The whole page tysmmmm plsss step by step explanation

1. Therefore, the exact value of cos(105°) is (√2 - √6)/4.

2. Therefore, the exact value of sin(75°) is (√6 + √2)/4.

3. Therefore, the exact value of tan(105°) is (√3 + 1)/(3 - √3).

4. Therefore, the exact value of cos(105°)cos(15°) is (2 + 2√3)/8.

A branch of mathematics known as trigonometry is concerned with the study of triangles and the correlations between their sides and angles.

It entails computing different triangle measurements and attributes using trigonometric functions including sine, cosine, and tangent.

Trigonometry is an essential component of calculus and other advanced mathematical studies, and it has applications in many disciplines including engineering, physics, navigation, astronomy, and architecture.

1. We can use the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with A = 60° and B = 45°. Then:

cos(105°) = cos(60° + 45°)

= cos(60°)cos(45°) - sin(60°)sin(45°)

= (1/2)(√2/2) - (√3/2)(√2/2)

= (√2 - √6)/4

Therefore, the exact value of cos(105°) is (√2 - √6)/4.

2. We can use the formula sin(A + B) = sin(A)cos(B) + cos(A)sin(B) with A = 45° and B = 30°. Then:

sin(75°) = sin(45° + 30°)

= sin(45°)cos(30°) + cos(45°)sin(30°)

= (√2/2)(√3/2) + (√2/2)(1/2)

= (√6 + √2)/4

Therefore, the exact value of sin(75°) is (√6 + √2)/4.

3. We can use the formula tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B)) with A = 60° and B = 45°. Then:

tan(105°) = tan(60° + 45°)

= (tan(60°) + tan(45°))/(1 - tan(60°)tan(45°))

= (√3 + 1)/(3 - √3)

Therefore, the exact value of tan(105°) is (√3 + 1)/(3 - √3).

4. We can use the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with A = 60° and B = -45°. Then:

cos(105°)cos(15°) = cos(60° - 45°)cos(15°)

= [cos(60°)cos(-45°) - sin(60°)sin(-45°)]cos(15°)

= [(1/2)(√2/2) - (√3/2)(-√2/2)]cos(15°)

= (√2 + √6)/4 * cos(15°)

= (√2 + √6)/4 * (√6 + √2)/4

= (2 + 2√3)/8

Therefore, the exact value of cos(105°)cos(15°) is (2 + 2√3)/8.

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The maximum profit that for the equation p(x) = 2800x - 85x² - x³ - 109000 is $672500

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

Given the profit function:

p(x) = 2800x - 85x² - x³ - 109000

The profit is maximum at:

p'(x) = 0

p(x) = 2800 + 170x - 3x²

2800 + 170x - 3x² = 0

x = 70

p(70) = 2800(70) - 85(70)² - (70)³ - 109000 = 672500

The maximum profit is $672500

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When a student is chosen at random, the student is more likely to be from Mrs Johnson's class.

The probability that the student got A in the first semester will be 0.15.

When a student is chosen at random, the student is more likely to be from Mrs Johnson's class. It should be noted that this is because 152 students out of 300 are from her class compared to Dixon who has 148 students.

The probability that the student got A in the first semester will be:

= 46 / 300

= 0.15

The probability for the last question will be:

= 14 / 148

= 0.095.

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The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.

In statistics, mean is a measure of central tendency that represents the average value of a set of data. It is commonly referred to as the "arithmetic mean" or simply the "average." To calculate the mean, you add up all the values in the data set and divide the total by the number of values. For example, if you have the following data set: 2, 5, 8, 9, 12, the mean would be calculated as follows:(2 + 5 + 8 + 9 + 12) ÷ 5 = 7.2 . So the mean of this data set is 7.2. The mean is a useful measure of central tendency because it takes into account all the values in the data set and provides a single representative value that can be used to describe the overall characteristics of the data.

given

For a population receiving pharmacological treatments, the mean wake time was estimated with a 95% confidence interval.

where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.

When we enter the provided values, we obtain:

s = 23.3

n = 23

t0.025,22 = 2.074

The mean wake time estimate with a 95% confidence interval for a population receiving medication is thus:

82.1 ± 2.074 * (23.3/√23)

which is equivalent to:

(71.4, 92.8)

The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.

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Answer:

Step-by-step explanation:

To determine which flight will have the most no-shows, we need to compare the probabilities of no-shows for each flight.

The probability of a no-show for the afternoon flight is 1/10, which means that on average, 1 out of every 10 passengers on the afternoon flight will not show up.

