(a) If tan² A = 1 + 2tan² B, prove that cos² B = 2cos² A​

Answer:

b. Low balance alert

Step-by-step explanation:

Because if you know that you have a low balance, you will presumably stop withdrawing money from the account so that you don't have an overdraft (which is when you withdraw more money than you have).

The equation of the circle given at the end of the image is:

(x - 2)² + y² = 16.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.

The center of the circle given at the end of the image has the coordinates given as follows:

(2,0).

The center is at (2,0), while one x-intercept of the circumference is at x = 6, that is, point (6,0), hence the radius is given as follows:

r = 6 - 2

r = 4.

Thus the equation of the circle is given as follows:

(x - 2)² + y² = 16.

The circle is given by the image presented at the end of the answer.

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The value of y for the ordered pair (9, y) is -5

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

A(-6,1), B(4,1), and C(4,-3)

The line AC would form a linear equation. when extended

A linear equation is represented as

y = mx + c

Using the points A and C, we have

-6m + c = 1

4m + c = -3

When evaluated, we have

-10m = 4

This gives

m = -0.4

So, we have

-6(-0.4) + c = 1

Evaluate

c = 1 + 6(-0.4)

c = -1.4

So, the equation is

y = -0.4x - 1.4

When x = 9, we have

y = -0.4 * 9 - 1.4

Evaluate

y = -5

So, the ordered pair is (9, -5) and y = -5

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Answer:

y = 6x²+15x-2x-5

dy/dx = 6*2(x) ²-¹ +15*1(x)¹-¹ -5*1¹-⁰

dy/dx = 12x + 15

There are [tex]4[/tex] students in total who went down the slide during recess after counting the sequence.

To determine the total number of students who went down the slide during recess, we need to count the number of times the slide was used and consider that each use represents one student. By analyzing the given data, we can count the occurrences of the letter 'X' in the provided sequence:

[tex]\[ x \quad x \quad xx \quad xx \quad x \quad x \quad xx \quad xx \quad xx \quad xx \quad 0 \quad 1 \quad X \quad XXX \quad xx45 \quad xxxxx \quad X \][/tex]

Counting the 'X's, we find that there are [tex]4[/tex] occurrences. Since each 'X' represents one student going down the slide, the total number of students is [tex]4[/tex].

Therefore, there are [tex]4[/tex] students in total who went down the slide during recess.

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The maximum, minimum, and median values include the following: D. maximum = 8, minimum = –8, median = 4.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

Minimum (Min) = -8.

First quartile (Q₁) = -4.

Median (Med) = 4.

Third quartile (Q₃) = 6.

Maximum (Max) = 8.

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Answer:

0.225

Step-by-step explanation:

5 + 7 + 8 = 20 crayons.

we want 4 blue crayons from 15 draws. p(blue) = 5/20.

p(4 from 15 draws) = 0.225

a)  Note that the the probability that on a given day, no machines break down is 0.3487

b) the probability that all printing   requirements on a particular day will be met is 0.2323

a) To find the probability that no machines break down, we can use the binomial distribution with

n = 10 (number of machines) and

p = 0.1 (probability of a machine breaking down).

The probability of no breakdowns  is

P(X = 0), where X is the number of breakdowns.

Using the binomial distribution formula: P(X = k) = (n choose k) * [tex]p^{k}[/tex] * (1 - p)[tex]^{n-k}[/tex]

P(X = 0) = (10 choose 0) * 0.1⁰ * 0.9¹⁰ = 0.3487

So it is right to stay that  the probability that on a given day, no machines break down is 0.3487

(b)

P(8 or more machines are functioning) = P(X = 8) + P(X = 9) + P(X = 10)

P(X = 8) = (10 choose 8) * 0.1⁸ *   0.9² = 0.1937

P(X = 9) = (10 choose 9) * 0.1⁹ * 0.9¹ = 0.0386

P(X = 10) = (10 choose 10) * 0.1¹⁰ * 0.9⁰ = 0.0000001

P(8 or more machines are functioning) = 0.1937 + 0.0386 + 0.0000001 = 0.2323

Hence, the probability that all printing requirements on a particular day will be met is 0.2323 or approximately 23.23%.

