Find. The unit vector. Multiple choice

Step-by-step explanation:

Consider the LHS, after the 5th step, consider the RHS

[tex]2 \csc(2x) = \csc {}^{2} (x) \tan(x) [/tex]

[tex]2 \frac{1}{ \sin(2x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex]2 \times \frac{1}{2 \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex] \frac{1}{ \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex] \csc(x) \sec(x) = \csc {}^{2} (x) \tan(x) [/tex]

Consider the RHS

[tex] \csc(x) \sec(x) =( 1 + \cot {}^{2} (x) ( \tan(x)) [/tex]

[tex] \csc(x) \sec(x) = \tan(x) + \cot(x) [/tex]

[tex] \csc(x) \sec(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } [/tex]

[tex] \csc(x) \sec(x) = \frac{1}{ \sin(x) \cos(x) } [/tex]

[tex] \csc(x) \sec(x) = \csc(x) \sec(x) [/tex]

Answer:

So our unknown width is X and the unknown length is X + 3.  We know the perimeter is 2 times the length plus 2 times the width so let's set up that equation:

2 X + 2 (X+3) = 24

Now solve for X

2 X + 2 X + 6 = 24

4 X + 6 = 24

4 X = 18

X = 4.5 - this is the width

X + 3 = 4.5 + 3 = 7.5 - this is the length

Step-by-step explanation:

Answer:

x²-8x-84

Using quadratic Formular -b±√b²-4ac/2a

--8±/8²-4×1×-84 /2×1

8±/64+336/2

8±/400/2

8±20/2

8+20/2, 8-20/2

28/2, -12/2

14,-6

Answer:

Step-by-step explanation:

1.5 x 4.5 x 4.5 = 30.375

30.375  ÷ 3 = 10.125

10.125= volume of the triangle

3 x 4.5 x 4.5 = 60.75

60.75 = volume of rectangle

60.75 + 10.125 = 70.875

70.875 = total volume

Answer:

By multiplying both side with the inverse of the coefficient of x

Step-by-step explanation:

coefficient of x = -6/4

inverse of coeefficient =-4/6.

multiply both sides.

x = 12(-4/6) = -8

Step-by-step explanation:

we can easily count this, as the diagonal lines are squares truly in half. so, 2 such cut squares are in total 1 full square.

there is one central rectangle of 4×6 squares = 24.

then in the upper left corner there is a small 2×2 square = 4.

and then we have in the bottom left 2 and the bottom right also 2 small triangles (4 in total) with each having 1 full square and 2 half-squares (2 squares in total) as area.

so, 4×2 = 8 squares.

so, the whole area is

24 + 4 + 8 = 36

The percentage of the time will Oliver get a written warning when  he is more than 16 minutes late for his shift at work is 46.7%.

The density curve is a type or way of representation of numbered distribution data over a graph. Here, the outcomes are continues. The density curve can not be below the x-axis or horizontal line of the graph.

In a density curve,

Records show that Oliver is typically 10-30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.

Oliver will get a written warning if he is more than 16 minutes late for work. The time remain after the 16 minutes is,

t=30-16

t=14 min

Thus, the percentage of the time will Oliver get a written warning is,

p=(14/30)*100

p=46.7 %

Thus, the percentage of the time will Oliver get a written warning when  he is more than 16 minutes late for his shift at work is 46.7%.

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Answer:

46.7%

Step-by-step explanation:

Answer:

y = 4 * sec x - 1

Step-by-step explanation:

From looking at the graph we can safely determine it's either CSC x or SEC x.

It SEC x because at the origin of it is exactly the same. Now we determine whether it has a vertical/horizontal stretch/shrink and translation shift.

Seeing it is a vertical stretch by 4 and translation 1 down.

I am not sure how to explain it in the more correct way. I have graphed it just to confirm if it is similar to your graph.

Answer:

B

Step-by-step explanation:

Probability of apple :

Probability of banana :

Probability of lemon :

Probability of orange :

Probability of pear :

The correct probability distribution for the 50 pieces of fruit, in the order listed is shown in option B. 0.2  0.3  0.12  0.28  0.1

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Total pieces of fruits = 50 pieces

Number of apple pieces = 10

Probability of apple pieces from the whole pieces = 10/50 = 0.2

Number of banana pieces = 15

Probability of banana pieces from the whole pieces = 15/50 = 0.3

Number of lemon pieces = 6

Probability of lemon pieces from the whole pieces = 6/50 = 0.12

Number of orange pieces = 14

Probability of orange pieces from the whole pieces = 14/50 = 0.28

Number of pear pieces = 5

Probability of pear pieces from the whole pieces = 5/50 = 0.1

Hence the correct probability are B. Probability 0.2 0.3 0.12 0.28 0.1.

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The angle of elevation is = 70° and the distance the airplane travelled in the air is = 17,557ft

tan x° = opposite/adjacent

where opposite = 16,500 feet

adjacent = 6,000 ft

tan x° = 16,500 / 6,000

tan x° = 2.75

X = arctan ( 2.75)

X = 70°

C² = a² + b²

C² = 16,500² + 6,000²

C² = 272250000 + 36000000

C² = 308250000

C= √308250000

C= 17,557ft

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Answer:

y = -3x - 3

Step-by-step explanation:

The line intercepts the y-axis at -3, and moves down 3 on the y for moving to the right 1 along the x-axis

Answer:

the answer is 27

Step-by-step explanation:

because 45 divided by 5 equals 9

and 9 times 3 equals 27

Answer:

Its skewed right

Step-by-step explanation:

I did the quiz and that was the answer

The distribution of this graph is Uniform.

The correct option is A.

Based on the provided dot plot, where there are 4 dots above each value from 5 to 10, the distribution can be described as uniform.

