The number of fish in a pond decreased by 10% this

year compared to last year.

Last year, there were 60 fish in the pond.

How many fish are in the pond this year?

Using lateral limits, it is found that the limit of the function does not exist.

The function is defined by parts, that is, it's rule depends on the input. The function is given by:

\(f(x) = -1 + x^2, x < 2\)

\(f(x) = -1 + x, x \geq 2\)

A limit is given by the value of function f(x) as x tends to a value. If the function is piece-wise, that is, it has multiple definitions, at the point of which the values of x changes, lateral limits have to be calculated.

The lateral limits are given by:

\(\lim_{x \rightarrow 2^{-}} f(x) = \lim_{x \rightarrow 2} -1 + x^2 = -1 + 2^2 = 3\)

\(\lim_{x \rightarrow 2^{+}} f(x) = \lim_{x \rightarrow 2} -1 + x = -1 + 2 = 1\)

Since the lateral limits at x = 2 are different, the limit of f(x) as x goes to 2 does not exist.

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The divergence theorem, also known as Gauss's theorem, relates the flux of a vector field through a closed surface to the divergence of the vector field in the region enclosed by the surface.

It states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the vector field over the region enclosed by the surface. In mathematical notation, this can be expressed as:

∫∫(F⋅n)dS=∫∫∫(divF)dV

where F is the vector field, n is the outward unit normal to the surface, dS is the surface element, and dV is the volume element.

To use the divergence theorem to calculate the flux of the vector field through the sphere of radius R centered at the origin and oriented outward, we need to first calculate the divergence of the vector field in the region enclosed by the sphere.

Assuming the vector field is given as F = (P, Q, R), the divergence of F can be found by taking the partial derivatives of each component with respect to the corresponding coordinate and summing them up. That is, divF = ∂P/∂x + ∂Q/∂y + ∂R/∂z. Once we have the divergence, we can use the divergence theorem to calculate the flux as:

∫∫(F⋅n)dS=∫∫∫(divF)dV = ∫∫∫(∂P/∂x + ∂Q/∂y + ∂R/∂z)dV

The volume integral can be evaluated in spherical coordinates since the region is a sphere. After integrating over the volume, the resulting flux will give the total amount of the vector field that passes through the surface of the sphere.

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Answer:

b

Step-by-step explanation:

dfghdfhjdfjdfj

We get the age of Jack is 29 years and the age of Jill is 16 years.

We are given that the sum of Jack's age and Jill's age is 45 years.

Let Jack's age be x.

Let Jill's age be y.

x + y = 45

x = 45 - y

Now, we are also given that jack's age next year will be twice Jill's age last year.

Jack's age next year = x + 1

Jill's age last year = y - 1

ATQ, We get the equation as:

x + 1 = 2( y - 1)

x + 1 = 2 y - 2

x = 2 y - 2 - 1

x = 2 y - 3

We get that:

45 - y = 2 y - 3

2 y + y = 45 + 3

3 y = 48

y = 48 / 3

y = 16 years.

x + y = 45

x + 16 = 45

x = 45 - 16

x = 29 years.

Therefore, we get the age of Jack is 29 years and the age of Jill is 16 years.

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The p-value is very small, likely less than 0.0001, providing strong evidence against the null hypothesis that the proportion of fathers who take no responsibility for childcare in Littleton is the same as for American fathers.

What is null hypothesis?

The null hypothesis is a statement that assumes there is no significant difference or relationship between two variables in a population, and any observed difference is due to chance.

what is proportion?

A proportion is a ratio of two quantities that represent a part of a whole, typically expressed as a fraction or a percentage. It measures the relative size of one quantity compared to another.

According to the give information:

To find the p-value for the hypothesis test, we need to follow these steps:

State the null and alternative hypotheses:

Null hypothesis (H0): The proportion of fathers who take no responsibility for childcare in Littleton is the same as the proportion for American fathers, which is 0.34.

Alternative hypothesis (Ha): The proportion of fathers who take no responsibility for childcare in Littleton is higher than the proportion for American fathers, which is greater than 0.34.

Determine the test statistic, which follows a normal distribution under the null hypothesis:

z = (p - P) / √[P(1-P) / n]

where p is the sample proportion, P is the hypothesized proportion under the null hypothesis, and n is the sample size.

In this case, we have:

p = 97/225 = 0.4311

P = 0.34

n = 225

So, the test statistic is:

z = (0.4311 - 0.34) / √[(0.34)(0.66) / 225] = 3.583

Calculate the p-value using the test statistic:

The p-value is the probability of observing a test statistic as extreme or more extreme than the one obtained, assuming the null hypothesis is true.

Since this is a one-tailed test in the upper tail (Ha: proportion is greater than 0.34), we need to find the area to the right of the test statistic in the standard normal distribution.

