A bridge is to be built across a small lake from a gazebo to a dock. The bearing from the gazebo to the dock is S 41° W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E, respectively (see figure). Find the distance from the gazebo to the dock

By using factoring and the zero product property the two numbers that multiply to make -14 and add to make -3 are -7 and 4.

The zero product property is a fundamental property of algebra that states that if the product of two or more factors is zero, then at least one of the factors must be zero. In other words, if a × b = 0, then either a = 0 or b = 0 or both a and b are zero. This property is often used to solve equations and factor polynomials. For example, if we have the equation (x - 3)(x + 5) = 0, we know that the only way the product can be zero is if one of the factors is zero, so we set each factor equal to zero and solve for x:

(x - 3)(x + 5) = 0

x - 3 = 0 or x + 5 = 0

x = 3 or x = -5

Thus, the solutions to the equation are x = 3 and x = -5.

We can solve this problem by using factoring and the zero product property.

First, we need to find two numbers that multiply to make -14. The factors of -14 are (-1, 14) and (1, -14), so the two numbers could be -1 and 14, or 1 and -14.

Next, we need to find which pair of numbers adds up to -3. The only pair of numbers that works is -7 and 4 because (-7) + 4 = -3.

Therefore, the two numbers that multiply to make -14 and add to make -3 are -7 and 4.

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An exponential function in terms of x is [tex]P(x) = 140,000(1.05)^x[/tex]

The population would be 291049.95 after 15 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

[tex]P(x) = I(1 + r)^x[/tex]

Where:

By substituting given parameters, we have the following:

[tex]P(x) = 140,000(1 + 0.05)^x\\\\P(x) = 140,000(1.05)^x[/tex]

After 15 years, we have:

[tex]P(15) = 140,000(1.05)^{15}[/tex]

P(15) = 291049.95 units.

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Answer:

Pe^(.0475 × 20) = $20,000

P = $7,734.82

Answer:

4x² + 24x + 35

Step-by-step explanation:

Total area = (7 + 2x)(5 + 2x)

= 35 + 10x + 14x + 4x²

= 4x² + 24x + 35

The minimum surface area of fabric needed for the sleeve is approximately 628.32 cm².

Based on the given model arm, a right circular cylinder would best represent the model for the sleeve.

To calculate the minimum surface area of fabric needed for the sleeve, we need to find the lateral surface area of the right circular cylinder.

The lateral surface area of a right circular cylinder is given by the formula:

Lateral surface area = 2πrh

where r is the radius of the cylinder, h is the height of the cylinder.

In this case, the height of the cylinder needs to be 20 cm (to cover the distance from the shoulder to the elbow), and the radius can vary depending on the desired fit. Let's assume a radius of 5 cm for the purposes of this calculation.

Plugging in the values, we get:

Lateral surface area = 2π(5 cm)(20 cm)

= 628.32 cm²

Therefore, the minimum surface area of fabric needed for the sleeve is approximately 628.32 cm².

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The maximum height of the arrow is 105 feet. To find the maximum height of the arrow, we need to determine the vertex of the quadratic function h = -16[tex]t^{2}[/tex] + 80t + 25.

The vertex is the highest point on the graph of the function, which represents the maximum height of the arrow.

To find the t-value at the vertex, we use the formula t = -b/2a, where a = -16 and b = 80. Plugging these values into the formula gives us t = -80/(2(-16)) = 2.5 seconds.

To find the maximum height, we plug t = 2.5 into the equation to get h = -16[tex](2.5)^{2}[/tex] + 80(2.5) + 25 = 105 feet. Therefore, the maximum height of the arrow is 105 feet.

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The sample space for this experiment contains a total of 12 possible outcomes.

The sample space for this experiment is the set of all possible outcomes. In this case, we have two independent events: flipping a coin and rolling a number cube.

The possible outcomes for flipping a coin are H (heads) and T (tails).

The possible outcomes for rolling a number cube are 1, 2, 3, 4, 5, and 6.

To determine the sample space for the experiment, we need to consider all possible combinations of these outcomes. Therefore, the sample space consists of all possible pairs of outcomes:

Sample space = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}

So the sample space for this experiment contains a total of 12 possible outcomes.

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BD = CA is proved using the Pythagorean theorem.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

From the trapezium ABCD,

BA = CD ______(A)

Now,

We can have two triangles:

ΔABD and ΔACD

Using the Pythagorean theorem.

BD² = AB² + AD² _____(1)

And,

CA² = CD² + AD² ______(2)

From (1), (2), and (A).

BD² = BA² + AD²

CA² = BA² + AD²

This means,

BD² = CA²

BD = CA

Proved

Thus,

BD = CA can be Proven as above.

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Answer:

Step-by-step explanation:

In the expression πr² + πrℓ, the part of the expression that is π is a constant.

