8) What does the mathematical symbol TT represent? 9) What does the mathematical symbol E represent?

a) After 30 years, the amount in the account will be approximately $499,355.18.

b) The total money deposited over 30 years will be $144,000.

c) The total interest earned over 30 years will be approximately $355355.18.

We have,

Given:

Monthly deposit: $400

Interest rate: 5% (expressed as a decimal, 0.05)

Time: 30 years (in months, 30 * 12 = 360 months)

a.

To calculate the amount in the account after 30 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Amount in the account

P = Initial deposit (first deposit)

r = Annual interest rate

n = Number of times interest is compounded per year

t = Time in years

In this case:

P = $400 x 360 = $144000

r = 0.05

n = 12 (compounded monthly)

t = 30

Substituting the values into the formula:

A = 144000(1 + 0.05/12)^(12 * 30)

A ≈ $499,355.18

b.

The total money deposited can be calculated by multiplying the monthly deposit by the number of months:

Total Money Deposited = Monthly deposit * Number of months

Total Money Deposited = $400 * 360

Total Money Deposited = $144,000

c.

The total interest earned can be calculated by subtracting the total money deposited from the amount in the account:

Total Interest Earned = Amount in the account - Total Money Deposited

Total Interest Earned = $499,355.18 - $144,000

Total Interest Earned ≈ $355355.18

Therefore,

After 30 years, the amount in the account will be approximately $499,355.18.

The total money deposited over 30 years will be $144,000.

The total interest earned over 30 years will be approximately $355355.18.

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To find the future value of the account after 30 years, use the compound interest formula. Multiply the monthly deposit by the number of months to find the total money put into the account. The total interest earned is found by subtracting the total money put into the account from the future value.

To calculate the future value of the account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (initial deposit), r is the interest rate in decimal form, n is the number of times interest is compounded per year, and t is the number of years.

a. Plugging in the values, we have [tex]A = 400(1 + 0.05/12)^(12*30)[/tex]. Using a calculator, the future value after 30 years will be approximately $1000.40.

b. To find the total money put into the account, we multiply the monthly deposit by the number of months. In this case, it will be $[tex]400 * 12 * 30 = $144,000.[/tex]

c. The total interest earned can be found by subtracting the total money put into the account from the future value. In this case, it will be $[tex]1000.40 - $144,000 = -$143,999.60.[/tex]

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Answer:

The length of the original rectangle is 14 meters and the width of the original rectangle is 12 meters

Step-by-step explanation:

Let

l ----> the length of the original rectangle

w ----> the width of the original rectangle

we know that

[tex]l=2w-10[/tex] ----> equation A

[tex]196=(w+2)^{2}[/tex] ----> area of a square

Solve for w

square root both sides

[tex](w+2)=(+/-)14[/tex]

[tex]w=14=(+/-)14-2[/tex]

[tex]w=14=14-2=12\ m[/tex]

[tex]w=14=-14-2=16\ m[/tex] -----> this solution not make sense

so

[tex]w=12\ m[/tex]

Find the value of L

[tex]l=2(12)-10=14\ m[/tex]

therefore

The length of the original rectangle is 14 meters and the width is 12 meters

Final answer:

The dimensions of the original rectangle are 12 meters (width) and 14 meters (length).

Explanation:

To find the dimensions of the original rectangle, let's first set up an equation.

Let the width of the rectangle be x meters.

The length of the rectangle is given as 10 m less than twice its width, so the length is (2x - 10) meters.

When 2 m are added to the width, the resulting figure is a square with an area of 196 m2.

The side length of a square with area A is √A, so the side length of the square is √196 = 14 meters.

Since adding 2 m to the width creates a square with side length 14 meters, we have:

x + 2 = 14

Subtracting 2 from both sides gives:

x = 12

Therefore, the dimensions of the original rectangle are 12 meters (width) and

(2*12 - 10)

= 14 meters (length).

Final answer:

Using the least squares line equation given, by substituting 844 for the number of reported dead birds, we calculate an expected number of approximately 31 human cases of West Nile virus.

Explanation:

To estimate the number of human cases of West Nile virus based on the number of reported dead birds using the least squares line equation ŷ = −10.2638 + 0.0491x, we need to substitute x with the number of reported dead birds. In this case, x = 844.

