9. The Star Point Ranger Station and the Twin Pines Ranger Station are 30 miles apart along a straight, mountain road. Each station gets word of a cabin fire in a remote area known as Ben's Hideout. A straight path from Star Point to the fire makes an angle of 34° with the road, while a straight path from Twin Pines makes an angle of 14° with the road. Find the distance, d, of the fire from the road. 34° Star Point Ben's Hideout D d 30 mi 14° Twin Pines 10. In problem 9 we had two expressions that were both equal to d. Use both of your expressions and the value you found for d in problem 7 to check your answers. Explain why they were not exactly equal. Does it matter if this application were real life? Why or why not?​

The rate at which the volume of water in the tank is changing is 58π(dr/dt).

To find the rate at which the volume of water in the tank is changing if the rate at which the height is decreasing is 8 centimeters per minute when the height is 4 meters, we need to use the formula for the volume of a cylinder, which is given by:

V = πr²hwhere V is the volume of the cylinder, r is the radius, and h is the height.

We also need to differentiate the formula for the volume of a cylinder with respect to time to get an equation for the rate of change of the volume of the cylinder. Differentiating the formula for the volume of a cylinder with respect to time, we get:

dV/dt = πr²dh/dt + 2πrhdr/dt

where dV/dt is the rate of change of the volume of the cylinder, dh/dt is the rate of change of the height of the cylinder, and dr/dt is the rate of change of the radius of the cylinder.

Substituting the given values into the formula and simplifying, we get:

dV/dt = π(5²)(-8/100) + 2π(5)(6)(dr/dt) = -2π + 60π(dr/dt) = 58π(dr/dt)

Therefore, the changes in water volume in the tank is 58π(dr/dt).

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Answer: c

Step-by-step explanation:

The arithmetic equation that correctly describes the following real-world situation is (s x 10) ÷ 5 = 225.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given: 10 pieces of candy are given to s students from a bag of candy containing 225 pieces. There are 5 pieces left over.

We have to find the equation that correctly describes the following real-world situation.

(s x 10) ÷ 5 = 225

2s = 225

s = 112.5

Hence, the value of s is 112.5

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Answer: ( s x 10 ) `-. = 225

Step-by-step explanation:

Answer:

After 16 years Mr. Jibril will be twice as old as his son.

Step-by-step explanation:

t - age Mr. Jibril

s - son age

t=4s (father is 4 times older than son)

t-4=7(s-4) (4 years ago they both have 4 year old less and father was 7 times older than son)

t=7s-28+4

t=7s-24

7s-24=4s

3s=24

s=8

t=32

x- years after Mr. Jibril will be twice as old as his son.

32+x=2(8+x)

32+x=16+2x

16=x

x=16

Note that the transformation for the above vertices are given as follows.

From the given graph, we can determine the transformations as follows:

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

Answer: x = -5, y = 1

Step-by-step explanation:

These are simultaneous equations

I will use the substitution method

BTW [1] means the top equation, and [2] the bottom equation

Rearrange [2] for x

-x = -4 + 9y

x = 4 - 9y

Substitute 4 - 9y into [1]

3(4 - 9y) - 2y = -17

Expand the bracket

12 - 27y - 2y = -17

Simplify

12 - 29y = -17

Rarrange for y

12 = 29y - 17

29y = 12 + 17 = 29

Now substitute y into either equation to solve for x

I will use [2] as it looks easier

-x - 9(1) = -4

Expand the bracket

-x -9 = -4

-x = 5

Now lets substitute x and y into [1] to check our answer

3(-5) - 2(1) = -17

-15 - 2 = -17

The answer of the given question based on the graph  transformations  is  option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.

Reflection is a transformation that flips an object over a line, plane, or point. The line, plane, or point is called the "line of reflection", the "plane of reflection", or the "point of reflection", respectively. Reflection is a fundamental concept in geometry, and it has applications in various fields of mathematics, physics, and engineering. It is often used in symmetry analysis, transformation geometry, and computer graphics.

The series of transformations that would carry the rectangle onto itself is option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.

To see why, we can analyze each transformation and its effect on the rectangle:

(x-4, y+0) translates the rectangle left by 4 units.

90° counterclockwise rotation preserves the right angles and parallel sides of the rectangle.

