The table below shows information about the distance walked by some hikers.
a) Work out the minimum number of hikers who could have walked between
7 miles and 18 miles.
b) Work out the maximum number of hikers who could have walked between
7 miles and 18 miles.
Distance, a (miles) Frequency
0< x≤5
2
5< x≤ 10
3
8
7
1
10< x≤15
15 < x≤20
20< x≤25

The function operation g(f(8) in the given functions f(x) = 3x+2 and g(x) = √(x-1) is 5.

A function is simply a relationship that maps one input to one output.

Given that:

First, set up the composite result function:

Evaluate g( 3x + 2 ) by substituting in the value of f into g.

g( 3x + 2 ) = √( ( 3x + 2 ) - 1 )

Simplify

g( 3x + 2 ) = √( 3x + 2 - 1 )

g( 3x + 2 ) = √( 3x + 1 )

Evaluate the result function by replacing the x with 8.

g( f(x) ) = √( 3(8) + 1 )

g( f(x) ) = √( 24 + 1 )

g( f(x) ) = √( 25 )

g( f(x) ) = 5

Therefore, the composite result function g( f(x) ) is 5.

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Prove of expression tan² θ - sin² θ = tan² θ × sin² θ is shown below.

Given that;

Expression is,

⇒ tan² θ - sin² θ = tan² θ × sin² θ

Now, We can simplify as;

⇒ tan² θ - sin² θ

⇒ sin² θ / cos² θ - sin²θ

⇒ sin² θ (1 / cos² θ - 1)

⇒ sin² θ (sec² θ - 1)

⇒ sin² θ × tan² θ

Thus, Prove of expression tan² θ - sin² θ = tan² θ × sin² θ is shown.

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The perimeter of the regular nonagon is approximately 29.7 feet.

The apothem of a regular nonagon divides each of its interior angles into two congruent angles.

Therefore, each of the interior angles of the nonagon measures:

(180 - 360/9)/2 = 140 degrees

The sum of the interior angles of a nonagon is (9-2) * 180 = 1260 degrees. Therefore, the measure of each exterior angle of the nonagon is:

360/9 = 40 degrees

In a regular nonagon, all the sides and angles are congruent, so we can divide it into 9 congruent isosceles triangles. Each of these triangles has base s and height a, and its legs are given by:

l =√s² - (a/2)²

The perimeter P of the nonagon is given by:

P = 9s

Substituting the values of s and a, we get:

l = √3.3²- (1.65/2)²

= 3.018 ft (rounded to 3 decimal places)

P = 9(3.3) = 29.7 ft

Therefore, the perimeter of the regular nonagon is approximately 29.7 feet.

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Answer:

If x < -12, then (-x) > 12, and we have:

x - (-12) = x + 12

So, the simplified expression without using the absolute value symbol is:

x + 12

Step-by-step explanation:

Answer:

Since x is less than -12, then x-(-12) = x+12.

Here is a table of values for x and x-(-12):

x | x-(-12)

-13 | -1

-14 | -2

-15 | -3

...

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

4k-6=2k-16-2

-16-2= -18

4k-6=2k-18

+6= +6 from both sides

4k=2k-12

-2k = -2k from both sides

2k = -12

/2 /2

k= -6

Answer:

buying price = $11764.70

Step-by-step explanation:

selling price = $10000

loss = 15%

85% = 10000

100% = 10000/85 × 100

= $ 11764.70

Answer:

The correct equation is D. 13x - 2y = 40

13(2) - 2(-7) = 26 + 14 = 40

13(4) - 2(6) = 52 - 12 = 40

Answer:

≈226.1947

Step-by-step explanation:

have a great day and thx for your inquiry :)

The surface area of the triangular prism in square meters is:

549.15 m²

The total surface area of the given prism would be the sum of the areas of the individual faces that make up the prism.

The formula for area of a triangle is:

Area = ¹/₂ * base * height

The formula for area of a rectangle is:

Area = Length * width

Thus:

Total surface area of prism is:

TSA = (15 * 13) + (15.81 * 15) + 2(¹/₂ * 9 * 13)

TSA = 549.15 m²

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The construction being demonstrated is constructing a perpendicular bisector.

In this construction, a line is drawn to bisect a given line segment and is perpendicular to that line segment. The perpendicular bisector divides the line segment into two equal parts and creates a right angle at the point of intersection. It is useful in various geometric constructions and applications, such as finding the midpoint of a line segment or constructing equilateral triangles. By constructing a perpendicular bisector, we ensure that the distances from any point on the line to the endpoints of the line segment are equal.

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Let's first start by rewriting the denominator to have a base of 3.

9 = 3^2

9^(n - 1) = 3^2(n - 1)

Now that we have two terms with the same base, we can subtract the exponents.