The calculation would be:
ŷ = −10.2638 + (0.0491 × 844)

This simplifies to:
ŷ = −10.2638 + 41.4474

Which further simplifies to:
ŷ = 31.1836

After rounding the result to the nearest whole number, we get that approximately 31 human cases of West Nile virus can be expected.

The expected number of human cases of West Nile virus when 844 dead birds are reported is approximately 31, calculated using the given least squares line equation.

To predict the number of human West Nile virus cases when 844 dead birds are reported, we use the least squares line equation:

Here, x represents the number of dead birds, which is 844.

Y = -10.2638 + 0.0491 * 844

0.0491 * 844 = 41.4404

Y = -10.2638 + 41.4404

Y = 31.1766

Rounding to the nearest whole number, the expected number of human cases of West Nile virus is 31.

Answer:

Yes, the triangles are congruent by Hypotenuse angle congruence

Step-by-step explanation:

we know that

The Hypotenuse-Angle Congruence  states that If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the triangles are congruent.

In this problem

The hypotenuse and an acute angle of the right triangle in the left are congruent to the hypotenuse and corresponding acute angle of the right triangle in the right

therefore

The triangles are congruent by Hypotenuse angle congruence

The answer is:

Center: (4,3)

Radius: 3 units.

To solve the problem, using the given formula of a circle, we need to find its standard equation form which is equal to:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

Where,

"h" and "k"are the coordinates of the center of the circle and "r" is its radius.

So, we need to complete the square for both variable "x" and "y".

The given equation is:

[tex]x^2+y^2-8x-6y+16=0[/tex]

So, solving we have:

[tex]x^2-8x+y^2-6y=-16[/tex]

[tex](x^2-8x+(\frac{8}{2})^{2} )+(y^2-6y+(\frac{6}{2})^{2})=-16+(\frac{8}{2})^{2}+(\frac{6}{2})^{2}\\\\(x^2-8x+16)+(y^2-6y+9)=-16+16+9\\\\(x^2-4)+(y^2-3)=9[/tex]

Now, we have that:

[tex]h=4\\k=3\\r=\sqrt{9}=3[/tex]

So,

Center: (4,3)

Radius: 3 units.

Have a nice day!

Note: I have attached a picture for better understanding.

By completing the square on the given equation, the center of the circle is found to be (4, 3) and the radius is 3.

This process will transform the equation into a standard form of a circle equation, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius of the circle.

To start, we can rewrite the original equation by adding and subtracting the necessary constants inside the square terms:

Therefore, after completing the square, we get (x - 4)^2 + (y - 3)^2 = 1. Hence, the center of the circle is (4, 3) and the radius is 3.

Answer:

72

Step-by-step explanation:

In order to find the acceleration we need first to defined it, so:

acceleration=((final velocity)-(initial velocity))/time interval

[tex]a=(vf-vi)/dt[/tex]

But (vf-vi) actually represents the velocity change, so (vf-vi)/dt represents the velocity change rate. This means that in our case:

[tex]a=(36miles/hour)/(0.5hours)[/tex]

[tex]a=72miles/hour^2[/tex]

In conclusion the acceleration is [tex]a=72miles/hour^2[/tex], without units just 72.

Answer:

(c) 5x - 3y = 11

Step-by-step explanation:

using slope intercept form

we know equation of line is

y= mx+c........(1)

where m is slope which  can be written as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-7-3}{-2-4} =\frac{-10}{-6} =\frac{5}{3}[/tex]

substituting value in equation (1)

[tex]y=\frac{5}{3} x+c[/tex]

now inserting value of point (4,3)

[tex]3=\frac{5}{3}\times 4+c[/tex]

[tex]c=\frac{-11}{3}[/tex]

[tex]y=\frac{5}{3} \times x-\frac{11}{3}\\[/tex]

on solving we get

[tex]5x - 3y = 11[/tex]

Answer:

postpositivist

Step-by-step explanation:

Of the all four options "post positivist" philosophical assumption are reflected in quantitative research designs

"post positivist" believes that, theory, hypothesis, background knowledge,believes and values of researchers can alter the actual observations. Post positivist consider both quantitative and qualitative methods to be a valid form of approaches unlike "positivist" which emphasize only on quantitative methods.

