please explain and show all steps
а Assume X is normally distributed with a mean of 11 and a standard deviation of 3 Determine the value of x that solves P (X> x) = 0.8

The surface area of the solid formed by the net = 150.72 in²

From the figure we can observe that the solid formed by the net is the net of a cylinder.

The cylinder bases are the 2 circles and the curved surface of the cylinder is the rectangle.

The surface area of the cylinder = Area of the 2 circles + area of the rectangle

Here, the diameter of circle is 4 in

So, the radius of circle = ½ × 4

                                     = 2 in

So, the area of the 2 circles would be,

2(πr²)

= 2 × 3.14 × 2²

= 25.12 in²

Here the width of the rectangle is 10 in. and the length is nothing but the circumference of the circle.

so, length L =  πd

                   = π × 4

                   = 12.56 in

Now the area of rectangle would be,

L × W

= 12.56 × 10

= 125.6 in²

The total surface area of net would be,

Area of the 2 circles + area of the rectangle

= 25.12 + 125.6

= 150.72 in²

Learn more about the surface area of cylinder here:

https://brainly.com/question/22074027

#SPJ1

Five other iterated integrals that are equal to the given iterated integral are:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dx dz dy

∫₀⁷ ∫₀ʸ ∫y²₂ f(x, y, z) dx dz dy

∫y²₂ ∫₀⁷ ∫₀ʸ f(x, y, z) dx dy dz

∫y²₂ ∫₀ʸ ∫₀⁷ f(x, y, z) dx dy dz

∫₀ʸ ∫y²₂ ∫₀⁷ f(x, y, z) dz dx dy

To find the five other iterated integrals that are equal to the given iterated integral, we need to rearrange the order of integration. We can do this by changing the order of the limits of integration and writing the integral with respect to a different variable first.

The original integral is:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dz dx dy

Now, we can change the order of integration in the following ways:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dx dz dy

∫₀⁷ ∫₀ʸ ∫y²₂ f(x, y, z) dx dz dy

∫y²₂ ∫₀⁷ ∫₀ʸ f(x, y, z) dx dy dz

∫y²₂ ∫₀ʸ ∫₀⁷ f(x, y, z) dx dy dz

∫₀ʸ ∫y²₂ ∫₀⁷ f(x, y, z) dz dx dy

Each of these integrals has the same value as the original integral, but with a different order of integration. It is important to note that changing the order of integration can sometimes make the integral easier to evaluate, especially if the integrand has certain symmetries.

For more questions like Integral click the link below:

https://brainly.com/question/22008756

#SPJ11

The selling price of the computer was $8507.52.

We have,

If the businessman incurred a loss of 21% on the cost price, then the selling price (SP) must have been 79% of the cost price (CP), since:

SP = CP - Loss

SP = CP - 0.21 x CP

SP = 0.79 x CP

We know that the cost price was $10768, so we can substitute this value into the equation above to find the selling price:

SP = 0.79 x CP

SP = 0.79 x $10768

SP = $8507.52

Therefore,

The selling price of the computer was $8507.52.

Learn mroe about profit and loss here:

https://brainly.com/question/31452402

#SPJ1

The value of x that would make M the midpoint of PQ if PM = 3x-1 and PQ = 5x+3 include the following: 2.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since M is the midpoint of line segment PO, we have the following:

Line segment PM = Line segment PQ

3x - 1 = 5x + 3

5x - 3x = 3 + 1

2x = 4

x = 4/2

x = 2

PM = 3x - 1 = 3(2) - 1 = 6 - 1 = 5 units.

PQ = 5x + 3 = 5(2) + 3 = 10 + 3 = 13 units.

Read more on midpoint here: brainly.com/question/17918978

#SPJ1

1) the cross product of R1 and R2 is -4i + 2j + 3k.

2) the inner angle between R1 and R2 is given by:56.35 degrees

3) the area of the triangle OP1P2 is (1/2) sqrt(29).

4)the circumference of the triangle OP1P2 is: C

(1) Cross product of R1 and R2:

The cross product of two vectors R1 and R2 is given by:

R1 × R2 = (R1yR2z - R1zR2y)i - (R1xR2z - R1zR2x)j + (R1xR2y - R1yR2x)k

Substituting the values of R1 and R2, we get:

R1 × R2 = (2×0 - 2×1)i - (1×0 - (-1)×2)j + (1×1 - 2×(-1))k

= -4i + 2j + 3k

Therefore, the cross product of R1 and R2 is -4i + 2j + 3k.