3^n / 3^2(n - 1) = 3^[n - 2(n - 1)]

3^[n - 2n + 2]

3^[-n + 2]

3^-(n - 2)

Answer: 3^(-n + 2) OR 3^-(n - 2)

Hope this helps!

Using the ASA Triangle Congruence Theorem, we can prove that triangles GHJ and PQR are congruent because they have Angle G and angle P are congruent, both being right angles.

The two triangles are congruent by rigid motions.

Using the ASA Triangle Congruence Theorem, we can prove that triangles GHJ and PQR are congruent because they have:

Angle G and angle P are congruent, both being right angles.

Side GH and side PQ are congruent, both having a length of 5 units.

Angle H and angle Q are congruent, both having a measure of 63.43 degrees (rounded to two decimal places).

Since the two triangles have two congruent angles and a congruent side between them, they are congruent by the ASA Triangle Congruence Theorem.

b. We can also prove that triangles GHJ and PQR are congruent using rigid motions.

Specifically, we can use a translation followed by a reflection to map triangle GHJ onto triangle PQR.

Translation: We can translate triangle GHJ 2 units to the left and 3 units down to get triangle G'H'J', where G'(-2, 1), H'(-2, -2), and J'(2, -2).

Reflection: We can reflect triangle G'H'J' across the x-axis to get triangle PQR, where P(-2, -4), Q(-2, -1), and R(2, -1).

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The required equation is y = 200 - (0.025)t

Hence option C is correct.

According to the given information:

The soil's water content is dropping by 2.5% weekly.

And here, Begin with the 200 gram of water that were initially present in the soil sample on July 1.

Then deduct the weekly water loss,

Which is determined by multiplying the original water amount by 25%  and the number of weeks (t).

Now forming the equation,

⇒ y = 200 - (2.5/100)t

⇒ y = 200 - (0.025)t

Hence, the expression be,

y = 200 - (0.025)t

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The perimeter of the triangle is 73 unit.

We know that tangents drawn from external point are equal in length.

So, HE = EI = 16 unit

IF = GF = 9.5 unit

DG = DH = 11 unit

So, the length of sides are

DE = 16 + 11 = 27

EF = 9.5 + 16 = 25.5

FD = 11 + 9.5 = 20.5

Now, the perimeter of Triangle DEF is

= DE + EF + FD

= 27 + 25.5 + 20.5

= 73 unit

Therefore, the perimeter of the triangle is 73 unit.

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The length of AC by the given data is about 11.0 cm.

We are given that;

ABCD is a trapezium AB=16cm, AD=11cm, BC=4cm

Now,

We can use these values to find DC. Since ABCD is a trapezium, we know that AB and DC are parallel. Therefore, the distance between them is constant. We can write:

AB−BC=AD−DC

Plugging in the given values, we get:

16−4=11−DC

Solving for DC, we get:

DC=11−12=−1

We can ignore the negative sign since we are only interested in the length of DC. So, DC = 1 cm.

Now we can plug in AD = 11 cm and DC = 1 cm into the Pythagorean theorem and get:

AC2=112+12

AC2=122

Taking the square root of both sides, we get:

AC=122​≈11.045

Rounding to one decimal place, we get:

AC≈11.0 cm

Therefore, by algebra the answer will be 11.0 cm.

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The correct statement is:
As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

I understand that you are asking about the behavior of the function g(z) as x approaches positive and negative infinity. Let's analyze the given function:
g(z) = 4x³ - 3r + 2r³ - 1
First, I believe "r" should be "x" to keep the variables consistent. So, the corrected function is:
g(x) = 4x³ - 3x + 2x³ - 1
Now, let's find the end behavior of this function as x approaches positive and negative infinity.
As x → ∞:
The highest degree term, x³, will dominate the function's behavior. The coefficients for x³ are 4 and 2, so the function will behave like 6x³. Since this term is positive and has an odd exponent, as x → ∞, f(x) → ∞.
As x → -∞:
Again, the x³ term will dominate the function's behavior. Since the exponent is odd, as x → -∞, f(x) → -∞.
So, the correct statement is:
As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

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To obtain a mixture of coffee that can be sold for $60 a pound, the merchant must mix the $20 coffee with the $80 coffee in such a way that the resulting mixture is worth $60 per pound.

To determine how many pounds of the $20 coffee should be used, we can set up a system of equations using the weights of each type of coffee and their corresponding values per pound.

Let x be the number of pounds of the $20 coffee to be used. Then, the total weight of the mixture is 80 + x pounds. The value of the $20 coffee is $20 per pound, and the value of the $80 coffee is $80 per pound. The value of the mixture must be $60 per pound. Therefore, we can write the following equation:

$20x + 80(80) = 60(80 + x)$

Simplifying and solving for x, we get:

$x = 200$

Therefore, the merchant should use 200 pounds of the $20 coffee and mix it with 80 pounds of the $80 coffee to obtain a mixture that can be sold for $60 a pound.

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The solution of expression after divide is, 70.83333...

We have to give that,

Divide 425 by 6.

Now, Divide the numbers as,

425 ÷ 6

6 ) 425 ( 70.833

   - 42

  --------

        050

         - 48

       -----------

               20

             - 18

             --------

                 20

               - 18

             ----------

                    2

Hence, The solution of expression after divide is, 70.83333...

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The relative speed between the jogger and the walker during the 500 second interval is 2.24 m/s.

To solve this problem, we need to first find the distances traveled by each person.

The jogger travels 10 blocks x 100 meters/block = 1000 meters south.

The walker travels 5 blocks x 100 meters/block = 500 meters west.

Using the Pythagorean theorem, we can find the distance between them: √((1000m)² + (500m)²) = 1118.03 meters.

To find their relative speed, we divide this distance by the time interval: 1118.03 meters / 500 seconds = 2.24 m/s.

Therefore, their speed relative to each other during this interval is 2.24 m/s.

The jogger traveled 1000 meters south, while the walker traveled 500 meters west. Using the Pythagorean theorem, the distance between them is 1118.03 meters. Dividing this distance by the time interval of 500 seconds, we get their relative speed, which is 2.24 m/s.

: The relative speed between the jogger and the walker during the 500 second interval is 2.24 m/s.

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The utilization factor can be calculated as the ratio of the arrival rate to the service rate. In this case, the arrival rate (lambda) is 15 per hour, and the service rate (mu) is 25 per hour. Therefore, it is important for the clinic to monitor the utilization factor and adjust staffing levels as needed to ensure efficient and effective patient communication.

So the utilization factor is:
Utilization factor = lambda / mu
Utilization factor = 15 / 25
Utilization factor = 0.6
This means that on average, the operator is utilized 60% of the time. In other words, there is a 40% idle time during which no phone calls are being processed. This is a relatively low utilization factor, which suggests that there is some capacity to handle more phone calls if necessary. However, it is important to note that if the arrival rate were to increase, the utilization factor would increase as well, which could lead to longer wait times for patients and potential bottlenecks in the phone system.

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The probability of choosing exactly two $50 tickets and no other money winners is:

34,320 / 21,455 ≈ 0.

we can use the hypergeometric    probability   distribution to solve this problem, since we are drawing without replacement from a finite population of tickets with different values.

the total number of tickets in the box is:

13 + 11 + 11 + 20 = 55

the number of ways to choose exactly two $50 tickets from the 13 available is:

${13 \choose 2} = 78$

the number of ways to choose one dummy ticket from the 20 available is:

${20 \choose 1} = 20$

the number of ways to choose one ticket from the remaining non-$50 tickets is:

11 + 11 = 22

, the total number of ways to choose exactly two $50 tickets and no other money winners is:

78 x 20 x 22 = 34,320

the number of ways to choose any three tickets from the 55 available is:

${55 \choose 3} = 21,455$ 60 or about 60%

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The temperature of the water after 4.5 minutes is approximately 153°F.

Using Newton's Law of Cooling to find the value of the decay constant k: T = [tex]Ta + (T0 - Ta) * e^-k*t[/tex]

Substituting the given values, we get:

185 = [tex]69 + (203 - 69) * e^-k*1.5[/tex]

Simplifying, we get:

[tex]116 = 134 * e^ \\^{-1.5k}[/tex]

Dividing both sides by 134, we get:

[tex]0.8657 = e^{-1.5k}[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.8657) = -1.5k

Solving for k, we get:

k ≈ 0.232

Therefore, the value of the decay constant is approximately 0.232.

To find the temperature of the water after 4.5 minutes, we can use Newton's Law of Cooling again, with t = 4.5:

[tex]T = Ta + (T0 - Ta) * e^-k*t[/tex]

[tex]T = 69 + (203 - 69) * e^-0.232*4.5[/tex]

T ≈ 153°F

Therefore, the temperature of the water after 4.5 minutes is approximately 153°F.

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By definition of volume of sphere, The volume of the basketball is,

V = 3052.08 inches³

We have to given that;

The radius of a basketball is 9 inches.

Since, We know that;

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

And,  We know that;

Volume of sphere = 4/3πr³

Where, r is radius of sphere.

And, pi is stand for 3.14.

Hence, We get;

The volume of the basketball is,

⇒ V = = 4/3πr³

Substitute radius (r) = 9 inches, pi = 3.14 in above equation, we get;

⇒ V = 4/3 × 3.14 × 9³ inches³

⇒ V = 4/3 × 3.14 × 243 inches³

⇒ V = 3052.08 inches³

Therefore, The volume of the basketball is,

⇒ V = 3052.08 inches³

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The missing length indicated has the value given as follows:

x = 25.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases in this problem are given as follows:

x and 144.

