Determine which function is represented by the graph. Do not use a calculator. (a) f ( x ) = 4 cos ( x + π ) (b) f ( x ) = 4 cos 4 x (c) f ( x ) = 4 sin ( x − π ) (d) f ( x ) = − 4 cos ( x + π ) (e) f ( x ) = 1 − sin x 2

Answer:

There are 10 1/4 cups of water that fit inside a 2 1/2 cup water bottle.

To see why, note that 2 1/2 cups is equivalent to 10 quarter cups (2 x 4 = 8 and 8 + 2 = 10). Therefore, you can fill the water bottle with 10 1/4 cups of water.

The calculated value of the probability of winning is 3.06501854e-7

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

Select 6 numbers out of 39 to win

This means that when a number is selected, the number is returned and the total numbers reduces by 1

i.e. P(Current) = n/(39 - n)

Using the above as a guide, we have the following:

P(Win) = 6/39 * 5/38 * 4/37 * 3/36 * 2/35 * 1/34

Evaluate the product of tthe expressions

So, we have

P(Win) = 3.06501854e-7

Hence, the probability of winning is 3.06501854e-7

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Complete question

In a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win You purchase one lottery ticket What is the probability that you will win?

The probability of winning is

Answer:

289

Step-by-step explanation:

Let's call the height of the building "h" and the distance from the point on the ground to the base of the building "d".

From the point on the ground, the distance to the top of the antenna is d + 138, and the distance to the bottom of the antenna is d.

Using trigonometry, we can set up two equations:

tan(30.5°) = (d + 138) / h (1)

tan(23.5°) = d / h (2)

We can solve equation (2) for d:

d = h tan(23.5°)

Substituting this into equation (1), we get:

tan(30.5°) = (h tan(23.5°) + 138) / h

Simplifying:

tan(30.5°) = tan(23.5°) + 138/h

tan(30.5°) - tan(23.5°) = 138/h

h = 138 / (tan(30.5°) - tan(23.5°)) ≈ 289.12 feet

Therefore, the height of the building is approximately 289.12 feet.

If the company has 33% more employees than it did a year ago and there are currently 66,500 employees, the number of employees the company had a year ago was proportionately, 50,000 employees.

Proportion refers to the ratio of one quantity or value compared to another.

Proportions are fractional values, representing using fractions, decimals, or percentages.

The current population of a company's employees = 66,500

The percentage increase in the population from last year's = 33%

Proportionately, last year's population = 100%, while this year's population is 133% (100 + 33).

If 66,500 = 133% (1.33), then 100% = 50,000 (66,500 ÷ 1.33)

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The actual distance between the two cities is  [tex]7\frac{1}{2}[/tex] miles .

A scale drawing is the reduced version of a larger image. The scale drawing is reduced at a constant proportion to the original image using a scale. An example of a scale drawing is a map of the city.

Actual distance between the cities can be determined by multiplying the distance in the scale drawing by the scale.

Actual distance = 1[tex]\frac{1}{2}[/tex] x 5

= [tex]\frac{3}{2}[/tex] x 5 = [tex]\frac{15}{2}[/tex] = [tex]7\frac{1}{2}[/tex] miles

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Answer:

1.75 Bags of Lemons

Step-by-step explanation:

1 2/5 = 1.4

1 1/4 = 1.25

1.4 * 1.25 = 1.75 Bags of Lemons

We can actually see here that the triangle ABC is an isosceles triangle. This is because two sides of the triangle are equal.

An isosceles triangle is actually a geometric shape having three sides, two of which are equal in length. Consequently, two of the angles that are across from those sides are also equal.

In order to prove that the triangle is an isosceles triangle, we will find the following:

Distance between  vertices A and B:

AB = √((8-5)² + (8-3)²) = √(3² + 5²) = √34 = 5.83mm

Then, we also find the distance between vertices B and C:

BC = √((11-5)² + (3-3)²) = 6mm

Finally, we find the distance between vertices A and C:

AC = √((11-8)² + (3-8)²) = √(3² + 5²) = √34  = 5.83mm

Thus, we see here that AB and AC are actually equal which makes the triangle an isosceles.