(2) Inner angle between R1 and R2:

The inner angle between two vectors R1 and R2 is given by:

cos θ = (R1 · R2) / (|R1||R2|)

where R1 · R2 is the dot product of R1 and R2, and |R1| and |R2| are the magnitudes of R1 and R2, respectively.

Substituting the values of R1 and R2, we get:

R1 · R2 = 1×(-1) + 2×1 + 2×0 = -1 + 2 = 1

|R1| = sqrt(1^2 + 2^2 + 2^2) = sqrt(9) = 3

|R2| = sqrt((-1)^2 + 1^2 + 0^2) = sqrt(2)

Therefore, the inner angle between R1 and R2 is given by:

cos θ = 1 / (3sqrt(2))

θ = cos^(-1) (1 / (3sqrt(2)))

θ ≈ 56.35 degrees

(3) Area of a triangle OP1P2:

Let R = R2 - R1 be the vector connecting P1 to P2. Then the area of the triangle OP1P2 is given by:

A = (1/2) |R1 × R2|

= (1/2) |(-4i + 2j + 3k)|

= (1/2) sqrt((-4)^2 + 2^2 + 3^2)

= (1/2) sqrt(29)

Therefore, the area of the triangle OP1P2 is (1/2) sqrt(29).

(4) Circumference of the triangle OP1P2:

Let a, b, and c be the side lengths of the triangle OP1P2 opposite to the points O, P1, and P2, respectively. Then the circumference of the triangle is given by:

C = a + b + c

To find the length of side c, we can use the distance formula:

c = |R2 - R1| = sqrt((-1 - 1)^2 + (1 - 2)^2 + (0 - 2)^2) = sqrt(18)

To find the length of sides a and b, we can use the fact that the triangle isisosceles (since the angles at P1 and P2 are equal), so a = b:

a = b = |P1 - O| = sqrt(1^2 + 2^2 + 2^2) = sqrt(9) = 3

Therefore, the circumference of the triangle OP1P2 is:

C

To learn more about circumference visit:

https://brainly.com/question/28757341

#SPJ11

The volume of the figure is given as follows:

V = 132 ft³.

The volume of a triangular prism is given as half the multiplication of the dimensions of the triangle, as follows:

V = 0.5 x l x w x h.

The dimensions of the triangle in this problem are given as follows:

3 ft, 8 ft and 11 ft.

Hence the volume of the prism is given as follows:

V = 0.5 x 3 x 8 x 11

V = 132 ft³.

More can be learned about the volume of a triangular prism at https://brainly.com/question/29663752

#SPJ1

Check the picture below.

The closest answer choice to the probability that a patient has the disease given a positive test result is 0.16.

To determine the probability that a patient has the disease given a positive test result, we need to use Bayes' theorem:

[tex]P_{(disease| positive test)} = P_{(positive test)} \times P_{(disease)} / P_{(positive test)}[/tex]

where,

[tex]P_{(disease |positive test)}[/tex] = probability of having the disease given a positive test result

[tex]P_{(positive test|disease)[/tex] = sensitivity = 0.7

[tex]P_{ (disease)[/tex]  = unconditional probability of having the disease = 0.04

[tex]P_{(positive test)} = probability of testing positive = (P_{(positive test |disease)}\times P_{(disease)}) + (P_{(positive test |no disease)}\times P_{(no disease)})[/tex]

To calculate P(positive test |no disease), we need to use the specificity of the test, which is:

[tex]P_{(negative test |no disease)}[/tex]  = specificity = 0.85

Therefore,

[tex]P_{(positive test |no disease)} = 1 - P_{(negative test |no disease)} = 1 - 0.85 = 0.15[/tex]

And,

[tex]P_{(positive test)} = (0.7 \times 0.04) + (0.15 \times 0.96) = 0.0676[/tex].

Now we can calculate the probability of having the disease given a positive test result as follows:

[tex]P_{(disease |positive test)} = 0.7 \times 0.04 / 0.0676 = 0.413.[/tex]

For similar question on probability.

https://brainly.com/question/24055383

#SPJ11

In a case whereby Sami wants to find the measurements of the sides and angles of the parallelogram shown the tools she can use to find these measurements are;

The protractor serves as one of the tools that can be used in making the parallelogram whih which be used in the mearement of the angles of the paralleolgram.