The length of the altitude segment is given as follows:

60.

60 is the geometric mean of x and 144, hence the value of x is obtained as follows:

144x = 60²

x = 3600/144

x = 25.

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Answer:Therefore, the solutions to the equation x^4 - 5x^3 + 7x^2 - 5x + 6 = 0 are x = 0, x = 1, x = 5.

Step-by-step explanation:

To solve the equation x^4 - 5x^3 + 7x^2 - 5x + 6 = 0, we can use factoring by grouping.

First, we can group the first two and last two terms:

x^4 - 5x^3 + 7x^2 - 5x + 6 = (x^4 - 5x^3) + (7x^2 - 5x + 6)

Next, we can factor out x^3 from the first group and factor out 1 from the second group:

(x^3(x - 5)) + (7x^2 - 5x + 6)

Now, we can group the last two terms of the second group:

x^3(x - 5) + (7x^2 - 3x - 2x + 6)

Then, we can factor out 1 from the terms inside the parentheses and group them:

x^3(x - 5) + (7x^2 - 3x) + (-2x + 6)

Now, we can factor out x from the second and third groups:

x^3(x - 5) + x(7x - 3) - 2( x - 3)

We can simplify the third group by distributing the negative sign:

x^3(x - 5) + x(7x - 3) - 2x + 6

Finally, we can combine the second and third groups:

x^3(x - 5) + x(7x - 5) + 6

So, the factored form of the equation x^4 - 5x^3 + 7x^2 - 5x + 6 = 0 is:

(x^3(x - 5) + x(7x - 5) + 6) = 0

This equation can be solved by setting each factor equal to zero and solving for x:

x^3(x - 5) + x(7x - 5) + 6 = 0

(x^3 - 7x^2 + 5x) + (6 - 5x) = 0

x(x^2 - 7x + 5) - (5x - 6) = 0

x(x - 5)(x - 1) - (5x - 6) = 0

x(x - 5)(x - 1) = 5x - 6

x^3 - 6x^2 + 10x - 6 = 5x - 6

x^3 - 6x^2 + 5x = 0

x(x^2 - 6x + 5) = 0

x(x - 1)(x - 5) = 0

Therefore, the solutions to the equation x^4 - 5x^3 + 7x^2 - 5x + 6 = 0 are x = 0, x = 1, x = 5.

In order to plot points H I and J on the coordinate planeIdentify the x-coordinate and y-coordinate of each point (H, I, and J). For example, let's say the coordinates are as follows:

Point H: (xH, yH)

Point I: (xI, yI)

Point J: (xJ, yJ)

Locate the origin (0, 0) on the coordinate plane. This is the starting point for plotting any point.

Move along the x-axis according to the x-coordinate of each point. If the x-coordinate is positive, move to the right; if it's negative, move to the left. Mark a point on the x-axis at the appropriate location.

Move along the y-axis according to the y-coordinate of each point. If the y-coordinate is positive, move upward; if it's negative, move downward. Mark a point on the y-axis at the appropriate location.

The point where the x and y axes intersect is the location of the point. Mark that point on the coordinate plane.

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How to Plot points H I and J on the coordinate plane

The values of x, y and z in the parallelogram 1 are x = 80, y = 100 and z = 80

Parallelogram 1

Adjacent angles of a parallelogram add up to 180

So, we have

x = 180 - 100

x = 80

Opposite angles are equal

So, we have

y = 100

z = 80

Using the above theorem, we have the values of x, y and z in the other parallelograms to be

Parallelogram 2

x = 180 - 50

x = 130

y = 130

z = 130 --- by corresponding angle theorem

Parallelogram 3

x = 90 --- by vertical angle theorem

Then, we have

y = 60 --- sum of angles in a triangle

z = 60 --- by corresponding angle theorem

Parallelogram 4

x = 100

y = 80

z = 80 --- by corresponding angle theorem

Parallelogram 5

y = 112

x = 180 - 112 - 40 --- sum of angles in a triangle

x = 28

z = 28  --- by corresponding angle theorem

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The equation will be y = kx²z², where k is the proportionality constant.

Given that y varies jointly as the square of x, the square of z,

And when x = 3 and z = 4, then y = 72,

So, we can write,

y ∝ x²z²

or,

y = kx²z² [k = proportionality constant]

Now, given x = 3 and z = 4, then y = 72,

Therefore,

72 = 3²·4²·k

72 = 9·16 k

k = 72 / 144

k = 0.5

Therefore, the value of proportionality constant k is 0.5.

Hence the equation will be y = kx²z², where k is the proportionality constant.

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