Using a standard normal distribution table or calculator, we find that the area to the right of z = 3.583 is very close to 0.

Therefore, the p-value is very small, likely less than 0.0001 (the exact value depends on the level of precision used in the standard normal distribution table).

In conclusion, the p-value is very small, which provides strong evidence against the null hypothesis and suggests that the proportion of fathers who take no responsibility for childcare in Littleton is higher than the proportion for American fathers.

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The given permutation can be written as the product of disjoint cycles: (1 3 5 7)(2 8 5 6 3 7 1 4).

The product of disjoint cycles can be obtained from the given permutation by tracing the path of each element as it moves in the permutation.

The elements in each cycle should be listed in cyclic order, with the first element being the one that the permutation maps to.The given permutation is (1 3 5 7 1 4)(1 7 8 5 6 3 2 4).

The first cycle starts with 1 and follows the path 1 → 3 → 5 → 7 → 1, forming the cycle (1 3 5 7).

The second cycle starts with 2 and follows the path 2 → 8 → 5 → 6 → 3 → 7 → 1 → 4 → 2, forming the cycle (2 8 5 6 3 7 1 4).

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the coodrinates of JKLM is,

J(1,3) , K(3,1), L(-1,-3) and M(-3,-1)

the length JK is ,

length KL is,

Length LM is,

length MJ

so, the perimeter = sum of sides,

= JK + KL + LM + MJ

= 2 root 2 + 4root2 + 2root2 + 4root2

= 12 root 2

thus, the perimeter is 12 root 2

Answer:

0.00284090909

Step-by-step explanation:

It’s basicly a unit conversion that converse whatever you have to miles/h, so you are getting a miles and get a time and do the math, the final answer will be 180/(5280*12)=0.00284090909

The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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The answer is -178 :))))))))))))))))))))))))))

Answer:

15 units

Step-by-step explanation:

13 - (-2) = 15

So the horizontal distance from (-2), -8)

to (13, -8 is 15 units,

Answer:

15 units

Step-by-step explanation:

The given (x, y) points are (-2, -8) and (13, -8).

The two given points have the same y-coordinate, y = -8.

Therefore, the horizontal distance between the points is the difference between their x-coordinates.

The x-coordinate of the first point is -2, and the x-coordinate of the second point is 13.

To find the horizontal distance, subtract the x-coordinate of the first point from the x-coordinate of the second point:

13 - (-2) = 13 + 2 = 15

Therefore, the horizontal distance from (-2, -8) to (13, -8) is 15 units.

Answer:

D. Use the equivalent ratio in lowest terms to plot the numerator on the x-axis and the denominator on the y-axis, then connect the two points.

The probability to wait more than 15 seconds to connect is 50% and the probability to wait at least 10 more seconds after waiting 10 seconds is 33.33%.

x = old modem establish connection = [0, 30]

Probability density function or PDF is

f(x) = \(\frac{1}{b-a}\); 0 ≤ x ≤ 30

Probability to wait more than 15 seconds to connect is

f(X>5) = \(\int\limits^{30}_{15} {f(x)} \, dx\)

= \(\int\limits^{30}_{15} {\frac{1}{b-a}} \, dx\)

= \(\frac{1}{30-0} \, [x]^{30}_{15}\)

= \(\frac{30-15}{30}\)

= 0.5 or 50%

Probability if already waited 10 seconds and having to wait at least 10 more seconds is equal to wait at least 20 seconds from start. So,

f(X>5) = \(\int\limits^{30}_{20} {f(x)} \, dx\)

= \(\int\limits^{30}_{20} {\frac{1}{b-a}} \, dx\)

= \(\frac{1}{30-0} \, [x]^{30}_{20}\)

= \(\frac{30-20}{30}\)

= 0.3333 or 33.33%

Thus, the 50% probability to wait more than 15 seconds to connect and 33.33% probability to wait at least 20 seconds to connect.

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The intervals on which f(x) = 2 - x² is increasing include the following: [-∞, 0].

For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.

On the other hand (conversely), if the output value (range) is decreasing when the input value (domain) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of this quadratic function above, we can reasonably infer and logically deduce that it is increasing over the interval [-∞, 0].

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The surface area that can be painted with one complete rotation of the roller is 1508 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 8 inches

h = height of the cylinder = width = 30 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(8*30)

SA = 150.7.966 = 1508 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 1508inches².

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Answer: 2 one

Step-by-step explanation:

Answer:

last one

Step-by-step explanation:

Sinkholes are cavities in the ground that form when water erodes an underlying rock layer.

Answer: the answer is 661.55

Step-by-step explanation:

interest formula: F = Pe^(rt)

Answer:

Step-by-step explanation:

To find the missing side lengths in the given right triangles, use trigonometric ratios.

