Please help, Thanks so much!!

The distance between both Amanda and Jasper and the bear is approximately 66.05 feet.

To determine the distance between Amanda and Jasper and the bear, we can use the law of sines, which states that for any triangle ABC with side lengths a, b, and c, and opposite angles A, B, and C, we have:

a/sin(A) = b/sin(B) = c/sin(C)

Let's label the distance between Amanda and the bear as a, the distance between Jasper and the bear as b, and the angle between Amanda and Jasper as C. We can then set up two equations using the law of sines:

a/sin(90 - C) = 28/sin(A)

b/sin(90 - C) = 28/sin(B)

Note that the angles A and B are supplementary, so sin(B) = sin(180 - A) = sin(A).

We can simplify these equations to:

a/cos(C) = 28/sin(A)

b/cos(C) = 28/sin(A)

Dividing the second equation by the first, we get:

b/a = cos(C)/cos(C) = 1

Therefore, a = b, which means that the distances between both Amanda and Jasper and the bear are equal.

To find this distance, we can use the law of cosines, which states that for any triangle ABC with side lengths a, b, and c, and opposite angles A, B, and C, we have:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

Substituting a = b and C = 180 - A, we get:

\(c^2 = 2a^2 - 2a^2 cos(A)c^2 = 2a^2(1 - cos(A))\)

Taking the square root of both sides, we get:

\(c = a \sqrt{(2 - 2 cos(A))\)

Substituting the given values for A and the width of the river:

A = 42 degrees

width of river = 28 feet

We get:

c = a sqrt(2 - 2 cos(42))

Using a calculator, we find that:

cos(42) ≈ 0.7431

Therefore:

c ≈ a \(\sqrt{(2 - 2 cos(42))\) ≈ 66.05 feet

So, the distance between both Amanda and Jasper and the bear is approximately 66.05 feet.

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The proportions of the population identified as intellectually disabled or as gifted differ, with a relatively small percentage being identified as intellectually disabled and a slightly larger percentage identified as gifted.

The identification of individuals as intellectually disabled or gifted is based on specific criteria and assessments. Intellectual disability refers to individuals who have significantly below-average intellectual functioning and limitations in adaptive behavior. Giftedness, on the other hand, refers to individuals who demonstrate exceptional abilities or potential in one or more areas.

The proportion of the population identified as intellectually disabled tends to be relatively small. According to the World Health Organization, approximately 1-3% of the global population has an intellectual disability.

In contrast, the proportion of the population identified as gifted is also relatively small but can vary depending on the criteria used for identification. Estimates suggest that around 2-5% of the population may be considered gifted.

Therefore, the proportions of the population identified as intellectually disabled or as gifted differ, with a relatively small percentage being identified as intellectually disabled and a slightly larger percentage identified as gifted.

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Answer:

5/4 8.10.............0.0 5=7=9

Answer:

C. 600 m²

Step-by-step explanation:

A parallelogram is a quadrilateral (has four sides and four angles) with two pairs of parallel sides. Opposite sides and angles of a parallelogram are equal to each other. Also, the diagonals are equal.

The area of a parallelogram is the product of its base and its height. It is given by the formula:

Area = base * height

We can see that for this parallelogram, the height = 15 m, the base = 40 m, hence:

Area = base * height = 40 m * 15 m = 600 m²

Therefore, the level of production that yields the maximum profit is 80 and maximum profit is $5400.

To find the level of production that yields the maximum profit, we need to determine the x-value at which the profit function P(x) reaches its maximum. We can do this by finding the vertex of the quadratic function P(x).

The profit function is given by \(P(x) = 160x - x^2 - 1000.\)

To find the x-value of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic function in the form \(ax^2 + bx + c.\)

In this case, the quadratic function is \(-x^2 + 160x - 1000\), so a = -1 and b = 160.

Substituting the values into the formula, we have:

x = -160 / (2*(-1))

x = -160 / -2

x = 80

To find the maximum profit, we substitute this value of x back into the profit function:

\(P(80) = 160(80) - (80)^2 - 1000\)

P(80) = 12800 - 6400 - 1000

P(80) = 6400 - 1000

P(80) = 5400

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Answer:

(x+4)(x+25)

Step-by-step explanation:

x*x=x^2

x*20=20x

4*x=4x

4*25=100

x^2+20x+4x+100

put the commons together and you will get

x^2+29x+100

A probability model consists of the sample space and the way to assign probabilities. The sample space is the collection of all possible outcomes of a random experiment.  It can be finite, countably infinite, or uncountably infinite.