The philosophical assumption reflected in quantitative research designs is postpositivist. Postpositivism believes in the existence of an objective reality that can be studied through empirical observation and measurement.

The philosophical assumption reflected in quantitative research designs is postpositivist. Postpositivism is a philosophical stance that believes in the existence of an objective reality that can be studied through empirical observation and measurement. Quantitative research designs aim to gather numerical data that can be analyzed statistically to uncover patterns and relationships in the data. A postpositivist approach to research values objectivity, generalizability, and the use of rigorous methodologies.

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This ODE is separable:

[tex]yy'-\cot t=0\implies y\,\mathrm dy=\cot t\,\mathrm dt[/tex]

Integrate both sides to get

[tex]\dfrac12y^2=\ln|\sin t|+C[/tex]

Given that [tex]y\left(\frac\pi2\right)=-1[/tex], we get

[tex]\dfrac12(-1)^2=\ln|\sin\dfrac\pi2\right|+C\implies C=\dfrac12[/tex]

Then

[tex]\dfrac12y^2=\ln|\sin t|+\dfrac12[/tex]

[tex]y^2=2\ln|\sin t|+1[/tex]

[tex]y^2=\ln\sin^2t+1[/tex]

[tex]\implies\boxed{y(t)=\pm\sqrt{\ln\sin^2t+1}[/tex]

Answer:

3 cm

Step-by-step explanation:

The perimeter of the square is 24 cm, so the side length is 6 cm.

I assume B is the point between A and C where the tangent line intersects the circle.  If so, B is the midpoint of AC, so it is half the length.  Therefore, BC = 3 cm.

The length of line segment BC is 3 cm.

A square is a polygon with four sides , all the sides of the square are equal.

It is given that the tangents of the circle are forming a square ,

The perimeter of the square is 24 cm.

the length of line segment BC = ?

The perimeter of the square is 4a

where a is the side of the square.

Substituting the values

24 = 4 * a

a = 6 cm

B is the mid point of the tangent length and therefore

BC = 6 /2 = 3 cm

Therefore , the length of line segment BC is 3 cm.

The missing image is attached with the answer.

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Answer:

The arrow diagram and the matrix representation for the relation is shown below.

Step-by-step explanation:

The given relation is

R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)}

If a relation is defined as

[tex]R=\{(x,y)|x\in R,y\in R\}[/tex]

Then the set of x values is domain and set of y values is range.

The domain of the function is

Domain={1, 2, 3, 4)

The range of the function is

Range={1, 2, 3, 4)

In arrow diagram, we have two sets first set represents the domain and second set represents the range. The arrow connecting the element represent the relation.

In matrix representation,

[tex]M_{ij}=\begin{cases}1 & \text{ if } (x_i,y_j)\in R \\ 0 & \text{ if } (x_i,y_j)\notin R\end{cases}[/tex]

The arrow diagram and the matrix representation for the relation is shown below.

The arrow diagram and matrix representation offer effective visualizations to understand and communicate the relationships within the given relation R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)}.

The given relation R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)} can be analyzed step by step. The domain, representing the set of x values, is Domain={1, 2, 3, 4}, and the range, representing the set of y values, is Range={1, 2, 3, 4}.

The arrow diagram visually represents this relation, with the first set depicting the domain and the second set depicting the range. Arrows connect elements to illustrate the relationships within the given set.

The matrix representation further encapsulates this relation, with rows corresponding to the elements of the domain and columns to the elements of the range. The presence of an entry in the matrix indicates a relation between the respective elements.

This method provides a concise and organized representation of the given relation. Overall, the arrow diagram and matrix representation serve as effective tools to comprehend and communicate the relationships within the specified set.

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1. A coin is tossed four times. What is the probability of getting four heads?

Each toss has a 1/2 chance of getting a head.

So the chance of getting all four heads can be calculated as :

[tex]1/2\times1/2\times1/2\times1/2=1/16[/tex]

2. A coin is tossed four times. What is the probability of getting two heads?

Each toss can have 2 results, so 4 flips will have [tex]2^{4}[/tex] or 16 results.

Getting two heads means getting two tails also. So, we can get the number of times two heads come = [tex]\frac{4!}{2!2!}[/tex] = 6

We can write the groups like - {HHTT,HTHT,HTTH,THHT,THTH,TTHH}

So, the required probability is : 6/16 or 3/8.