A constant is a value that does not change in an expression, and in this case π represents a fixed value of approximately 3.14159. It is not a coefficient, which is a numerical factor that multiplies a variable, nor a variable or term, which represent varying quantities in an expression.

The coordinates of P and Q are P(5, 5) and Q(7, 7) respectively.

Let the centres of the circles be:

P (a, r)  and

Q (b, s)

where r and s are the radii of the circles.

Since the circles are tangent to the x-axis, we know that r = a and s = b.

Also, since the circles are tangent to each other, we have

a + b = PQ = 26

Let the point of contact of circle P with the x-axis be (p, 0)

Let the point of contact of circle Q with the x-axis be (q, 0).

Then, we know that

p + q = AB = 24

Using Pythagorean theorem, we can write:

(r² - p²) + (r² - (24 - p)²) = (s²- q²) + (s² - (24 - q)²)

Expanding and simplifying, we get:

2r² - 24r + 576 = 2s² - 24s + 576

Substituting r = a and s = b, and using the fact that a + b = 26, we get:

2a² - 24a + 576 = 2b² - 24b + 576

Simplifying further, we get:

a² - 12a + 288 = b² - 12b + 288

(a - b)(a + b - 12) = 0

Since a + b = 26, we have a - b = 0 or a + b - 12 = 0. The first case gives us a = b, which is not possible since the circles are tangent to each other. Therefore, we have a + b = 12.

Using substitution method to solve  the simultaneous equations:

a + b = 12

a + b = 26

We get a = 7 and b = 5.

Therefore, the centres of the circles P and Q are (7, 7) and (5, 5) respectively.

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Answer:

Step-by-step explanation:

Given cos(θ) = 5/9, you want the six trig functions of θ.

The relevant identities are ...

The sine of θ is ...

  sin(θ) = √(1 -(5/9)²) = √(81 -25)/9 = (√56)/9

  sin(θ) = (2/9)√14

Then the cosecant is ...

  csc(θ) = 1/sin(θ) = (9/2)/√14

  csc(θ) = (9√14)/28

The tangent of θ is ...

  tan(θ) = sin(θ)/cos(θ) = ((2/9)√14)/(5/9)

  tan(θ) = (2/5)√14

Then the cotangent is ...

  cot(θ) = 1/tan(θ) = (5/2)/√14

  cot(θ) = (5√14)/28

The secant of θ is ...

  sec(θ) = 1/cos(θ) = 1/(5/9)

  sec(θ) = 9/5

The cosine is given in the problem statement.

None of the other statements necessarily follow from (x-4) being a factor of f(x). So the correct statement is Of(4) = 0

What is a statement?

A statement is a proposition that is either true or false, but not both. It may be a mathematical equation, an inequality, or a proposition that can be tested for its truth value.

What is meant by factor?

A factor refers to a number or algebraic expression that is multiplied by another number or expression to obtain a product. Factors can be either integers or polynomials.

According to the given information

If (x-4) is a factor of f(x), then f(4) = 0. This is because when you divide f(x) by (x-4), the remainder is zero when x=4.

Therefore, the correct statement is: f(4) = 0

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If Liquid a has a density of 1. 2 g/cm³, 150 cm of Liquid a is mixed with some of Liquid b to make Liquid c whose mass is 220 g and has a density of  1.1 g/cm³, then the density of liquid B is 0.8 g/cm³.

To find the density of liquid B, you can follow these steps:
1. Calculate the mass of liquid A using its density and volume:
Liquid A has a density of 1.2 g/cm³ and a volume of 150 cm³.

Mass of A = Density of A × Volume of A = 1.2 g/cm³ × 150 cm³ = 180 g

2. Calculate the mass of liquid B using the mass of liquid C and mass of liquid A:
Liquid C has a mass of 220 g.
Mass of B = Mass of C - Mass of A = 220 g - 180 g = 40 g

3. Calculate the volume of liquid C using its mass and density:
Liquid C has a density of 1.1 g/cm³.
Volume of C = Mass of C ÷ Density of C = 220 g ÷ 1.1 g/cm³ = 200 cm³

4. Calculate the volume of liquid B using the volume of liquid C and the volume of liquid A:
Volume of B = Volume of C - Volume of A = 200 cm³ - 150 cm³ = 50 cm³

5. Calculate the density of liquid B using it's mass and volume:
Density of B = Mass of B ÷ Volume of B = 40 g ÷ 50 cm³ = 0.8 g/cm³

So, the density of liquid B is 0.8 g/cm³.

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Answer: 2,2

Step-by-step explanation:  if you have the 2,-2 then that would be your answer because the reflection is the same as the 2,-2 but on a different thing

The probability of a bulb lasting for at most 624 hours is 0.9861, rounded to four decimal places.

