A plane is coming in for a landing on a runway that is 270m long as shown below. The planes angle of depression to the ends of the runway are 38 degrees and 44degreez respectively. Determine the height of the plane before it comes in for its landing.

If the paint gallon cost $12 and carton cost is $5 , then the amount saved per gallon buying the larger can is $8  .

We know that 1 gallon is = 4 quarts. So , a one-gallon can is equal to four one-quart cans.

To buy one gallon of paint, we need to buy 4 one-quart cans.

Each one-quart can costs $5, so 4 one-quart cans will cost:

⇒ 4 × $5 = $20 ,

Now, the cost of one gallon of paint if it is bought in one one-gallon can.

⇒ One one-gallon can costs $12.

So , if we buy the larger one-gallon can, we will save:

⇒ $20 - $12 = $8

Therefore, We will save $8 per gallon buying the larger can.

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Answer:

option D

Step-by-step explanation:

y-intercept=-8

point(0,-8)

m=4

Using point slope form:

y-y1=m(x-x1)

y-(-8)=4(x-0)

y+8=4x

y=4x-8

Answer:

The equation in point-slope form is: y - 5 = 4(x - 2).

The equation in standard form is: 4x - y + 3 = 0.

Answer:

Standard form

4x - y = 3

Step-by-step explanation:

Point slope form of a line equation is:
y - y1 = m(x - x1)

where
(x1, y1) is a point on the line and m is the slope

The standard form of a line equation is:
Ax + Bc = C
where
A, B, C are integers

Slope Point Form

Given
(x1, y1) = (2, 5)
m = 4

The slope-point equation is
y - y1 = m(x - x1)

which is

y - 5 = 4(x - 2)

Expanding the bracket on the right side:
y - 5 = 4x  - 8

Move constant -5 to the right to become +5
y = 4x - 8 + 5 = 4x - 3

Move 4x to left becoming -4x

y - 4x = -3

or

-4x + y = -3

same as

4x - y = 3

This is the standard form with A = -4, B = 1 and C = 13

Answer:

Im going to give them as ordered pairs, you can pick out the range (Y values): (-2,-4), (-1,-1), (2,8)

Step-by-step explanation:

All that needs to be done for this problem is one thing: substitute the given domain values for the "x" in the equation. Domain is just a fancy way of saying x coordinate. All f(x) is is "function of x." This can still be your Y coordinate, or your range. I hope this process helps!

Answer:

-10/3 \(\leq\) x \(\leq\) -13/6

Step-by-step explanation

-3 \(\leq\) 3x +7 \(\leq\) 1/2

-10 \(\leq \\\) 3x \(\leq\) -13/2

-10/3 \(\leq\) x \(\leq\) -13/6

The needed angle measurement's value is; <a = 125°, <b = 55°, <c = 125°, <e = 125°, <f = 55°, <h = 55° and <g = 125°.

An angle is a measure of a turn or a rotation. It is usually measured in degrees, radians, or gradians. An angle is formed by two rays that share a common endpoint, called the vertex. Angles can be measured in a variety of ways, including the degree of rotation between the two rays, the ratio of the lengths of the sides of the angle, or the angle between two lines. An angle can also be used to describe the orientation of an object relative to another object or point.

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(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

What is Quadrant?

(i) When sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=41.81°,138.18°

So it lies in Ist and IInd quadrant.

A suitable graph is not provided here.

(ii) when cosФ=-1/2

Ф=cos^(-1)(-1/2)

Ф=120°,240°

So it lies in IInd and IIIrd quadrant.

A suitable graph is A and D.

(iii) when cotФ=3/4

Ф=cot^(-1)(3/4)

Ф=53.13°,233,13°

So it lies in Ist and IIIrd quadrant.

A suitable graph is E.

(iv) when cosecФ=3/2 or sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=0.729°

So it lies in Ist quadrant.

A suitable graph is not provided here.

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

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Answer:

a , c , e

Step-by-step explanation:

just took it ;)

The statements about the clock are accurate are;

1.  Note that the face of a clock is divided into 12 equal parts and the Angle of each part is= 30°

If one hand points at 2 and the other points at 4, then it is divided into two parts that is 2 to 3 and 3 to 4.

The angle that will be formed then will be = 2 (30) = 60°

So therefore option one is correct

111. When a person place one hand at 5 and the other hand at 10, then it is divided into 5 parts.

The angle that is formed= 30(5) = 150°.

Therefore, the arc length =(37.68) = 15.7.

So therefore, Option three is correct.

V.  When the length of the minor arc ranges from 11 to 2, then this is divided is 3 parts.

So therefore, 3(30) = 90°  

The minor arc is said to ranges from 7 to 10 and it is represented by  3(30) = 90°  

So therefore option five is correct.

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Answer: 0.13 cents per minute.

Step-by-step explanation:

7.80 divided by 60(min per hour.)= .13 cents.

Answer:

C. 2,637 square inches

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

Use PEMDAS, in this case, start with multiplication: (2)(-7), don't forget there is a minus sign in front of the two which is important later, then move on to dividing (-9) by (-3). Then you are left with 20-(-14)+3, which is the same as 20+14+3, which equals 37.

