Evaluate the function requested. Write your answer as a fraction in lowest terms.
Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 41, adjacent B C is 9, opposite A C is 40.
Find cos B.
a.
Cosine B = StartFraction 41 Over 40 EndFraction
c.
Cosine B = StartFraction 40 Over 41 EndFraction
b.
Cosine B = StartFraction 9 Over 41 EndFraction
d.
Cosine B = StartFraction 9 Over 40 EndFraction

Answer: 11 1/3 gallons of lemonade

The range stays 48°.

To determine how the range changes when a value of 80.4° is added, we need to follow these steps:
Identify the minimum and maximum values in the original data set.
Calculate the original range by subtracting the minimum value from the maximum value.
Add the new value (80.4°) to the data set.
Identify the new minimum and maximum values.
Calculate the new range.
Compare the original and new ranges.

The minimum value is 57°, and the maximum value is 105°.
The original range is 105° - 57° = 48°.
Add the new value: [58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 80.4].
The new minimum value is still 57°, and the new maximum value remains 105°.
The new range is still 105° - 57° = 48°.
Since the original range and the new range are both 48°, the range does not change.
The range stays 48°.

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Answer:

Mean of given observations = Sum of given observations Total number of observations

∴11=x+(x+2)+(x+4)+(x+6)+(x+8)÷5

⇒55=5x+20

5x=55-20

5x=35

x=35/5

x=7

Hence, the value of x is 7.

Answer:

The value of a+b+c is -2

Step-by-step explanation:

rewrite equation: a+b+c

substitute: (-1) + (2) + (-3)

simplify: -1 + 2 - 3

PEMDAS: 1 - 3

Which equals: -2

Answer:

z = 66

y = 120

Step-by-step explanation:

First, we can solve for z because it is supplementary to 114°.

114° + z° = 180°

-114°         -114°

z° = 66°

z = 66

Now, we can solve for y using the fact that the interior angles of a quadrilateral add to 360° (think about a rectangle: 4 x 90°).

We have to use the z value that we solved for earlier.

81° + 93° + y° + z° = 360°

↓ substituting in z-value

81° + 93° + y° + 66° = 360°

↓ combining like terms

240° + y° = 360°

-240°         -240°

y° = 120°

y = 120

Compounded Principal Interest Rate per Compounding Period Number of Compounding Periods Final Amount

Annually $9,200 6% / year 1 $20,101.83

Semi-Annually $9,200 3% / 6 months 30 $20,480.73

Quarterly $9,200 1.5% / 3 months 60 $20,740.64

Monthly $9,200 0.5% / month 180 $21,027.54

Weekly $9,200 0.12% / week 780 $21,118.33

Daily $9,200 0.016% / day 5,475 $21,183.05

What is compound interest ?

Compound interest is a method of calculating interest where interest is added to the principal amount, and the interest is also calculated on the accumulated interest. This results in the growth of the principal amount over time. Compound interest is often used in investments, loans, and savings accounts. The formula for calculating compound interest is [tex]A = P (1 + r/n)^{nt}[/tex], where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

According to the question:
Compound Interest Formula: [tex]A = P(1 + r/n)^{nt}[/tex]

where A is the final amount, P is the principal invested, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested.

Compounded Principal Interest Rate per Compounding Period Number of Compounding Periods Final Amount

Annually $9,200 6% / year 1 $20,101.83

Semi-Annually $9,200 3% / 6 months 30 $20,480.73

Quarterly $9,200 1.5% / 3 months 60 $20,740.64

Monthly $9,200 0.5% / month 180 $21,027.54

Weekly $9,200 0.12% / week 780 $21,118.33

Daily $9,200 0.016% / day 5,475 $21,183.05

Note: The final amounts have been rounded to the nearest cent.

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The correct answer is that the average age of all the students at City College could not be exactly 22, but it could be close to it. Since the average age of a sample of 190 students at City College is 22, it can be concluded that the average age of all the students at City College could not be exactly 22 because the sample is only a part of the population.

