The diagram shows a swimming course set out on a lake. Angle BCA = 90°. B 80m 145m C A Not to scale C is due north of A. Calculate the bearing of B from A.
​

Answer:

3 seconds

proofi took the test

The object reaches its maximum height after 3 seconds.

The correct option is 3 seconds.

To find the time at which the object reaches its maximum height, we need to determine the vertex of the parabolic function[tex]h(t) = -16t^2 + 96t + 6[/tex] . The vertex form of a parabola is given by [tex]h(t) = a(t - h)^2 + k[/tex], where (h, k) represents the vertex.

In this case, a = -16, so the vertex is given by t = -b/2a. Plugging in the values, we get t = -96/(2 x (-16)) = 96/32 = 3 seconds.

Therefore, the object reaches its maximum height after 3 seconds.

Option B, 3 seconds, is the correct answer.

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The complete Question:

The function [tex]h(t) = -16t^2 + 96t + 6[/tex] represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.

After how many seconds does the object reach its maximum height?

A. 2 seconds

B. 3 seconds

C. 6 seconds

D. 9 seconds

The mean is  6394530.35 and the median is = 3355572.5

The missing data is attached in the answer.

Mean is the average value of the data points , it is determined by dividing the total sum of the data points to the number of data points.

Mean and Median is the measure of the central; tendency of the data.

Mean is given by

Sum of the observations/number of observations

= (741894 + 6931071....)/20

= 6394530.35

2) To find median

The data needs to be arranged in ascending order

Then the median is the middle number of the arranged data

Here the median is = 3355572.5

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Answer:

Step-by-step explanation:

1)   = f(x - a) + b

Coordinate change

(x, y) → (x + a, y + b)

2) RFy(x, y) = f(-x)

Coordinate change

(x, y) → (-x, y)

3) RFx(x, y) = -f(x)

Coordinate change

(x, y) → (-y, x)

4) RCCW90(x, y) = f⁻¹(-x)

Coordinate change

(x, y) → (-y, x)

5) RCCW180(x, y) = -(f(-x))

Coordinate change

(x, y) → (-x, -y)

6) A 270 degrees counterclockwise rotation gives;

RCCW270(x, y) = -(f⁻¹(x))

Coordinate change

(x, y) → (y, -x)

Step-by-step explanation:

1) Horizontal translation a units right = f(x - a)

The vertical translation b units up = f(x) + b

Therefore, we get;  = f(x - a) + b

The coordinate change

(x, y) → (x + a, y + b)

2) A reflection across the y-axis = RFy(x, y) = f(-x)

The coordinate change

(x, y) → (-x, y)

3) A reflection across the x-axis gives RFx(x, y) → (x, -y)

Therefore, in function notation, we get;

RFx(x, y) = -f(x)

4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)

In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)

5) A 180 degrees counterclockwise rotation about the origin gives;

(x, y) → (-x, -y)

Therefore, we get;

In function notation RotCCW180(x, y)  = -(f(-x))

6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)

In function notation RotCCW270(x, y) = -(f⁻¹(x))

Answer:

The answer will be 38° + 32° = 70°

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The total length of the wire needed to make this shape is 162cm

The perimeter of a triangle is the sum of the external side of the triangle.

Given the following parameters

Length of one side of the outside shape = 24cm

The side length of the smaller triangle = 24/4 = 6cm

The perimeter of the smallest triangle  3(6) = 18cm

The perimeter of the smaller triangle (at the middle) = 12(3) = 36cm

Total length of wire needed. = 3(24) + 3(18) + 36

Total length of wire needed = 72 + 54 + 36

Total length of wire needed = 162cm

Hence the total length of the wire needed to make this shape is 162cm

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Their speed in terms of square feet per minute is 3/10 square feet per minute.

We know that the speed formula is the rate at which an object travels a given distance. Speed is defined as the distance traveled by a body in a given amount of time. Speed in the SI is measured in m/s.

Given that the distance = 1/5 square feet.

The time = 2/3 minute.

Speed = distance/time = (1/5)/(2/3) = (1/5)*(3/2) = 3/10

Therefore, we can conclude that their speed in terms of square feet per minute is 3/10 square feet per minute.

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Answer: 19

Step-by-step explanation:

g(4) = 4² + 3

g(4) = 16 + 3

g(4) = 19

The set A satisfying the given inequality is A = (-[tex]\infty[/tex], -10].

Following are some facts which are true for an inequality relation:

[tex]\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)[/tex]

Since y ∈ B, -2 ≤ y ≤ 7. So,

[tex]\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\; y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.[/tex]

The set {-x | inequality (1) holds ∀ y ∈ B} is [10, [tex]\infty[/tex]) i.e.

10 ≤ -x ≤ [tex]\infty[/tex].

Multiplying -1 throughout gives

-10 ≥ x ≥ -[tex]\infty[/tex].

x, thus, lies in the range A = (-[tex]\mathbf{\infty}[/tex], -10}.

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Disclaimer: The question was incomplete. Please find the full content below.

Find the set A such that for x ∈ A

[tex]\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y[/tex]

∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.

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Answer:

134

Step-by-step explanation:

the "nth" term of a sequence means that you can plug in the term number to get the term value

so, if

  11n + 2 is the sequence

  11(12) + 2 is the 12th term

  132 + 2 is the 12th term

  134 is the 12th term

By plugging in the term "place" (1st, 2nd, 3rd, 4th, etc.) for the variable "n", we get a term value.

hope this helps!!

The 12th term of the sequence is 133

The nth term is given as:

Tn = 11n + 1

The 12th term is calculated as:

T(12) = 11(12) + 1

Evaluate

T(12) = 133

Hence, the 12th term of the sequence is 133

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Answer:

1, 17, 33, 49

Step-by-step explanation:

given the first term is 1 then the next 3 terms are

1 + d, 1 + 2d, 1 + 3d ( d is the common difference )

the sum of the first 4 terms is 100 , then

1 + 1 + d + 1 + 2d + 1 + 3d = 100 , that is

4 + 6d = 100 ( subtract 4 from both sides )

6d = 96 ( divide both sides by 6 )

d = 16

1 + d = 1 + 16 = 17

1 + 2d = 1 + 2(16) = 1 + 32 = 33

1 + 3d = 1 + 3(16) = 1 + 48 = 49

the first 4 terms are

1, 17, 33, 49

Answer:

see the file attached!!!!

The cost of renting a community center for x guest is given as y = 10x + 100

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the y intercept.

Let y represent the cost of renting a community center for x guest. Hence:

y = 10x + 100

The cost of renting a community center for x guest is given as y = 10x + 100

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Answer:

[tex]|{\sf XY}| = 10\; {\rm cm}[/tex].

Step-by-step explanation:

Refer to the diagram attached. The dashed segment attached to [tex]\!{\sf Z}[/tex] points to the north. Rotating this segment clockwise with point [tex]{\sf Z}\!\![/tex] as the fixed center of rotation would eventually align this segment with the one between point [tex]\!\!{\sf Z}[/tex] and point [tex]\!\!{\sf X}[/tex]. The bearing of point [tex]{\sf X}[/tex] from point [tex]{\sf Z}[/tex] is the size of the angle between these two line segments when measured in the clockwise direction.

Subtract the bearing of [tex]{\sf Y}[/tex] from [tex]{\sf Z}[/tex] from the bearing of [tex]{\sf X}[/tex] from [tex]{\sf Z}[/tex] to find the measure of the angle [tex]\angle {\sf YZX}[/tex]:

[tex]\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}[/tex].

Thus, triangle [tex]\triangle {\sf YZX}[/tex] is a right triangle ([tex]90^{\circ}[/tex]) with segment [tex]{\sf YX}[/tex] as the hypotenuse. It is given that [tex]|{\sf XZ}| = 6\; {\rm cm}[/tex] whereas [tex]|{\sf ZY}| = 6\; {\rm cm}[/tex]. Thus, by Pythagorean's Theorem:

[tex]\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}[/tex].

Answer:

x = 6

Step-by-step explanation:

.16x + 2 * .02 = (x + 2) * .17
.16x + .4 = .17x + .34
.06 = .01x
6 = x

Answer:

B

Step-by-step explanation:

using the addition identity for sine

sin(A + B) = sinAcosB + cosAsinB

using the sine and cosine ratios in the right triangle

sinABC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{4}{5}[/tex]

cosABC = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{3}{5}[/tex]

using the exact values

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex]

Then

sin(ABC + 60)

= sinABC cos60 + cosABC sin60

= ( [tex]\frac{4}{5}[/tex] × [tex]\frac{1}{2}[/tex] ) + ([tex]\frac{3}{5}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )

= [tex]\frac{4}{10}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]

= [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]

sin<ABc

cos<ABC

Now

Based on the given probability events, we can calculate that Events A and B are independent, because P(B) = P(B|A) = 1/2.

Events are independent if P(B) = P(B|A)

The probability of event B is:

= 3 odd numbers / 6 numbers

= 1 / 2

The probability of A is:

= 3 prime numers / 6

= 1/2

P(B|A) = ((1 / 2) x (1 / 2)) / (1 / 2)

= 1/2

So P(B) = P(B|A) = 1/2.

The events are independent.

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Answer:

No

Step-by-step explanation:

I will not do hard questions

Answer:

12

Step-by-step explanation:

Direct Variation. I think it's gonna be like this.

SInce Z is not inversely to y , its varies directly to both.

Then it's,

Z=kxy, where k is constant.

subst. Z=6,x=2 and y=6.

6=k×2×6

6=k×12=12k

6=12k=½

the formula connecting them is

Z=½xy

Z=½×3×8

Z= 1×3×8÷2

Z=24÷2

Z=12.

That's my solution.

Considering the direction of the wind, it is found that the ground speed needs to be of 510 knots.

The ground speed, considering that the wind is flowing from Wyoming to Colorado, and the same direction as the trip, is given by:

G = Plane speed + Wind speed.

In this problem, we have that the speeds are given as follows:

Hence the ground speed is given by:

G = 400 + 110 = 510 knots.

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Answer:

Good idea for thanks......

The amount of oil required for 1 liter of fuel is 111.11 mL.

Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.

Given that the fuel is the mixture where 8 parts are petrol and 1 part is oil in the whole part of the fuel.

The total part of the fuel is 8+1=9

the portion of the petrol is = parts of petrol/total parts of the fuel= 8/9

the portion of the oil = parts of oil /total parts of the fuel= 1/9

Now we have to calculate the amount of oil required for 1 liter of fuel.

As discussed before, 1/9 parts of the fuel is oil.

So the amount of oil is= (1/9)*1 liter= (1/9)litre= 1/9* 1000 mL= 111.11 mL

Similarly, we can calculate the amount of petrol which will be

the amount of petrol= (8/9)*1 liter= (8/9) liter= 8/9*1000 mL= 888.88 mL

Therefore the amount of oil required for 1 liter of fuel is 111.11 mL.

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Answer:

y = x/2 -3

Step-by-step explanation:

x - 2y = 6

Slope intercept form is y = mx+b  where m is the slope and b is the y intercept

We need to solve for y

Subtract x from each side

x-2y-x = -x+6

-2y = -x+6

Divide each side by -2

-2y/-2 = -x/-2 +6/-2

y = x/2 -3

The slope intercept form is

y = x/2 -3

Answer: slope intercept form is

y = x/2 -3

Step-by-step explanation:

hope this helps ; )

cos N = 14/20 = 0.70

For this question, I will be writing 'csc' instead of 'cosec'

[tex]\sin 30^{\circ}=\frac{1}{2} \implies \csc 30^{\circ}=2\\\\\sin 45^{\circ}=\frac{1}{\sqrt{2}}\\\\\cos 60^{\circ}=\frac{1}{2} \implies \sec 60^{\circ}=2\\\\\\\therefore \csc^{2} 30^{\circ}-\sin^{2} 45^{\circ}-\sec^{2} 60^{\circ}=2^{2}-\left(\frac{1}{\sqrt{2}} \right)^{2}-2^{2}=\boxed{-\frac{1}{2}}[/tex]

Answer:

Option (C)

Step-by-step explanation:

The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.

So, this means that adding 1 to this, the range matches with option C.

Answer:

b step by step explanation

The function that represents exponential growth is:

f(x) = x³

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

Exponential growth is a phenomenon that occurs when the rate of change of a quantity is proportional to its current value. In other words, as the value of the quantity increases, the rate at which it increases also increases. This can be represented mathematically using an exponential function of the form f(x) = abˣ, where a is the initial value, b is the growth factor, and x is the time or number of periods.

The function that represents exponential growth is:

f(x) = x³

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Answer:

sin C = cos A

Step-by-step explanation:

sinC = opp/hyp

=12/13

cosA = adj/hyp

12/13

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

Expression in scientific notation :

[tex]\qquad \tt \rightarrow \:3.45 × {10}^{-4} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 0.000345[/tex]

[tex]\qquad \tt \rightarrow \: 0.000345 \times \cfrac{10000}{10000} [/tex]

[tex]\qquad \tt \rightarrow \: (0.000345 \times 10000) \times \cfrac{1}{10000} [/tex]

[tex]\qquad \tt \rightarrow \: 3.45 \times \cfrac{1}{10 {}^{4} } [/tex]

[tex]\qquad \tt \rightarrow \: 3.45 \times{10 {}^{ - 4} } [/tex]

[tex] \textsf{Correct option - D} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

3.45 x 10-4

Step-by-step explanation:

Rationalizing the numerator, it is found the result of the limit is given as follows:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{1}{2\sqrt{x}}[/tex]

A limit is given by the value of function f(x) as x tends to a value.

The first step to find the limit is replace the variable by the value, hence:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{0}{0}[/tex]

Undefined limit, hence we have to find another way. The numerator includes square roots, hence it should be rationalized using the subtraction of perfect squares, as follows:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} \times \frac{(\sqrt{x + h} + \sqrt{x})}{(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{(\sqrt{x + h})^2 - (\sqrt{x})^2}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{x + h - x}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{h}{h(\sqrt{x + h} + \sqrt{x})}[/tex]

Then we simplify the h, so:

[tex]\lim_{h \rightarrow 0} \frac{1}{\sqrt{x + h} + \sqrt{x}} = \frac{1}{2\sqrt{x}}[/tex]

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Answer:

Tax 3.78 $ and tip 7.56 $

Step-by-step explanation:

42*0.09 = 3.78

42*0.18 = 7.56