Answer:

9 attendees

Step-by-step explanation:

1+4=5

46/5=9 R1 the slash is dividing it hope it help's

Answer:

9 attendees

Hope I helped

129 students had a private scholarship.

Out of the 843 students,

To calculate the total number of students with a private scholarship, we need to add the number of students who had a private scholarship (112) and the number of students who had both scholarships (17). This gives us a total of 129 students with a private scholarship. The rest of the students, who had either a government scholarship (80) or no scholarship (651), do not have a private scholarship.

209 students had only one of the two scholarships, so 209 - 129 = 80 students had a government scholarship.

So in total, 112 + 80 = 192 students had either a private or a government scholarship.

Therefore, 843 - 192 = 651 students did not have either a private or a government scholarship.

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Answer:

43

Step-by-step explanation:

A circle can be defined as a geometric shape consisting of all points in a plane that are equidistant from a given point, which is known as the center. The distance between the center of the circle and any point on the circle is referred to as the radius.

In order to find the center and radius of a circle, we need to have three points on the circle's circumference, and then we can use algebraic formulas to solve for the center and radius. Let's look at the given problem to find the center and radius of the circle that passes through the points (-1,5), (5,-3), and (6,4).

Center of the circle can be determined using the formula:

(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)

Let's plug in the values of the given points and simplify:

(x,y)=(−(−1)−5−6/3,−5+3+4/3)=(2,2/3)

Next, we need to find the radius of the circle. We can use the distance formula to find the distance between any of the three given points and the center of the circle:

Distance between (-1,5) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(2+1)2+(2/3−5)2=√10.111

Distance between (5,-3) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(5−2)2+(−3−2/3)2=√42.222

Distance between (6,4) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(6−2)2+(4−2/3)2=√33.361

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Answer:

1=137 2=43 3=137 4=43 5=137 6=43

Step-by-step explanation:

it should be c because the puthagorean theorem is c^2=a^2+b^2 so subtract b^2 to the other side to keep a by itself and then sqare root both sides to get ride of the square on the a

Answer:

15,539 gallons will remain after 192 days

Step-by-step explanation:

16,307 - 4x = y

Plug in 192 for x since that's how many days will have passed.

16,307 - 4(192) = y

4 x 192 = 768

Then, subtract 768 from 16,307 to see how many gallons will remain.

16,307 - 768 = 15,539

Answer:

15,539 gallons

Step-by-step explanation:

16,307 - 4x = y;

16,307 - 4(192) = y;

4 x 192 = 768;

16,307 - 768 = 15,539

Maximum 8A/144 people are allowed to entire the park.

The entire space taken up by the surface of the park is called area.

If the park is rectangular shaped, then the area is the product of length and breadth. If it is square shaped, area can be determined by the square of the side length.

Given, length of unused space = 12 foot

    breadth of unused space = 12 foot

Area of unused space = 12 x 12 = 144 square feet

Maximum 8 people is allowed for every 144 squares feet space

Let, area of the entire park is A square feet

Now maximum number of people allowed = (8 × A)/ 144

hence, 8A/144 people is allowed.

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The obtained answers for the given piecewise function are:

(a) The cost of a call that is under six minutes is 0.70 (m < 6)

(b) The cost of a 14-minute call is 2.62 (m > 6; m is an integer)

(c) The cost of a 9 1/2 minute call is 1.66 (m > 6; m is not an integer)

A piecewise function is given by different functions at different intervals.

It is given that,

phone company set the following rate schedule for an m-minute call from any of its pay phones.

C(m) = 0. 70 when m ≤ 6

        = 0.70 + 0.24(m - 6) when m > 6 and m is an integer

        = 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer

(a) The cost of a call that is under six minutes:

Since m < 6, the cost is C(m) = 0.76

Thus, the cost of a call that is under six minutes is 0.76

(b) The cost of a 14-minute call:

Since 14 > 6, the cost is C(m) = 0.70 + 0.24(m - 6) when m > 6 and m is an integer.

C(14) = 0.70 + 0.24(14 - 6)

        = 0.70 + 0.24(8)

        = 0.70 + 1.92

        = 2.62

Thus, the cost of a 14-minute call is 2.62.

(c) The cost of a 9 1/2 minute call:

9 1/2 = 19/2 = 9.5

Since 9.5 > 6, the cost is C(m) = 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer.

C(9.5) = 0.70 + 0.24([9.5 - 6] + 1)

          = 0.70 + 0.24([3.5] + 1)

Since we know that if [x] is a function then its domain is R and the range is Z(integer)

So, [3.5] = 3(is an integer)

Then,

C(9.5) = 0.70 + 0.24(3 + 1)

          = 0.70 + 0.96

          = 1.66

Therefore, the cost of a 9 1/2 minute call is 1.66.

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The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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To show that the location parameter of the minimum extreme value distribution is the mode of the distribution, we set the first derivative of the density function, f(t), equal to zero and solve for t. The resulting value of t is the mode of the distribution.

The minimum extreme value distribution is characterized by its density function, which is given by:

f(t) = (1/β) * exp((t-α)/β) * exp(-exp((t-α)/β))

where α is the location parameter and β is the scale parameter. The mode of a distribution represents the value at which the density function has the highest point.