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Answer: [tex]8(\sqrt{x} -10)[/tex]

Step-by-step explanation:

[tex]8\sqrt{x} - 80[/tex]

[tex]8(\sqrt{x} -10)[/tex]

The number of users that are 30 and older is 10,500.

We have,

From the histogram,

The number of users that are 30 and older.

= 7 + 9 + 3 + 2

= 21

Now,

The percentage of 30 and older users.

= 21/50 x 100
= 21 x 2

= 42%

Now,

Total users = 25,000

So,

The percentage of 30 and older users.

= 42% of 25,000

= 42/100 x 25,000

= 42 x 250

= 10500

Thus,

The number of users that are 30 and older is 10,500.

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Answer:

A,E

Step-by-step explanation:

Operation: Minus

To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.

6.8 km - 2.3 km = 4.5 km

Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.

Answer:

a and e

Step-by-step explanation:

got it right on homework

The required pair of points that are both located less than 3 units from points (3, 8) is (2, 7).

Following the condition given in the question,
Assuming there are 3 points on the graph beside (3, 8) are (2, 7), (5, 5), and (6, 10)

The distance formula between two points is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, for each point, we can plug in the coordinates and simplify the following:

Point (2, 7):

d = √[(2 - 3)² + (7 - 8)²]

d = √[1² + 1²]

d = √2  (<3)

Points (6, 10):

d = √[(6 - 3)² + (10 - 8)²]

d = √[3² + 2²]

d = √13  (>3)

Point (5, 5):

d = √[(5 - 3)² + (5 - 8)²]

d = √[2² + 3²]

d = √13   (>3)

Point (1, 1):

d = √[(1 - 3)² + (1 - 8)²]

d = √[(-2)² + (-7)²]

d = √53  (>3)

Thus, the pair of points that are both located less than 3 units from points (3, 8) is (2, 7).

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The average rate of change for function f(x) = 1.85x² to the nearest tenth over the interval 10 ≤ x ≤ 20 is equal to 55.5 (Rounding to the nearest tenth).

Function models the cost of a square carpet

f(x) = 1.85x²

The average rate of change of a function f(x) over an interval [a, b] is,

Average rate of change = [f(b) - f(a)] / (b - a)

The average rate of change of f(x) over the interval 10 ≤ x ≤ 20.

Using the given function, we have,

f(10) = 1.85(10)²

       = 185

f(20) = 1.85(20)²

        = 740

Now calculate the average rate of change,

average rate of change

= [f(20) - f(10)] / (20 - 10)

= (740 - 185) / 10

= 55.5 (Rounding to the nearest tenth)

Therefore, the average rate of change of function f(x) over the interval 10 ≤ x ≤ 20 is approximately 55.5.

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Given that the diameter of a circle is 8.4 inches.

The radius (r) of the circle can be found by dividing the diameter by 2:

r = d/2 = 8.4/2 = 4.2 inches

The area (A) of a circle can be found using the formula:

A = πr^2

Substituting the value of r, we get:

A = 3.14 x 4.2^2 = 55.3896 ≈ 55.39 square inches

The circumference (C) of a circle can be found using the formula:

C = 2πr

Substituting the value of r, we get:

C = 2 x 3.14 x 4.2 = 26.3896 ≈ 26.39 inches

Therefore, the area of the circle is approximately 55.39 square inches and the circumference of the circle is approximately 26.39 inches.

We know that the area of a circle is given by the formula A = π×r²

Given the diameter of the circle = 8.4 in

Therefore radius of the circle = 8.4/2 = 4.2 in    (diameter/2 = radius)

Now Area of the circle = π × 4.2²

                                     = 3.14 × 17.64
                                     = 55.3896

                                     = 55.39   (round up to the nearest hundredth)

Circumference of the circle = 2 × π × r

                                              = 2 × 3.14 × 4

                                              = 26.376

                                              = 26.38 (round up to the nearest hundredth)

Therefore the area of the circle is 55.39 in² and the circumference is 26.38 in.

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Answer:

Step-by-step explanation:

The third side of Patricia's garden should be approximately 10.64 feet long.

To determine the length of the third side of Patricia's garden, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we have two known side lengths (6 feet and 7 feet) and the angle between them (110 degrees).