The ruler is also useful in the creation of the parallelogram because it can be used to meausre the lenght of the fiqure, hence the first as well as the third option is right

Learn more about  parallelogram at:

https://brainly.com/question/970600

#SPJ1

The equation that represents the company's fare structure, based on the amount of time it is rented is y = 60x + 120.

Option C is the correct answer.

We have,

From the table, we can make an equation.

Take two ordered pairs.

i.e

(1, 180) and (2, 240)

Now,

Let the equation be y = mx + c

So,

m = (240 - 180)/ (2 - 1) = 60/1 = 60

And,

(1, 180) = (x, y)

180 = 60 x 1 + c

180 = 60 + c

c = 180 - 60

c = 120

Now,

y = mx + c

y = 60x + 120

Thus,

The equation that represents the company's fare structure, based on the amount of time it is rented is y = 60x + 120.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

3.6 kilograms

Step-by-step explanation:

divide the mass value by 2.205

If two functions are f(x) and k(x), then, The correct option is C.

A mapping demonstrates the pairings of the components. It displays the input and output values of a function, much like a flowchart would.  Every element of the domain is associated with exactly one element of the range in a function, which is a unique kind of relation. A mapping demonstrates the pairings of the components.

It displays the input and output values of a function, much like a flowchart would. The two parallel columns of a mapping diagram.

The calculation is as follows:

If two functions are f(x) and k(x),

(f o g)(x) = f[g(x)]

Now according to the picture

We have to find the value of (h o k)(1).

(h o k)(x) = h[k(x)]

             = h[k(1)]

             = h(3) [Since, k(1) = 3]

             = 28 [Since, h(3) = 28]

Learn more about functions visit: brainly.com/question/28989903

#SPJ4

Correct Question:

Select the correct answer. Consider functions h and k. What is the value of ?

It is important to recognize and be aware of confirmation bias to engage in more unbiased and evidence-based thinking.

(a) To calculate the probability of dying from COVID conditional on being unvaccinated, Pr(D|U), using Bayes' rule, we can write:

Pr(D|U) = (Pr(U|D) * Pr(D)) / Pr(U)

Where:

Pr(D) is the probability of dying from COVID (unknown)

Pr(U|D) is the probability of being unvaccinated given that the person died from COVID (given as 0.53)

Pr(U) is the probability of being unvaccinated (unknown)

Similarly, to calculate the probability of dying from COVID conditional on being vaccinated, Pr(D|V), we can write:

Pr(D|V) = (Pr(V|D) * Pr(D)) / Pr(V)

Where:

Pr(V|D) is the probability of being vaccinated given that the person died from COVID (1 - Pr(U|D) = 1 - 0.53 = 0.47)

Pr(V) is the probability of being vaccinated at least once (given as 0.93)

The relative likelihood of dying with and without vaccination can be assessed by comparing Pr(D|U) and Pr(D|V). If Pr(D|U) is significantly higher than Pr(D|V), it suggests that being unvaccinated increases the likelihood of dying from COVID. If Pr(D|V) is close to or higher than Pr(D|U), it suggests that vaccination provides a protective effect against severe outcomes of COVID.

However, without knowing the value of Pr(D) (the overall probability of dying from COVID), we cannot make a specific comparison between Pr(D|U) and Pr(D|V). The calculation only provides conditional probabilities based on the given information.

To further analyze the relative likelihood, additional data or information on the overall probability of dying from COVID is needed.

(b) The type of error that people who believe vaccinations are not effective based on the almost equal fractions of vaccinated and unvaccinated deaths from COVID are committing is known as a "base rate fallacy."

The base rate fallacy occurs when individuals ignore or downplay the prior probabilities or base rates of events and focus solely on the conditional probabilities or specific outcomes. In this case, the base rate would be the overall vaccination rate in the population, which is not taken into account when comparing the fractions of vaccinated and unvaccinated deaths.

While it may be true that the fractions of vaccinated and unvaccinated deaths are similar, the base rate of vaccination in the population also needs to be considered. If a significant portion of the population is vaccinated, it is expected that there will be vaccinated individuals among the deaths, simply due to the larger number of vaccinated individuals.