3. Not getting two heads means getting 3 tails and 1 head or all tails.

Probability of having all tails = [tex]1/2\times1/2\times1/2\times1/2=1/16[/tex]

Probability of one head(1st trial) and three tails = 1/16

Probability of one head (2nd trial) and three tails (the 1st, 3rd and 4th trials) = 1/16

Probability of one head (3rd trial) and three tails (the 1st, 2nd and 4th trials) = 1/16

Probability of one head (4th trial) and three tails (the 1st, 2nd and 3rd trials) = 1/16

So, the total probability showing only one or none head and at least three tails = [tex]1/16+1/16+1/16+1/16+1/16=5/16[/tex]

Answer:

Hyperbola.

Step-by-step explanation:

We start from the function:

[tex]x^{2} +y^{2} -z^{2} =36[/tex]

We may get the traces if we cut the surface in planes x=k. This is equivalent to replace x for k:

[tex]k^{2}+y^{2} -z^{2}=36\\y^{2} -z^{2}=36-k^{2}[/tex]

The last equation is the equation of an hyperbola, which varies its characteristics depending on K (the plane cut).

When x=k or y=k is substituted into the equation of the quadric surface x² + y² - z² = 36, the resulting traces are hyperbolas. These traces represent intersections of planes parallel to coordinate planes with the quadric surface.

The trace of a quadric surface can be found by substituting a constant into the equation for one of the variables. The given quadric surface equation is x² + y² - z² = 36. If we substitute x = k into the equation, we get k² + y² - z² = 36. This is an equation of a hyperbola.

Similarly, for the case when y = k, we substitute this into our original equation to get x² + k² - z² = 36. This also represents a hyperbola.

The traces given by these equations represent the intersection of planes parallel to the coordinate planes and the quadric surface. In these particular cases, the traces are hyperbolas.

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Answer:

The company needs to sell 9000 units in order to turn a profit of $40,000

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

From the question we can get some important hints before creating our formula. First the Selling Price will be profit so it will be a positive number, but both unit cost and fixed costs are losses so they will be negative values in our formula. Also our formula will depend on the amount sold which we can represent as the variable x. With these hints we can create our formula as the following

[tex](60x-20x)-400,000 = y[/tex]

Where:

Now that we have our formula the question asks how many units need to be sold in order to earn a profit of $40,000. We can calculate this by replacing the $40,000 with y and solving for x like so,

[tex](60x-20x)-400,000 = 40,000[/tex] .... add 400,000 on both sides

[tex]40x= 360,000[/tex] ... divide both sides by 40

[tex]x= 9000[/tex]

The company needs to sell 9000 units in order to turn a profit of $40,000

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

There are 19 questions worth 7 points.

There are 17 questions worth 8 points.

Step-by-step explanation:

Assign variables:

Let x = number of questions worth 7 points.

Let y = number of questions worth 8 points.

First we deal with the number of questions.

There are 36 questions, so our first equation is:

x + y = 36

Now we deal with the points.

x questions worth 7 points each are worth 7x points.

y questions worth 8 points each are worth 8y points.

The total worth of all the questions is 7x + 8y.

The total worth of the exam is 269, so our second equation is

7x + 8y = 269

We have a system of 2 equations in 2 variables.

x + y = 36

7x + 8y = 269

Let's use the substitution method to solve the system of equations.

Solve the first equation for x.

x + y = 36

x = 36 - y

Substitute 36 - y in for x in the second equation.

7x + 8y = 269

7(36 - y) + 8y = 269

Distribute the 7.

252 - 7y + 8y = 269

Combine like terms.

252 + y = 269

Subtract 252 from both sides.

y = 17

There are 17 questions worth 8 points.

x + y = 36

x + 17 = 36

x = 19

There are 19 questions worth 7 points.

Check:

What does 19 questions at 7 points each and 17 questions at 8 points each add to?

19 * 7 + 17 * 8 = 133 + 136 = 269

The points add to 269, so our answer is correct.

Answer:

(-2,2)

Step-by-step explanation:

Let's find the answer.