The population is always larger than the sample. Therefore, it cannot be concluded that the average age of all the students at City College must be more than 22 or must be less than 22.In addition, the standard deviation of the sample is needed to determine the exact range of ages for the population.

It is possible that the population has a higher or lower average age than the sample, but without the standard deviation, it is impossible to say for sure.In conclusion, the given statement that the average age of all the students at City College must be more than 22 or must be less than 22, since the population is always larger than the sample, is not accurate. It could not be exactly 22 but could be close to it, depending on the standard deviation of the sample.

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During the sale, the stereo system was sold for 30% less than its original price of $710, so the discount amount was:

0.30 x $710 = $213

Therefore, the sale price of the stereo system was:

$710 - $213 = $497

After the sale, the discounted price of $497 was marked up by 30%. The markup amount is:

0.30 x $497 = $149.10

So the final price of the stereo system after the markup is:

$497 + $149.10 = $646.10

Therefore, the price of the stereo system after the markup is $646.10.

1. Battling the stereotypes architects face.

2. Arguing for good design over cheap construction.

3. Making time for hand sketching

4. Finding great materials to match great designs.

5. Bridging the generation gap (making a design appealing to different generations)

The value of a is obtained as 7, for the given expression, obtained using the scientific notations.

Numbers that are either too little or too huge to put in conventional decimal form can be expressed using scientific notation. Scientific notation is often known as standard index form simply scientific form among experts.

This notation is frequently used in the work of engineers, mathematicians, and scientists to make it considerably simpler to write large numbers. By using the "SCI" display option on the calculator, you can utilise scientific notation when using one.

The given number is:

63,000,000,000

Write the number in its scientific notation:

6.3 x 10¹⁰

Comparable number is 6.3 x 10³ which is 10ᵃ times larger than the 6.3 x 10¹⁰.

Dividing:

=  6.3 x 10¹⁰ / 6.3 x 10³

= 10⁷

Now, 10⁷ = 10ᵃ

As the base is same , thus the value of a = 7.

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The equation of the straight line is y = -2x - 4, the value of x₁ is -1 and the value of y₁ is -2.

To find the equation of a straight line given its slope and one point, we use the point-slope form of the equation:

−y − y₁​ = m(x−x₁ )

where m is the slope of the line, and (x₁, y₁) is the given point.

In this case, m = -2 and the point is (-1, -2). So we have:

x₁ = -1

y₁ = -2

m = -2

Substituting these values into the point-slope form, we get:

y−(−2)=−2(x−(−1))

Simplifying and rearranging terms, we get the equation of the line:

y + 2 = -2x - 2

y = -2x - 4

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Euler's theorem lets us draw the conclusion that a polyhedron cannot contain [tex]6[/tex] vertices or [tex]7[/tex] edges.

Four or even more plane face (all polygons) that meet in pairs along an edge and at least three edges that meet at a vertex make up a solid figure. Full solution, step-by-step Polyhedron: A three-dimensional object with only polygonal faces. There must be a minimum of different faces on a polyhedron.

A two-dimensional shape composed of line segments is known as a polygon. Square, triangle, hexagonal, etc. are a few examples. A polyhedron, on the other hand, is a three-dimensional object formed of polygons. For instance, a cube, a tetrahedron, etc.

[tex]V - E + F = 2[/tex]

In the case of a polyhedron with [tex]6[/tex] vertices and [tex]7[/tex] edges, we can plug in the values [tex]V=6[/tex] and [tex]E=7[/tex] to obtain:

[tex]6 - 7 + F = 2[/tex]

Simplifying this equation, we get:

[tex]F = 3[/tex]

Therefore, we can conclude that it is not possible for a polyhedron to have [tex]6[/tex] vertices and [tex]7[/tex] edges, based on Euler's theorem.

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Answer:

x = 138°

Step-by-step explanation:

The measure of the angle formed by two tangents drawn from outside point of circle is half the difference of intercepted arcs.