The Law of Cosines states that for a triangle with side lengths a, b, and c, and angle C opposite side c:

c² = a² + b² - 2ab*cos(C)

We want to find the length of the third side, so let's call it c. Plugging in the known values:

c² = 6² + 7 - 267*cos(110°)

Simplifying the equation:

c² = 36 + 49 - 84*cos(110°)

Now, we can calculate the value of cos(110°) using a calculator or trigonometric tables. Once we have that value, we can substitute it back into the equation to find c². Taking the square root of c² will give us the length of the third side.

Note: The value of cos(110°) is approximately -0.342.

c² = 36 + 49 - 84*(-0.342)

c² ≈ 36 + 49 + 28.248

c^2 ≈ 113.248

Taking the square root:

c ≈ √113.248

c ≈ 10.64

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Let’s solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons.

The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x.

Setting these two expressions equal to each other, we get:

5500 + 200.25x = 4995 + 225.50x

Solving for x, we get:

25.25x = 505

x = 20

So, the two companies charge the same when the amount of sugar is 20 tons.

The cost when the two companies charge the same is:

5500 + 200.25 * 20 = $9505

So, when the two companies charge the same, the cost is $9505.

Received message. Let's solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons. The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x. Setting these two expressions equal to each other, we get: 5500 + 200.25x = 4995 + 225.50x Solving for x, we get: 25.25x = 505 x = 20 So, the two companies charge the same when the amount of sugar is **20 tons**. The cost when the two companies charge the same is: 5500 + 200.25 * 20 = $9505 So, when the two companies charge the same, the cost is **$9505**.

Answer:

To solve m^2 - 6m = 3 using the quadratic formula, we first need to put the equation in standard form, which is ax^2 + bx + c = 0.

m^2 - 6m - 3 = 0

Now we can identify a, b, and c:

a = 1, b = -6, c = -3

Next, we can plug these values into the quadratic formula:

m = (-b ± sqrt(b^2 - 4ac)) / 2a

m = (-(-6) ± sqrt((-6)^2 - 4(1)(-3))) / 2(1)

m = (6 ± sqrt(48)) / 2

Simplifying the square root of 48, we get:

m = (6 ± 4sqrt(3)) / 2

Now we can simplify by factoring out a 2 from the numerator:

m = 3 ± 2sqrt(3)

So the solutions to the equation are:

m = 3 + 2sqrt(3) or m = 3 - 2sqrt(3)

Step-by-step explanation:

Answer: 3±2√3

Step-by-step explanation:

see image for explanation

Let me know if you more explanation with simplifying the root.  That is a whole lesson in itself.

The probability representing the no heads in the outcome of flipping a coin 200 times is given by 25%.

Total number of times coin flipped = 200

Number of times we get,

Heads, Heads  = 40

Heads, Tails  = 75

Tails, Tails  = 50

Tails, Heads =  35

The probability of getting no heads that is two tails in a coin toss. Probability is frequency of the outcome 'Tails, Tails' divided by the total number of trials.

⇒P(No Heads) = Frequency of 'Tails, Tails' / Total number of trials

From the table, the frequency of 'Tails, Tails' is 50,

And the total number of trials is 200.

This implies,

P(No Heads)

= 50 / 200

= 0.25

= 25%

Therefore, the probability of the no heads is equal to 25%.

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Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.

We have,

Dela uses a ratio of 4 teaspoons of vinegar to 12.5 teaspoons of olive oil.

So, for 6 containers

= 4 x 6

= 24 teaspoons of vinegar

and, = 12.5 x 6

= 75 teaspoons of olive oil

Thus, Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.

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Answer: In one week, Nursen saves $5 and shares $3.75, so she has $5 + $3.75 = $8.75 per week.

She spends $4.95 on bus fare, so she has $8.75 - $4.95 = $3.80 per week to spend.

This week, Nursen earned $24 babysitting, so she has an additional $24 to spend.

Therefore, Nursen has $3.80 + $24 = $27.80 to spend.

Step-by-step explanation:

A graph of y = 2x + 3 for values of x from -3 to 3 is shown in the image attached below.