A probability model is a way of assigning probabilities to events in the sample space.The probability of an event is a measure of the likelihood that the event will occur. The probability of an event is always between 0 and 1, inclusive. A probability of 0 means that the event will never occur, while a probability of 1 means that the event is certain to occur. If an event has a probability of 0.5, then it is just as likely to occur as not to occur.The probability of an event can be calculated using different methods, depending on the type of experiment. For example, if the experiment is a coin toss, then the probability of getting heads is 0.5, and the probability of getting tails is also 0.5. If the experiment is rolling a six-sided die, then the probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on.In summary, a probability model consists of the sample space and the way to assign probabilities. It is a mathematical framework used to quantify uncertainty in various fields such as statistics, physics, economics, and engineering. The probability of an event is a measure of the likelihood that the event will occur and is always between 0 and 1, inclusive.

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Answer:

11/12

Step-by-step explanation:

2/3 + 1/4

Get a common denominator of 12

2/3 *4/4   + 1/4 *3/3

8/12 + 3/12

11/12

Answer:

Step-by-step explanation:

I don't see a graph from which to choose.  Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?

The graph of functions

(F(x) = (x+1), and

(F(x) = |x+1| are both attached.

Given the numbers:

Let's find their greatest common factor:

Step 1: Let's determine the factors of the numbers.

a.) 570

The factors of 570 are: 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570

b.) 615

The factors of 615 are: 1, 3, 5, 15, 41, 123, 205, 615

Their common factors are: 1, 3, 5, 15

But the greatest among all factors is 15.

Therefore, their greatest common factor (GCF) is 15.

Answer:

We can estimate a population of 500 birds.

Step-by-step explanation:

We can estimate the total bird population using a rule of three with the information given:

If we find 5 birds with the foot band among 100 birds captured, how many birds there are in total if inicially we put foot bands in 25 birds?

5 birds with foot band -> 100 birds captured

25 birds with foot band -> X total birds

X * 5 = 25 * 100

X = 25 * 100 / 5 = 500 birds

We can estimate a population of 500 birds.

mean marks of 100 students was 40.. It was discovered that 53 was misread as 83. Find the actual mean.

Total mean score = 40

\(mean \: = \frac{sum \: of \: observation}{number \: of \: observations} \)

sum of observations

= mean × no of observations

= 40×100

= 4000

After the replacement, sum of new observation will be

=4000-83+53

= 3970

mean of new the observation will be

\( = \frac{3970}{100} \)

\( = 39.7\)

[Hence, the actual mean is 39.7]

Answer:

The focus of the parabola is (10, 10.0\(\overline 5\))

The directrix of the parabola is, y = 1.0\(\overline 5\)

The maximum height reached by the ball = 5.\(\overline 5\) meters

The vertex of the parabola is (10, 5.\(\overline 5\))

Step-by-step explanation:

The general equation of a parabola is y = a·(x - h)² + k

The vertex of the parabola = (h, k)

At 2 meters (horizontal) before landing, the height, h = 2 meters

∴ We have;

2 = a·(2 - h)² + k

2 = a·(18 - h)² + k

(2 - h)² = (18 - h)²

h² - 4·h + 4 = h² - 36·h + 324

36·h - 4·h = 324 - 4

h = 320/32 = 10

h = 10

2 = ut -0.5×9.81×t²

The

The time it takes the ball to fall 2 meters =

y = a·x² + b·x + c

h = -b/(2·a)

At y = 0, x = 0, therefore, c = 0

2 = a·2² + b·2 + c = 4·a + 2·b

2 = 324·a + 18·b

k = a·10² + b·10

20·a = -b

k = 100·a - 200·a = -100·a

2 = a·(2 - 10)² + k = 64·a + k

2 = 64·a + k = 64·a - 100·a = -36·a

a = 2/(-36) = -1/18

a = -1/18

a = 1/(4·p)

∴ 4·p = -18

p = 18/4 = 4.5

The focus of the parabola = (h, k + p) = (10, 10.0\(\overline 5\))

The directrix, y = k - p = 1.0\(\overline 5\)

k = 100× -1/18 = 5.\(\overline 5\)

The maximum height reached by the ball = 5.\(\overline 5\) meters

The vertex of the parabola = (10, 5.\(\overline 5\))

Step-by-step explanation:

Using Cosine rule, we have:

q² = r² + s² - 2(r)(s)(cosQ)

= 380² + 390² - 2(380)(390)(cos48°)

= 98169.688cm²

Hence q = 313cm. (nearest centimeter)

The required value of side q is 313 cm for the triangle ΔQRS.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

In triangle QRS side r = 380 cm, side s = 390 cm and angle Q = 48°.