The standard deviation of the lifetime is a measure of how spread out the lifetimes are. In other words, it tells us how much the lifetimes of bulbs vary from the mean. In this case, the standard deviation of the lifetime is 20 hours.

Now, let's get to the question at hand. We want to find the probability of a bulb lasting for at most 624 hours. To do this, we need to use the properties of the normal distribution.

First, we need to calculate the z-score, which tells us how many standard deviations a value is from the mean. We can use the formula z = (x - mu) / sigma, where x is the value we are interested in, mu is the mean, and sigma is the standard deviation. In this case, x = 624, mu = 580, and sigma = 20.

Plugging these values into the formula, we get z = (624 - 580) / 20 = 2.2.

Next, we need to find the probability of a bulb lasting for at most 624 hours, which is the same as finding the area under the normal curve to the left of z = 2.2. We can use a standard normal distribution table or a calculator to find this probability.

Using a calculator, we can use the normal cdf function with the values -9999 (a very large negative number) and 2.2 to find the probability. This gives us a probability of 0.9861.

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630 calories of total calory intake of Mrs. Ramirez should be from proteins.

From the circle graph we can see that,

percentage of calories from fruits is = 15%

percentage of calories from grains is = 15%

percentage of calories from vegetables is = 25%

percentage of calories from proteins is = 35%

percentage of calories from Dairy is = 10%

Here it is also given that Mrs. Ramirez need to eat 1800 calories.

So the calories should be from proteins

= 35% of 1800 calories

= (35/100)*1800 calories

= 35*18 calories

= 630 calories.

Hence, 630 calories should be from proteins.

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The question is incomplete. The complete question will be -

Applying the inscribed angle theorem, the measure of the size of angle ∅ = 85 degrees.

If an inscribed angle in a circle is subtended by an arc, the inscribed angle theorem states that the measure of the intercepted arc would be twice the measure of the inscribed angle.

Therefore, we have:

measure of arc DF = 2(31) = 62 degrees [inscribed angle theorem]

measure of arc BD = 2(54) = 108 degrees.[inscribed angle theorem]

∅ = 1/2(measure of arc BDF) [inscribed angle theorem]

∅ = 1/2(m(DF) + m(BD))

Substitute:

∅ = 1/2(62 + 108)

∅ = 1/2(170)

∅ = 85 degrees.

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Answer:

let x be the no.

So, 5 less than the square of a number in an algebraic expression is:

x^2 - 5

In this scenario, the dependent variable is "how many jumps I can do," while the independent variable is "how long I am jumping (2 minutes)."

The relationship between these variables can be described as follows: The number of jumps completed depends on the duration of time spent jumping, with a specific focus on a 2-minute interval.

When we say the dependent variable is "how many jumps I can do," it means that the number of jumps completed is determined by or depends on the independent variable, which is the duration of time spent jumping.

This suggests that as the duration of time increases or decreases, it will likely have an impact on the number of jumps performed.

In this particular case, you have specified a 2-minute interval as the focus. It suggests that you are examining the relationship between the number of jumps completed and the specific duration of 2 minutes.

This implies that you are interested in understanding how the number of jumps varies within this fixed time frame.

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The percentage of the games that Natasha scores between 93 and 142 is given as follows:

96.9%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 115, \sigma = 11[/tex]

The proportion of games with scores between 93 and 142 is the p-value of Z when X = 142 subtracted by the p-value of Z when X = 93, hence:

Z = (142 - 115)/11

Z = 2.45

Z = 2.45 has a p-value of 0.992.

Z = (93 - 115)/11

Z = -2

Z = -2 has a p-value of 0.023.

0.992 - 0.023 = 0.969, hence the percentage is of 96.9%.

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The measure of the exterior angle of the triangle is 128°.

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Trigonometric functions are the functions that denote the relationship between angle and sides of a right-angled triangle.

Sin θ = Opposite Side/Hypotenuse

Cos θ = Adjacent Side/Hypotenuse

Tan θ = Opposite Side/Adjacent

Recall that the measure of the exterior angle of a triangle is the sum of the opposite interior angles. That is:

x = 38 + 90

x = 128°

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A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.

The probability that the first customer's VCR is not defective is 23/25, as there are 23 working VCRs out of the total 25.

Since one VCR has already been sold, there are 24 VCRs left and 1 defective VCR. Thus, the probability that the second customer gets a defective VCR is 1/24.

To find the probability that both events occur, we multiply the individual probabilities:

P = (23/25) x (1/24)

P = 0.077 or 0.0778 when rounded to the nearest thousandth.

Therefore, A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.

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1) If Amy deposits $2,300 in an account that pays 8.5% interest, after 4 years, the future value will be $3,187.48.

2) If Andres deposits $10,000 in an account that pays 8% interest, after 4 years, the future value will be A. $13,604.89.

3) If Kara deposits $500 in an account that pays 5% interest, after 2 years, the future value will be C. $551.25.