To properly evaluate the effectiveness of vaccinations, it is important to compare the rates of COVID-related hospitalizations or deaths between vaccinated and unvaccinated individuals while taking into account the overall vaccination rate in the population. This broader analysis provides a more accurate assessment of the effectiveness of vaccines in preventing severe outcomes of COVID.

(c) The bias that is at work in this situation is known as "confirmation bias."

Confirmation bias refers to the tendency to selectively focus on or interpret information in a way that confirms pre-existing beliefs or hypotheses while ignoring or discounting evidence that contradicts those beliefs. In this case, individuals who already believe that vaccinations are not effective are exhibiting confirmation bias by concentrating their attention on the death rates of the entirely unvaccinated and disregarding the strong evidence for the efficacy of the vaccine.

Despite the information provided that only 1.7% of the deceased have received three doses of the vaccine while approximately 53% of the population has received three doses, individuals with confirmation bias tend to dismiss or downplay this evidence. They may actively seek out information or arguments that align with their preconceived notions while ignoring or dismissing information that challenges their beliefs.

Confirmation bias can hinder rational decision-making and prevent individuals from objectively evaluating new information or updating their beliefs based on the available evidence. It is important to recognize and be aware of confirmation bias to engage in more unbiased and evidence-based thinking.

To learn more about probability visit:

https://brainly.com/question/15124899

#SPJ11

A 5% risk of being wrong, as accepted by convention in psychology, is an acceptable level of risk as it balances decisions making and potential for error well. The costs of lowering the risk to 1% requires more time and efforts.

In my opinion, a 5% risk of being wrong is a generally acceptable level of risk in many situations in psychology. This is because it balances the need for making decisions with the potential for error.

If we were to lower the risk to 1%, it might require more time, resources, and effort to gather additional evidence and conduct more in-depth analysis. This could slow down the decision-making process, which might not be desirable in certain situations.

Ultimately, the acceptable level of risk depends on the context and the potential consequences of the decision being made. If the consequences of a wrong decision are severe, it may be worthwhile to invest in reducing the risk to 1% or lower.

However, for most everyday decisions, a 5% risk of being wrong is a reasonable compromise between accuracy and efficiency.

Know more about psychology here:

https://brainly.com/question/12011520

#SPJ11

Each gift tag costs $0.16.

We have,

To solve this problem, we need to determine the price of each gift tag given that it costs $1.12 to buy 7 tags.

Let "x" be the price of each gift tag in dollars.

Then, if we buy 7 tags, the total cost would be 7 times the price of each tag:

7x

We know that this total cost is $1.12, so we can set up a proportion:

7x / 1 = 1.12 / 1

Simplifying, we get:

7x = 1.12

Now we can solve for "x" by dividing both sides by 7:

x = 1.12 / 7

Simplifying, we get:

x = 0.16

Therefore,

Each gift tag costs $0.16.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The HR administrator must collect a sample size of 108 employees to be accurate within 0.09 at the 95% confidence interval.

To determine the necessary sample size, we need to use the formula:

[tex]n = \frac{(z^2 )(p) (1-p)}{E^2}[/tex]

Where:
- n = sample size
- z = the z-score for the desired level of confidence (in this case, 1.96 for 95%)
- p = the estimated proportion of employees using the benefit (since we have no preliminary notion, we will use 0.5 as the most conservative estimate)
- E = the desired margin of error (0.09)

Plugging in these values, we get:

[tex]n = \frac{(1.96^2 )(0.5) (1-0.5)}{0.09^2}[/tex]
n = 107.92 = 108

We round up to the next whole number since we can't have a fraction of a person in our sample.

To know more about the confidence interval visit:

brainly.com/question/29680703

#SPJ11

An inequality that represents the situation is s > 140.

Let's use "s" to represent the number of milligrams of sodium in a serving.

Since a serving of food does not qualify as low sodium if it contains more than 140 milligrams of sodium, we can write the inequality:

s > 140

This inequality reads "s is greater than 140", indicating that any value of "s" that is greater than 140 milligrams of sodium per serving does not qualify as low sodium.

To graph this inequality, we can represent "s" on the vertical axis and mark the value of 140 with a dashed line.