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Answer: tan(O) = 3/4

Step-by-step explanation:

The following triangle is a right triangle so we can use the pythagorean theorem to find side QP.

4^2 + b^2 = 5^2

16 + b^2 = 25

b^2 = 9

b = 3

tangent is equal to opposite over adjacent.

The side opposite O is QP which we found to be 3

The side adjacent to O is OP which is given to be 4

tan(o) = 3/4

(a) The Goran's monthly payment is  605.9.

(b) His total amount to repay the loan is 50,895.6.

(c) The amount of interest he will pay is 10,395.6.

The Goran's monthly payment, is calculated using the following formula;

P = r(PV) / (1 - (1 + r)⁻ⁿ)

where;

r = 6.7% / 12 = 0.00558

PV = 40,500

n = 7 years x 12 months/year = 84 months

P = 0.00558(40,500) / (1 - (1 + 0.00558)⁻⁸⁴)

P  = 605.9

Total amount = 84 x 605.9 = 50,895.6

The total interest paid on the loan is the difference between the total amount repaid and the amount borrowed.

= 50,895.6 - 40,500

= 10,395.6

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Using this fact, we can find the measure of arc MN. Since angle MSN has a measure of 129 degrees, arc MN must have a measure of 2*129 = 258 degrees.



. Let's call the point where the circle intersects with the line that passes through the center point M.

We also know that the measure of angle MSN (where N is the point where the circle intersects with the line opposite to M) is 129 degrees.

Now, there are a few things we can deduce from this information. First of all, we know that angle MSN is an inscribed angle, since it intercepts an arc of the circle.

We also know that the measure of an inscribed angle is equal to half the measure of the intercepted arc.

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1/5 = 200 pennies

5/5 = 1000 pennies

The measure of angle x of the intersecting lines is x = 7.4°

Given data ,

Let the measure of angle be x

Now , the measure of angle ∠PON = 105.3°

And , the measure of angle ∠NOR = 153.1°

Now , the measure of angle ∠QOR = 94.2°

So , the intersecting lines are solved and

The measure of x = 360° - ( 153.1° + 105.3° + 94.2° )

On simplifying , we get

x = 7.4°

Hence , the measure of angle x = 7.4°

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(26) The length FE in the intersecting chords is 6.

(27) The length of arc AE is 64⁰.

The length FE is calculated by applying intersecting chord theorem as follows;

The intersecting chord theorem, also known as the power of a point theorem, states that:

If two chords of a circle intersect inside the circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

FE ≅ AB = 6

The length of arc AE is calculated as follows;

arc AE + arc AB + arc ED = 180 (sum of angles of a semi circle)

arc AE + 58 + 58 = 180

arc AE + 116 = 180

arc AE = 64

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To solve the inequality 2x < 12, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides by 2:

2x < 12

x < 6

Therefore, the solution to the inequality is x < 6. This means that all values of x that are less than 6 satisfy the inequality. We can represent this graphically on a number line:

<=======()------6-------------->

The open circle () indicates that x cannot be equal to 6, but can be any value less than 6. The arrow indicates that the inequality is true for all values of x to the left of the open circle.

In summary, the solution to the inequality 2x < 12 is x < 6.

I'm 15 BTW

The proof is shown in the solution.

Given is an expression (2k + x)", we need to expand and prove,

Expand the binomials and cancel the 2k's:

n(n−1) / 2 (2k) = n(n−1)(n−2) / 6

Solving,

3(2k) = n−2

n = 6k+2

Hence proved.

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There are distance of 1.3 miles does Lucy walk before stopping.

Given that;

A hiking trail is 2 3/5 miles long. Lucy walks 1/2 of the trail before stopping for water break.