Based on the information provided above, the required table can be constructed or developed as follows;

x                    y = 2x + 3              y___

-3                  y = 2(-3) + 3          -3

-2                  y = 2(-2) + 3          -1

-1                  y = 2(-1) + 3             1

0                  y = 2(0) + 3              3

1                   y = 2(1) + 3               5

2                  y = 2(2) + 3              7

3                  y = 2(3) + 3              9

In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set in the table on a graph as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the domain of this linear function y = 2x + 3 is [-3, 3] and the range is [-3, 9].

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The ratio of sec θ is determined as 5/3.

option A.

The ratio is sec θ is calculated by applying the following method;

sec θ =  1/cosθ

Given that tanθ = -4/3 = oppo/adjacent

The hypotenuse side is calculated by applying Pythagoras theorem as shown below;

h = √ 4² + 3²

h = 5

The ratio of sec θ is calculated as follows;

sec θ =  1/cosθ

1/cosθ = 1/(3/5)

1/cosθ = 5/3

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Answer:

2(1/2)(11)(13) + 2(1/2)(10)(13.2) + 10(11)

= 143 + 132 + 110 = 385 square feet

B is the correct answer.

32% of the students surveyed preferred grilled cheese, so in a group of 3500 students, about 1120 students will prefer grilled cheese.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of people surveyed is given as follows:

80 + 40 + 50 + 20 + 60 = 250.

80 students preferred grilled cheese sandwich, hence the percentage is obtained as follows:

p = 80/250 x 100%

p = 32%.

Hence the expected amount of 3500 students is given as follows:

0.32 x 3500 = 1120 students.

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Selective serotonin reuptake inhibitors (SSRIs) are drugs that A. prevent unused neurotransmitters from being transported back to the neuron.

By inhibiting the serotonin transporter, SSRIs prevent the reuptake of serotonin into neurons after synapse release, thereby increasing available serotonin in the brain. Such changes help to alleviate symptoms associated with anxiety, depression and other mood disorders.

Overall, a rise in serotonin activity is significant in transforming an individual's mood pattern. When more serotonin remains within synapses, it binds with and activates its receptors, leading to increased levels of hormonal activity proven to be effective in treating various mood imbalances in patients.

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The value of x is 13°

When two lines intersect, four angles are formed. There are two pairs of nonadjacent angles. These pairs are called vertical angles.

In a coordinate plane, a line parallel to the Y-axis is called Vertical Line. It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate.

We have:

The angles are:

m ∠ A=(2x−2) ∘ and ∠ B=(3x−15) ∘

We have to find the value of x

Now, We know that :

m ∠A = m ∠B  (Def. of Vertical Angles)

(2x−2) = (3x−15)

Combine the like terms:

2x - 3x = -15 + 2

-x = -13

x = 13

The value of x is 13°

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The difference between 13.56 and 10.02 is 3.54.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The difference between 13.56 and 10.02 can be calculated by doing the subtraction. As,

(13 + 0.56) - (10 + 0.02)

= (13 - 10) + (0.56 - 0.02)

= 3 + 0.54

= 3.54

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An appropriate tip for a waiter at a restaurant is at least 15% of the total bill. For a tab of $20, the tip would be:

Tip amount = 15% of $20

Tip amount = 0.15 x $20

Tip amount = $3

Therefore, the total amount of money that should be left, including tip, is:

$20 (tab) + $3 (tip) = $23.

Result:

sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).

For us to write the expression, we shall use this formular formula:

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

where:

a = tan⁻¹(x)

b = tan⁻¹(y)

Next, we have:

tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))

= (x - y) / (1 + xy)

From both sides, we have sine:

sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))

So, sin(tan⁻¹(x) - tan⁻¹(y))  

= sin(tan⁻¹(x) - tan⁻¹(y))

= (x - y) / (1 + xy) in terms of x and y.

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The blanks are filled as follows

1. Commutative

2. Distributive

3. Identity

4. Associative

5. Commutative

6. Inverse

7. Identity

8. Associative

9. Distributive

10. A. Identity

11. A. Identity

12. B. Commutative

13. C. Associative

14. E. Distributive

The distributive law of multiplication is a distinct attribute in mathematics that distinguishes how multiplication interacts with the operations of addition or subtraction.

It is exemplified in the problem as

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Answer: 19.1 is correct

Step-by-step explanation:

where a and c are the lengths of two sides of the triangle and C is the angle between them. To use this formula, we need to find side b and angle A.

We can use the Law of Cosines to find side b: