kieran is flying a kite. he gets tired, so he stakes the kite into the ground. the kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. how high is the kite

ANSWER

The correct answer is A

EXPLANATION

If the two functions are inverses , then

[tex]f(g(x)) = g(f(x)) = x[/tex]

Given

[tex]f(x) = 5x - 11[/tex]

and

[tex]g(x) = \frac{1}{5}x + 11[/tex]

[tex]f(g(x)) = f( \frac{1}{5} x + 11)[/tex]

This implies that,

[tex]f(g(x)) = 5(\frac{1}{5} x + 11) - 11[/tex]

Expand to get;

[tex]f(g(x)) =x + 55 - 11[/tex]

[tex]f(g(x)) =x +44[/tex]

Since

[tex]f(g(x)) \ne \: x[/tex]

The two functions are not inverses

The correct answer is A

Answer:

Correct choice is A.

Step-by-step explanation:

Given functions are [tex]f\left(x\right)=5x-11[/tex] and [tex]g\left(x\right)=\frac{1}{5}x+11[/tex].

Then [tex]f\left(g\left(x\right)\right)=f\left(\frac{1}{5}x+11\right)=5\left(\frac{1}{5}x+11\right)-11=x+55-11=x+44[/tex]

By definition of inverse we says that if f(x) and g(x) are inverse of each other then f(g(x)) must be equal to x.

But in above calculation we can see that f(g(x)) is not equal to x.

Hence correct choice is A.

The slope is 7/4 and the intercept is -10

Answer:

a.)The total 4-letters passwords when repetition of letters is allowed are 456976

b.)The total 4-letters passwords when repetition of letters is not allowed are 358800

Step-by-step explanation:

Some situations of probability involve multiple events. When one of the events affects others, they are called dependent events. For example, when objects are chosen from a list or group and are not returned, the first choice reduces the options for future choices.

There are two ways to sort or combine results from dependent events. Permutations are groupings in which the order of objects matters. Combinations are groupings in which content matters but order does not.

How many 4-letter passwords can be made using the letters A throught Z if...

a)Repetition of letters is allowed?

There are only 26 possible values for each letter of the password (The English Alphabet consists of 26 letters). The total 4-letters passwords when repetition of letters is allowed are [tex]26^{4} =456976[/tex]

b) Repetition of letters is not allowed?

If repetition of  letters is not allowed, we can only choose 4 letters out of 26. Using the permutation equation [tex]nP_{k} =\frac{n!}{(n-k)!}[/tex]

The total 4-letters passwords when repetition of letters is not allowed are [tex]26P_{4} =\frac{26!}{(26-4)!}=26.25.24.23=358800[/tex]

.

When repetition of letters is allowed, there are 456,976 possible 4-letter passwords that can be made using the letters A through Z. When repetition of letters is not allowed, there are 358,800 possible passwords that can be made.

a) When repetition of letters is allowed, we have 26 choices for each of the 4 positions in the password. Therefore, the number of 4-letter passwords that can be made is 26 * 26 * 26 * 26 = 456,976.

b) When repetition of letters is not allowed, the number of choices for the first position is 26. For the second position, there are 25 choices left, since we can't repeat the letter used in the first position. Similarly, for the third position, there are 24 choices, and for the fourth position, there are 23 choices. Therefore, the number of 4-letter passwords that can be made without repetition is 26 * 25 * 24 * 23 = 358,800.

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ANSWER

72km/h

EXPLANATION

The average speed of the car can be calculated using the formula:

Average Speed=total distance/ total time taken.

The car covers a distance of 108km in 1½ hours.