The probability of a no-show for the morning flight is 1/20, which means that on average, 1 out of every 20 passengers on the morning flight will not show up.

Since 1/10 is greater than 1/20, the afternoon flight will have a higher number of no-shows, on average. Therefore, the afternoon flight is more likely to have the most no-shows.

Total area to paint: (15 + 10) - 1.5 = 23.5 sq ft

Calculate the area of each wall, subtract the door area, and sum the areas.

Front and back walls: (3 * 2.5) * 2 = 15 sq ft

Next, we calculate the area of the side walls:

Side walls: (2 * 2.5) * 2 = 10 sq ft

Door area: 1.5 * 1 = 1.5 sq ft

Total area to paint: (15 + 10) - 1.5 = 23.5 sq ft

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The Complete Question

Kara wants to paint the four outside walls of her dog's house, excluding the roof and door. The dog house measures 3 feet in length, 2 feet in width, and 2.5 feet in height. The door is 1.5 feet tall and 1 foot wide. What is the area of the surface she needs to paint?

Thus, the solution set for the cost of each notebook that can be bought by George is:  (0 ≤ x ≤ 6).

A linear equation is a one-variable equation of the a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.

Given that:

So, the linear equation follows

Amount for 4 notebooks + Left amount  = total amount

4*x + 12 ≤ 36

4x ≤ 36 - 12

4x ≤ 24

x ≤ 24/4

x ≤ 6

So, (0 ≤ x ≤ 6)

Thus, the solution set for the cost of each notebook that can be bought by George is:  (0 ≤ x ≤ 6).

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The difference in what you have as a balance in your check register versus your online statment by 11/18 is $34.78.

The combined total of the 2 transactions they have in common is $206.99.

Use the amount in 11/1 as your balance, then compute by deducting the checks (chk) and debit purchases and adding the deposits. Then get the difference.

Check Register:

Total = 397.45 - 50.32 - 16.32 + 190.67

Total = 521.48

Online Statement:

Total = 486.44 - 84.80 - 19.73 - 16.32 + 190.67

Total = 556.26

Difference = online - check register

Difference = 34.78

On 11/10 and 11/18, check and online have the same transactions (same date, same amount) which are 16.32 and 190.67. Add them together to get 206.99

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Answer:

the car's angular speed is 72,000π radians per hour.

the car's linear speed is approximately 100.53 miles per hour.

Step-by-step explanation:

To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.

The formula for angular speed is:

ω = 2πf

where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.

In this case, the wheel is spinning at a rate of 10 revolutions per second, so:

ω = 2π(10) = 20π radians per second

To convert this to radians per hour, we can multiply by the number of seconds per hour:

20π radians per second × 3600 seconds per hour = 72,000π radians per hour

To find the car's linear speed in miles per hour, we can use the formula:

v = rω

where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.

The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:

9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles

Now we can substitute the values we have found:

v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)

v ≈ 100.53 miles per hour

Answer:

(i) 10 revolutions = 10(2π) = 20π radians

10 revolutions/sec =

(20π radians/sec)(3,600 sec/hr) =

72,000π radians/hr

(ii) C = 18π inches

10 revolutions × 18π inches =

180π inches

(180π in./sec)(3,600 sec/hr) =

(648,000π in./hr)(1 mi./63,360 in.)

= 225π/22 miles/hour

= about 32.13 miles/hour

The three types of rock are igneous, sedimentary, and metamorphic.

There are three types of rocks as explained below.

Igneous rocks are formed from the cooling and solidification of molten rock, either on the Earth's surface (extrusive) or beneath the surface (intrusive). Examples of igneous rocks include basalt, granite, and pumice.

Sedimentary rocks are formed from the accumulation and cementation of sediment particles (such as sand, silt, and clay) or the precipitation of minerals from a solution. Examples of sedimentary rocks include sandstone, limestone, and shale.

Metamorphic rocks are formed from the alteration of pre-existing rocks by heat, pressure, and chemical reactions. Examples of metamorphic rocks include marble, slate, and gneiss.

The rock cycle is the process by which one type of rock can be changed into another type of rock.

The rock cycle involves three main processes:

Therefore, one type of rock can be changed into another type of rock through the rock cycle by undergoing weathering, erosion, deposition, lithification, metamorphism, melting, and solidification, depending on the specific conditions and processes involved.

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The minimum grade you need to get a B in the course is given as follows:

x = 80.625.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The grades and their percentages are given as follows:

You want a grade of 80, hence the minimum test average is obtained as follows:

0.15 x 73 + 0.2 x 79 + 0.25 x 84 + 0.4x = 80

47.75 + 0.4x = 80

x = (80 - 47.75)/0.4

x = 80.625.