\(\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

From inspection of the first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:

\(\implies \tan 18^{\circ}=\dfrac{15}{x}\)

\(\implies x\tan 18^{\circ}=15\)

\(\implies x=\dfrac{15}{\tan 18^{\circ}}\)

\(\implies x=46.165253...\)

\(\implies x=46.2\;\;\sf(nearest\;tenth)\)

----------------------------------------------------------------------------------------

Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.

Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.

As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.

As KL is parallel to NM, then m∠K = 90°.  Therefore, m∠KLN = 40°.

(Refer to the attached diagram).

For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:

\(\implies \tan 50^{\circ}=\dfrac{LN}{45}\)

\(\implies LN=45\tan 50^{\circ}\)

LN is the hypotenuse of right triangle KLN.

If we use ∠KNL as θ, then side KN is adjacent to the angle.

Therefore, to find the KN use the cosine ratio:

\(\implies \cos 50^{\circ}=\dfrac{KN}{LN}\)

\(\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}\)

\(\implies KN=45\tan 50^{\circ}\cos 50^{\circ}\)

\(\implies KN=34.471999...\)

\(\implies KN=34.5\;\; \sf (nearest\;tenth)\)

As KL is the side opposite ∠KNL, to find KL use the sine ratio:

\(\implies \sin 50^{\circ}=\dfrac{KL}{LN}\)

\(\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}\)

\(\implies KL=45\tan 50^{\circ}\sin50^{\circ}\)

\(\implies KL=41.0821297...\)

\(\implies KL=41.1\;\;\sf (nearest\;tenth)\)

----------------------------------------------------------------------------------------

From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:

\(\implies \cos 70^{\circ}=\dfrac{x}{46}\)

\(\implies x=46\cos 70^{\circ}\)

\(\implies x=15.732926...\)

\(\implies x=15.7\;\;\sf(nearest\;tenth)\)

Answer:

See below

Step-by-step explanation:

3 * 3 = 9 obviously

a negative number times a negative number equals a positive number

  so   -3  * -3 = + 9

a) Rocky Mountain should order 200 tires each time it places an order.

b) The total cost of this policy is $17,160.

a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:

If fewer than 200 tires are ordered: The purchase price is $25 per tire.

If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.

If 8,000 or more tires are ordered: The purchase price is $13 per tire.

Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.

b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:

Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200

Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950

Therefore, the total cost of this policy is $40,950.

Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.

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Answer:

50% chance of drawing a spade, 17% chance of drawing 7

Step-by-step explanation:

The score that separates the top 59% from the bottom 41% is 39.3.

To solve this problem, we need to find the z-score that separates the top 59% from the bottom 41%, and then use the z-score formula to find the corresponding raw score.

The z-score for the top 59% is the z-score that corresponds to a cumulative area of 0.59 to the left of it. We can find this using a standard normal table or a calculator:

z = invNorm(0.59) = 0.24

The z-score for the bottom 41% is the z-score that corresponds to a cumulative area of 0.41 to the left of it:

z = invNorm(0.41) = -0.24

The score that separates these two z-scores can be found using the z-score formula:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation. Solving for x, we get:

x = z * σ + μ

Plugging in the values we found earlier, we get:

x = 0.24 * 7.6 + 37.6 = 39.3

Therefore, the score that separates the top 59% from the bottom 41% is 39.3.

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The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.

The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.

We have,

The absolute value function f(x) = |x – 2| is a piecewise function that returns the positive distance between the input value x and the number 2.

Geometrically,

It represents the distance of a point on the number line from point 2.

On the coordinate plane,

The graph of the absolute value function is V-shaped, with its vertex at the point (2, 0).

The two arms of the V extend indefinitely in opposite directions, passing through the points (-∞, 2) and (2, +∞) on the positive and negative sides of the x-axis, respectively.

Thus,

The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.

The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.

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The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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Answer:0.6

Step-by-step explanati

Answer:

First tell me what's Carnegie

Answer:

answer: 510 square feet

To write the equation in standard form for the circle passing through (–2, 4) centered at the origin, we need to find the radius and the center of the circle.

Since the circle passes through (–2, 4), we can use the distance formula to find the radius, which is the distance from the origin to (–2, 4).

The distance formula is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, x1 = 0, y1 = 0, x2 = –2, and y2 = 4. So, the radius is:

radius = sqrt((-2 - 0)^2 + (4 - 0)^2) = sqrt(20) = 2sqrt(5)

The center of the circle is the origin, since the circle is centered at the origin. Therefore, the equation of the circle in standard form is:

x^2 + y^2 = (2sqrt(5))^2 = 20

So, the equation of the circle passing through (–2, 4) centered at the origin is x^2 + y^2 = 20.

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