We substitute the values into the formula to obtain,

[tex]Average \: \: Speed= \frac{108}{1.5} [/tex]

[tex]Average \: \: Speed=72 {kmh}^{ - 1} [/tex]

Therefore the average speed of the journey is 72km/h

Answer:

242 mm²

Step-by-step explanation:

Given 2 similar figures with

ratio of sides = a : b, then

ratio of areas = a² : b² and

ratio of volumes = a³ : b³

Here the ratio of volumes = 27 : 1331, hence

ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11, thus

ratio of areas = 3² : 11² = 9 : 121

let x be the surface area of the larger figure then by proportion

[tex]\frac{18}{9}[/tex] = [tex]\frac{x}{121}[/tex] ( cross- multiply )

9x = 18 × 121 ( divide both sides by 9 )

x = [tex]\frac{18(121)}{9}[/tex] = 2 × 121 = 242

The surface area of the larger figure is 242 mm²

Answer: OC

Step-by-step explanation: exact answer is 64.6

To estimate how many shoppers received free earbuds, 19% of 340 is calculated. The closest equivalent fraction to 19% is 20%, which means dividing 340 by 5, resulting in 68 shoppers receiving free earbuds, making option C correct.

The question revolves around the application of percentage calculations to a real-world scenario, where 340 shoppers at an electronics store are given various specials. To estimate how many shoppers received a free set of earbuds, we must calculate 19% of 340 shoppers.

Using equivalent fraction to estimate, 19% is close to 20%, and 20% of 340 can be found by dividing 340 by 5 (because 20% is the same as 1/5th).:

Therefore, about 68 shoppers received a free set of earbuds. This makes option C the correct choice. To note, we have not used the given table and information in the question as they do not relate to the calculation required for the current problem.

For this case we have by definition, that the volume of a cone is given by "

[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]

Where:

h: It's the height

r: It is the cone radius

They tell us as data that the volume is 8 [tex]\pi[/tex]and the height is 6 cm, we must find an expression that allows to clear the radius, then:[tex]8 \pi = \frac {1} {3} \pi * r ^ 2 * 6[/tex]

Answer:

Option D

Step-by-step explanation:

Formula:

d×3.14=C

or

r×3.14×2=C

d=diameter

r=radius

Answer: Second option.

Step-by-step explanation:

By the Right Triangle Altitude Theorem, we know that the altitude "h" (Observe the figure attached) is:

[tex]h=\sqrt{9*3}\\h=3\sqrt{3}[/tex]

Then, since we know the value of the altitude, we can calculate the value of "y" with the Pythagorean Theorem:

[tex]a=\sqrt{b^2+c^2}[/tex]

Where "a" is the   hypotenuse and "b" and "c" are the legs of the right triangle.

We can identify that:

[tex]a=y\\b=9\\c=h=3\sqrt{3}[/tex]

Then, substituting values, you get that "y" is:

[tex]y=\sqrt{9^2+(3\sqrt{3})^2}=6\sqrt{3}[/tex]

Answer:

Step-by-step explanation:

Y=20. X=10. Y=5. X=2.5

X is half of Y so 20 is y

Answer:

20

Step-by-step explanation:

The area of the two smaller squares are shown as 25 and 144, add them together to get 25 + 144 = 169.

The area of the larger square is shown as 169, which is the same as the sum of the two smaller ones.

The answer is Yes.

yes the sum of the smaller squares is equal to the largest one. 25 + 144 = 169

The area of the largest squares is 169, so the area of the smaller squares is equal to the largest square.

Answer:

D:The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

hope this helps you

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Step-by-step explanation:

i just took the test on E2020 & got 100%

d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Number of tree purchased                            Total Cost ($)

                1                                                                 60

                2                                                                120

                3                                                                180

                4                                                                240

                5                                                                290

For the linear function rate of change is constant.

Now, between 2 and 3 trees rate of change is given by

[tex]=\frac{180-120}{3-2} \\\\=60\\[/tex]

Now, between 3 and 5 trees rate of change is given by

[tex]=\frac{200- 180}{5-3} \\\\=55[/tex]

This is clearly that the rate of change isn't constant. Therefore, the function is non-linear.

so,

d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Learn more about linear function here

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Answer:

A

Step-by-step explanation:

Solving for x:

-3x + 8 ≥ 14

-3x ≥ 6

x ≤ -2

Notice the sign gets reversed when you divide or multiply by a negative number.

The only option less than -2 is -3, A.

Here's a tip: on multiple choice questions, sometimes it's faster to try each answer instead of solving the equation.  This can save time on tests like the SAT or ACT.

Let's try it:

-3(-3) + 8 = 9 + 8 = 17

-3(-1) + 8 = 3 + 8 = 11

-3(0) + 8 = 0 + 8 = 8

-3(3) + 8 = -9 + 8 = -1

So you can see the answer is A.

Answer:

A. [tex]y-5=1.5(x-4)[/tex].

B. [tex]y=1.5x-1[/tex].

Step-by-step explanation:

The given line passes through (2,2) and (4,5).

The slope the given line can be found using the formula;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{5-2}{4-2}[/tex]

This gives [tex]m=\frac{3}{2}=1.5[/tex].

The slope-intercept form is [tex]y-y_1=m(x-x_1)[/tex].

We substitute the second point to get:

[tex]y-5=1.5(x-4)[/tex].

We expand to get:

[tex]y-5=1.5x-6[/tex].

[tex]y=1.5x-6+5[/tex].

[tex]y=1.5x-1[/tex].

Answer:

13

Step-by-step explanation:

(x + 3)^3/2 = 64

√(x + 3)^3 = 64

(x + 3)^3 = 64^2

(x + 3)^3 = (4^3)^2

(x + 3)^3 = (4^2)^3

Same exponent

So

x + 3 = 4^2

x + 3 = 16

x = 13

Answer:

The length of the largest table that can be brought in the house on a diagonal is [tex]9.5\ ft[/tex]

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

Find the length of the diagonal of the frame

[tex]d^{2} =3^{2} +8^{2} \\\\ d^{2}=90\\\\ d=\sqrt{90}\ ft\\\\ d=9.5\ ft[/tex]

Answer:

Step-by-step explanation:

Alright, lets get started.

The height of the door is 8 feet.

The width of the door is 3 feet.

The largest size of the table that can be brought in this house from this given door is diagonally from this door.

So, lets find the diagonal of this door.

If we apply Pythagorean theorem ,

[tex]c^2=a^2+b^2[/tex]

[tex]c^2=3^2+8^2[/tex]

[tex]c^2=9+64=73[/tex]

taking square root on both sides

[tex]c=\sqrt{73}=8.5[/tex]

So, the maximum length of the table would be 8.5 feet.  :  Answer

Hope it will help :)

[tex]63:21=3:1[/tex]

Hope this helps.

r3t40

Final Velocity = Initial Velocity + (Acceleration * time)

Final Velocity = ?

Initial Velocity = 3

Acceleration = 1.5

Time = 7

Plug in and solve

3+(1.5*7)

3+10.5

Velocity = 13.5m/s

Answer:

[tex]6050(1+\frac{0.031}{12})^{3}(1+\frac{0.206}{12})^{9}[/tex]

Step-by-step explanation:

p = $6050

The card offered an introductory APR of 3.1% for the first 3 months

r = 3.1% or 0.031

t = 3

n = 12

So, compound interest formula for this period is :

[tex]6050(1+\frac{0.031}{12})^{3}[/tex]

And a standard APR of 20.6% thereafter,

r = 20.6% or 0.206

t = 9

n = 12

So, compound interest formula for this period is :

[tex]6050(1+\frac{0.206}{12})^{9}[/tex]

Now as the p is common, we can re write the expressions as :

[tex]6050(1+\frac{0.031}{12})^{3}(1+\frac{0.206}{12})^{9}[/tex]

Answer:

The probability is 0.953

Step-by-step explanation:

We know that the mean [tex]\mu[/tex] is:

[tex]\mu=10:30\ p.m[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=0:15\ minutes[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

We seek to find

[tex]P(10:00\ p.m.<x<11:00\ p.m.)[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{10:00-10:30}{0:15}[/tex]

[tex]Z=\frac{-0:30}{0:15}[/tex]

[tex]Z=-2[/tex]

The score of Z =-2 means that 10:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%

and

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{11:00-10:30}{0:15}[/tex]

[tex]Z=\frac{0:30}{0:15}[/tex]

[tex]Z=2[/tex]

The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=100\%-2.35\%-2.35\%[/tex]

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=95.3\%[/tex]

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=0.953[/tex]

the probability is 0.4772, or 47.72%.

To find the probability that Flight 202's arrival time is between 10:00 p.m. and 11:00 p.m., we need to standardize the times and use the properties of the normal distribution. The mean arrival time is 10:30 p.m., and the standard deviation is 15 minutes.

First, convert the times to minutes past 10:00 p.m.: 10:30 p.m. is 30 minutes past, and 11:00 p.m. is 60 minutes past. Now, standardize these times using the formula for z-scores:

Using the z-table or a standard normal distribution calculator, we find the area under the curve to the left of z = 0 is 0.5, and to the left of z = 2 is approximately 0.9772. Therefore, the probability that the arrival time is between 10:00 PM and 11:00 PM is the difference of these probabilities:

P(10:00 PM < X < 11:00 PM) = P(Z < 2) - P(Z < 0) = 0.9772 - 0.5 = 0.4772

So, the probability is 0.4772, or 47.72%.

Answer: 100 cm = 1 m

Step-by-step explanation:

Like most metric measurements, 100 centimeters are equal to 1 meter.

No, if you were to have three right angles, the fourth angle would also have to be a right angle. As a result, it would make the shape either a square or a rectangle.

f(x) = x³ + 2x² + x

f(x) = x.(x² + 2x + 1)

f(x) = x.(x + 1)²

So, f(x) = 0 when x = 0 or when x = -1

But

f(x) = x.(x + 1)² = x.(x + 1).(x + 1)

So we have three roots, x = 0, x = -1 and x = -1, although two of them are equal.

So we have a multiple zero x = -1 with a multiplicity 2.

Alterativa A.

Answer:

A

Step-by-step explanation:

For this case we must divide the following expression:

[tex]\frac {\frac {14x ^ 2} {15}} {7x}[/tex]

And in this way we get the amount of money that each person will receive.

Then applying double C we have:

[tex]\frac {14x ^ 2} {15 * 7x} =\\\frac {14x ^ 2} {105x} =\\0.133x[/tex]

Thus, each person has 0.133x of money!

Answer:

0.133x

Answer:

x<3/-2

Step-by-step explanation:

4x>6x+3

4x-6x>3

-2x>3

x<3/-2

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ANSWER

The graph in option D.

EXPLANATION

The given function is:

[tex]y = 3 {x}^{2} - 12x + 10[/tex]

We complete the square to obtain:

[tex]y = 3( {x}^{2} - 4x) + 10[/tex]

[tex]y = 3( {x}^{2} - 4x + {( - 2)}^{2} ) + 10 - 3 {( - 2)}^{2}[/tex]

[tex]y = 3{( x- 2)}^{2}+ 10 - 12[/tex]

[tex]y = 3{( x- 2)}^{2} - 2[/tex]

The graph of this function opens upwards and has its vertex at (2,-2).

The y-intercept is 10.

From the options the graph that satisfies all these properties is D.

Answer: The area is  [tex]320m^2[/tex]

Step-by-step explanation:

The formula for calculate the area of a rectangle is:

[tex]A=lw[/tex]

Where "l" is lenght and "w" is the width.

We know the width and the perimeter, then we can solve for the lenght from the following formula, which is used to calculate the perimeter of a rectangle:

[tex]P=2l+2w[/tex]

Then:

[tex]72m=2l+2(16m)\\72m-32m=2l\\\l=\frac{40}{2}\\\\l=20m[/tex]

Substituting values into the formula [tex]A=lw[/tex], we get that the area of the rectangle is:

[tex]A=(16m)(20m)[/tex]

[tex]A=320m^2[/tex]

Answer:

The area of rectangle = 320 m²

Step-by-step explanation:

Points to remember

Area of rectangle = lb

l - length and b - width

It is given that, perimeter of rectangle is 72 m. And width of rectangle = 16 m

To find the value of length

Perimeter = 2(l + b)

72 = 2(l + 16)

36 = l + 16

l = 36 - 16 = 20

To find the area of rectangle

Area = lb

 = 20 * 16

 = 320 m²

Therefore area of rectangle = 320 m²

Answer:

It's the second one:

yes; 4+5=6

Step-by-step explanation:

The answer is B. I think. Hope that helps!