To find the length of the side q,

Use cosine rule,

\(cos Q = \frac{(r^2 + s^2 - q^2)}{(2\times r \times s)}\)

Substitute the values here,

\(cos 48 = \frac{(380)^2 + (390)^2- q^2}{2\times380 \times390} \\\)

\(0.67 = \frac{144400 + 152100 - q^2}{296400}\)

198,588 = 296500 - q²

q² = 97912

q = 312.90

q = 313 cm

The value of side q is 313 cm.

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the algae that is present with the scientist to research upon covers a surface area of 2004 inches² in the rectangular prism.

The dimensions of the rectangular prism is given by:

Height = h = 18 inches

Width = w = 14 inches

Length = l = 30 inches

Now, we have to calculate the surface area of the tank excluding the top of the tank to find out how much algae has been present there for the scientist to test.

So, the formula for surface area will become:

A = 2(w l + h l + h w) - l w ( as the top has to be excluded)

Now substituting the values of l, w and h, we get that:

A = 2 [ (14) (30) + (18) (30) + (18) (14) ] - (30) (14) inches²

A = 2 [ 420 + 540 + 252 ] - 420 inches²

A = 2 [ 1212 ] - 420 inches²

A = 2424 - 420 inches²

A = 2004 inches²

Therefore, we get that, the algae that is present with the scientist to research upon covers a surface area of 2004 inches² in the rectangular prism.

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Answer:

6

Step-by-step explanation:

\(\sqrt{41-5} \\\\\sqrt{36} \\\\6\)

He borrowed $24,000.

The dimensions of the lawn are 24 meters by 16 meters or 32 meters by 12 meters.

Let's start by considering the formula for the perimeter of a rectangle. The perimeter of a rectangle is the sum of the length of all its sides, which can also be written as 2 times the length plus 2 times the width. In this case, we know the total fence length, which is 88 meters. Therefore, we can write the equation as:

2L + 2W = 88 ------(1)

Next, we are given the area of the rectangle, which is 384 square meters. The formula for the area of a rectangle is length multiplied by width. Therefore, we can write:

L x W = 384 ------(2)

We now have two equations with two unknowns. We can solve this system of equations by substitution or elimination method. Let's use the substitution method to solve this problem.

From equation (1), we can express L in terms of W as:

L = (88 - 2W)/2

Substituting this value of L into equation (2), we get:

(88 - 2W)/2 x W = 384

Simplifying the equation, we get:

44W - W² = 384 x 2

Rearranging and simplifying further, we get:

W² - 44W + 768 = 0

We can now solve this quadratic equation to find the value of W. Factoring the equation, we get:

(W - 24) (W - 32) = 0

Therefore, W can be either 24 meters or 32 meters. We can find the corresponding value of L using equation (1).

When W = 24, L = (88 - 2 x 24)/2 = 20 meters

When W = 32, L = (88 - 2 x 32)/2 = 12 meters

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9514 1404 393

Answer:

  x² +3x -3 +3x/(5x² +6x +2)

Step-by-step explanation:

As with any long division, you formulate a partial quotient, then subtract the product of that and the divisor from the dividend. The result is a new dividend. You're done when the degree of the dividend is less than the degree of the divisor.

The partial quotient term is simply the ratio of the highest-degree terms in the dividend and the divisor. (That is what makes it easier than numerical long division.)

_____

Web page formatting cut off part of the "Hints" in the first attachment. The second attachment shows the full "Hints."

1) The Excel function RAND() generates a random number from a uniform distribution.

The Sanotronics example has a director labor cost of $46, parts cost of $95, and 1st year demand of 10,000. The profit value is calculated as follows -  

profit = revenue - cost

revenue = demand * price

price = 100 - director labor cost - parts cost

Plugging in the values, we get -  

profit = 10,000 * 100 - 46 - 95 = $49,544

Therefore, the profit value is $49,544.

2) The second argument  in Excel's IF function isthe value if the condition is true.