Uniform distribution refers to a distribution where the data points are evenly spread out across the range without any noticeable skewness or clustering. In this case, since there are an equal number of dots above each value within the given range, the distribution is uniform.

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Answer:

9.

Step-by-step explanation:

1) the condition 'One x-intercept of y = x2 – 6x + c is 3' means, that x=3 and y=0;

2) it is possible to substitute the values x=3 and y=0 into the given equation and to calculate 'c':

0=9-18+c; ⇒ c=9.

Answer:

We need to find 74% of 84 (that's the amount that was sold// If you would have been asked for the amount left, it would be (100%-74%), but here it's easier since it's already given to us)

Now, let's write the percentage as a fraction

74/100 of 84

**Trick, for percentages, anytime you see a "of" replace it with a multiplication symbol

74/100 x 84

Now, it's just a simple multiplication

(74x84)/100

*You can use a calculator and find your answer

It would give you 62.16 and you will need to round it to a whole number, so 62 gallons

*If you can't use a calculator, simplify the fraction as much as you can and try to approximate

Step-by-step explanation:

~62

Answer:

12n + 16

Step-by-step explanation:

2 (6n + 8)

= (2*6n) + (2*8) [distributive property]

= 12n + 16

Hope it helps ⚜

Answer:

12n + 16

Step-by-step explanation:

Distributive Property

Distributing the terms

Answer:

618 391 .87

Step-by-step explanation:

5 years 6 months = 22 quarters

8% = .08      .08/4 = .02 interest per period

400 000 ( 1 + .02)^22 = 618 391.87

Answer:

x = 2

Answer is explained in image itself.

By concepts of trigonometry and of perpendicularity, the angles AKL and AKC from respective right triangles have measures of 90° and 32.3°, respectively.

As planes ABCD and BCLK are perpendicular to each other, the triangles AKL and AKC are right angled. The required angles can be found by using the following trigonometric relationships:

[tex]\angle AKL = 90^{\circ}[/tex] (As line segments AK and KL are perpendicular to each other)

[tex]\angle AKC = \tan^{-1} \left(\frac{AC}{KC} \right) = \tan^{-1} \left(\frac{\sqrt{2}\cdot a}{\sqrt{5} \cdot a} \right) = \tan^{-1} \sqrt{\frac{2}{5} }[/tex] (as line segments AC and KC are perpendicular to each other)

[tex]\angle AKC \approx 32.312^{\circ}[/tex]

By concepts of trigonometry and of perpendicularity, the angles AKL and AKC from respective right triangles have measures of 90° and 32.3°, respectively.

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Answer:

g(x) = 5|(x - 2) - 2| - 2

Step-by-step explanation:

To shift 5 units right :

⇒ f(x) = 5|(x - 2) - 2| - 7

⇒ Applied rule : a units right → f(x) = (x - a)

To shift 5 units up :

⇒ g(x) = 5|(x - 2) - 2| - 7 + 5

⇒ g(x) = 5|(x - 2) - 2| - 2

Answer:

[tex]g(x)=5|x-4|-2[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

Parent function:

[tex]f(x)=5|x-2|-7[/tex]

Translate 2 units right:

[tex]\begin{aligned}\implies f(x-2)& =5|x-2-2|-7\\ & =5|x-4|-7 \end{aligned}[/tex]

Then translate 5 units up:

[tex]\begin{aligned}\implies f(x-2)+5& =5|x-4|-7+5\\ & =5|x-4|-2 \end{aligned}[/tex]

Therefore:

[tex]\implies g(x)=5|x-4|-2[/tex]

Answer: A. No; the graph fails the vertical line test.

The vertical line test is a tool used to determine if we have a function. If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test. Consequently, this leads to the relation not being a function.

For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.

Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.

Applying the leg rule, the value of x in the right triangle is: 8.9 units.

The leg rule is given as:

hypotenuse/leg = leg/part

Given the following:

Plug in the values

16/x = x/5

x² = 16×5

x² = 80

x = √80

x = 8.9 units.

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The measure of the unknown angle in the full circle is calculated as: 310 degrees.

The angle measure of a full circle equals 360 degrees.

The full circle given is divided into two angles, of which 50 degrees is a measure of one of the angles.

The unknown angle = 360 - 50 = 310 degrees.

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Answer:

b = 40

Step-by-step explanation:

Solve system of equations.

1) w = y

2) c + b = 90

3) y + c = 180

Since we want to solve for b, second equation would be a good starting point.

c + b = 90

b = 90 - c

But what is c?

Let's make c the subject in 3rd equation.

y + c = 180

c = 180 - y

Insert c back in second equation.

b = 90 - c

b = 90 - (180 - y)

b = 90 - 180 + y

b = -90 + y

All we need now is y. Notice that in the first equation w equals y and w is 130°, which means y is also 130°. Substitute again.

b = -90 + y

b = -90 + w

b = -90 + 130

b = 40

---

This is how it looks like if you solve it in one go (same procedure as above but in one place).

c + b = 90

b = 90 - c

b = 90 - (180 - y)

b = -90 + y

b = -90 + w

b = -90 + 130

b = 40

Answer:

Bias compare results implement treatments

Step-by-step explanation:

Answer: 70

Step-by-step explanation:

By the corresponding angles theorem, [tex]4x-50=2x+30 \longrightarrow x=40[/tex]

This means that [tex]2x+30=110[/tex].

Now, if we notice the linear pair, this means that [tex]y=\boxed{70}[/tex]

Answer:

c=-9x^2-15x

Step-by-step explanation:

Answer:

c = 6.25

Step-by-step explanation:

For this to occur, the discriminant of the quadratic formula must = 0

b^2 - 4ac = 0

15^2 - 4(9)(c) = 0

36c = 225

c = 6.25