The future values represent the present investment compounded at an interest rate.

The future values can be determined using an online finance calculator as follows:

1) N (# of periods) = 4 years

I/Y (Interest per year) = =8.5%

PV (Present Value) = $2,300

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $3,187.48

Total Interest = $887.48

2) N (# of periods) = 4 years

I/Y (Interest per year) = =8%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $13,604.89

Total Interest = $3,604.89

3) N (# of periods) = 2 years

I/Y (Interest per year) = 5%

PV (Present Value) = $500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $551.25

Total Interest = $51.25

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Answer:

B

Step-by-step explanation:

1 1/2 x 1/3

=1/2

So therefore the answer is B (1/2 cup)

Answer:

The answer is B ( 1/2 cup)

The interest accrued after one month at a rate of 15.5% on a principal amount of $1,000 is $12.92.

To use the formula I=Prt to calculate the interest accrued after one month at a rate of 15.5%, we need to know the principal amount (P) and the time period (t) in years.

Assuming that the principal amount is $1,000, and the time period is one month, which is equivalent to 1/12 of a year, we can calculate the interest as follows:

[tex]I = Prt[/tex]

[tex]I[/tex] [tex]= 1000 x 0.155 x (1/12)[/tex]

[tex]I = $12.92[/tex]

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After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.

To compute the first 10 iterations of Newton's method for the given function and initial approximation, follow these steps:

1. Write down the function and its derivative:

[tex]f(x) = 4 * tan(x) - 6 * x  

f'(x) = 4 * sec^2(x) - 6[/tex]
2. Define the initial approximation, X₀ = 1.4.

3. Apply Newton's method formula to find the next approximation, X₁:
  X₁ = X₀ - f(X₀) / f'(X₀)

4. Repeat steps 3-4 for a total of 10 iterations (X₁ to X₁₀).

Note that I'm unable to perform calculations on this platform, but I'll provide a general outline for performing the iterations:

Iteration 1 (X₁):
[tex]X₁ = 1.4 - (4 * tan(1.4) - 6 * 1.4) / (4 * sec^2(1.4) - 6)[/tex]

Iteration 2 (X₂):
[tex]X₂ = X₁ - (4 * tan(X₁) - 6 * X₁) / (4 * sec^2(X₁) - 6)[/tex]

Repeat these steps up to the 10th iteration (X₁₀).

After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.

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a) To find y for the given x and Δx values, first calculate x + Δx:
x + Δx = 3 + 0.03 = 3.03

Now, use the function y = f(x) = 9x to find the y values:
y = 9(3) = 27 (for x = 3)
y = 9(3.03) = 27.27 (for x = 3.03)

b) To find dy, we first need to find the derivative of the function (f'(x)). The function is y = f(x) = 9x, and its derivative (using differentiation) is:
f'(x) = 9

c) To find dy for the given x and Δx values, we can now use the formula dy = f'(x)dx:
dy = f'(x)dx = 9(0.03) = 0.27

So, for the given x and Δx values, a) y is 27 and 27.27, b) dy is equal to 9, and c) dy for the given x and Δx values is 0.27.

Using the straight-line method, we can find the depreciation expense per year by dividing the depreciable value (cost - residual value) by the estimated life:

Depreciable Value = Cost - Residual Value

Depreciable Value = $40000 - $10000

Depreciable Value = $30000

Annual Depreciation Expense = Depreciable Value / Estimated Life

Annual Depreciation Expense = $30000 / 6

Annual Depreciation Expense = $5000

To create a depreciation schedule, we can subtract the annual depreciation expense from the cost each year until we reach the residual value:

| Year | Cost |   Depreciation | Accumulated Depreciation | Book Value |

|------|---------------|-----------------  |----------------------------------------|------------|

| 1     | $40000  | $5000                | $5000                             | $35000     |

| 2    | $35000  | $5000                 | $10000                           | $30000     |

| 3    | $30000  | $5000                  | $15000                           | $25000     |

| 4    | $25000  | $5000                  | $20000                          | $20000     |

| 5    | $20000  | $5000                  | $25000                         | $15000     |

| 6    | $15000  | $5000                    | $30000                        | $10000     |

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Answer:

k=0.3

Step-by-step explanation:

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get  2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get  16 = 2x Dividing both sides by 2, we get x=8

The volume of the given shape is 125 unit³ if the length is 5 unit, breadth is 5 unit, and height is 5 unit.

A cube is a three-dimensional geometric shape that has six identical square faces, where each face meets at a right angle with the adjacent faces. It is a regular polyhedron, meaning that all of its faces are congruent (identical) and its edges are of equal length.

Volume of cube = length × breadth × height

length = 5 unit

breadth = 5 unit

height = 5 unit

Volume = 5 × 5 × 5

= 125 unit³

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