At an altitude Of 2000 feet, a skydiver measures the angle of depression from himself to the landing zone. The measure of that angle is 36ﾟ. How far is the skydiver from the landing zone? Round to the nearest foot. ​

Answer:

Step-by-step explanation:

well, domain is the input of a function

example

f(x) =2x+5

if the domain (x) = 2

so:

f(x) =2(2) +5

f(x) = 9

range is the output whish is :

f(x) = 9

Answer:

75%

Step-by-step explanation: i know the answer

...................................................                                              

Hello there!

This triangle is equilateral. Therefore, all the sides are equal.

We are given one of them. It is 12 units.

Therefore, all the other sides are 12 units long.

So a=12

Hope this helps you! :)

#HaveAnAmazingDay

\(GraceRosalia\)

Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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Answer:

\(x<-8\)

Step-by-step explanation:

So we have the inequality:

\(3x-1>4x+7\)

Add 1 to both sides. The left side cancels:

\(3x>4x+8\)

Subtract 4x from both sides. The right side cancels:

\(-x>8\)

Divide both sides by -1. Since we're dividing by a negative, we flip the sign:

\(x<-8\)

And we're done!

Our solution is all numbers less than -8.

Answer:

x = -8

Step-by-step explanation:

I will be the brainliest, its hard to explain on a document, i could make you avideo how to do these problems, im a math teacher.

Answer:

Step-by-step explanation:

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

horizontal shift- right four units

vertical shift- up 2 units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: Stretched

Answer:

  c. 33.0%

  d. 14.5%

Step-by-step explanation:

For answering questions about percentages in different categories or combinations of categories, it is convenient to find the totals of rows and columns in the table. These totals are shown in the attached.

__

Students who surf total 32+65 = 97. Of those, 32 also skateboard. The requested percentage is ...

  32/97 × 100% ≈ 33.0% . . . . surfers who also skateboard

__

The total number of students is 166. Of those, the number who neither surf nor skateboard is 24. That percentage is ...

  24/166 × 100% ≈ 14.5% . . . . students who don't surf or skateboard

_____

Additional comment

a. 97/166 ≈ 58.4% surf

b. 89/166 ≈ 53.6% do not skateboard

__

This sort of table is called a "two-way table." One set of categories is represented in rows, another set is represented in columns. This table is filled with frequencies. Such tables can also display relative frequencies by dividing the entire table by the total of totals in the lower right corner.

Answer:

3×7000:5×X

21000:5X

so X= 4200

So expenditure on food will be Rs4200

Answer:

y = 2x^2 + 4x +6

perimeter = length plus

breadth

8cm +7cm + 5cm

= 20

The magnitude of ab -> is 7.28 units and the direction is 111.8°.

To find the magnitude and direction of ab ->, we first need to find the components of the vector ab ->. The components can be found by subtracting the coordinates of a from the coordinates of b.

So, the x-component of ab -> is (-2) - (-4) = 2 and the y-component of ab -> is 13 - 6 = 7.

The magnitude of ab -> can be found using the Pythagorean theorem:

|ab ->| = sqrt((2)^2 + (7)^2) = 7.28 units (rounded to two decimal places).

The direction of ab -> can be found using trigonometry.

tan(theta) = (y-component of ab ->) / (x-component of ab ->) = 7/2

theta = arctan(7/2) = 111.8° (rounded to one decimal place)

Therefore, the magnitude of ab -> is 7.28 units and the direction is 111.8°.

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Answer:

m∠C = 102°

Step-by-step explanation:

This is a quadrilateral inscribed in a circle

The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

We know what m∠B

We have external angles outside the circle.

m∠CDA is opposite m∠B

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

m∠CDA is the sum of m∠CD and m∠DA

m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

m∠DAB is an exterior angle also, hence,

m∠DAB is the sum of m∠DA and m∠AB

m∠DAB = m∠DA + m∠AB

m∠DAB = 84° + 120°

m∠DAB = 204°

Finally we can solve for m∠C

m∠DAB is Opposite m∠C

So, m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

Answer:

Can't see the problem. Send a picture of it.

Answer:

C.

Step-by-step explanation:

-1/4(12x+8)<=-2x+11

Distribute:

-3x-2<=-2x+11

Add 2x on both sides:

-1x-2<=0+11

Additive identity property applied:

-1x-2<=11

Add 2 on both sides:

-1x+0<=13

Additive identity property applied:

-1x<=13

Divide both sides by -1:

x>=-13 (dividing or multiplying both sides of an inequality by a negative means we must flip inequality sign)

Answer x>=-13

So the solution set includes any number greater than or equal to -13. That means we have everything to right of -13 including -13.

Answer:

\( {2}^{2} + {3}^{2} - {4}^{2} \\ 4 + 9 - 16 \\ 13 - 16 \\ - 3\)

I hope it helped U

stay safe stay happy

Answer:

-3

Step-by-step explanation:

\( {2}^{2} + {3}^{2} - {4}^{2} \)

\( = 4 + {3}^{2} - {4}^{2} \)

\( = 4 + 9 - {4}^{2} \)

\( = 4 + 9 - 16\)

\( = - 3\)

Answer:

y = 2x - 4

Step-by-step explanation:

Can I ask which variable you are solving?

PS I will assume you need the formula y=mx+b

-2x + y = - 4

Here you would translate the m and x variables to the right side making them positive.

y = 2x - 4

Now the formula is in proper form

Hey :)

If you are solving for x, the answer is: x = y/2 + 2

-2x + y = -4

Subtract y from both sides

−2x = −4 − y

The equation is in standard form:

−2x = − y −4

Divide both sides by −2:

-2x/-2 = -y - 4/-2

Dividing by −2 undoes the multiplication by −2

x = -y -4/-2

Divide −4 −y by −2

x = y/2 + 2

However, if you are solving for y, the answer is: y = −4 + 2x

−2x + y = −4

Add 2x to both sides:

y = −4 + 2x

Hope this helps!

Answer:

39

Step-by-step explanation:

37 = 96 %

x  = 100%

\(x =\frac{37(100)}{96} =38.54= 39\)

\(\huge\boxed{39\ \text{students}}\)

Note: The numbers in this problem are a little weird and don't work out perfectly. I'll demonstrate at the end of this answer how something seems a little off in the problem, but we'll get as close as possible.

We know from the problem that 37 students are equal to 96% of the class.

Let's write this as an equation:

\(37=0.96x\)

Divide both sides of the equation by \(0.96\) to isolate \(x\).

\(38.54\approx x\)

We'll round this to \(39\) as the final answer.

It's important to note that you can't have partial students, only whole numbers.

If we do the math here, 37 out of 39 students is about 95%.
Also, 37 out of 38 is about 97%.

I'm not sure how the original writer of the question got 96%, but I suppose 39 is the best answer with what's been given.

Answer:

180

Step-by-step explanation:

Answer:

B 180

Step-by-step explanation:

180÷2=90

180÷3=60

180÷4=45

180÷6=30

180÷10=18

Answer:

1. a.) The x intercepts are 7 and negative 3.

b.) The y-intercept is -21

2. C

3. a.) 4

b.) 4 and 1

Step-by-step explanation:

1 a.)The x intercepts can be found by setting y to 0, and solving for x for each factor individually.

0=x-7

7=x

0=x+3

-3=x

b.)The y-intercept can be found by multiplying the factors and looking the stand-alone number at the end of the equation. This can also be solved mathematically by replacing the x's in the equation with 0.

\(y=(x-7)(x+3)\\y=x^2-7x+3x-21\\y=x^2-4x-21\\y=(0)^2-4(0)-21\\y=-21\)

2.) Based on the graph we can see the line intercepts the x-axis at -1 and 3. So if we were to put this into factored form, the numbers would be opposite when paired with x. Hence

(x-3)(x+1)

3 a.)  Again, this can be found by observing the number by itself at the end of the equation or mathematically by changing x to 0

\(y=(0)^2-5(0)+4\\y=4\)

b.) As stated previously, this can be found by setting the y to 0 and solving the factors.