Reflection over the x-axis preserves the right angles of the rectangle and also preserves the orientation of its parallel sides.

Therefore, the final image after all three transformations would be congruent to the original rectangle, i.e., the rectangle would be carried onto itself.

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The given statement "for continuous random variables, the probability of any specific value of the random variable is one." is false because the random variable taking on any specific value is then given by the area under the PDF curve at that value, which is zero.

In fact, for continuous random variables, the probability of any specific value is zero. This may seem counterintuitive at first, but it is a fundamental property of continuous random variables.

The PDF is a function that describes the relative likelihood of the random variable taking on a particular value within its range. The probability of the random variable taking on a specific value is then given by the area under the PDF curve at that value.

Since the PDF is a continuous function, the probability of the random variable taking on any specific value is zero. This is because the area under a continuous curve at any single point is zero.

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The standard deviation of the sampling distribution of  30 seconds songs then the total number of songs are 36.

The mean and the standard deviation of the sampling distribution of x:

The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:

The mean is the same as the population mean. The standard deviation is the division of the population standard deviation by the square root of the sample size. The central limit theorem states that as long as the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution for the mean will be normal whether the population is normally distributed, Poisson, binomial, or any other distribution.

Now,

The parameters for this problem are given as follows:

Population mean of 225 seconds.

Population standard deviation of 60 seconds.

Sample size of 10 seconds.

Hence the standard deviation for the sampling distribution of x is given as follows:

s = 60/√(10) = 19 seconds.

if the sampling distribution of the songs is 30second tehn the tottal number of songs are 36

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Therefore, the scale factor of triangle ABC to triangle UVW is  5 and option C is the correct choice.

Two triangles are shown to us in the photograph. We must determine the ABC to UVW scale factor.

To find the scale factor of our given triangles, we will divide one side of triangle UVW by its corresponding side of triangle ABC.

Original side  ×scale factor = new side

5 × scale factor =25

By multiplying both sides of the equation by 5, we obtain:

5/5×scale factor/5 =25/5

scale factor = 5

What exactly is scale factor?

A scale factor is a figure that, when multiplied by a certain amount, creates a smaller or bigger replica of the original figure. It is the ratio of a blueprint, map, model, or actual thing to the distance or object1. Every inch on a home layout, for instance, would correspond to 4 inches in real life if the scale factor was 1/41.

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Answer: ANSWER IS 5

Step-by-step explanation:

The volume of the pyramid is 4480ft³

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.

The volume of a pyramid is expressed as:

V = 1/3 b × h

b = base area

h = height

Here, base are = 17.5 × 32

= 560ft²

Height = 24ft

V = 1/3 × 560 × 24

V = 560 × 8

V = 4480 ft³

Therefore the volume of the pyramid is 4480ft³

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Answer:

1047

Step-by-step explanation:

a_n = a_1 + (n - 1)d

a_19 = 243

a_11 = 147

243 = a_1 + (19 - 1)d

147 = a_1 + (11 - 1)d

243 = a_1 + 18d

147 = a_1 + 10d

a_1 = 243 - 18d

a_1 = 147 - 10d

243 - 18d = 147 - 10d

-8d = -96

d = 12

a_1 = 147 - 10d

a_1 = 147 - 10(12)

a_1 = 27

The first term is 27. The common difference is 12.

a_86 = a_1 + (n - 1)d

a_86 = 27 + 85(12)

a_86 = 1047

We can conclude after answering the presented question that Use the equation data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

The procedures that a manufacturing organisation might take to undertake a time study analysis are as follows:

List the tasks performed by the workers and describe what constitutes a complete unit of labour.

Choose a representative sample of employees to observe. The sample size should be high enough to be statistically significant, but not so large that observing all workers becomes unfeasible.

Use the data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.

By doing a time study analysis, the manufacturing organisation may acquire useful insights into their workers' productivity and find chances for process changes that will help them fulfil the rising demand for their products.

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Answer:

Step-by-step explanation:

To write the ratio of baking soda to salt, we need to compare the amount of baking soda to the amount of salt in the recipe.

The recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt, so the ratio of baking soda to salt is:

3/4 : 3

To simplify this ratio, we can divide both numbers by the greatest common factor (GCF) of 3 and 4, which is 1.

