5/6 minus what equals 1/3

Answer:1968ft^2

Step-by-step explanation:

Perimeter(p)=178feet

P=2L+2w

178=2L+2w

178=2(L+w)

L+w=178 ➗ 2

L+w=89.............(1)

W+7=L

L-w=7...................(11)

L+w=89... ..........(1)

L-w=7...................(11)

Subtract (11) from (1)

2w=89-7

2w=82

w=82 ➗ 2

w=41 width=41feet

Substitute w=41 in (11)

L-w=7

L-41=7

L=7+41

L=48feet

Area= length x width

Area=48 x 41

Area=1968ft^2

The area of the garden is 1968 square feet by setting up and solving equations based on the information about the garden's length, width, and perimeter.

The problem is asking for the area of a rectangular garden where the length is 7 feet longer than its width. We also know the perimeter of the garden is 178 feet. Normally in a rectangle, the formula for the perimeter is P = 2(length + width).

Since the length is 7 feet longer, let's denote the width as 'w' and therefore the length as 'w+7'. Substituting in the perimeter formula we get: 178 = 2(w + w + 7).

By simplifying and solving the equation we find that the width, w = 41 feet. Therefore, the length is w+7 = 48 feet.

Lastly, the area of a rectangle is calculated as length * width, so substituting the values we found we get the area = 48 feet * 41 feet = 1968 square feet.

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Answer:

Required results are [tex]\nabla .\vec{F}[/tex]=8\cos(8x+5z)-8ye^x[/tex]  and  [tex]\nabla\times \vec{F}=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]

Step-by-step explanation:

Given vector function is,

[tex]\vec{F}=\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k}[/tex]

To find [tex]\nabla .\vec{F}[/tex] and [tex]\nabla \times \vec{F}[/tex] .

[tex]\nabla .\vec{F}[/tex]

[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]

[tex]=\frac{\partial}{\partial x}(\sin(8x+5z))-\frac{\partial}{\partial z}(8ye^xz)[/tex]

[tex]=8\cos(8x+5z)-8ye^x[/tex]

And,

[tex]\nabla \times \vec{F}[/tex]

[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})\times(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]

[tex]\end{Vmatrix}[/tex]

[tex]=\uvec{i}\Big[\frac{\partial}{\partial y}(-8ye^xz)\Big]-\uvec{j}\Big[\frac{\partial}{\partial x}(-8ye^xz)-\frac{\partial}{\partial z}(\sin(8x+5z))\Big]+\uvec{k}\Big[-\frac{\partial}{\partial y}(-\sin(8x+5z))\Big][/tex]

[tex]=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]

Hence the result.

Answer:

You can use the graph of a trigonometry function to show sales amounts over a given period of time. Here’s an example: Even though people in many parts of the world play soccer year-round, certain times of the year show an increase in the sales of outdoor soccer shoes.

Step-by-step explanation:

Answer:7^6

Step-by-step explanation:

Answer:

7^6

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

8*5

Answer:

720

Step-by-step explanation:

96 * 7.5

Answer:

This would be -9 to the 5th power. (-9^5)

Step-by-step explanation:

-9 to the 5th power when put in a calculator equals -59,049.

The exponent is how many times the number is multiplied by itself.

Answer:

-59049

Step-by-step explanation:

(-9).(-9).(-9).(-9).(-9)

=81.(-9).(-9).(-9)

= -729.(-9).(-9)

= 6561.(-9)

= -59049

Answer:

160°

Step-by-step explanation:

∠C and ∠D are both inscribed angles of arc AB.  Therefore, they are equal.

5w + 20 = 7w − 4

24 = 2w

w = 12

Therefore, ∠C = ∠D = 80°.

Inscribed angles are half the central angle, so mAB = 2 × 80° = 160°.