           Near arc = 42°

           Far arc    = 360 - 42 = 318°

            [tex]\boxed{\bf x = \dfrac{1}{2}(Far \ arc - near \ arc)}[/tex]

                 [tex]= \dfrac{1}{2}*(318-42)\\\\= \dfrac{1}{2}*276\\\\= 138^\circ[/tex]

Answer:

e. y = sin(x) + π

Step-by-step explanation:

We can see that the graph of y = sin(x) has been shifted vertically. This means that the added π should be outside the trigonometric function.

Therefore, e. y = sin(x) + π is the correct answer.

See the attached image for how a, b, c, and d values change the graphs of sine and cosine.

Answer:

0.9375

Step-by-step explanation:

In summary, 15/16 inches is the same as 0.9375 inches and 15/16 inches is also the same as 0.078125 feet.

The time at which the population reaches 4,000 is t ≈ 2.51 hours after 12 pm or approximately 2:30 pm. A) The growth constant can be found using the formula for exponential growth:

$-N = N_0 e^{kt}$

where N₀ is the initial population, N is the final population, t is the time elapsed, and k is the growth constant.

Using the given information, we can set up two equations:

500 = N₀e^(0k)

1500 = N₀e^(2k)

Dividing the second equation by the first, we get:

3 = e^(2k)

Taking the natural logarithm of both sides, we get:

ln(3) = 2k

Therefore, the growth constant k is (ln(3))/2, approximately 0.549.

The population as a function of time can now be expressed as:

N(t) = 500e^(0.549t)

B) To find the population at 5 pm, we need to substitute t = 5 into the equation we found in part A:

N(5) = 500e^(0.549*5) ≈ 4,206

Therefore, the population at 5 pm is approximately 4,206 bacteria.

C) To find the time the population reaches 4,000, we need to solve the equation N(t) = 4,000 for t:

4,000 = 500e^(0.549t)

Dividing both sides by 500, we get:

8 = e^(0.549t)

Taking the natural logarithm of both sides, we get:

ln(8) = 0.549t

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The average adult have 02 liters of blood in the body.

The amount of blood circulating in a person depends on their height and weight, but the average adult has more than 5 liters. Blood volume is tightly regulated and linked to various organ systems. Additionally, it is closely related to sodium levels and hydration status. Maintenance of blood volume is essential for normal functioning as it is necessary for the continuous perfusion of body tissues.

According to the Question:

Given that:

The average adult has 1. 2 to 1. 5 gallons of blood in their body.

Now,

Based on the given conditions, formulate: 1.2 ×1.5

Calculate the product or quotient: 1.8

Round the number: 2 gallons.

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The probability of Bob and Joan's fourth child having sickle cell disease, given that their first three children are healthy, is 6.25%.

When Bob and Joan have children, each child has a 25% chance of inheriting two copies of the sickle cell gene and thus developing the disease, a 50% chance of inheriting one copy of the sickle cell gene and being a carrier like their parents, and a 25% chance of inheriting two copies of the normal gene and not carrying the disease.

To understand this probability calculation mathematically, we can use the laws of probability. We can define the probability of the fourth child inheriting the sickle cell gene as P(s), and the probability of the fourth child inheriting the normal gene as P(n).

Since Bob and Joan are each heterozygous carriers for the sickle cell gene, we know that P(s) = 0.25 (25%), and P(n) = 0.75 (75%). We can use the multiplication rule of probability to calculate the probability of their fourth child inheriting two copies of the sickle cell gene, which is:

P(sickle cell disease) = P(s) x P(s) = 0.25 x 0.25 = 0.0625 or 6.25%

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Complete Question:

Bob and Joan know from a blood test that they are each heterozygous (carriers) for the autosomal recessive gene that causes sickle cell disease. If their first three children are healthy, what is the probability that their fourth child will have the disease?

We have that, the probability of hitting the coin toss at least 6 out of 7 times is approximately 0.0625. Which corresponds to option d. 0.0625.