Since the inequality is greater than 140, we shade the area above the line to represent all the possible values of "s" that do not qualify as low sodium.

The resulting graph would look like given in the attached image.

To learn more about inequality;

brainly.com/question/28823603

#SPJ1

The complete question:

Write and graph an inequality that represents the number of sodium 's' in a serving that does not qualify as low sodium.

For a food to be labeled low sodium, there must be no more than 140 milligrams of sodium per serving.

The median weight of the players is 225 pounds.

To find the median weight of the players, we need to find the weight value that separates the 24th and 25th ordered weights. We can do this by looking at the box plot and determining the boundaries of the box, which contains the middle 50% of the data.

From the box plot, we can see that the box extends from 170 pounds to 250 pounds, so these are the weights that make up the middle 50% of the data. The median weight will be the weight that is in the middle of this range.

To find the median weight, we can take the average of the two middle values in this range. The two middle values are 220 and 230 pounds. So the median weight is:

(220 + 230) / 2 = 225 pounds

Therefore, the median weight of the players is 225 pounds.

To learn more about median visit:

https://brainly.com/question/1153198

#SPJ11

a. The null hypothesis is H0: p1 = p2, meaning that there is no difference in the proportion of B2B and B2C marketers who commonly use the business social media tool. The alternative hypothesis is Ha: p1 ≠ p2, indicating that there is a difference in the proportion of B2B and B2C marketers who commonly use the business social media tool.

To determine the test statistic, we can use the formula:

[tex]Z = (\frac{p1-p2}{\sqrt{p(1-p)} } (\frac{1}{n1} +\frac{1}{n2})[/tex]

where p is the pooled sample proportion, n1 and n2 are the sample sizes for B2B and B2C marketers, respectively.

Plugging in the values, we get:

[tex]p = \frac{(x1 + x2)}{(n1 + n2)} = \frac{525+244}{584+417} = 0.677[/tex]

[tex]Z= \frac{ (0.9 - 0.59)}{\sqrt{0.677(1-0.677)(\frac{1}{584}+\frac{1}{417}) } } } = 12.72[/tex]

The rejection region for a two-tailed test with alpha = 0.05 is ±1.96. Since our test statistic (12.72) is outside this range, we reject the null hypothesis and conclude that there is strong evidence of a difference in the proportion of B2B and B2C marketers who commonly use the business social media tool.

b. The p-value is the probability of observing a test statistic as extreme as the one calculated or more extreme, assuming the null hypothesis is true. We can find it using a Z-table or a calculator. Here, the p-value is essentially zero, indicating very strong evidence against the null hypothesis.

Interpreting the p-value, we can say that if the true proportion of B2B marketers who commonly use the business social media tool were equal to that of B2C marketers, the probability of observing a difference as extreme as the one in our sample or more extreme would be very small. Therefore, we can reject the null hypothesis and conclude that the proportion of B2B marketers who commonly use the business social media tool is significantly different from that of B2C marketers.

c. The null hypothesis is H0: p1 = p2, meaning that there is no difference in the proportion of B2B and B2C marketers who commonly use the video social media tool. The alternative hypothesis is Ha: p1 ≠ p2, indicating that there is a difference in the proportion of B2B and B2C marketers who commonly use the video social media tool.

To determine the test statistic, we can use the same formula as in part (a), but with the sample proportions and sizes for the video social media tool:

[tex]p = \frac{(x1 + x2)}{(n1 + n2)} = \frac{309+241}{584+417} = 0.444[/tex]

[tex]Z= \frac{ (0.53 - 0.58)}{\sqrt{0.444(1-0.444)(\frac{1}{584}+\frac{1}{417}) } } } = -1.33[/tex]

The p-value for a two-tailed test with alpha = 0.05 is approximately 0.18. Since this is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support a difference in the proportion of B2B and B2C marketers who commonly use the video social media tool.

To know more about "Null hypothesis" refer here:

https://brainly.com/question/30535681#

#SPJ11

The probabilities of the three events are:

P(sum < 6) = 1/2

P(sum = 11) = 1/18

P(sum > 8) = 1/3

We have,

There are 6 possible outcomes for the spinner and 6 possible outcomes for the number cube, so there are 6 x 6 = 36 equally likely outcomes in total.