Answer:

[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]    

[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]    

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

Step-by-step explanation:

Data provided

[tex]\bar X=9797[/tex] represent the sample mean for the steps

[tex]\mu[/tex] population mean

s=2313 represent the sample standard deviation

n=61 represent the sample size  

Solution

The confidence interval for the true population mean is given by :

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

Since we need to find the critical value [tex]t_{\alpha/2}[/tex] we need to calculate first the degrees of freedom, given by:

[tex]df=n-1=61-1=60[/tex]

The Confidence is 0.90 or 90%, the value for the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,60)".And we see that [tex]t_{\alpha/2}=1.67[/tex]

Now we have everything in order to replace into formula (1):

[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]    

[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]    

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps.

To construct a 90% confidence interval for the mean number of steps taken on a typical workday for people working in New York City who wear activity trackers, you can use the following formula:

Confidence Interval = X ± Z * (σ/√n)

Where:

X is the sample mean (9,797 steps).

Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645, but you can use a Z-table or calculator to get the exact value).

σ is the population standard deviation (2,313 steps).

n is the sample size (61).

Now, let's plug in the values and calculate the confidence interval:

Z for a 90% confidence level is approximately 1.645.

Confidence Interval = 9,797 ± 1.645 * (2,313/√61)

Confidence Interval = 9,797 ± 1.645 * (299.98)

Confidence Interval ≈ 9,797 ± 494.06

Now, calculate the lower and upper bounds of the confidence interval

Lower Bound = 9,797 - 494.06 ≈ 9,302.94

Upper Bound = 9,797 + 494.06 ≈ 10,291.06

Interpretation:

We are 90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps. This means that if we were to take many random samples and calculate a 90% confidence interval for each sample, we would expect about 90% of those intervals to contain the true population mean.

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Answer:

Step-by-step explanation:

So, we do not have enough evidence to conclude that the number of adolescent relationships is equal between those with an older sibling and those without.

check the attached file for explanation and solution

Answer:

330+77= 407

Step-by-step explanation:

*Danganronpa flashbacks*

Answer:

The correct option is (a).

Step-by-step explanation:

According to the Centers for Disease Control and Prevention, 0.22 or 22% of US adults of 25 years or older smoke.

But a researcher suspects that this percentage is lower if the US adults of 25 years or older have a bachelor's degree or higher education level.

So, the researcher needs to test whether the proportion of US adults  of 25 years or older who smoke is less in case the adults have bachelor's degree or higher.

To test his suspicion the researcher can use a one-proportion z-test.

The hypothesis of the test can be defined as:

H₀: The proportion of smokers among US adults of 25 years or older who have a bachelor's degree or higher is 0.22, i.e. p = 0.22.

Hₐ: The proportion of smokers among US adults of 25 years or older who have a bachelor's degree or higher is less than 0.22, i.e. p < 0.22.

Thus, the correct option is (a).

Final answer:

The alternative hypothesis for the scenario where a researcher suspects a lower smoking rate among U.S. adults with higher education is that the proportion of smokers in this group is less than .22.

Explanation:

The alternative hypothesis in this research scenario is that the proportion of U.S. adults age 25 or older who have a bachelor's degree or higher education level and smoke is lower than .22. The alternative hypothesis translates the researcher's suspicion into a testable statement and is essential for conducting a hypothesis test. The correct alternative hypothesis based on the research question would be: 'The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is less than .22.'

Answer:

90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)

Step-by-step explanation:

We have the following data:

Sample size = n = 1000

Proportion of travelers who prefer window seat = p = 60%

Standard Error = SE = 0.015

We need to construct a 90% confidence interval for the proportion of travelers who prefer window seat. Therefore, we will use One-sample z test about population proportion for constructing the confidence interval. The formula to calculate the confidence interval is:

[tex](p-z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}}, p+z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}})[/tex]

Since, standard error is calculated as:

[tex]SE=\sqrt{\frac{p(1-p)}{n} }[/tex]

Re-writing the formula of confidence interval:

[tex](p-z_{\frac{\alpha}{2}} \times SE, p+z_{\frac{\alpha}{2}} \times SE)[/tex]

Here, [tex]z_{\frac{\alpha}{2}}[/tex] is the critical value for 90% confidence interval. From the z-table this value comes out to be 1.645.