The   IF function is a logical function that returns onevalue if a condition is true, and another value if the condition is false. The   syntax for the IF function is -  

IF(condition,   value_if_true,value_if_false)

The second   argument, value_if_true, isthe value that will be returned if the condition is true. The third argument, value_if_false, is the value that will be returned if the condition is   false.

For example,the following IF function   will return "Yes" if the value in cell A1 is greater than 10, and "No" if the value in cell A1 is less than or equal to 10 -  

=IF(A1>10, "Yes", "No")

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MJ Supply distributes bags of dog food to pet stores. Its markup rate is 28%. Which equation represents the nee price of a bag, y, given an original price, p?​

we know that

100%+28%=128%=128/100=1.28

so

the value of y is equal to

The head circumference of a newborn boy who marks the start of the 75th percentile is approximately 35.38 cm.

To find the head circumference of a newborn boy who marks the start of the 75th percentile, we need to first find the z-score corresponding to the 75th percentile using the standard normal distribution.

The z-score formula is

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

To find the z-score that corresponds to the 75th percentile, we need to look up the z-score associated with a cumulative area of 0.75 under the standard normal distribution curve. This value can be found using a table or calculator and is approximately 0.674.

Now we can use the formula for the z-score to solve for the head circumference of a newborn boy at the 75th percentile

z = (x - μ) / σ

0.674 = (x - 34.5) / 1.3

0.674 × 1.3 = x - 34.5

0.8762 + 34.5 = x

x = 35.3762

x ≈ 35.38 cm

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Answer: x=5.4

Step-by-step explanation:

5x+18=45

-18 on both sides

45-18=27

5x=27

divide 5 on both sides

x=5.4

Answer: x=5.4

Step-by-step explanation:

5x=27

x=5.4

After considering the given data and performing series of calculations we finally conclude that the total number of butterflies are expected in the habitat after 12 months is 480 butterflies which is Option A, under the condition that the logistic growth function \(f(t) = 400/1+9.0e^{-0.22t} .\)

To evaluate the total number of butterflies expected in the habitat after the duration of 12 months, we could simply apply the logistic growth function
\(f(t) = 400/1+9.0e^{-0.22t}\) and stage t = 12.
\(f(12) = 400/1+9.0e^{-0.22(12)}\) = 480 butterflies
Hence after performing the given set of evaluation we find, the answer is (A) 480 butterflies.
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Answer:

( h − 4 ) ( h + 12 )

Step-by-step explanation:

I'm not even sure if this helps but it factored

The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth.

1. The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth. These factors have led to numerous challenges, including increased traffic congestion, inadequate infrastructure, and strain on public services. The city's population is growing at a rapid pace, resulting in overcrowding, housing shortages, and environmental concerns.

2. To mitigate the present traffic jam situation in Dhaka City, a restructuring of the population can be pursued through various strategies. One approach is to promote decentralization by developing satellite towns or encouraging businesses and industries to establish themselves in other regions. This would help reduce the concentration of population and economic activities in the city center. Additionally, improving public transportation systems, including expanding the metro rail network, introducing dedicated bus lanes, and enhancing cycling and pedestrian infrastructure, can provide viable alternatives to private vehicles. Encouraging telecommuting and flexible work arrangements can also help reduce the number of daily commuters. Moreover, urban planning should focus on creating mixed-use neighborhoods with residential, commercial, and recreational spaces to minimize the need for long-distance travel.

By implementing these measures, the population of Dhaka City can be restructured in a way that reduces the strain on transportation systems, alleviates traffic congestion, and creates a more sustainable and livable urban environment.

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The best method to estimate the size of a population of rabbits living in a large urban park is the Capture a set of rabbits, mark and release them, and then recapture a second set of rabbits, which is option C.

Later, a second sample of rabbits is captured, and the number of marked rabbits in this sample is recorded. The ratio of marked rabbits to the total number of rabbits in the second sample can be used to estimate the total population size.

The CMR method is considered one of the most accurate methods for estimating the size of a population of animals, as it accounts for the potential biases in other methods like counting individual animals within quadrants or along transects.

This method assumes that the marked and unmarked animals have an equal chance of being captured and that there is no migration or mortality between the two sampling periods.

In conclusion, the CMR method is the best option to estimate the size of a rabbit population in a large urban park as it is more accurate than other methods and accounts for potential biases in other methods. Therefore, correct option is C.

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Answer:

Step-by-step explanation:

3245