered at the point beginning at point (1,2), we can think of C as both beginnings and ending at point ( 1, 3).

c[tex]\int\limits gradf.dr[/tex] = f(1, 3) - f(1, 3)

                  = 68 - 68

                  = 0

Answer:

10[tex]\sqrt{3}[/tex]

Step-by-step explanation:

assumed the radius of the pond was r

∴tan60°=[tex]\sqrt{3}[/tex]= [tex]\frac{30}{r}[/tex]

∴r=[tex]10\sqrt{3}[/tex]

The length of radius of the pond will be 108.76 metres.

Given the values we have,

length of the pole = 30 metres

the angle of elevation of the pole from a point on the circumference = 60°

From this information, we get a right-angled triangle with a perpendicular of 30 m and a base angle of 60°

Therefore we can say that the radius of the pond will be the base of the triangle.

Let the radius of the pond be r

Using the trigonometric ratio of tan, we get,

[tex]tan \alpha = \frac{perpendicular}{base}[/tex]

[tex]tan 60 = \frac{30}{r}[/tex]

The value of tan 60° is [tex]\sqrt{3}[/tex]

[tex]\sqrt{3}=\frac{30}{r}[/tex]

[tex]r= \frac{30}{\sqrt{3}}[/tex]

[tex]r = 17.32[/tex] metres

Therefore the base of the triangle or the radius of the pond is 17.32 metres.

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The p-value of ay distribution given can be calculated using the formula P(Z < X) where X is any sample data.

To find the p-value for a left-tailed test of hypothesis for a mean when the test statistic has been calculated as -1.03, you can use the following formula:

p-value = P(Z < -1.03)

Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is less than -1.03. The resulting p-value will be the probability that the test statistic is as extreme or more extreme than the observed value, given that the null hypothesis is true.

To find the p-value for a right-tailed test of hypothesis for a mean when the test statistic has been calculated as 2.58, you can use the following formula:

p-value = P(Z > 2.58)

Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is greater than 2.58. The resulting p-value will be the probability that the test statistic is as extreme or more extreme than the observed value, given that the null hypothesis is true.

To find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as 1.91, you can use the following formula:

p-value = 2 * P(Z > 1.91)

Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is greater than 1.91. The resulting p-value will be twice this probability, since the test is two-tailed and we need to consider both tails of the distribution.

To find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as -1.16, you can use the following formula:

p-value = 2 * P(Z < -1.16)

Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is less than -1.16. The resulting p-value will be twice this probability, since the test is two-tailed and we need to consider both tails of the distribution.

Note that in all of these cases, you need to assume that the population standard deviation is known. If the population standard deviation is not known, you will need to use a different test statistic and a different approach to calculate the p-value.

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False. The maximum likelihood estimator (MLE) is a method for estimating the parameters of a statistical model based on the maximization of the likelihood function. In the context of linear regression, the MLE would be the values of the parameters that maximize the likelihood of the observed data given the model.

The least squares estimator, on the other hand, is a method for estimating the parameters of a linear regression model by minimizing the sum of squared residuals, which is the difference between the observed response values and the fitted values predicted by the model. While the least squares estimator and the MLE can sometimes lead to similar estimates of the parameters, they are not the same thing and are derived using different principles.

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part (a) =the model's necessary solution is [tex]y=\frac{20}{1+19e^{0.779t} }[/tex] in logistic function.

part (b) =The weight of the culture is 14.425 grams after five hours.

part (c)=After 6.6 years, the culture has an 18 gram weight.

part (d)= The logistic differential equation used to simulate how quickly a culture's weight increases is [tex]\frac{dy}{dy}= 0.779y(1-\frac{y}{20})[/tex]

5. hours later, the culture weighs 11.571 grams.

part (e)= According to portion (c) of this question, the culture's weight will be 18 grams when t=6.6, which is why the weight of the culture increases most quickly at that time.

Given a growth rate, r, and a carrying capacity, K, the logistic equation is a straightforward differential equation model that can be used to connect the change in population, d P d t, to the existing population, P.

given

a bacterial culture weighs 1 gram in time(t)=0

the culture weighs 4 after 2 hours

culture  maximum weight is 20 grams.

for part (a)

The general solution for the logistic differential equation is [tex]y(t)=\frac{L}{1+be^{-kt} }[/tex]

The culture can weigh up to 20 grams , so put value of L= 20 grams

The value of [tex]e^{0}[/tex]is 1.

1+b Equals 20 when multiplied on both sides.

on solving b=19

[tex]y(t)= \frac{20}{19e^{-kt} }[/tex]

The culture weights 4 grams at the end of two hours, or y(2)=4.

value of  t and y in [tex]y(t)= \frac{20}{19e^{-kt} }[/tex]

on simplifying k≈0.779

b and k values should be substituted in the general solution [tex]y(t)= \frac{20}{19e^{-kt} }[/tex]

Therefore, the model's necessary solution is [tex]y=\frac{20}{1+19e^{0.779t} }[/tex] in logistic equation.

for part (b)

The weight of the culture is 14.425 grams after five hours.

for part (c)

After 6.6 years, the culture has an 18 gram weight.

for part (d)

The logistic differential equation used to simulate how quickly a culture's weight increases is [tex]\frac{dy}{dy}= 0.779y(1-\frac{y}{20})[/tex]

5. hours later, the culture weighs 11.571 grams.

for part (e)

According to portion (c) of this question, the culture's weight will be 18 grams when t=6.6, which is why the weight of the culture increases most quickly at that time.

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The expressions representing the length and width of the garden is (5x-1)(2x+7)

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given that, Lillian has a rectangular garden with an area of 10x²+33x-7 square feet.

To find the expressions that would represent the length and width of the garden, we will factorize the expression representing the area of the garden,

10x²+33x-7

= 10x²+35x-2x-7

= 5x(2x+7)-1(2x+7)

= (5x-1)(2x+7)

Hence, The expressions representing the length and width of the garden is (5x-1)(2x+7)

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The ordered pairs for the coordinates of the fire department and of the hospital are given as follows:

The y-coordinate is the same for both the fire department and for the hospital.

The notation of an ordered pair is given as follows:

(x-coordinate,y-coordinate).

From the graph, each coordinate is defined as follows:

For this problem, as the fire department and the hospital are aligned horizontally, it means that they have the same y-coordinate.

The image containing the location of the fire department and of the hospital is shown at the end of the answer.

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Answer:

B) 7.077

Step-by-step explanation:

From the problem, n = 24

Since n is the number of term.

Just input n into the equation.

[tex]a_n= \frac{n^{2}-n}{4n-18}\\[/tex]

[tex]= \frac{24^{2}-24}{4(24)-18}\\[/tex]

[tex]= 7.0769...[/tex]

≈ [tex]7.077[/tex]

From the provided topics to select, For the analytical data we need something where we can extract information from it. The answer is page bounce rate revenue and revenue per session.

In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.

The systematic computational analysis of data or statistics is known as analytics. It is employed for the identification, explanation, and dissemination of significant data patterns. It also involves using data patterns to make smart decisions.

Page bounce rate revenue and revenue per session are the topics which contains some data and facts from which an analysis process can extract some information for other uses.

So, The metrics for understanding analytical data are page bounce rate revenue and revenue per session.

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The probability, to the nearest 10 th of a percent, that both marbles drawn will be green is 0.02

Given :

A bag contains 4 red marbles, 7 blue marbles and 8 green marbles. If two marbles are drawn out of the bag

Probability :

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

total number of possible outcomes = 4 + 7 + 8

= 11 + 8

= 19

Total number of favourable outcomes = 7

probability = favourable outcomes / possible outcomes

= 7 / 19 * 18

= 7 / 342

= 0.02

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You have a 5% chance of being wrong with a 95% confidence interval. With a 90 percent certainty span, you have a 10 percent chance of being incorrectly.

A confidence interval of ninety-nine percent would be larger than a confidence interval of ninety-five percent (for instance, plus or minus 4.5 percent as opposed to 3.5 percent).

We now have: 32 125 0.256 1 At a confidence level of 95 percent:

Zenit = 20.05/2 = 2196 95 percent confidence interval:

Considering the estimated proportion (P) = 0.256 n = = Zverit PL1-P) E 1.96 12 0.015) 0.256 (1-0.256) = 3251.94 3252

Zerit = 20.05/2 = 1.96 At 95%

confidence lovel margin of error (E) = 0.015

Now P = zerit / PL1-£) = 0.256  1.96 X 0.2561-0.256 125 = 0.256  0.0765.

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The data collection method used by Ana Maria for sampling is; simple random sample

There are different methods of sampling such as;

Simple random sampling whereby each individual is chosen completely by chance & each member of the population has an equal chance, or probability, of being selected.

Systematic sampling whereby the Individuals are being selected at regular intervals from the sampling frame.

Stratified sampling whereby the population is first of all divided into subgroups or called strata who all share a similar characteristic.

Clustered sampling whereby subgroups of the population are used as the sampling unit, rather than individuals.

Convenience sampling whereby participants are selected based on availability and willingness to take part

Now, since she decides to walk around the campus and ask people that she meets about the book club. This will be an example of Simple random sampling.

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The value of x is 8.

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Given that, a right triangle,

Solving for x,

y² = 12×4

y = 4√3

y²+4² = x²

(4√3)² +4² = x²

x² = 64

x = 8

Hence, The value of x is 8.

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PQ,MN=5x-10 , and PQ=4x+10 , then MN=90. x-10=10 this equation is proved.

Congruent Addition is the  Substitution segments to  have the Property of   Equality Given  equally lengths; Substitutions Property's of Equality.

As per the given question

MN≈PQ

MN = 5x-10

And PQ=4x+10

Congruent segment have equal lengths:; Substitution property of equality

MN=PQ

5x-10 = 4x+10

Substitution property of equality

X-10=10

Addition property of equality

X=20

Substitution property of equality

MN= 5(20)-10

MN= 90

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So a linear equation in the form p is P(n) = -$0.004*n + $79.

We have two data points:

6000 shirts can be sold for $55 each.

8000 shirts can be sold for $47 each.

Then we can define the relation:P(n).

Where P is the price, and n is the number of shirts.

Now, we know that we can model this as a linear relationship that passes through the points (6000, $55) and (8000, $47)

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, the slope is:

a = ($47 - $55)/(8000 - 6000) = -$0.004

Then our equation is:

P(n) = -$0.004*n + b

Now let's find the value of b, we know that:

P(6000) = $55= -$0.004*6000 + b

$55 = -$24 + b

b= $79

Our equation is:

P(n) = -$0.004*n + $79.

The linear equation P(n) = -$0.004*n + $79 has the form p.

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The value of x in first part = 16

The value of x in second part = 10

Part a

The angle U = angle Z = 54 degrees

Angle V = angle Y = 67 degrees

Therefore angle W = angle X

The sum of the angles in  a triangle is 180 degrees

Then, the equation will be

54 + 67 + a = 180

121 + a = 180

a = 180 - 121

a =  59 degrees

Then

4x - 5 = 59

4x = 59 + 5

4x = 64

x = 64/4

x = 16

Part 2

Similarly the unknown angle as b

Sum of the the angles in a triangle is 180 degrees

58 + 74 + b = 180

132 + b = 180

b = 180 - 132

b = 48 degrees

Then the equation will be

5x - 2 = 48

5x = 48 + 2

5x = 50

x = 50/5

x = 10

Therefore, the value of x in the part a and part b are 16 and 10 respectively

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