Substituting all the values in the formula gives us:

[tex](0.6 - 1.645 \times 0.015, 0.6 + 1.645 \times 0.015)\\\\ = (0.575, 0.625)[/tex]

Therefore, the 90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)

Answer:

...

Step-by-step explanation:

...

Answer:

25

Step-by-step explanation:

Answer:

72 degrees

Step-by-step explanation:

We need to know the total circumference in order to determine the arc measure for ABC before we figure out AC

Circumference   =2πr   →  =2π(10)   →   =20π

We know the length of ABC

so we set up a proportion to figure out its arc measure.

arc length/ circumference = arc measure/ degrees in a circle

16π/ 20π = arc measure/ 360 degrees

arc measure= 360 x 16π/ 20π =228 degrees

The arc measure of ABC is 228 degrees

If we combine the major arc ABC, and the minor arc AC we have the entire circle.

288 degrees  +m  AC= 360

m  AC= 72 degrees

The measure of AC is 72 degrees

(i got the explanation off of Klan Academy when i answered the question)

Answer:

Indicate whether each of the following statements is true or false (brie y explain your reason). (a) [1pt] Consider a standard LP with four variables and three constraints. Then two basic solutions (0; 0; 0; 4; 0; 12; 18) and (3; 0; 0; 1; 0; 2; 0) are adjacent. (b) [1pt] If a linear program has no optimal solution, then it must have an unbounded feasible region. (c) [1pt] Consider the shadow prices of a standard form of LP. The vector formed by the shadow prices is a feasible solution of the dual problem of this LP. (d) [1pt] A linear program can have exactly 10 feasible solutions. (e) [1pt] Consider a primal problem of maximizing c^Tx and a dual problem of minimizing b^Ty (both subject to some constraints). If for a primal feasible solution x and a dual solution y, we have c^Tx > b^Ty, then y must be dual infeasible. (i.e not a feasible solution for the dual problem). (f) [1pt] In a two player zero sum game, there exists at least one Nash equilibrium.

Step-by-step explanation:

a. true

Because two basic feasible solution stands to be adjacent in case they possess basic variable in common. Two distinct basic solutions with respect to set related with linear constraint under is considered to be adjacent.

b.False.

If a linear problem has no solution it may have null feasible region not important to have unbounded feasible region.

c.True.

If Shadow price is feasible for standard form of LP then it will be feasible solution of dual problem of this LP.

d. False.

As there will be 'n' variables 'm' constraints having nCm feasible solutions.

e.True.

As stated in weak duality theorem

f.True

For every zero-sum 2-player normal-form game, a Nash equilibrium exists. Moreover, a pair of mixed strategies (p,q)(p,q) for the two players is a Nash equilibrium if and only if each strategy is a maximin strategy.

Step-by-step explanation:

a) 24 / 250 = 0.096

b) Standard error for a proportion is:

σ = √(pq/n)

σ = √(0.096 × 0.904 / 250)

σ = 0.0186

c) At 98% confidence, the critical value is 2.326.  The margin of error is therefore:

2.326 × 0.0186 = 0.0433

d) At 95% confidence, the critical value is 1.960.  The margin of error is therefore:

1.960 × 0.0186 = 0.0365

So the confidence interval is:

(0.0960 − 0.0365, 0.0960 + 0.0365)

(0.0595, 0.1325)

e) 0.10 is within the 95% confidence interval, so the null hypothesis would not be rejected.

Final answer:

a) The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is 9.6%. b) The standard error of the estimated proportion is 1.9%. c) The margin of error at the 98% confidence level is 4.4%. d) The 95% confidence interval estimate for the true proportion is approximately 5.9% to 13.3%. e) The null hypothesis that the proportion is 0.10 is rejected if the z-test statistic falls outside the range (-1.96, 1.96).