Because a tangent line for a parabola function is equal to 0 only at its vertex then:

[tex]f(x)=(x+2)^{2}+2[/tex]

[tex]f'(x)=2*(x+2)[/tex]

[tex]f'(x)=2x+4[/tex] so then:

[tex]f'(x)=0[/tex] when

[tex]0=2x+4[/tex]

[tex]-2=x[/tex]

For x=-2 f(x) is:

[tex]f(x)=(x+2)^{2}+2[/tex]

[tex]f(1)=(-2+2)^{2}+2[/tex]

[tex]f(x)=2[/tex]

In conclusion, the vertex of the given parabola is (-2,2), so the answer is C. Although in your answer is reported as (-2.2) but I think was a typing mistake.

Answer:

y=5x-6

Step-by-step explanation:

Hello

let´s see  , we have   P1(3,9) and P2(4.14)

first let's find its slope

[tex]m=\frac{y2-y1}{x2-x1}   = \frac{14-9}{4-3}[/tex]

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

the slope is 5.

[tex]y-y_{0} = m(x-x_{0} )\\\\using P1\\\\ y-9 = 5(x-3)\\\\y=5x-15+9\\\\y=5x-6[/tex]

where x is the independent variable and y is the dependent variable

Have a great day.

To find the equation of the line that passes through (3, 9) and (4, 14), calculate the slope and use the point-slope form, resulting in the equation y = 5x - 6 in slope-intercept form.

To find an equation of the line that passes through the points (3, 9) and (4, 14), we will first calculate the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula, we have m = (14 - 9) / (4 - 3) = 5. With the slope known, we can use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1). Using the point (3, 9), the equation becomes y - 9 = 5(x - 3). To put this into slope-intercept form, we simplify to get y = 5x - 6.

The probability that the time between two unplanned shutdowns of a power plant is between 18 and 24 days, following an exponential distribution with a mean of 30 days, is approximately 0.0033.

For an exponential distribution, the probability density function (PDF) is given by:

[tex]\[ f(x) = \lambda e^{-\lambda x} \][/tex]

where [tex]\( \lambda \)[/tex] is the rate parameter, and for an exponential distribution, [tex]\( \lambda = \frac{1}{\text{mean}} \)[/tex].

Given a mean of 30 days, [tex]\( \lambda = \frac{1}{30} \)[/tex].

Now, to find the probability that the time between two unplanned shutdowns is between 18 and 24 days, integrate the PDF over this interval:

[tex]\[ P(18 < X < 24) = \int_{18}^{24} \lambda e^{-\lambda x} \, dx \]\[ P(18 < X < 24) = \int_{18}^{24} \frac{1}{30} e^{-\frac{x}{30}} \, dx \][/tex]

Let's complete the calculations step by step.

[tex]\[ P(18 < X < 24) = \int_{18}^{24} \frac{1}{30} e^{-\frac{x}{30}} \, dx \]\[ P(18 < X < 24) = -\frac{1}{30}e^{-\frac{x}{30}} \Big|_{18}^{24} \][/tex]

Now, evaluate the integral at the upper and lower limits:

[tex]\[ P(18 < X < 24) = -\frac{1}{30} \left(e^{-\frac{24}{30}} - e^{-\frac{18}{30}}\right) \]\[ P(18 < X < 24) = -\frac{1}{30} \left(e^{-0.8} - e^{-0.6}\right) \][/tex]

Using a calculator:

[tex]\[ P(18 < X < 24) \approx -\frac{1}{30} \left(0.44933 - 0.54881\right) \]\[ P(18 < X < 24) \approx -\frac{1}{30} \times (-0.09948) \]\[ P(18 < X < 24) \approx 0.003316 \][/tex]

Therefore, the probability that the time between two unplanned shutdowns is between 18 and 24 days is approximately 0.0033 (rounded to four decimal places).

Answer:

The constant of variation is -4

Step-by-step explanation:

If y is directly proprtional to x, then we write:

[tex]y \propto \: x[/tex]

If we introduce the constant of proportionality or variation k, then we obtain:

[tex]y = kx[/tex]

When x=1, y=-4 (We can choose any ordered pair from the table)

[tex] - 4 = k(1)[/tex]

[tex]k = - 4[/tex]

Therefore the constant of variation is -4.

Answer:

-4

Step-by-step explanation:

Answer: [tex]H_0:p\leq0.72[/tex]

[tex]H_a:p\neq0.72[/tex]

Step-by-step explanation:

Given :  A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 72% .

Let 'p' be the new proportion of high school seniors who felt that "getting rich" was an important personal goal .

Claim : [tex]p\neq0.72[/tex]

We know that the null hypothesis has equal sign.

Therefore , the null hypothesis for the given situation will be opposite to the given claim will be :-

[tex]H_0:p=0.72[/tex]

And the alternative hypothesis must be :-

[tex]H_a:p\neq0.72[/tex]

Hence,  the null hypothesis and the alternative hypothesis that we would use for this test :

[tex]H_0:p\leq0.72[/tex]

[tex]H_a:p\neq0.72[/tex]

Final answer:

To test the belief that the proportion of high school seniors valuing wealth has changed, we would use H0: p = 0.72 as the null hypothesis and Ha: p

Explanation:

To conduct a hypothesis test regarding the proportion of high school seniors who believe that "getting rich" is an important goal, we state the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis is the statement that the proportion remains the same, while the alternative hypothesis states that the proportion has changed.

For a proportion of high school seniors who believe that getting rich is an important goal, if the decade-old study showed a proportion of 72%, we would have:

H0: p = 0.72

Ha: p ≠ 0.72

In the hypothetical scenario with a disease prevalence of 9.5% in the general population and finding 7% in a local survey, we would determine the null and alternative hypotheses regarding whether the local proportion is less than the national average as follows:

H0: p ≥ 0.095

Ha: p < 0.095

When conducting a hypothesis test, the null hypothesis typically represents no change or no effect, while the alternative hypothesis represents a change, difference, or effect that we are trying to detect.

Answer:

see below

Step-by-step explanation:

A horizontal line has the same y value and is a constant y value

y = -5

A vertical line has the same x value and is a constant x value

x = -6

A vertical line is a line where all of the [tex]x[/tex] values are the same. In this case, [tex]\boxed{x=-6}[/tex], so that is the equation of the line.

A horizontal line is a line where all of the [tex]y[/tex] values are the same.  Here, [tex]\boxed{y=-5}[/tex], so that is the second line.

Answer: 0.4052

Step-by-step explanation:

Given : Mean : [tex]\mu=\text{307 ​grams}[/tex]

Standard deviation : [tex]\sigma = \text{4.1 grams}[/tex]

The formula for z -score :

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x=308 ,

[tex]z=\dfrac{308-307}{4.1}=0.24390\approx0.24[/tex]

The p-value = [tex]P(z>0.24)=1-P(z<0.24)[/tex]

[tex]=1-0.5948348= 0.4051652\approx0.4052[/tex]

Hence, the probability that a can will be sold that holds more than 308 ​grams =0.4052.

The confidence interval is [tex]\fbox{(5.8, 8.1)}[/tex] and [tex]\fbox{\text{Option A}}[/tex] is correct.

Further Explanation:

Given:

The least value is [tex]1[/tex] that is the least attractive.

The highest value is [tex]10[/tex] that is the most attractive.

The observations are,

7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9.

Calculation:

The sum of all observations is [tex]83[/tex].

The population mean is [tex]\mu[/tex].

The standard deviation [tex]s[/tex] is [tex]1.832[/tex].

The sample mean [tex]\bar^{X}[/tex] is [tex]6.92[/tex].

Level of significance [tex]\alpha[/tex] =  [tex]5\%[/tex].

Formula for confidence interval = [tex]\left( \bar{X} \pm t_{n-1, \frac{\alpha}{2}\%} \frac{s}{\sqrt{n}} \right)[/tex]

Confidence interval =[tex]\left( 6.92 \pm t_{12-1, \frac{5}{2}\%} \frac{1.832}{\sqrt{12}} \right)[/tex]

The value of [tex]t_{11, \frac{5}{2}\%[/tex]=[tex]2.201[/tex]

Confidence interval = [tex]( 6.92 \pm 2.201}\times \frac{1.832}{\sqrt{12}}) \right)[/tex]

Confidence interval = [tex]( 6.92 - 2.201}\times 0.5288 ,6.92 + 2.201}\times \0.5288) \right)[/tex]

Confidence interval = [tex](6.92-1.1639,6.92+1.1639)[/tex]

Confidence interval = [tex]\fbox{(5.8, 8.1)}[/tex]

The [tex]95\%[/tex] confidence interval gives us an idea that [tex]95\%[/tex] chances of the true mean or population mean lies in the interval.

A. We are [tex]95\%[/tex] confident that the interval from [tex]5.8[/tex] to [tex]8.1[/tex] actually contains the true mean of attractiveness rating of all adult females.

B. The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females.

C. We are confident that [tex]95\%[/tex] of all adult females have attractiveness ratings between [tex]5.8[/tex] and [tex]8.1[/tex].

[tex]\fbox{\text{Option A}}[/tex] is Correct as we are [tex]95\%[/tex] confident that the interval from [tex]5.8[/tex] to [tex]8.1[/tex] actually contains the true mean of attractiveness rating of all adult females.

Option B is not correct as the confidence interval tells us about the population mean.

Option C is not correct as the individual rating can be more than [tex]5.8[/tex] or less than the [tex]8.1[/tex].

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Answer Details:

Grade: College Statistics

Subject: Mathematics

Chapter: Confidence Interval

Keywords:

Probability, Statistics, Speed dating, Females rating, Confidence interval, t-test, Level of significance , Normal distribution, Central Limit Theorem, t-table, Population mean, Sample mean, Standard deviation, Symmetric, Variance.

The confidence interval for the population mean attractiveness rating of all adult females is 5.8 to 8.1, and we are 95% confident that this interval contains the true mean attractiveness rating.

In this study of speed dating, male subjects were asked to rate the attractiveness of their female dates on a scale from 1 (not attractive) to 10 (extremely attractive). A sample of attractiveness ratings was provided: 7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9. The objective is to construct a confidence interval with a 95% confidence level to estimate the true mean attractiveness rating of all adult females.

The calculated confidence interval is 5.8 to 8.1. This means that we are 95% confident that the interval from 5.8 to 8.1 contains the true mean attractiveness rating of all adult females. The margin of error, represented by the range of the interval, provides a level of precision in our estimation.

The confidence interval suggests that the true mean attractiveness rating for all adult females falls within the specified range. It does not provide an exact value for the mean, but it indicates a plausible interval within which the true mean is likely to be found. Additionally, the confidence interval does not imply a causal relationship, but rather a statistical estimate based on the observed sample.

Final answer:

By using the divisibility rules for 9 and 11, we can conclude that the integer 176521221 is divisible by 9 but not by 11, and the integer 149235678 is divisible by 9 but not by 11.

Explanation:

To determine whether the integers 176521221 and 149235678 are divisible by 9 or 11 without performing the division, we can use divisibility rules:

Divisibility by 9: Add up all the digits in the number. If the sum is divisible by 9, then the original number is also divisible by 9.

Divisibility by 11: Take the alternating sum of the digits. If the result is divisible by 11 (including 0), the original number is divisible by 11.

Divisibility of 176521221 by 9

1+7+6+5+2+1+2+2+1 = 27; Since 27 is divisible by 9, 176521221 is also divisible by 9.

Divisibility of 176521221 by 11

(1-7+6-5+2-1+2-2+1) = -3; Since -3 is not divisible by 11, 176521221 is not divisible by 11.

Divisibility of 149235678 by 9

1+4+9+2+3+5+6+7+8 = 45; Since 45 is divisible by 9, 149235678 is also divisible by 9.

Divisibility of 149235678 by 11

(1-4+9-2+3-5+6-7+8) = 9; Since 9 is not divisible by 11, 149235678 is not divisible by 11.

Answer:

  C.  Hyperbola opening up and down

Step-by-step explanation:

A graph tells the tale.

___

The term with the positive coefficient identifies the axis along which the hyperbola opens. Here, that is the y-axis, so the figure opens up and down.

The minus sign between the squared terms indicates it is a hyperbola, rather than a closed curve (ellipse or circle). The fact that both terms are squared indicates it is not a parabola.

Answer:

The proposition is false if p is true.

Step-by-step explanation:

I made the truth table in the picture, to fill it you need to know:

v : only is false when both propositions are false.

^ : only is true when both propositions are true.

⇒: only is false when the left proposition is true and the right proposition is false.

So, the answer is the third option.

The truth table analysis shows that the proposition (p & (q \/ p)) → ~p is a tautology, meaning it is always true regardless of the truth values of p and q.

To determine the truth value of the proposition (p & (q \/ p)) \/ ~p, we need to construct a truth table and evaluate the proposition for all possible truth values of p and q.

Truth Table Construction

Let's go step by step:

Construct two initial columns for the variables p and q with their possible truth values.

Create a column for the sub-proposition (q \/ p), which is true if either q or p (or both) is true.

Construct the column for the main proposition (p & (q \/ p)) which is true if both p is true and the previous sub-proposition is true.

Determine the negation of p (~p), which is true when p is false.

Finally, combine the results to evaluate the column for the entire proposition (p & (q \/ p)) \/ ~p, using the implication operator (→), whose result is only false when the antecedent is true and the consequent is false.

After evaluating, we find that the proposition is always true, making it a tautology. Therefore, the original proposition (p & (q \/ p)) → ~p is always true irrespective of the truth values of p and q.

Answer:

Part 42) Yes, It is possible o form a triangle using the segments with the given measurements

Part 43) Yes, It is possible o form a triangle using the segments with the given measurements

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Part 42) we have

8ft, 9ft, 11ft

Applying the triangle inequality theorem

a) 8+9 > 11

17 ft > 11 ft ----> is true

b) 9+11 > 8

20 ft > 8 ft  ----> is true

c) 8+11 >  9

19 ft > 9 ft ----> is true

therefore

Yes, It is possible o form a triangle using the segments with the given measurements

Part 43) we have

7.4cm, 8.1cm, 9.8cm

Applying the triangle inequality theorem

a) 7.4+8.1 > 9.8

15.5 cm > 9.8 cm ft ----> is true

b) 8.1+9.8 > 7.4

17.9 cm > 7.4 cm  ----> is true

c) 7.4+9.8 >  8.1

17.2 cm > 8.1 cm ----> is true

therefore

Yes, It is possible o form a triangle using the segments with the given measurements

Answer:

y=-8

Step-by-step explanation:

So if you draw a circle with center at the origin (0,0) with radius 8.  

So we have:

That means the radius stretches to (0,-8); down 8 units from (0,0).

The radius stretches to (0,8); up 8 units from (0,0).

The radius stretches to (8,0); right 8 units from (0,0).

The radius stretches to (-8,0); left 8 units from (0,0).

We are looking for a line tangent to our circle at (0,-8). Since this was down 8 units.  Then our equation is horizontal and y=a number. They-coordinate in (0,-8) is -8, so the we have y=-8.

If someone said tangent at (0,8), we would have said y=8 .

If someone said tangent at (8,0), we would have said x=8.

If someone said tangent at (-8,0), we have have said x=-8.

The equation of the line that is tangent to the circle with radius 8 at (0,-8) and center at the origin is y=-8. This is because the tangent line is horizontal at that point as it is perpendicular to the radius line lying along the y-axis.

In the context of Mathematics, particularly geometry, the line that is tangent to a circle at a given point is perpendicular to the radius drawn to that point. Since the circle's center is at the origin (0,0) and the radius is extended to the point (0,-8), this radius lies along the y-axis. Therefore, the equation of the tangent line which is perpendicular to this radius would be a horizontal line through the point (0,-8), given by the equation y=-8.

Remember that tangent line by definition touches the circle at only one point without intersecting it and the line is perpendicular to the radius at that point of tangency. In this particular scenario, the radius and tangent are perpendicular lines in the coordinate system: the radius aligns with the y-axis, hence the tangent aligns with the x-axis.

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Answer:

The annual rate of return is 13.14%.

Step-by-step explanation:

As it is not mentioned whether the amount was compounded, so we will assume this to be simple interest.

Given is - A $3500 loan was settled ten years later with a payment of $8100.

Means total amount paid back was = $8100

And original principle was = $3500

So, interest paid = [tex]8100-3500=4600[/tex] dollars

Now simple interest formula is :

[tex]I=p\times r\times t[/tex]

Where p = 3500

I = 4600

r = ?

t = 10

Now putting these values in formula we get;

[tex]4600=3500\times r\times10[/tex]

[tex]r=4600/35000[/tex]

r=  0.1314

So, rate of interest = 13.14%