1. Determine the probability of success and failure.

Since the coin is fair, the probability of success (flipping it correctly) is 0.5, and the probability of failure (flipping it incorrectly) is also 0.5.

2. Calculate the probability of flipping the coin correctly exactly 6 times.

Using the binomial probability formula

[tex]P(X = 6) = C(7, 6) * (0.5)^6 * (0.5)^1\\P(X = 6) = 7 * (0.5)^6 * (0.5)^1\\P(X = 6) \approx 0.0547\\[/tex]

3. Calculate the probability of performing the toss correctly all 7 times.

Using the binomial probability formula.

[tex]P(X = 7) = C(7, 7) * (0.5)^7 * (0.5)^0\\P(X = 7) = 1 * (0.5)^7 * 1\\P(X = 7) \approx 0.0078\\[/tex]

4. Calculate the probability of calling the flip correctly at least 6 times.

[tex]P(X \geq  6) = P(X = 6) + P(X = 7)\\P(X \geq  6) \approx 0.0547 + 0.0078\\P(X \geq  6) \approx 0.0625\\[/tex]

Thus, the probability of hitting the coin toss at least 6 out of 7 times is approximately 0.0625, which corresponds to option d. 0.0625.

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Answer:

The system is consistent.

Step-by-step explanation:

Answer:

  (b)  There is not enough information to know whether the system is consistent or inconsistent.

Step-by-step explanation:

Given a system of equations consists of two lines with the same slope, you want to know whether the system is consistent or inconsistent, whether the lines are perpendicular, or if there is enough information to tell.

Lines with the same slope are either parallel or coincident. If they are parallel, the system of equations is inconsistent. If they are coincident, the system of equations is consistent.

Parallel or coincident lines are not perpendicular. Perpendicular lines have opposite reciprocal slopes.

Since we cannot tell whether the lines are parallel or coincident from the given description, we have to say, "there is not enough information to know."

The height of the building is about 364 feet.  

Let's use a proportion to solve the problem. We know that the height of the building and the length of its shadow are proportional to the height of the pole and the length of its shadow. That is:  

height of building/length of building shadow = height of pole/length pole shadow

We are given that the height of the pole is 10 feet, and its shadow is 5.5 feet long. We are also given that the length of the building shadow is 200 feet. We don't know the height of the building, so we'll use "h" to represent it. Substituting the given values into the proportion, we get:

h / 200 = 10 / 5.5

We can solve for "h" by cross-multiplying:

h = 200 * 10 / 5.5

h ≈ 363.6

Therefore, the height of the building is approximately 363.6 feet. Rounding to the nearest foot gives us the final answer:

The height of the building is about 364 feet.

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Answer:

x = 2

x = 1/2

Step-by-step explanation:

To solve the given equation (x-2)(2x-1) = 0, we need to find the values of 'x' that make the left-hand side of the equation equal to zero. For this, we need to use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Using the zero product property, we can set each factor equal to zero and solve for 'x'.

First factor: x - 2 = 0

Adding 2 to both sides, we get:

x = 2

Second factor: 2x - 1 = 0

Adding 1 to both sides, we get:

2x = 1

Dividing by 2 on both sides, we get:

x = 1/2

Therefore, the solutions to the given equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

We can verify our solutions by plugging them back into the original equation and checking if the left-hand side equals zero.

When x = 2, we have:

(x-2)(2x-1) = (2-2)(2(2)-1) = 0, which is true.

When x = 1/2, we have:

(x-2)(2x-1) = (1/2-2)(2(1/2)-1) = (-3/2)(0) = 0, which is also true.

Therefore, our solutions are correct.

FYI, you could've also multiplied the polynomials to get a quadratic equation, though this is terribly inefficient for this case.

Answer:

In short, to solve the equation (x-2)(2x-1) = 0, we use the zero product property by setting each factor equal to zero and solving for x. The solutions are x = 2 and x = 1/2.

Step-by-step explanation:

The equation (x-2)(2x-1) = 0 can be solved by finding the values of x that make the left-hand side of the equation equal to zero.