\(0=(x-4)(x-1)\\0=(x-4)\\4=x\\0=x-1\\1=x\)

Answer:

True

Step-by-step explanation:

We know that \(tan\theta=\frac{sin\theta}{cos\theta}\), \(sin\theta<0\) in Quadrant III, and \(cos\theta<0\) in Quadrant III. Thus, x is indeed negative since \(cos\theta<0\).

Answer:

Step-by-step explanation:

The ratio for Purple People Eater can be expressed in fraction form as

✔ 3/5

.

The ratio for Purple Majesty can be expressed in fraction form as

✔ 4/7

.

To compare these fractions, rewrite them with a common denominator of

✔ 35

.

The ratio of red paint to blue paint in Purple People Eater is

✔ greater than

the ratio in Purple Majesty.

Answer:

x = 42

Step-by-step explanation:

166 + 93 + 127 + 112=498

 5-2=3

180 x 3=540

540-498=42

Answer:

The probability that a person has not been vaccinated is 37%.

\(1 - {.37}^{3} = .949347 = 94.9347\%\)

Answer:

Exterior angle = 20 degrees

Interior angle = 160 degrees

================================================

Explanation:

The phrasing "Each exterior angle measure is one eighth the measure of each interior angle" means,

exterior = (1/8)*(interior)

That rearranges to

interior = 8*(exterior)

Let's say x is the measure of the unknown exterior angle. That makes 8x the measure of the interior angle

The two must add to 180 to form a straight line.

interior + exterior = 180

8x + x = 180

9x = 180

x = 180/9

x = 20 is the measure of the exterior angle

8x = 8*20 = 160 is the measure of the interior angle

Note how 160+20 = 180 to verify our answers.

The option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is B) x1 = 5, x2 = 5.25, Z = 56.5

To determine the correct answer, we can substitute each option into the objective function and check if the constraints are satisfied. Let's evaluate each option:

A) x1 = 5, x2 = 4.63, Z = 52.78

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(4.63) = 85 + 37.04 = 122.04 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(4.63) = 15 + 18.52 = 33.52 ≤ 36 (constraint satisfied)

B) x1 = 5, x2 = 5.25, Z = 56.5

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5.25) = 85 + 42 = 127 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5.25) = 15 + 21 = 36 ≤ 36 (constraint satisfied)

C) x1 = 5, x2 = 5, Z = 55

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5) = 85 + 40 = 125 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5) = 15 + 20 = 35 ≤ 36 (constraint satisfied)

D) x1 = 4, x2 = 6, Z = 56

Checking the constraints:

17x1 + 8x2 = 17(4) + 8(6) = 68 + 48 = 116 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(4) + 4(6) = 12 + 24 = 36 ≤ 36 (constraint satisfied)

From the calculations above, we see that options B), C), and D) satisfy all the constraints. However, option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is: B) x1 = 5, x2 = 5.25, Z = 56.5.

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The appropriate test to use for constructing a confidence interval for the mean household income in the state is the t-test.

The t-test is the appropriate test to use when constructing a confidence interval for the mean household income because the population standard deviation is typically unknown in such cases. The t-test allows for estimating the population standard deviation using the sample standard deviation, making it suitable for situations where the population standard deviation is not known.

To construct a confidence interval, the researcher would typically collect a random sample of household incomes from the state. The sample mean and sample standard deviation are calculated from the data. The t-test uses these sample statistics, along with the desired confidence level and the sample size, to determine the margin of error for the confidence interval.

The margin of error is then added and subtracted from the sample mean to establish the lower and upper bounds of the confidence interval. The t-distribution is used instead of the normal distribution because it accounts for the additional uncertainty introduced by estimating the population standard deviation from the sample.

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The value of x and y from the given figure are 106 and 127 respectively.

For a circle geometry, the sum of the opposite angles of the quadrilateral is 180 degrees. Hence;

53 + y = 180

y = 180 - 53

y = 127 degrees

Also, the angle at the center is twice that at the circumference. Hence:

x = 2(53)

x = 106 degrees

Hence the value of x and y from the given figure are 106 and 127 respectively.

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