1. Trim is needed around the perimeter of the entire window. Calculate the perimeter of the window.​

Answer:

y = 7x - 27

Step-by-step explanation:

assuming you require the equation of the line

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 7 , then

y = 7x + c ← is the partial equation

to find c substitute (5, 8 ) into the partial equation

8 = 35 + c ⇒ c = 8 - 35 = - 27

y = 7x - 27 ← equation of line

Answer:

60°

Step-by-step explanation:

There is a supplementary angle, so we know that 180°-100° would give 80°.

A triangles angles add up to 180, so 80+40=120

180-120=60°

Answer:

60 degrees

Step-by-step explanation:

Hi there!

Angle NAB and angle CAB are supplementary angles, meaning they add up to 180 degrees. First, solve for angle CAB:

180 - 100 = 80

Therefore, angle CAB measures 80 degrees.

The sum of the interior angles of a triangle is always 180 degrees. Now, we can solve for angle B by subtracting 80 and 40 from 180:

180 - 80 - 40 = 60

Therefore, angle B measures 60 degrees.

Another way we can solve this is by viewing the 100-degree angle as an exterior angle of a triangle. The two opposite interior angles always add up to an exterior angle of a triangle.

100 = 40 + 60

Therefore, angle B measures 60 degrees.

I hope this helps!

Answer:

A

Step-by-step explanation:

The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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From one of the trigonometric ratios, tan(x), it is possible to find that x is equal to 52.1°.

The main trigonometric ratios for a right triangle are presented below.

                \(sin(x)= \frac{opposite\; side}{hypotenuse} \\ \\ cos(x)= \frac{adjacent\; side}{hypotenuse} \\ \\tan(x)= \frac{sin(x)}{cos(x)} =\frac{opposite\; side}{hypotenuse}* \frac{adjacent\; side}{hypotenuse}=\frac{opposite\; side}{adjacent\; side}\)

For solving this question, you need to apply the a trigonometric ratio . You have the dimensions of two sides and you need to find the angle x.

Thus, you can apply the tan(x).

                       \(tan(x)= \frac{opposite\; side}{adjacent\; side}=\frac{36}{28} =\frac{9}{7}\)

After that, you should calculate the arctan(x).

                           \(arctan\left(\frac{9}{7}\right)=52.1^{\circ \:}\)

Then x= 52.1°

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Answer:

464m^2

Step-by-step explanation:

Given data

Dimension of the regular playground

Length= 28m

Width= 15 m

We want to extend both sides by 1 m

Length= 28+1= 29m

Width= 15+1= 16m

Hence the area

Area=Length*Width

Area= 29*16

Area= 464m^2

The Area is 464m^2

Because the lines drawn are straight.

Explanation:

When the straight lines join together, the original point from where the first line started, becomes a right angle (90°)

Answer:

3rd choice: sec(a) = 1.06

Step-by-step explanation:

sec(a) = (hypotenuse)/(adjacent leg)

The statement that is accurate for the right triangle shown below is C. sec(a) = 1.06

The accurate statement is the one that can help us arrive at the correct angle in the diagram. That is sec(a) = 1.06. The formula is given as follows:

(hypotenuse)/(adjacent)

In the question we have, the hypotenuse is 50 while the adjacent is 47. Note that the hypotenuse is the longest side of the triangle, and the adjacent is often represented by the base.

So, we have;

50/47 = 1.06

Thus to find the angle for alpha in the triangle shown, the right statement would be; sec(a) = 1.06.

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Answer: 4.5 pounds

Explanation: To convert 72 ounces into pounds, we use the conversion factor for ounces and pounds which is 16 ounces = 1 pound.

Next, notice that we're going from a smaller unit, ounces, to a larger unit, pounds and when we go from a smaller unit to a larger unit, we divide. So here, we divide 72 by the conversion factor, 16, to get 4.5.

So 72 ounces equals 4.5 pounds.

Answer:

it should be C. and A. because it is a straight line and not curved and it has a positive slope

Step-by-step explanation:

Mr. clean

The total surface area of the cylinder is 548.13 square meters.

The curved surface area of a cylinder can be calculated using the formula:

CSA = 2πrh

where CSA is the curved surface area, r is the radius, and h is the height or length of the cylinder.

We are given that the curved surface area of the cylinder is 408 m² and the length is 17 m.