Hence, Number of miles does Lucy walk before stopping is,

⇒ 1/2 of (2 3/5)

⇒ 1/2 × 13/5

⇒ 13/10

⇒ 1.3 miles

Thus, Number of miles does Lucy walk before stopping is, 1.3 miles

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The correct option of system of equations that can be used to find the temperature at which the degrees Celsius and the degrees Fahrenheit would be equivalent is the option;

5·F - 9·C = 160

F - C = 0

A system of equation, is a set of equation that have common variables.

The equation for conversion of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is; 9·C = 5·F - 160

When the temperature in degrees Celsius is equivalent to the temperature in degrees Fahrenheit, we get;

F = C

Therefore;

F - C = 0

Similarly, from the specified equation, we get;

9·C = 5·F - 160

5·F - 9·C = 160

The system of equation that would give the temperature where the degrees Celsius and degrees Fahrenheit are equivalent is therefore;

5·F - 9·C = 160

F - C = 0

(Which yields a temperature of 40°)

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The probability of getting 14 successes out of 19 trials with a probability of success of 0.8 is approximately 0.0572.

Using the binomial probability formula, we have:

P(X=14) = (n choose x) * pˣ . (1-p)⁽ⁿ⁻ˣ⁾

Plugging in the values, we get:

P(X=14) = (19 choose 14) x 0.8¹⁴ x 0.2⁵

P(X=14) ≈ 0.0572

Therefore, the probability of getting 14 successes out of 19 trials with a probability of success of 0.8 is approximately 0.0572.

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Step-by-step explanation:

To determine which point is a solution of the linear inequality 92 + 3y < 6, we can substitute the values of each point into the inequality and check if the inequality holds true.

Let's evaluate the inequality for each point:

1. Point (1, -1):

92 + 3(-1) < 6

92 - 3 < 6

89 < 6

The inequality is not true for this point.

2. Point (2, -2):

92 + 3(-2) < 6

92 - 6 < 6

86 < 6

The inequality is not true for this point.

3. Point (1, 1):

92 + 3(1) < 6

92 + 3 < 6

95 < 6

The inequality is not true for this point.

4. Point (1, 3):

92 + 3(3) < 6

92 + 9 < 6

101 < 6

The inequality is not true for this point.

None of the given points satisfy the inequality. Therefore, none of the points (1, -1), (2, -2), (1, 1), or (1, 3) are solutions to the linear inequality 92 + 3y < 6.

Answer:

There are 6 children in the group and 4 adults

Step-by-step explanation:

Because the adult ticket cost $8, so there are 4 adults and a total of $32 for adults.

Then I took 62-32=$30

$30 (total for children price) / $5 (the children's tickets) = 6 children

Answer:

$677.25

Step-by-step explanation:

Money deposited: $375.45 + 614.20 + $187.60 = $1177.25

Money withdrawn: $500.00

Total deposit: $1177.25 - $500.00 = $677.25

Answer: $677.25

The expression y = sin(x²) cot(2x) when differentiated is 2xcot(2x)cos(x²) - 2csc²(2x)sin(x²)

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

y=sin x² cot 2x

Express properly

So, we have the following representation

y = sin(x²) cot(2x)

When each term of the expression are differentiated using the first principle and the product rule, we have

sin(x²) ⇒ 2xcot(2x)cos(x²)

cot(2x) ⇒ -2csc²(2x)sin(x²)

So, the solution is 2xcot(2x)cos(x²) - 2csc²(2x)sin(x²)

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To obtain 15 gallons of 24% alcohol, you would need to mix 14 gallons of 25% alcohol and 1 gallon of 10% alcohol.

To determine the amounts of 25% alcohol and 10% alcohol needed to obtain 15 gallons of 24% alcohol, we can set up an equation based on the principle of the mixture:

Let x represent the number of gallons of 25% alcohol.

Let y represent the number of gallons of 10% alcohol.