To find the mode of the minimum extreme value distribution, we differentiate the density function with respect to t and set it equal to zero:

d/dt [f(t)] = (1/β) * exp((t-α)/β) * exp(-exp((t-α)/β)) * (1/β) * (1/β) * exp((t-α)/β)

Setting the above expression equal to zero, we can simplify it to:

exp((t-α)/β) * exp(-exp((t-α)/β)) = (1/β)^2

By taking the logarithm of both sides, we have:

(t-α)/β - exp((t-α)/β) = -2 * log(β)

This equation does not have a closed-form solution. Therefore, to find the mode, we typically use numerical methods such as iterative algorithms or optimization techniques.

In conclusion, the mode of the minimum extreme value distribution can be obtained by setting the first derivative of the density function equal to zero and solving the resulting equation. However, due to the lack of a closed-form solution, numerical methods are generally used to find the mode.

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Answer:

\( {k}^{2} + 2k + \frac{15}{2} = 0 \\ {k}^{2} + 2k + 1 = - \frac {15}{2} + 1 \\ {k + 1}^{2} = - \frac{13}{2} \\ k + 1 = - \sqrt{ \frac{13}{2} } \\ k = 1 + or - - \sqrt{ \frac{13}{2} } \)

Answer:

x = 80

Step-by-step explanation:

\(\frac{1}{7}\) (x - 3) - 2 = 9 ( add 2 to both sides )

\(\frac{1}{7}\) (x - 3) = 11 ( multiply both sides by 7 to clear the fraction )

x - 3 = 77 ( add 3 to both sides )

x = 80 ← is the only solution

Answer:

D. x= -74 and x = 80

Explanation:

\(\sf \rightarrow \dfrac{1}{7} |x-3| -2 = 9\)

\(\sf \rightarrow \dfrac{1}{7} |x-3| = 9 + 2\)

\(\sf \rightarrow \dfrac{1}{7} |x-3| = 11\)

\(\sf \rightarrow |x-3| = 11 \times 7\)

\(\sf \rightarrow |x-3| =77\)

\(\sf \rightarrow x-3= \pm 77\)

\(\sf \rightarrow x-3= 77 \quad or \quad x - 3 = -77\)

\(\sf \rightarrow x= 77+3 \quad or \quad x = -77+3\)

\(\sf \rightarrow x= 80 \quad or \quad x = -74\)

The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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It will take Vincent 24 number of days to build the cubby house by himself.

Let's assume that Vincent can build the cubby house alone in h days.

From the given information, we know that Nadia takes 12 days to build the cubby house, and when Nadia and Vincent work together, they can finish it in 8 days.

We can use the concept of "work done" to solve this problem. The amount of work done is inversely proportional to the number of days taken.

Nadia's work rate is 1/12 of the cubby house per day, while the combined work rate of Nadia and Vincent is 1/8 of the cubby house per day.

When Nadia and Vincent work together, their combined work rate is the sum of their individual work rates:

1/8 = 1/12 + 1/h

To solve for h, we can rearrange the equation:

1/h = 1/8 - 1/12

1/h = (3 - 2) / 24

1/h = 1/24

Taking the reciprocal of both sides, we find:

h = 24

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To find the equation of a line that passes through a point and is parallel to another line, we can use the formula $y - y_1 = m(x - x_1)$ where $m$ is the slope of the given line and $(x_1,y_1)$ is the point through which the new line passes. The slope of the new line will be equal to that of the given line.

For part (a), we can use this formula with $(x_1,y_1) = (3,-2)$ and $m = -\frac{3}{4}$ (the slope of the given line). Thus, we get $y + 2 = -\frac{3}{4}(x - 3)$ which simplifies to $y = -\frac{3}{4}x + \frac{5}{2}$.

For part (b), we can use a similar formula with $(x_1,y_1) = (3,-2)$ and $m = \frac{4}{3}$ (the negative reciprocal of the slope of the given line). Thus, we get $y + 2 = \frac{4}{3}(x - 3)$ which simplifies to $y = \frac{4}{3}x - \frac{14}{3}$.

Jenna invested $3500 at a 6% interest rate and $1500 at a 4.5% interest rate to obtain a total income of $277.50.

Let's assume Jenna invested x dollars at a 6% interest rate and (5000 - x) dollars at a 4.5% interest rate. The total income from the investments is $277.50.

To find the amounts invested at each rate, we can set up an equation based on the interest earned. The interest earned from the first part of the investment at 6% is (x * 0.06), and the interest earned from the second part at 4.5% is ((5000 - x) * 0.045). The sum of these two interests should be equal to the total income of $277.50.

Therefore, we have the equation:

0.06x + 0.045(5000 - x) = 277.50

Simplifying the equation, we get:

0.06x + 225 - 0.045x = 277.50

0.015x = 277.50 - 225

0.015x = 52.50

x = 52.50 / 0.015

x = 3500

Therefore, Jenna invested $3500 at a 6% interest rate and $1500 (5000 - 3500) at a 4.5% interest rate.

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