The sum will be less than 6 if Michelle rolls a 1, 2, or 3 on the number cube, regardless of the result of the spinner.

There are 3 possible outcomes for the number cube and 6 possible outcomes for the spinner, so there are 3 x 6 = 18 outcomes where the sum is less than 6.

Therefore, the probability that the sum will be less than 6 is:

= P(sum < 6)

= 18/36

= 1/2

The sum will be equal to 11 if Michelle rolls a 5 or 6 on the spinner and a 6 on the number cube. There are 2 possible outcomes for the spinner and 1 possible outcome for the number cube, so there are 2 x 1 = 2 outcomes where the sum is equal to 11.

Therefore, the probability that the sum will be equal to 11 is:

= P(sum = 11)

= 2/36

= 1/18

The sum will be greater than 8 if Michelle rolls a 3, 4, 5, or 6 on the spinner and a 4, 5, or 6 on the number cube.

There are 4 possible outcomes for the spinner and 3 possible outcomes for the number cube, so there are 4 x 3 = 12 outcomes where the sum is greater than 8.

Therefore, the probability that the sum will be greater than 8 is:

= P(sum > 8)

= 12/36

= 1/3

Therefore,

The probabilities of the three events are:

P(sum < 6) = 1/2

P(sum = 11) = 1/18

P(sum > 8) = 1/3

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

The translations to the parent function f(x) = x² to generate the function g(x) = (x - 1)² - 3 are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The changes to the parent function in this problem are given as follows:

More can be learned about translations at brainly.com/question/28174785

#SPJ1

On solving this trigonometry, we find that (a) sec(sin⁻¹ [tex]\frac{12}{13}[/tex]) = [tex]\frac{13}{5}[/tex] and (b) tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) = [tex]\frac{12}{5}[/tex]

(a) To find the exact value of sec(sin⁻¹ [tex]\frac{12}{13}[/tex]), we can use the fact that sec(x) = [tex]\frac{1}{cos}[/tex](x). Let's draw a right triangle with opposite side 12 and hypotenuse 13. Using the Pythagorean theorem, we can find the adjacent side:

a² + b² = c²

a² + 12² = 13²

a² = 169 - 144

a = √25

a = 5

So our triangle has sides of length 5, 12, and 13. Now we can find cos(sin⁻¹  [tex]\frac{12}{13}[/tex]) by looking at the adjacent/hypotenuse ratio in this triangle:

cos(sin⁻¹ [tex]\frac{12}{13}[/tex]) =  [tex]\frac{5}{13}[/tex]

Therefore, sec(sin⁻¹(12/13)) = 1/cos(sin⁻¹ [tex]\frac{12}{13}[/tex])

                                            = 1/[tex]\frac{5}{13}[/tex]

                                            = [tex]\frac{13}{5}[/tex].

So the exact value of sec(sin⁻¹ [tex]\frac{12}{13}[/tex]) is [tex]\frac{13}{5}[/tex].

(b) To find the exact value of tan(sin⁻¹ [tex]\frac{12}{13}[/tex]), we can use the fact that tan(x) = sin(x)/cos(x). Let's use the same right triangle as before.

Then sin(sin⁻¹ [tex]\frac{12}{13}[/tex])=  [tex]\frac{12}{13}[/tex] and cos  [tex]\frac{12}{13}[/tex]) = [tex]\frac{5}{13}[/tex]  , so

tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) = sin(sin⁻¹ [tex]\frac{12}{13}[/tex])/cos(sin⁻¹[tex]\frac{12}{13}[/tex])

                        = [tex]\frac{12}{13}[/tex] / [tex]\frac{5}{3}[/tex]

                        = [tex]\frac{12}{5}[/tex]

So the exact value of tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) is [tex]\frac{12}{5}[/tex].

To learn more about trigonometry, refer to:

https://brainly.in/question/2685053

#SPJ4

The solution for b is y-mx in the equation y=mx+b.

The given equation is y=mx+b

y equal r=to m times of x plus b

We need to solve for b in the equation

To solve we have to isolate b from the equation

Subtract mx from both sides

y-mx=b

Hence, the solution for b is y-mx in the equation y=mx+b.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The values of x and y are given as follows:

x = y = 5.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The diagonal length of the rectangle is the hypotenuse of a right triangle of sides 6 and 8, hence:

d² = 6² + 8²

d² = 100

d = 10.

The segments x and y are each half the length of the diagonal, and the two diagonals have the same length for a rectangle, hence:

x = y = 5.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

Step-by-step explanation:

120 = 1000 e^(-.05t)

120/1000 = e^(-.05t)   take natural LN of both sides

-2.12 = - .05t

t = 42.4 days

To find the percent of the population that is likely greater than 5 kilograms, we need to determine the relationship between the given information and the desired result. However, we do not have enough information to directly calculate the percentage of cats weighing more than 5 kilograms based on the given data.

It is essential to have more details, such as the distribution of weights or a specific correlation between the two weight ranges (greater than 4.5 kg and greater than 5 kg), to provide an accurate answer to your question.

In summary, with the current information available, we cannot determine the percent of the cat population that is likely greater than 5 kilograms.

To know more about "Correlation" refer here:

https://brainly.com/question/31569444#

#SPJ11

all four properties are satisfied, we can conclude that (M,d) is a metric space.

What is metric space?

In mathematics, a metric space is a set of objects called points, together with a function called the distance function or metric, that defines a notion of distance between any two points in the space. The metric satisfies certain conditions to ensure that it is a useful measure of the "distance" between points, such as being non-negative, symmetric, and satisfying the triangle inequality. Metric spaces are used to study properties of objects that can be thought of as having a notion of distance, such as Euclidean space, graphs, and networks.

Let's check each of these properties:

Non-negativity: This property holds since d(x, y) is defined to be 0 or 1, both of which are non-negative.

Identity of indiscernibles: This property also holds since d(x, y) is defined to be 0 if and only if x = y.

Symmetry: This property holds since d(x, y) = d(y, x) for any x, y in M.

Triangle inequality: For any x, y, z in M, there are three cases to consider:

If x = y or y = z, then d(x, y) + d(y, z) = d(x, z) = 1 by definition, and the inequality holds.

If x = z, then both sides of the inequality are 0.

If x, y, and z are all distinct, then d(x, y) + d(y, z) = 2 and d(x, z) = 1, so the inequality holds.

Since all four properties are satisfied, we can conclude that (M,d) is a metric space.

Learn more about metric space, by the following link.

https://brainly.com/question/31129859

#SPJ4

The equivalent expression of the fraction 1/{5(n+45)} as,

1/{5(n+45)} = 1/ (5n + 225)

Equivalent expression of 1/{5(n+45)} can be expressed as,

By applying distributive property of addition in the denominator of the given fraction 1/{5(n+45)} , we get

5(n + 45) = 5·n + 5·45

⇒ 5(n + 45) = 5n + 225

The numerator of fraction 1/{5(n+45)} can be written in equivalent expression as,

1 = 1·1 = 1

Thus, we can write the equivalent expression of the fraction 1/{5(n+45)} as,

1/{5(n+45)} = 1/ (5n + 225)

Equivalent expressions are defined as expressions which work in same way even though they look different from each other.

To know more about equivalent expressions here

https://brainly.com/question/28170201

#SPJ1

Rounding to the nearest dollar, we get an account balance of $3,796. Therefore, the answer is (b) $3,796. Option b is Correct.

A financial repository's account balance represents the amount of money there is at the end of the current accounting period. It is the sum of the balance carried over from the previous month and the net difference between the credits and debits that have been recorded during any particular accounting cycle.

The future value of an annuity with monthly contributions:

FV = [tex]P * ((1 + r/12)^{n - 1}) / (r/12)[/tex]

Here FV is the future value, P is the monthly payment, r is the annual interest rate, and n is the number of months.

In this case, P = $150, r = 5.5%, and n = 24 months (2 years * 12 months/year). Plugging in these values, we get:

FV =[tex]150 * ((1 + 0.055/12)^24 - 1) / (0.055/12)[/tex]

≈ $3,795.88

Learn more about account balance visit: brainly.com/question/31393384

#SPJ4

The average rate at which the object falls during the first 3 seconds is given as follows:

-48.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The function for this problem is defined as follows:

h(x) = 400 - 16x².

The numeric values are given as follows:

Thus the average rate of change is obtained as follows:

r = (256 - 400)/(3 - 0)

r = -48.

More can be learned about the average rate of change of a function at brainly.com/question/11627203

#SPJ1