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The solution set for the inequality is x < -10

The different signs for representing inequalities are;

From the information given, we have that;

−4x−38<2

To solve for the value of x, take the steps;

collect the like terms

-4x> 2 + 38

Add the values

-4x> 40

Divide both sides by the coefficient of x, we have;

x > -10

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Answer:

$140,000

Step-by-step explanation:

7*20,000 = 140,000

The areas of the trapezoids is,

A = 48 sq units.

Since, The formula to find the area of a trapezoid of a trapezoid is,

⇒ A = 1/2(b₁ + b₂ )h.

Hence, it is stated that the height of each unit is 2.

Now let's substitute the variables in the formula with the actual bases and heights as;

A = 1/2(8 + 4)8,

A = 6 × 8,

A = 48 sq units.

Thus, the areas of the trapezoids is,

A = 48 sq units.

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The equation of the quadratic with a directrix of x = 2 and vertex of (0 , 0)  is: y² =  -8x

The equation of the quadratic with a directrix of y = 4 and vertex of (1, 3)  is: (x - 1)² = -4 (y - 3)

Quadratic equation when the directrix is at x direction is of the form:

(y - k)² =  4P (x - h)

OR

standard vertex form, x = a(y - k)² + h     where a = 1/4p

The vertex

v (h, k) = (0, 0)

P in this problem, is the distance between the vertex and the directrix

P = 0 - 2 = -2

substitution of the values into the equation gives

(y - k)² =  4P (x - h)

(y - 0)² =  4 x -2 (x - 0)

y² =  -8x

Quadratic equation when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The vertex

v (h, k) = (1, 3)

P in this problem, is the distance between the vertex and the directrix

P = 3 - 4 = -1

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - 1)² =  4 * -1 (y - 3)

(x - 1)² = -4 (y - 3)

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the cruising speed of the blue whale is approximately 3.16 meters per second.

What are  velocity?

a velocity is a unit of measurement for the Distance an object travels in a

the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by

dividing the total Distance traveled by the journey time.

In this case, we know the mass of the blue whale (m = 170,000 kg) and its kinetic energy (KE = 890,000 J), but we need to solve for its velocity (v).

Rearranging the formula, we get:

v = √(2 * KE / m)

Plugging in the values we know, we get:

v = √(2 * 890000 J / 170000 kg)

Simplifying this expression, we get:

v = √10 = 3.16 m/s

Therefore, the cruising speed of the blue whale is approximately 3.16 meters per second.

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The grams of each food she feeds this group of rats each day is 80 grams of food A and 100 grams of food B each day.

Let us consider that the researcher feeds x grams of food A and y grams of food B each day. Then we can restructure the  two equations on the basis of  the amount of niacin and retinol present in the food
0.11x + 0.35y = 28.4 (equation 1)
190x + 95y = 37,335 (equation 2)

We can evaluate this system of equations applying the substitution or elimination method.
Let us apply substitution method:
In case of equation 1, we can evaluate concerning x:
x = (28.4 - 0.35y) / 0.11
Staging this value for x in equation 2
190[(28.4 - 0.35y) / 0.11] + 95y
= 37,335
Applying simplification and evaluating for y
y = 100
Staging this value for y in equation 1 to evaluate x

x = 80

Then, the researcher feeds 80 grams of food A and 100 grams of food B each day.
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Answer:

the answer is:l only

because -10 only states the true statement while -1 and 6 gave False Staments...

The values of x, y, and z based on the system of equations will be (-2,4,7).

x + 3y + 5z = 45

6x - 3y + 2z = - 10

------------------------add

7x + 7z = 35

6x - 3y + 2z = -10

-2x + 3y + 8z = 72

----------------------add

4x + 10z = 62

7x + 7z = 35....multiply by 4

4x + 10z = 62...multiply by -7

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

28x + 28z = 140 (result of multiplying by 4)

-28x - 70z = - 434 (result of multiplying by -7)

--------------------add

- 42z = - 294

z = -294/-42

z = 7

4x + 10z = 62

4x + 10(7) = 62

4x + 70 = 62

4x = 62 - 70

4x = - 8

x = -8/4

x = -2

x + 3y + 5z = 45

-2 + 3y + 5(7) = 45

-2 + 3y + 35 = 45

3y + 33 = 45

3y = 45 - 33

3y = 12

y = 12/3

y = 4

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Solve the following system of equations algebraically for all values of x,y and z

x+3y+5z=45

6x-3y+2z=-10

-2x+3y+8z=72

The equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit is 15 in - (1.25 in/hr)t

Given  the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h

L(t) is a function of time, t:

L(t) = 15 in - (1.25 in/hr)t

Note that when the candle has burned down to nothing, L(t) = 0.

