1. Falls Canyon is roughly in the shape of a triangle. If the base of the triangle is 158 miles, the height is 25 miles, and if it has a population of 97,500 moose, what is the approximate population density of moose per square mile?
49
980
500
3,900

The function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the areas of the individual shapes

So, we have

Area = Rectangle + Triangle

Using the area formula, we have

M(x) = (x + 2)(x - 2) * 1/2 * x * (x + 2)

Factorize

M(x) = (x + 2)(x - 2 + x/2)

So, we have

M(x) = (x + 2)(3/2x - 2)

Hence, the function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

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Answer:

Step-by-step explanation:

The plant receives a total of 1.08 grams of magnesium in 20 weeks.It's important to note that when performing unit conversions, it's crucial to keep track of the units and ensure that they cancel out correctly. In this case, we converted milligrams to grams and then multiplied by the number of weeks to find the total amount of magnesium in grams.

To calculate the total amount of magnesium the plant receives in 20 weeks, we need to convert the milligrams to grams and then multiply it by the number of weeks.

Given that the plant food contains 54 milligrams of magnesium, we need to convert it to grams. Since there are 1,000 milligrams in 1 gram, we divide 54 by 1,000 to convert milligrams to grams:

54 milligrams ÷ 1,000 = 0.054 grams

Now, we multiply the amount of magnesium received per week (0.054 grams) by the number of weeks (20) to find the total amount of magnesium received in 20 weeks:

0.054 grams/week × 20 weeks = 1.08 grams.

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Answer:1.5

Step-by-step explanation:

Y=1/2 of x

Answer and Explanation:

We can check if these triangles are similar by comparing the ratios of their corresponding side lengths:

[tex]\dfrac{QP}{LK} \stackrel{?}{=} \dfrac{RP}{MK}[/tex]

[tex]\dfrac{6}{16} \ne \dfrac{11}{36}[/tex]

These triangles are not similar because the ratios of their corresponding side lengths is not the same.

The height of the TV is approximately 52.3 inches when rounded to the nearest tenth of an inch.Hence, the TV is approximately 52.3 inches tall.

To find the height of the TV, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal) of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the width and height of the TV form the legs of a right triangle, with the diagonal as the hypotenuse.

Let's denote the height of the TV as h. According to the Pythagorean theorem:

h² + 67² = 85²

Simplifying the equation, we have:

h² + 4489 = 7225

Subtracting 4489 from both sides, we get:

h² = 2736

Taking the square root of both sides, we find:

h ≈ 52.3.

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Answer:

Step-by-step explanation:

you have to find the mean of the two fractions, adding and then dividing by two

(1/5 + 1/9) : 2 =

14/45 : 2 =

7/45

The complete polynomial is f(x) = 2x⁴ - 3x² - 6 and the values are n = 4 and a = -3

From the question, we have the following parameters that can be used in our computation:

This means that

f(1) = 7

f(-3) = 129

So, we have

f(1) = 2(1)ⁿ + a(1)² - 6

f(-3) = 2(-3)ⁿ + a(-3)² - 6

Evaluate

f(1) = 2 + a - 6

f(-3) = 2(-3)ⁿ + a(-3)² - 6

Recall that

f(1) = -7 and f(-3) = 129

So, we have

2 + a - 6 = -7

2(-3)ⁿ + 9a - 6 = 129

This gives

a = -3

Recall that

2(-3)ⁿ + 9a - 6 = 129

So, we have

2(-3)ⁿ + 9(-3) - 6 = 129

2(-3)ⁿ = 162

Divide by 2

(-3)ⁿ = 81

Solve for n

n = 4

So, the complete polynomial is f(x) = 2x⁴ - 3x² - 6

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The smallest size that will allow this confidence interval to be built is given as follows:

n = 75.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is calculated as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The desired margin of error is of M = 0.5, as we have the time in hours, with [tex]\sigma = 2.2[/tex], hence the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = 1.96\frac{2.2}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 1.96 \times 2.2[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 2.2}{0.5}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 2.2}{0.5}\right)^2[/tex]

n = 75 -> rounded up.

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The final price of the textbook for an English literature course, which is 12% more than the listed price of $130 when tax and shipping costs are included, is $145.60.

The final price of the textbook includes the costs of tax and shipping of 12%, which is added to the listed price.

The final price of the textbook can be computed, using the increase factor, as follows:

The listed price = $130

The increase in the final price = 12%

12% = 0.12 (12/100)

Increase factor = 1.12%

The final price = $145.60 ($130 x 1.12)

Thus, when adding 12%, which represents the tax and shipping costs, to the listed price, the final price is $145.60.

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Answer: Congruent and Perpendicular

Step-by-step explanation:

If diagonals of a quadrilateral bisect each other then it is a rectangle and if they are perpendicular as well then it is a square.

K is a maximal subgroup of G, and we have[tex]H ⊆ K[/tex] since H is a proper subgroup of G and thus H is in M.