3/4 divided by 1 = 3/4

3 divided by 1 = 3

So the simplified ratio of baking soda to salt is:

3/4 : 3 = 3: 12

To find the value of the ratio, we can divide both the numerator and denominator by 3:

3/3 : 12/3 = 1: 4

Therefore, the value of the ratio of baking soda to salt is 1:4.

Answer: 113.10 inches squared

Step-by-step explanation:

formula for area: A=(pi)r^2

the diameter is 2x the radius so the radius would be 12/2=6. plug 6 in for r and solve. The answer is 113.097 so when you round to the nearest hundredth it becomes 113.10

Answer:

x1 ≈ 0,84; x2 ≈ 4,16

Step-by-step explanation:

Find the discriminant and then both values of x according to the formulas (I added a photo of my solution)

The minimum cost of fencing the rectangular field with an area of 900 square meters is approximately $2,375.15.

Let's solve for one variable in terms of the other using the area equation:

l x w = 900

l = 900/w (by dividing both sides by w)

Now we can substitute this expression for "l" into the perimeter equation:

P = 2l + 2w

P = 2(900/w) + 2w

P = (1800/w) + 2w

To minimize P, we can take the derivative with respect to w and set it equal to zero:

dP/dw = -1800/w² + 2 = 0

Solving for w, we get:

w = √(1800/2) = 30√(2)

We can now use this value of w to find the corresponding value of l from the area equation:

l = 900/w = 900/(30√(2)) = 30√(2)

Therefore, the dimensions of the rectangular field that require the least amount of fencing while still having an area of 900 square meters are l = 30√(2) meters and w = 30√(2) meters.

The total length of fencing required is:

P = 2l + 2w

P = 2(30√(2)) + 2(30√(2))

P = 120√(2)

The minimum cost of the fence can be found by multiplying the total length of fencing by the cost per meter of fencing:

Cost = 14 x P = 14 x 120√(2) = 1680√(2) dollars = $2,375.15.

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The unknown angle in the triangle is as follows;

m∠S = 38 degrees

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

In the triangle QRS,

m∠Q = 4m∠R

m∠R = 3 / 4 m∠S

Therefore, let's find the angle m∠S in the triangle as follows:

Therefore,

m∠Q + m∠R + m∠S = 180°

let

m∠R = x

4x + x + 4 / 3 x = 180

5x + 4 / 3 x  = 180

15x + 4x / 3 = 180

19x / 3 = 180

19x = 180 × 3

19x = 540

x = 540 / 19

x = 28.42

Therefore,

m∠S = 4 / 3 (28.42)

m∠S = 37.8947368421

m∠S = 38 degrees

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The old age dependency ratio as a decimal is 0.190.

The old age dependency ratio is a measure of the number of people who are considered "dependent" on those who are of working age.

Specifically, it is the ratio of the number of people aged 65 years and over to the number of people aged 15 to 64 years old.

Old Age Dependency Ratio = (Number of people over 65) / (Number of people aged 15-64)

Old Age Dependency Ratio = 40,809 / 214,965 = 0.1895

Therefore, Rounding this to the thousandths place the Old Age Dependency Ratio as a decimal is 0.190.

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Answer:

18 sides

Step-by-step explanation:

We know the relation between exterior angle, interior angle. Given that each interior angle is 8 times the exterior. So, there are 18 sides for such a polygon given in question.

Answer:

a₅ = 11

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 2 , with a₁ = 3 , then

a₂ = a₁ + 2 = 3 + 2 = 5

a₃ = a₂ + 2 = 5 + 2 = 7

a₄ = a₃ + 2 = 7 + 2 = 9

a₅ = a₄ + 2 = 9 + 2 = 11

The center of the hyperbola is the midpoint between the vertices, which is (-2,6).

The distance between the center and each vertex is 3, so the distance between the center and each focus is c = 7.

The distance between each vertex and focus is a = 4.

The equation of the hyperbola with center (h,k) is:

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

where b^2 = c^2 - a^2.

Plugging in the values we have:

- Center: (h,k) = (-2,6)

- a = 4

- c = 7

- b^2 = c^2 - a^2 = 49 - 16 = 33

So the equation of the hyperbola is:

(x + 2)^2 / 16 - (y - 6)^2 / 33 = 1

In this setting, a probability of 0.33 means that out of all the people who fly on United Airlines, 33% of them have a frequent flyer account and accumulate miles for free trips.