Set 15 in - (1.25 in/hr)t equal to zero and solve for t:

(1.25 in/hr)t = 15 in, or

t = 15/  1.25 in/hr

t = 12 hrs

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Answer:

The discriminant is:

(-3)^2 - 4(1)(18) = 9 - 72 = -63

Since this discriminant is negative, f(x) does not have any real number solutions.

Answer:

The quotient is

[tex]8 {x}^{2} + 15x - \frac{1}{8} [/tex]

and the remainder is

[tex] \frac{63}{64} [/tex]

Answer: 2.5

Step-by-step explanation:

the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5

hope it helped:)

The angle of the turn at Deer Trail is of 105 degrees.

Notice that both of the lines that go up to the left are parallel, thus, the angles formed betwen the intersections are all equal (for the respective lines).

Now, also know that two adjacent angles in an intersection should add up to 180°.

We can see that the angle to the right of deer trail has a measure of 75°, then the angle to the left (which is adjacent) must have a measure M such that:

M + 75° = 180°

M = 180° - 75°

M = 105°

That is the angle of the turn.

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Answer:

108

You rounded to the nearest tens place.

The 0 in the tens place rounds up to 1

Step-by-step explanation: because the digit to the right in the ones place is 8.

110

When the digit to the right is 5 or greater we round away from 0.

108 was rounded up and away from zero to 110

The next "three-umbers" in the pattern "2,0,6,-4,10,-8,..." are 14, -12, and 18.

To find the next three numbers in the pattern 2, 0, 6, -4, 10, -8, we need to analyze the pattern and identify the rule for it.

The pattern seems to be alternating between adding and subtracting the "odd-multiples" of 2.

The pattern is as follows : 2 - (2×1) = 0,

0 + (2×3) = 6,

6 - (2×5) = -4,

-4 + (2×7) = 10,

10 - (2×9) = -8,

Using this rule, we can find the next three numbers in the pattern as follows:

Add 22 because : -8 + (2×11) = 14,

Subtract 26 because : 14 - (2×13) = -12,

Add 30 , because : -12 + (2×15) = 18,

Therefore, the next three numbers in the pattern are 14, -12, and 18.

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Answer:

the surface area of the rectangular prism is 572cm².

Step-by-step explanation:

The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:

2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²

So the surface area of the rectangular prism is 572 square centimeters.

Answer:

25$ if the tickets were involved it would be 70$

Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.

The topic of this question is

Mathematics

, specifically about using multiplication and addition in problem-solving.

Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.

Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.

Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.

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the deductible, and the coinsurance. Here are the steps to calculate the total out-of-pocket expense: the total out-of-pocket expense for one month is $ [tex]154[/tex] .

To calculate the out-of-pocket expense for one month, we need to take into account the monthly premium.

Step 1: Calculate the deductible

The deductible is the amount that the insured person needs to pay before the insurance starts covering the costs.

In this case, the deductible is $500 because that's the threshold for the 90% coverage. Since the family will fill 6 prescriptions per month, we need to calculate the average cost per prescription:

Average cost per prescription = Total prescription costs / Number of prescriptions

Average cost per prescription = $ [tex]850 / 6 = $141.67[/tex]

Since the deductible is $500, the insurance will cover 90% of the first $500, which is $450. The remaining $50 will be paid by the insured person. Therefore, the deductible is $  [tex]500 - $450 = $50.[/tex]

Step 2: Calculate the coinsurance

After the deductible is met, the insurance will cover 80% of the remaining prescription costs, and the insured person will be responsible for the remaining  [tex]20[/tex] %.

To calculate the coinsurance, we need to subtract the deductible from the total prescription costs and multiply the result by 0.2:

Coinsurance = (Total prescription costs - Deductible) x 0.2

Coinsurance = [tex]($850 - $500) \times 0.2[/tex]

Coinsurance = $ [tex]70[/tex]

Step 3:

Calculate the total out-of-pocket expense

The total out-of-pocket expense is the sum of the monthly premium, the deductible, and the coinsurance:

Total out-of-pocket expense = Monthly premium + Deductible + Coinsurance

Total out-of-pocket expense = $  [tex]34 + $50 + $70[/tex]

Total out-of-pocket expense = $154

Therefore, the total out-of-pocket expense for one month is $ [tex]154[/tex] .

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