Let G be a finite group and let H be a subgroup of G. We want to show that H is contained in a maximal subgroup of G.

First, we note that if H is already a maximal subgroup of G, then we are done. So assume that H is not maximal.

Let M be the set of all subgroups of G that contain H. Note that M is non-empty, since G is itself in M. Since G is finite, M has a maximal element, say K. Then K is a maximal subgroup of G, and we have [tex]H ⊆ K[/tex] since H is in M.

To show that every subgroup H of G, where H is not equal to G itself, is contained in a maximal subgroup of G, we can use the same argument as above.

Let M be the set of all proper subgroups of G (i.e., subgroups that are not equal to G itself). Note that M is non-empty, since {e}, the subgroup consisting only of the identity element, is in M. Since G is finite, M has a maximal element, say K. Then K is a maximal subgroup of G, and we have[tex]H ⊆ K[/tex] since H is a proper subgroup of G and thus H is in M.

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Answer:

The circumference of the circle is 12pi cm.

Answer:

The circumference of the circle is 12π cm.

that's the answer

Based on the information, the town will run out of water in 1 hour.

The town has a total water consumption of 500 people * 10 liters/day = 5000 liters/day.

The town has a water supply of 5000 liters/day / 1000 liters/m³ = 5 m³

The town will run out of water in 5 m³/ 5000 liters/day = 0.01 days = 1 hour.

Time to run out of water = Total water supply / Total water consumption per day = 5000 liters / 5000 liters/day

= 1 hour

Therefore, the town will run out of water in 1 hour.

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[tex]A[/tex] — at least one of the children is a girl

[tex]A'[/tex] — none of the children is a girl

[tex]P(A)=1-P(A')\\\\|\Omega|=2^5=32\\|A'|=1\\\\P(A')=\dfrac{1}{32}\\\\P(A)=1-\dfrac{1}{32}=\dfrac{31}{32}\approx96.9\%[/tex]

Answer:

The probability that when a couple has five children, at least one of them is a girl is 31/32 or approximately  [tex]0.96875.[/tex]

Explanation:

We can determine the probability of having at least one girl by using the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring. In this case, the event of interest is having at least one girl among five children and the complement is having only boys among five children.

Since there are two equally likely outcomes (boy or girl) for each child and the events are independent, we can find the probability of having all boys by multiplying the probabilities of each individual event together: (1/2)^5 = 1/32.

So, the probability of having at least one girl is 1 - 1/32 = 31/32 or approximately 0.96875.

Step-by-step explanation:

70 x 68 = 4760 marks

# mrks / 70  papers =  68 marks/paper

# marks   =   70 papers * 68 marks/paper

The critical point in the solution of the equation -5x + 7y > 2 and 2x - 5y < -7 using graph is

(3.5, 2.8)

The solution of the inequality equation s given as

A) -5x + 7y > 2

B) 2x - 5y < -7

would be solved by graphical method

Using the graph the point of the intersection of the two lines is the critical points of the solution. The critical point from the graph is (3.5, 2.8)

The solution also entails the areas or points covered in the areas where the two shades superimpose.

The graph showing the solution is attached

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The length of each leg is 14.69  in the triangle

In an isosceles triangle, the median drawn from the vertex angle also acts as an altitude, dividing the triangle into two congruent right triangles.

Let the length of one of the legs of the triangle "x".

Using the Pythagorean theorem, we can write:

x²+ (15)² = (21)²

x² + 225 = 441

x² = 441 - 225

x² = 216

Taking the square root of both sides, we find:

x = √216

x =14.69

Therefore, the length of each leg is 14.69 in the triangle

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The measure of angle C is  13. 94 degrees

To determine the value of the angle, we need to know the six different trigonometric identities.

These identities are;

From the information given, we have that;

The Hypotenuse side of the triangle ABC =  34

the adjacent side of the triangle = 33

Using the cosine identity, we have that;

cos C= adjacent/hypotenuse

cos C = 33/34

Divide the values

cos C = 0. 9706

Find the inverse

C = 13. 94 degrees

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The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is approximately (17.569, 18.831), rounded to three decimal places.To determine the 90% confidence interval for the number of chocolate chips per cookie in Big Chip cookies, we can use the sample mean and standard deviation along with the appropriate formula.

Given that Jose randomly selected a sample of 57 cookies and found a sample mean of 18.2 and a standard deviation of 2.9, we can calculate the confidence interval using the following formula:

Confidence Interval = Sample Mean ± (Z * (Standard Deviation / √Sample Size))

Since the data is assumed to be from a normally distributed population and we want a 90% confidence interval, we need to find the Z-value for a 90% confidence level. Using a standard normal distribution table or a calculator, the Z-value for a 90% confidence level is approximately 1.645.

Substituting the values into the formula:

Confidence Interval = 18.2 ± (1.645 * (2.9 / √57))

Calculating the values:

Confidence Interval = 18.2 ± (1.645 * 0.383)Confidence Interval ≈ 18.2 ± 0.631.

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It would take Ofelia 1 hour to type a 3-page paper at her current typing rate.