Explanation:

a) Point estimate:
The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is the number of failed components divided by the total number of components tested. In this case, the point estimate is 24/250 = 0.096, or 9.6%.

b) Standard error:
The standard error of the estimated proportion is calculated using the formula SE = sqrt((phat * (1 - phat)) / n), where phat is the point estimate and n is the sample size. In this case, the standard error is sqrt((0.096 * (1 - 0.096)) / 250) = 0.019, or 1.9%.

c) Margin of error:
The margin of error is determined by multiplying the standard error by the appropriate critical value from the standard normal distribution. For a 98% confidence level, the critical value is approximately 2.33. Therefore, the margin of error is 2.33 * 0.019 = 0.044, or 4.4%.

d) Confidence interval:
The 95% confidence interval estimate for the true proportion of components that fail to meet the specifications is given by the formula phat +/- z * SE, where phat is the point estimate, z is the appropriate critical value from the standard normal distribution (for 95% confidence, z is approximately 1.96), and SE is the standard error. Therefore, the confidence interval is 0.096 +/- 1.96 * 0.019, or approximately 0.059 to 0.133.

e) Hypothesis test:
To test the null hypothesis H_0: p = 0.10 against the alternative hypothesis H_a: p != 0.10, we can use a two-tailed z-test. The test statistic is calculated as (phat - p_0) / sqrt((p_0 * (1 - p_0)) / n), where p_0 is the null hypothesis value (0.10), phat is the point estimate, and n is the sample size. The critical value for a significance level of 0.05 is approximately 1.96 from the standard normal distribution. If the test statistic is outside the range (-1.96, 1.96), we reject the null hypothesis. In this case, if the test statistic falls outside the range (-1.96, 1.96), we would reject the null hypothesis and conclude that the true proportion of components that fail to meet the specifications is not 0.10.

Answer:

  f(r) = (x -1)(x -4+√7)(x -4-√7)

Step-by-step explanation:

The signs of the terms are + - + -. There are 3 changes in sign, so Descartes' rule of signs tells you there are 3 or 1 positive real roots.

The rational roots, if any, will be factors of 9, the constant term. The sum of coefficients is 1 -9 +17 -9 = 0, so you know that r=1 is one solution to f(r) = 0. That means (r -1) is a factor of the function.

Using polynomial long division, synthetic division (2nd attachment), or other means, you can find the remaining quadratic factor to be r^2 -8r +9. The roots of this can be found by various means, including completing the square:

  r^2 -8r +9 = (r^2 -8r +16) +9 -16 = (r -4)^2 -7

This is zero when ...

  (r -4)^2 = 7

  r -4 = ±√7

  r = 4±√7

Now, we know the zeros are {1, 4+√7, 4-√7), so we can write the linear factorization as ...

  f(r) = (r -1)(r -4 -√7)(r -4 +√7)

_____

Comment on the graph

I like to find the roots of higher-degree polynomials using a graphing calculator. The red curve is the cubic. Its only rational root is r=1. By dividing the function by the known factor, we have a quadratic. The graphing calculator shows its vertex, so we know immediately what the vertex form of the quadratic factor is. The linear factors are easily found from that, as we show above. (This is the "other means" we used to find the quadratic roots.)

Answer:

   look for the x-intercepts

Step-by-step explanation:

A "zero" is a value of x where the function value is zero. On a graph, that point is where the graph meets the x-axis. Every x-intercept is a zero of the function.

__

If there are no x-intercepts, then there are no real zeros. The roots (zeros) will be complex.

Answer:

Heather rode the farthest

She rode 0.1km farther than Hailey.

Step-by-step explanation:

This is a conversion of units question.

Heather rode her horse 2 kilometers.

Hailey rode 1900 meters on her horse.

Each km has 1000 meters.

So 1900 meters = 1900/1000 = 1.9 km

This means that Hailey rode for 1.9 km.

Heather rode the farthest(2km is greather than 1.9km)

2 - 1.9 = 0.1km

She rode 0.1km farther than Hailey.

Answer:

the correct graph is pictured below

Step-by-step explanation:

the graph is below

Answer:

a) P=0.091

b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but it is still possible that there are 6 of each taste.

c) The probability of picking 4 vainilla in a row, if there are half of each taste, is P=0.030.

This is a very improbable case, so if this happens we would have reasons to think that there are more than half vainilla candies in the box.