The equation can be set up as follows:

0.25x + 0.10y = 0.24  (15)

0.25x + 0.10y = 3.6

To solve this equation, we need another equation. Since we know that the total volume of the mixture is 15 gallons, we can add a second equation:

x + y = 15

Now we have a system of equations:

0.25x + 0.10y = 3.6

x + y = 15

Now, solving

x = 15 - y

Substituting this value of x into the first equation:

0.25(15 - y) + 0.10y = 3.6

3.75 - 0.25y + 0.10y = 3.6

-0.15y = -0.15

y = 1

and, x + 1 = 15

x = 14

Therefore, to obtain 15 gallons of 24% alcohol, you would need to mix 14 gallons of 25% alcohol and 1 gallon of 10% alcohol.

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Answer:

Step-by-step explanation:

41 + 85 + 180 - x = 180

x = 126

Answer:

Step-by-step explanation:

There are 5 marbles

The standard deviation of this sample of shopping time is equal to 50.

In order to calculate the standard deviation of this sample of shopping time, we would have to first determine the mean of the data set.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

For the total sum of data, we have:

F(x) = 42 + 27 + 22 + 37 + 32

F(x) = 132.1.

Mean = 160/5

Mean = 32

Now, we can calculate the standard deviation by using this formula:

Standard deviation, S = √(1/n × ∑(xi - u₁)²)

Standard deviation, S = √(1/5 × ∑(42 - 32)² + 1/5 × ∑(27 - 32)² + 1/6 × ∑(22 - 32)² + 1/5 × ∑(37 - 32)² + 1/5 × ∑(32 - 32)²

Standard deviation, S = 250/5

Standard deviation, S = 50.

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Answer: 32 ounces

Step-by-step explanation:

1 pint = 16 ounces, 16 x 2 = 32 ounces.

a. The interest that would accrue at Bank A is $1484.32.

b. Kathy would owe $5984.32 at Bank A.

c. The interest that would accrue at Bank B is $201.82.

d. Kathy would owe $4776.82 at Bank B.

e. Kathy would save $1213.03 by using Bank B.

a. The annual interest at Bank A is 21.99%. The simple interest for 18 months can be calculated as:

I = Prt = 4500 x 0.2199 x (18/12) = $1484.32.

Therefore, the interest that would accrue at Bank A is $1484.32.

b. The total amount that Kathy would owe at Bank A is the sum of the principal and interest:

Total = Principal + Interest = $4500 + $1484.32. = $5984.32.

Therefore, Kathy would owe $5984.32 at Bank A.

c. The annual interest rate at Bank B is 2.99%, but there is also a one-time service fee of $75. The interest for 18 months can be calculated as:

I = Prt = 4500 x 0.0299 x (18/12) = $201.82.

Therefore, the interest that would accrue at Bank B is $201.82.

d. The total amount that Kathy would owe at Bank B is the sum of the principal, interest, and service fee:

Total = Principal + Interest + Service fee = $4500 + $201.82 + $75 = $4776.82

Therefore, Kathy would owe $4776.82 at Bank B.

e. By using Bank B, Kathy would save the difference between the total amount owed at Bank A and the total amount owed at Bank B:

Savings = Total at Bank A - Total at Bank B = $5989.85 - $4776.82 = $1213.03.

Therefore, Kathy would save $1213.03 by using Bank B.

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The nearest Whole number, the coordinator should use a sample size of 753.

To find the sample size needed when the population proportion is known, we can use the formula:

n = (z^2 * p * q) / E^2

where:

n= sample size

z = z-score for the desired level of confidence (we'll use 1.96 for 95% confidence)

p = population proportion

q = 1 - p (the proportion of the population that does not have the characteristic)

E = margin of error (we'll use 0.03 for 3% margin of error)

Substituting the values given in the problem:

n = (1.96^2 * 0.3 * 0.7) / 0.03^2

n ≈ 752.9

Rounding up to the nearest whole number, the coordinator should use a sample size of 753.

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