. Given that Ofelia typed 3/5 of a page in 1/5 hour, we can determine her typing rate. To do so, we can divide the amount of work completed (3/5 of a page) by the time it took (1/5 hour):

(3/5) / (1/5) = 3 pages/hour

This means Ofelia's typing rate is 3 pages per hour. Now, we need to find out how many hours it would take her to type a 3-page paper at this rate. We can use the formula:

Time = Work / Rate

Here, the work is the 3-page paper, and the rate is 3 pages/hour. Plugging in the values:

Time = 3 pages / 3 pages/hour = 1 hour
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Answer:

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

Original price is $66 and the sale price is 50% off, so the sale price is:

Janelle will pay $33 for the ticket.

Step-by-step explanation:

Future Value = Present Value ( 1 + i)^n  

                                    i = decimal interest per PERIOD (.0712/12)

                                    n = periods = 25 * 12 = 300 months

Future value = 8000 ( 1 + .0712/12)^300 = $ 47189.98

Answer:

Step-by-step explanation: Take the amount he started with, 8,000, our coefficient, and since it is being increased by 7.12 percent, therefore, we put it all together, and that will be 8000(1.712) to the power of five which is.. 117,654.56 dollars (you're welcome)

The measure of each arc is calculated as: 16. m(MN) = 72°;  17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 265°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°.

To determine the measures of each of the arcs, note that the central angle will have the same measure as the arc.

16. m(MN) = m<QRN [vertical angles are equal}.

m(MN) = 72°.

17. m(NQR) = 180° [half of a circle is 180 degrees]

18. m(NQ) = 180 - 72 = 108°

19. m(MRP) = 180 + (180 - 95)

m(MRP) = 180 + 85 = 265°

20. m(QR) = 72°

21. m(MR) = 180 - 72 = 108°

22. m(QMR) = 360 - 72 = 288°

23. m(PQ) = 180 - 95 - 72 = 13°

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Step-by-step explanation:

ab = 72    then  a = 72/b     sub into first equation

72/b  * b^4 = 48

72 b^3 = 48

b^3 = 48/ 72

b = .87358

then a = 72/b = 82.4194

The value of 'b' in the ordered pair that satisfies the equations ab^4 = 48 and ab = 72 can be found by expressing 'a' in terms of 'b' from the second equation, substituting into the first and solving for 'b'. The final answer is b = cuberoot(2/3).

The subject of this problem is about finding the value of b in an ordered pair (a, b) that satisfies the given equations ab^4 = 48 and ab = 72.

From the second equation, we could express 'a' as a = 72/b. Now, let's substitute 'a' into the first equation, the new equation becomes (72/b) * b^4 = 48. Simplifying this gives b^3 = 48/72 = 2/3, taking the cube root of both sides obtains the value of b which is cuberoot(2/3).

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The sum of the exterior angles of the heptagon in the given diagram is 51.43 degrees.

To find the sum of the exterior angles of a heptagon, we can use the formula:

Sum of exterior angles = 360 degrees

Since a heptagon has 7 sides, it also has 7 exterior angles.

Therefore, each exterior angle of a heptagon is equal to:

= 360 degrees / 7

= 51.43 degrees (rounded to two decimal places)

Hence, the sum of the exterior angles of the heptagon in the given diagram is 51.43 degrees.

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A graph and table for the linear equation y = 2x/5 - 2 in slope-intercept form is shown in the image attached below.

In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Next, we would rearrange and simplify the given given linear equation in slope-intercept form in order to enable us plot it on a graph;

2x - 5y = 10

5y = 2x - 10

y = 2x/5 - 2

In conclusion, we would use an online graphing calculator to plot the given linear equation in slope-intercept form as shown in the graph attached below.

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From the origin, move 3 units to the right, and then move 9 units up is the intersection of the graphs of the two equations be located on a coordinate grid

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that solution to a system of two linear equations is x = 3: y = 9.

We need to find how the intersection of the graphs of the two equations be located on a coordinate grid

As we know that the numbers on right side of zero are positive and number of upside of zero on y axis are positive.

As x=3 which is positive

y=9 which is positive.

So From the origin, move 3 units to the right, and then move 9 units up is the intersection of two equations

Hence, From the origin, move 3 units to the right, and then move 9 units up is the intersection of the graphs of the two equations be located on a coordinate grid

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There are 72 students in the school.

The number for Igbo language = 54

The number for Igbo language = 40

The Venn diagram is attached

Assuming that the total number of students in the school is x.

Information from the problem

3/4 of students credited Igbo language and

5/9 credited Agriculture.

every student in the school credited at least one of the two subjects. hence we have that

3/4x + 5/9x - 22 = x

Simplifying this equation gives

3/4x + 5/9x - x = 22

11x / 36 = 22

11x = 36 * 22

x = (36 * 22) / 11

x = 72

The number for Igbo language

= 3/4 * 72 = 54

The number for Igbo language

= 5/9* 72 = 40

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