Step-by-step explanation:

We can model this problem with the variable x: number of picked vainilla in a row, following a hypergeometric distribution:

[tex]P(x=k)=\dfrac{\binom{K}{k}\cdot \binom{N-K}{n-k}}{\binom{N}{n}}[/tex]

being:

N is the population size (12 candies),

K is the number of success states in the population (6 vainilla candies),

n is the number of draws (3 in point a, 4 in point c),

k is the number of observed successes (3 in point a, 4 in point c),

a) We can calculate this as:

[tex]P(x=3)=\dfrac{\binom{6}{3}\cdot \binom{12-6}{3-3}}{\binom{12}{3}}=\dfrac{\binom{6}{3}\cdot \binom{6}{0}}{\binom{12}{3}}=\dfrac{20\cdot 1}{220}=0.091[/tex]

b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but is possible.

c) In the case k=4, we have:

[tex]P(x=3)=\dfrac{\binom{6}{4}\cdot \binom{6}{0}}{\binom{12}{4}}=\dfrac{15\cdot 1}{495}=0.030[/tex]

This is a very improbable case, so we would have reasons to think that there are more than half vainilla candies in the box.

Using the hypergeometric distribution, it is found that:

The candies are chosen without replacement, hence the hypergeometric distribution is used to solve this question.

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Item a:

The probability that you would have picked three vanillas in a row is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,12,3,6) = \frac{C_{6,3}C_{6,0}}{C_{12,3}} = 0.0909[/tex]

0.0909 = 9.09% probability that you would have picked three vanillas in a row.

Item b:

The probability is above 5%, hence it is not an unusual event and gives no evidence that there might not have been 6 of each.

Item c:

Now n = 4, and the probability is P(X = 4), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,12,4,6) = \frac{C_{6,4}C_{6,0}}{C_{12,4}} = 0.0303[/tex]

The probability is below 5%, hence it is an unusual event and there is enough evidence to believe that there might not have been 6 of each.

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Answer:

24 guppies

Step-by-step explanation:

Assuming a linear relationship,  the volume required per guppy is given by:

[tex]g=\frac{576\ in^3}{3\ guppies}\\ g= 192\ in^3/guppy[/tex]

The volume of the fish tank is given by the product of its length, by its width and its height:

[tex]V = 24*12*16\\V=4,608\ in^3[/tex]

The number of guppies that this tank can safely hold is:

[tex]n=\frac{V}{g}=\frac{4,608}{192} \\n=24\ guppies[/tex]

The tank can safely hold 24 guppies.

By calculating the average speed of Tomos in the 525-meter race, we can estimate that he would take about 3 minutes 12 seconds to complete an 800-meter race if he maintains the same average speed.

To solve this problem, we first need to figure out Tomos's average speed in the 525-meter ski race that he completed in 2 minutes and 6 seconds. We convert the time to seconds for ease of calculation. So, 2 minutes 6 seconds equals 126 seconds. Now, we calculate his average speed by dividing the length of the race by the time he took to complete it:

Average speed = Distance / Time
Average speed = 525m / 126s
Average speed = 4.17 m/s

Now to calculate how long Tomos should take to complete an 800 m race, we rearrange the formula to solve for time. Time = Distance / Average Speed:

Time = 800m / 4.17 m/s
Time = 191.84 seconds

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Answer:

49.4 km

Step-by-step explanation:

you add 27.54 plus 21.86 so 49.4 km total between school and to your friends house

You drive a total distance of 49.4 kilometers when you travel 27.54 kilometers to school and then 21.86 kilometers to your friend's house.

When you drive 27.54 km to school and then 21.86 km to your friend's place, you are covering a total distance of 49.4 kilometers. To calculate this, you simply add the two distances together:

Distance to school: 27.54 km

Distance to friend's place: 21.86 km

Total distance = 27.54 km + 21.86 km = 49.4 km

So, you drive a total of 49.4 kilometers when you travel to both school and your friend's house. This cumulative distance is the sum of the individual distances you cover for each leg of your journey. It's important to keep track of such distances, especially if you want to estimate fuel consumption, plan your commute, or calculate travel time accurately. In this case, you've covered 49.4 kilometers in total, which is the combined distance for your trip.