To do this, we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

Therefore, we set each factor equal to zero and solve for x:

x-2 = 0 or 2x-1 = 0

Solving each equation for x, we get:

x = 2 or x = 1/2

So the solutions to the equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

Answer:

∠1 + ∠2 = 135°

Step-by-step explanation:

From the text, it is given that the two unknows are adjacent angles.

∠2x + ∠2x + 7 = 135°

∠4x + 7 = 135°

∠4x = 128°

x = 32

Answer:

[tex]\angle 1 = 64[/tex]°

[tex]\angle 2 = 71[/tex]°

Step-by-step explanation:

If two adjacent angles form at a resulting angle, this means that both angles form the full resulting angle.

This means [tex]\angle1[/tex] and [tex]\angle2[/tex] have a sum of [tex]135[/tex]°. This can also be written as:

[tex]135 = 2x+2x+7[/tex] or [tex]135 = 4x+7[/tex]

This can be worked out using simple rearrangement:

[tex]135 = 4x+7\\=135-7 = 4x\\=128 = 4x\\\therefore x = 32[/tex]

Therefore we can simply substitute to get our angles:

[tex]\angle 1 = 2x = 32\times2 = 64\\\angle 2 = 2x+7 = 32\times2+7 = 71[/tex]

Hope this helps!!!

The length of the bow of the circle is 9π/ 2 = 4.5 *3.14 = 14.13.  

The  bow time of a circle can be determined with the compass

and significant point of view exercising the bow time frame strategy.

 ⇒ angle =   arc/ radius  

⇒ 135 ° =   bow/ 6

 ⇒  arc =  135 ° * 6  

⇒  bow =  135 ° * π/ 180 ° * 6  

⇒  bow =  9π/ 2  

⇒ 9π/ 2 = 4.5 *3.14   ⇒14.13

  In calculation, a bow is characterized as a piece of the limit of a circle or a bend. It can likewise be indicated as an open bend. The limit of a circle is the border or the distance around a circle,  else called the circuit.

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Answer:

$110.2

Step-by-step explanation:

$76 × 45%

$34.2

$76 + $34.2

$110.2

Answer: If Sydney needs to make exactly 8 dozen items for a bake sale, that means she needs to make a total of 8 x 12 = 96 items

The nth term of the sequence 45, 40, 35, 30 is given by the formula a(n) = 50 - 5n.

To find the nth term of the sequence 45, 40, 35, 30, we need to first identify the pattern that governs the sequence. Here, we can see that each term is obtained by subtracting 5 from the previous term.

So, we can express the nth term of the sequence as:

a(n) = a(1) + (n-1)d

where a(1) is the first term of the sequence, d is the common difference between consecutive terms, and n is the index of the term we want to find.

In this case, a(1) = 45 and d = -5, since we are subtracting 5 from each term to get the next one. Substituting these values into the formula, we get:

a(n) = 45 + (n-1)(-5)

Simplifying, we have:

a(n) = 45 - 5(n-1)

Expanding the brackets, we get:

a(n) = 45 - 5n + 5

Simplifying further, we get:

a(n) = 50 - 5n

Therefore, the nth term of the sequence 45, 40, 35, 30 is given by the formula a(n) = 50 - 5n.

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Answer:

f = 2

Step-by-step explanation:

10 = 6 + 2f

subtract 6 from both sides

4 = 2f

divide both sides by 2

2 = f

The measure of the missing angle is 43 degrees.

What is triangle?

A triangle is a geometric shape with three sides and three angles. It is a closed, two-dimensional figure with straight sides. The sum of the angles in a triangle always adds up to 180 degrees.

To find the measure of the missing angles, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the measure of the missing angle by subtracting the sum of the other two angles from 180 degrees.

Let's call the missing angle x. Then we have:

105° + 32° + x = 180°

Simplifying, we get:

x = 180° - 105° - 32°

x = 43°

Therefore, the measure of the missing angle is 43 degrees.

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