The agent helping people confirm reservations and check baggage over the busy Thanksgiving day weekend is recording whether each passenger has a frequent flyer account, which means that for each individual passenger, there are two possible outcomes: either they have a frequent flyer account or they don't.

The probability of a passenger having a frequent flyer account is 0.33, which means that if the agent helps 100 passengers over the Thanksgiving weekend, we would expect approximately 33 of them to have a frequent flyer account, on average.

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Answer:

3

Step-by-step explanation:

do the brackets first

(5+3) = 8

24÷8=3

so the answer is 3

Answer:

The correct numerical expression using PEDMAS for "subtract the sum of 2 and 9 from the product of 4 and 3" is:

4 x 3 - (2 + 9)

Using the order of operations, first, we perform the addition inside the parentheses, then we multiply 4 and 3, and finally, we subtract the result of the sum from the product:

= 4 x 3 - 11

= 12 - 11

= 1

Therefore, the correct numerical expression is (4 x 3) - (2 + 9) = 1.

Step-by-step explanation:

The probability that Alice has the disease given that she tested positive is only about  0.00563

To solve this problem, we can use Bayes' theorem, which relates the conditional probabilities of two events. Let's define the following events

A: Alice has the disease.

B: Alice tests positive.

We want to find P(A|B), the probability that Alice has the disease given that she tested positive. Bayes' theorem tells us that

P(A|B) = P(B|A)× P(A) / P(B)

where

P(B|A) is the probability of testing positive given that Alice has the disease, which is 1 - the false negative rate = 0.85.

P(A) is the frequency of the disease in the population, which is 0.1% or 0.001.

P(B) is the overall probability of testing positive, which can be calculated using the law of total probability

P(B) = P(B|A) × P(A) + P(B|not A) × P(not A)

where

P(B|not A) is the probability of testing positive given that Alice does not have the disease, which is the false positive rate = 0.15.

P(not A) is the complement of P(A), i.e., the probability that Alice does not have the disease, which is 1 - P(A) = 0.999.

Therefore,

P(B) = 0.85 × 0.001 + 0.15 × 0.999 = 0.15084

Now we can substitute these values into Bayes' theorem

P(A|B) = 0.85 × 0.001 / 0.15084 = 0.00563

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Answer:  x=25.9

Step-by-step explanation:

Tan = opp / adj

Tan 67 ° = x / 11

11 Tan (67 °)= x

x = 25.914

  = 25.9 ( 3 significant figures)

Let a be the first, b be second and c be the third whole number.

Since the sum of these three numbers is 100.

So, [tex]a+b+c=100[/tex] (equation 1)

Since, The first number is a multiple of 15

Therefore, [tex]a = 15n[/tex]

And, the second number is ten times the third number.

[tex]b = 10c[/tex]

Substituting the values of 'a' and 'b' in equation 1

So, [tex]15n+10c+c=100[/tex]

[tex]15n+11c=100[/tex]

[tex]11c=100-15n[/tex]

[tex]c=\dfrac{100-15n}{11}[/tex]

Therefore, [tex]100-15n[/tex] should be exactly divisible by 11.

So, by taking [tex]n= 1[/tex] and 2, [tex]100-15n[/tex] is not divisible by 11

Let [tex]n =3[/tex]

[tex]c=\dfrac{100-15\times3}{11}[/tex]

[tex]c= 5[/tex]

Now, second number (b) [tex]= 10c = 10\times5=50[/tex]

As, [tex]a+b+c=100[/tex]

[tex]a+50+5=100[/tex]

[tex]a+55=100[/tex]

[tex]a=45[/tex]

Therefore, the three whole numbers are 45, 50, 5.

Answer:

1 and 19

Step-by-step explanation:

3(x-10)^2 = 3(x^2-20x+100) = 3x^2 - 60x + 300

If 3x^2 - 60x + 300 = 243, 3x^2 - 60x + 57 = 0

Divide by 3 to get x^2 - 20x + 19 = 0

use the quadratic equation (-b±√(b²-4ac))/(2a) to get

(20±√324)/2 = (20±18)/2 = 1 and 19