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B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and  it takes 2.6 hours when both drains are turned on.

Step-by-step explanation:

The given is,

                   A alone can empty the pool in 4.75 hours.

                   It takes 2.6 hours when both drains are turned on.

Step:1

            One hour work drains A and B =

                  One hour work of drain A + One hour work of Drain B.........(1)

            One hour work of Drain A = [tex]\frac{1}{4.75}[/tex]

                     One hour of ( A + B ) = [tex]\frac{1}{2.6}[/tex]

            Equation (1) becomes,

                     One hour work of B = One hour work of ( A + B )

                                                                  - One hour work of A

            Substitute the values,

                     One hour work of B =  [tex]\frac{1}{2.6} - \frac{1}{4.75}[/tex]

                                                       = [tex]\frac{4.75-2.6}{(4.75)(2.6)}[/tex]

                                                       = [tex]\frac{2.15}{12.35}[/tex]

                                                       = [tex]\frac{1}{5.744}[/tex]

                    One hour work of B  = [tex]\frac{1}{5.744}[/tex]

             B alone can empty the pool in 5.744 hours

Result:

           B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and  it takes 2.6 hours when both drains are turned on.

Answer: +/- 7

Step-by-step explanation:

3x² = 147

To solve for x divide through by three first.

3x² = 147

x² = 49, now we take the square root of both side by trying to apply laws of indices.

√x² = √49

The square root will neutralize the effect of the square because

√a = a¹/² so (x²)¹/², and (x²)¹/² =

x²×¹/² = x, therefore the solution is

x = +/- 7.

Answer:

a) y-intercept = 2.59

b) Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.

Step-by-step explanation:

(a) What is the y-intercept of the regression line? (Use 2 decimal places)

The given regression equation is

y = 2.59 + 0.0126x

The standard form of the regression equation is given by

y = a + bx

Where a is the y-intercept of the regression line and b is the slope of the regression line.

Comparing the given equation with the standard form,

y-intercept = 2.59

(b) What is the correct interpretation of the y-intercept?

The y-intercept is the value we get when x = 0

y = 2.59 + 0.0126(0)

y = 2.59 + 0

y = 2.59 minutes

Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.

The equation we've developed to represent the rabbit population over time, where 't' is the number of months since January, is P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650. This equation covers the oscillations in the population and the steady yearly increase.

The subject matter falls under the discipline of Mathematics, particularly in the topics involving functions. We can create a sinusoidal (sine or cosine) function to represent the oscillation of the population of rabbits.

Given that the population fluctuates 19 above and below the average, and the average increases by 160 each year, this suggests a sinusoidal period of 12 months (a year) with a vertical shift (midline) that increases linearly.

Considering t as the number of months since January, the equation for the population P in terms of the months since January t would be:

P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650

The 19 is the amplitude, (2π/12)t - π/2 represents the sinusoidal oscillation adjusted to start at the minimum in January, (160t/12) is the yearly change in population that increases per month, and 650 is the average population at the start.

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To find the population equation in terms of months since January considering oscillations and growth, use the formula p(t) = 650 + 160t + 19sin(2πt/12).

Population Equation: The equation for the population p in terms of the months since January t can be written as p(t) = 650 + 160t + 19sin(2πt/12). This equation takes into account the initial population of 650 rabbits, an increase of 160 rabbits per year, and the oscillation of 19 above and below the average population.

Answer:

  5.892×10^-2

Step-by-step explanation:

Scientific notation has one digit to the left of the decimal point. To write the number in scientific notation, it can work to start by writing the number with that as one of the factors:

  0.05891 = 5.891 × 0.01

  = 5.891 × 1/10^2

  = 5.891 × 10^-2

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You can also enter this number into your calculator and change the display mode to SCI.

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It helps to understand the decimal place-value number system in terms of the power of 10 that multiplies each number place.