We can use this information to solve for the radius:

CSA = 2πrh

408 = 2πr(17)

r = 408 / (2π × 17)

r ≈ 3.00 m (rounded to 2 decimal places)

Now that we know the radius, we can calculate the total surface area of the cylinder by adding the areas of the two bases and the curved surface area:

Total surface area = 2πr² + 2πrh

Total surface area = 2π(3.00)² + 2π(3.00)(17)

Total surface area ≈ 226.19 + 321.94

Total surface area ≈ 548.13

Therefore, the total surface area of the cylinder is approximately 548.13 square meters.

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Answer:

125 Dolphins

Step-by-step explanation:

The number of dolphins varied linearly with the number of fish.

The number of dolphins = D

The number of fish = F

Hence:

D ∝ F

D = kF

When 400 fish were present 250 dolphins appeared

Solving for k

250 = 400k...... Equation 1

Also

when 300 fish were present, 200 dolphins appeared.

200 = 300k...... Equation 2

So: we find k = Constant of Proportionality

250 = 400k...... Equation 1

200 = 300k...... Equation 2

We Subtract Equation 2 from Equation 1

50 = 100k

k = 50/100

k = 1/2

How many dolphins would appear if 250 fish were present?

D = kF

D = 1/2 × 250

D = 125 Dolphins

Let:

x = Speed of the jet

y = Speed of jetstream

so:

and

Solve the system using elimination method:

Replace x into (1)

Answer:

Rate of the jet in still air: 726 mph

Rate of the jetstream: 65mph

The internal rate of return on the investment for Burgundy Basins is 13.33%.

The internal rate of return on the investment for Burgundy Basins represents the percentage return expected from the investment, which is 13.33% in this case. It indicates the rate at which the investment's net present value is zero, meaning it is expected to generate returns equal to its cost. This makes the investment financially attractive as it offers a return higher than the company's cost of capital.

Burgundy Basins, a sink manufacturer, is considering an average-risk investment worth $36 million. The investment is projected to generate a perpetual annual return of $4.8 million. To evaluate the attractiveness of the investment, the internal rate of return (IRR) is calculated. The IRR represents the rate at which the net present value of the investment becomes zero.

In this case, the IRR is determined to be 13.33%, indicating that the investment offers a return higher than its cost. This implies that the investment is financially viable and can potentially enhance the company's profitability. However, it's important to note that other factors such as market conditions and potential risks should also be taken into consideration before making a final decision.

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\(\mathrm{\frac{\#\:of\:miles}{\#\:of\:hours}=\frac{5}{1\frac{1}{2}}}\)

First off, we have to convert 1 and half hours to minutes

1 hour = 60 mins

1 and a half is half of 1, which is 60 ÷ 2 = 30, then plus 1 hour, which is 60. So 60 + 30 = 90.

So we have:

\(\frac{5}{90}\)

Since we converted minutes to hours on one side of the equation, we have to do the same on the other side of the equation.

1 hour = 60 mins

6 hours would be 60 × 6 = 360 minutes

Now we can set up a variable, \(m\), as to how far it will take in miles.

\(\frac{5}{90}=\frac{m}{360}\)

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Nextly, we solve for \(m\)

\(\frac{5}{90}=\frac{m}{360}\)

Step 1: Multiply 10 to both sides

\(10\cdot[\frac{5}{90}]=[\frac{m}{360}]\cdot10\)

10 and 90. Cancel the zeros. We are left with 9, so \(\frac{5}{9}\)

360 and 10. Cancel the zeros. We are left with 36, so \(\frac{m}{36}\)

So we have \(\frac{5}{9}=\frac{m}{36}\)

Step 2: Multiply 36 to both sides

\(\frac{36m}{36}=\frac{5\cdot \:36}{9}\)

\(20\)

Therefore, Goerge could walk 20 miles in 6 hours.

Answer:

The pressure exerted by gas number 3 is 159 mmHg

Step-by-step explanation:

To answer this question, the law to Use is Dalton’s law of partial pressure

Dalton’s law of partial pressure states that for a mixture of gases which do not mix, the total pressure exerted by such gases is equal to the sum of the individual pressure.

Now for the three gases, the total pressure Pt is equal to P1 + P2 + P3

Now we have Pt = 950 mmHg, P1 = 335 mmHg and P2 = 456 mmHg

P3 = Pt-P1-P2

Plugging the values above, we have ; 950-335-456 = 159 mmHg

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m.

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m. This is because the conjunction "and" (∧) is used to connect two statements that must both be true in order for the overall statement to be true. In this case, both s (It is sunny today) and m (I will bring my umbrella) must be true in order for the statement to be true.

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(B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."


The logical operator ∧ (conjunction) connects two propositions and represents the idea of "and." Therefore, s∧m means "It is sunny today and I will bring my umbrella." This is the logical expression that represents the statement given in the question.


To summarize, the correct answer is (B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."
Main Answer: The correct logical expression is (B) s∧m.

In the given statement, "Despite the fact that it is sunny today, I will bring my umbrella," both propositions s (It is sunny today) and m (I will bring my umbrella) are true at the same time. The logical expression that represents this is s∧m, which means "s AND m" are both true.

The statement "Despite the fact that it is sunny today, I will bring my umbrella" is best represented by the logical expression (B) s∧m, as it shows that both s and m are true.

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Answer:

The information we have is:

The boat can hold 170 L of fuel

The boat uses 34L each hour.

With this information, we can find the total amount of time that the boat can be used.

If the boat is used x hours, then it needs:

x*34L of fuel.

And the maximum amount of fuel that the boat can use uis170 L

Then we can solve:

x*34L = 170L

Now we can divide both sides by 34L to isolate x.

x = 170L/34L = 5

This means that the boat can be used for 5 hours.

Answer:

390 square miles I think

The sampling soldiers until her margin of error for a 82% confidence interval is less than 0.004, soldiers should Haley sample is 12,724 soldiers.

The degree of inaccuracy in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced chance of relying on a survey's or poll's findings, meaning that there will be less trust in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

A confidence interval is a measure of how unpredictable a given statistic is. It is typically used in conjunction with the margin of error to indicate how confidently a statistician feels that the findings of an online survey or online poll are worthy of being considered representative of the total population.

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi (1-\pi)}{n} }\)

In which, z is the z-score that has a p-value of 1+∝/2.

The margin of error is of:

\(M=z\sqrt{\frac{\pi (1-\pi)}{n} }\)

Estimate of the proportion of 64%, hence π = 0.64.

94% confidence level

So , ∝ = 0.94 z is the value of Z that has a p-value of , so z = 1.88

Margin of error of less than 0.008 is wanted, hence, we have to find n when M = 0.008.

\(M=z\sqrt{\frac{\pi (1-\pi)}{n} }\\0.008 =1.88\sqrt{\frac{0.64(0.36)}{n} } \\0.008\sqrt{n} = 1.88\sqrt{0.64(0.36)} \\n = 12723.84\\\)

Therefore, Haley should sample 12,724 soldiers.

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The distance between the two skew lines that measure along the line Perpendicular to the two lines is \(\frac{13}{\sqrt{70}}\).

To find the distance between the skew lines and measure the distance along the line perpendicular to the two lines, it is necessary to find a vector n perpendicular to both lines. Then project rAC onto that vector.

Here's the step-by-step explanation:

Step 1 Finding vector AB and vector CD

Step 2 Finding the vector n perpendicular to both lines.

The vector that is perpendicular to both lines is the cross-product of the vectors AB and CD.

Step 3 Finding the projection of rAC onto the vector n.

Therefore, the distance between the two skew lines is \(\frac{13}{\sqrt{70}}\).

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Answer:

$72

Step-by-step explanation:

Just add it together

Answer:

Step-by-step explanation:

The terms x and y must be substituted to isolate one side of the equation.

First, you have to substitute by the y=5/6x+10.

\(\sf{-x+6\left(\dfrac{5}{6}x+10\right)=-12}\)

Solve.

\(\sf{4x+60=-12}\)

Subtract by 60 from both sides.

4x+60-60=-12-60

Solve.

4x=-72

Divide by 4 from both sides.

4x/4=-72/4

Solve.

Divide the numbers from left to right.

-72/4=-18

x=-18

Substitute: x=-18

\(\sf{y=\dfrac{5}{6}\left(-18\right)+10}\)

Solve.

y=5/6(-18)+10=-5

y=-5

I hope this helps you! Let me know if my answer is wrong or not.

Let's denote the cost of a large pizza as CC and the number of toppings as TT. From the given information, we have the following two scenarios:

A large pizza with 2 toppings costs $13.50.

This can be represented as the ordered pair (2,13.50)(2,13.50).

A large pizza with 5 toppings costs $17.75.

This can be represented as the ordered pair (5,17.75)(5,17.75).

To find the equation representing the situation, we need to determine the additional charge per topping. Let's denote this charge as AA

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

C+2A=13.50C+2A=13.50 (for the first scenario)

C+5A=17.75C+5A=17.75 (for the second scenario)

Solving this system of equations, we find that C=10C=10 and A=1.75A=1.75.

Therefore, the equation representing the situation is C+TA=10+1.75TC+TA=10+1.75T, where CC is the cost of the pizza and TT is the number of toppings.

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We conclude that there is no such limit N such that sN < 1.5.

(a)  The sequence is defined recursively by s₁ = 2 and sₙ₊₁ = 1 + sₙ. So, s₁ = 2,s₂ = 1 + s₁ = 1 + 2 = 3, ands₃ = 1 + s₂ = 1 + 3 = 4. Thus, s₁ > s₂ > s₃ , (b)  We claim that the sequence is bounded below. The basis step is that s₁ = 2 is greater than 1. We shall demonstrate that sₙ > 1 for all n by induction. Let n be a positive integer. Since sₙ > 1, we have sₙ₊₁ = 1 + sₙ > 1 + 1 = 2. Thus, by induction, the sequence is bounded below by 1 , (c)  Let n be a positive integer. To show that sₙ is a decreasing sequence, it suffices to show that sₙ > sₙ₊₁. Now, sₙ − sₙ₊₁ = sₙ − (1 + sₙ) = −1. Since −1 < 0, it follows that sₙ > sₙ₊₁. Thus, the sequence (sₙ) is a decreasing sequence , (d)  We know that s₁ = 2 and that sₙ₊₁ = 1 + sₙ for all n. Now, sₙ₊₂ = 1 + sₙ₊₁ = 1 + 1 + sₙ = sₙ + 2. Therefore, it follows that sₙ₊ₖ = sₙ + k for all n and k. Since sₙ is decreasing, we have sₙ ≥ 2 for all n. Now, suppose that (sₙ) converges to a limit L. Then L = L + 1, which is impossible. Therefore, the sequence (sₙ) does not converge, (e)  We want to find an N such that sN < 1.5. Since sₙ is decreasing and bounded below, it follows that (sₙ) converges to some real number L. Now, we claim that sₙ > 1.5 for all n. Suppose, to the contrary, that there exists a positive integer N such that sN < 1.5. Since sₙ is decreasing and converges to L, it follows that sₙ → L as n → ∞. But this is impossible, since sₙ > 1.5 for all n.

Therefore, we conclude that there is no such N such that sN < 1.5.

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Answer: To find the magnitude of a vector, we need to use the formula:

|v| = sqrt(v1^2 + v2^2)

where v1 and v2 are the components of the vector.

Let's first find the components of vector a. Using the given magnitude (15) and direction (80 degrees), we can use the following formulas to find its x and y components:

a1 = |a| * cos(theta) = 15 * cos(80) = 2.977

a2 = |a| * sin(theta) = 15 * sin(80) = 14.479

Therefore, vector a can be written as a = [2.977, 14.479].

Now, let's find the components of vector b. From the given expression, we can see that its x and y components are 12 and -16, respectively.

b = [12, -16]

To find the vector a-b, we need to subtract the corresponding components of the two vectors:

a-b = [2.977 - 12, 14.479 - (-16)] = [-9.023, 30.479]

Finally, we can find the magnitude of a-b using the formula:

|a-b| = sqrt((-9.023)^2 + (30.479)^2) = 31.75 (rounded to two decimal places)

Therefore, the magnitude of a-b is approximately 31.75.

Step-by-step explanation:

The magnitude of the vector a-b is the length of the vector resulting from subtracting vector b from vector a. To find this, we will use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, we will use it to find the magnitude of a-b.

The first step is to calculate the length of each side. For vector a, the magnitude is the length of the hypotenuse of a right triangle, so it is equal to the square root of (15^2 + 80^2). This gives us a magnitude of 85.02. For vector b, the magnitude is equal to the square root of (12^2 + (-16)^2). This gives us a magnitude of 20.
Now we can use the Pythagorean Theorem to find the magnitude of a-b. We know that the hypotenuse is the magnitude of a-b, and the lengths of the other two sides are the magnitudes of a and b, so we have 85.02^2 - 20^2 = (a-b)^2. Solving for a-b gives us a magnitude of 85.

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Answer:

A is correct

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