A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree. Note that the two triangles are proportional to one another.

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[tex]\displaystyle\\\frac{5}{\sqrt{11}-\sqrt{3}}=?\\\\\\\text{We rationalize the denominator.}\\\\\frac{5}{\sqrt{11}-\sqrt{3}}=\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}=\frac{5(\sqrt{11}+\sqrt{3})}{(11-3)}=\boxed{\bf\frac{5\sqrt{11}+5\sqrt{3})}{8}}[/tex]

Answer:

The correct option is b) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]

Step-by-step explanation:

We need to find the quotient of [tex]\frac{5}{\sqrt{11}-\sqrt{3}}[/tex],

Rationalizing the above,

By multiply and divide by conjugate of its denominator,

[tex]\frac{5}{\sqrt{11}-\sqrt{3}} \times \frac{\sqrt{11}+\sqrt{3}}{\sqrt{11}+\sqrt{3}}[/tex]

[tex]\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}[/tex]

Since, [tex](a+b)(a-b)=a^{2}-b^{2}[/tex]

[tex]\frac{5\sqrt{11}+5\sqrt{3}}{(11-3)}[/tex]

simplify,

[tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]

Therefore, the correct option is b) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]

Answer:

1. 37

2. 25

Step-by-step explanation:

In order to find a percentile of a given number set, you must first put the values in ascending order:

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

70% = 0.7

Since there are 10 numbers in the set, we'll multiply 10 by 0.7

10 × 0.7 = 7

So we are going to look at the seventh number in the set.

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

1     2     3    4    5    6    7    8    9   10

The seventh number in the set is 37.

We're going to do the same for finding the 40th percentile:

40% = 0.4

10 × 0.4 = 4

Finding the fourth number in the set...

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

1     2     3    4    5    6    7    8    9   10

... We get 25

And those are you answers, 37 and 25.

Answer:

6ft for 30°

8.5ft for 45°

10.4ft for 60°

Step-by-step explanation:

12(sin 30°)=x

x=6

12(sin 45°)=x

x=8.5

12(sin 60°)=x

x=10.4

By using right angle trigonometry and the cosine function (x = L cos θ), we find that a 12-ft ladder reaches 10.4 ft, 8.5 ft and 6 ft up a wall when it is leaned at 30°, 45° and 60° respectively.

The problem described here involves the use of right angle trigonometry, specifically the use of the cosine function. In order to determine how high up the wall the ladder reaches at an angle of 30°, 45° and 60°, we can use the formula: x = L cos θ.

Firstly, let's calculate the height at 30 degrees (θ = 30°). We know that cos 30° = √3/2, so we substitute into the formula: x = 12ft * √3/2 which approximately equals 10.4 ft.

Next, for 45 degrees (θ = 45°), cos 45° = √2/2. Substituting into the formula: x = 12ft * √2/2 = 8.5 ft.

Finally, for 60 degrees (θ = 60°), cos 60° = 1/2. Therefore, x = 12ft * 1/2 = 6ft). So, the ladder reaches 10.4 ft up the wall when the angle is 30°, 8.5 ft when the angle is 45°, and 6 ft when the angle is 60°.

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Answer:

531,441·g^6·h^8

Step-by-step explanation:

The operative rule of exponents is ...

(a^b)^c = a^(b·c)

Working from the inside out, according to the order of operations, we get ...

= (9^3·g^3·h^4)^2

= 729^2·g^(3·2)·h^(4·2)

= 531,441·g^6·h^8

Answer:4(3y-5)

Yes. 4(3y-5) is the factored version

The domain is the input values, which are the X- values.

The domain would be -6, -1 , 0, 3

The first answer is the right one.

For this case, we have that by definition, the domain of a function is given by all the values of "x" for which the function is defined. The values of the domain are represented in the starting point.

Then, it is observed in the figure that the values of the domain are:

[tex]{x | x = -6, -1,0,3}[/tex]

ANswer:

Option A

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$950\\ r=rate\to 1.5\%\to \frac{1.5}{100}\dotfill &0.015\\ t=years\dotfill &6 \end{cases} \\\\\\ A=950e^{0.015\cdot 6}\implies A=950e^{0.09}\implies A\approx 1039.5\implies \stackrel{\textit{rounded up}}{A=1040}[/tex]

The answer would be 3/12 was used on the recipe. If 3/12 was used on the recipe and we know 2/12 was used to make a sandwich, 3/12 + 2/12 =5/12 used and that holds true being as there is 7/12 of the loaf left. 12/12 - 5/12 = 7/12

Hope I helped. Please mark me brainliest! :)

Answer:

Part 1) The commission is $35.6 and the total salary for week 1 is $285.6

Part 2) The commission is $45.04 and the total salary for week 2 is $295.04

Part 3) The commission is $39 and the total salary for week 3 is $289

Part 4) The commission is $32.96 and the total salary for week 4 is $282.96

Step-by-step explanation:

Let

x-----> the amount in sales

y----> Cindy Nelson’s salary

we know that

4%=4/100=0.04

so

The linear equation that represent this situation is

y=250+0.04x

case 1) week 1

Sales  $890

For x=890

substitute in the linear equation

y=250+0.04(890)

y=250+35.6=$285.6

therefore

The commission is $35.6

The total salary for week 1 is $285.6

case 2) week 2

Sales  $1,126

For x=1,126

substitute in the linear equation

y=250+0.04(1,126)

y=250+45.04=$295.04

therefore

The commission is $45.04

The total salary for week 1 is $295.04

case 3) week 3

Sales  $975

For x=975

substitute in the linear equation

y=250+0.04(975)

y=250+39=$289

therefore

The commission is $39

The total salary for week 1 is $289

case 4) week 4

Sales  $824

For x=824

substitute in the linear equation

y=250+0.04(824)

y=250+32.96=$282.96

therefore

The commission is $32.96

The total salary for week 1 is $282.96

Answer:

(a) 110 mm Hg

(b) 70 mm Hg

(c) 3/4 second

(d) see the attachment

Step-by-step explanation:

(a) The sine function has a maximum value of +1, so the maximum value of p is ...

pmax = 20·(+1) +90 = 20+90 = 110 . . . . . mm Hg

__

(b) The sine function has a minimum value of -1, so the minimum value of p is ...

pmin = 20·(-1) +90 = -20+90 = 70 . . . . . mm Hg

__

(c) The period of the sine function is 2π, so the value of t that makes the argument be 2π will be the period.

8π/3·t = 2π

t = 2π·3/(8π) = 3/4 . . . . . . multiply by the inverse of the coefficient of t

The period of her heartbeat cycle is 3/4 seconds.

__

(d) a graph is attached.

Answer:

X-intercept: (0,4)

Y-intercept: (-4,0)

Answer:

recursive: f(0) = 7; f(n) = f(n-1) -8

explicit: f(n) = 7 -8n

Step-by-step explanation:

The sequence is an arithmetic sequence with first term 7 and common difference -8. Since you're numbering the terms starting with n=0, the generic case will be ...

recursive: f(0) = first term; f(n) = f(n-1) + common difference

explicit: f(n) = first term + n·(common difference)

To get the answer above, fill in the first term and common difference values.

Answer:

The vertices are (3 , -5) , (-5 , -5)

The foci are (4 , -5) , (-6 , -5)

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1

- The length of the transverse axis is 2 a

- The coordinates of the vertices are  (h  ±  a  ,  k)

- The coordinates of the foci are (h ± c , k), where c² = a² + b²

- The distance between the foci is  2c

* Now lets solve the problem

- The equation of the hyperbola is (x + 1)²/16 - (y + 5)²/9 = 1

* From the equation

# a² = 16 ⇒ a = ± 4

# b² = 9 ⇒ b = ± 3

# h = -1

# k = -5

∵ The vertices are (h + a , k) , (h - a , k)

∴ The vertices are (-1 + 4 , -5) , (-1 - 4 , -5)

* The vertices are (3 , -5) , (-5 , -5)

∵ c² = a² + b²

∴ c² = 16 + 9 = 25

∴ c = ± 5

∵ The foci are (h ± c , k)

∴ The foci are (-1 + 5 , -5) , (-1 - 5 , -5)

* The foci are (4 , -5) , (-6 , -5)

Answer:

Vertices: (3,-5) (-5,-5)

Foci: (-6,-5) (4,-5)

Step-by-step explanation:

(x+1)^2/16-(y+5)^2/9 =1

formula: (x-h)^2/a^2 -(y-k)^2/b^2=1

in this case...

a^2=16      b^2=9

h=-1 k=-5

a=4           b=3

v=(h+/-a,k)

v1=(-1+4,-5)=

v1=(3,-5)

v2=(-1-4, -5) =

v2=(-5,-5)

Foci=(h+/-c,k)

F1=(h-c,k)

=(-1-5,-5)

f1=(-6,-5)

F2=(h+c,k)

=(-1+5, -5)

F2=(4,-5)

Hope this helps! :)

Answer:

44%

Step-by-step explanation:

If p represents the number of portions and q represents the quantity in each portion, then the original amount needed was p·q.

After p is increased by 20%, its number is ...

p + 0.20·p = 1.20·p

After q is increased by 20%, its amount is ...

q + 0.20 ·q = 1.20·q

Then the new amount the parents must buy is ...

(1.20p)(1.20q) = 1.20²·pq = 1.44pq

This amount is ...

(1 + 44/100)·pq = pq + 44%·pq

It is 44% more than the original planned purchase.

Answer:

44 percent

Step-by-step explanation:

Step-by-step explanation:

Did they define mechanical pencils using the variable m?

Answer:

Yes , i thinks so because have letter and the result is perfect and have two statement.

See the attached picture for the solution.

Answer:

a. 20.5

Step-by-step explanation:

because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x

therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a

Answer:

The correct answer option is a. 20.5 feet.

Step-by-step explanation:

We are given that the angle of elevation of the ladder is 70° and the height of the ladder is 25 feet from the ground.

We are to find the distance of the building from the base of the ladder.

For this, we will use tan:

[tex] tan 70 = \frac { 2 5 } { x } [/tex]

[tex] x = \frac { 2 5 } { tan 7 0 } [/tex]

x = 20.5 feet

Answer:

$162

Step-by-step explanation:

Discount = percentage discount ÷ 100 × original cost

Discount = [tex]\frac{40}{100}[/tex] × $405 = $162

Cash flow from operating activities is $43,000. Calculated by adjusting net income for changes in working capital items.

To calculate the cash flow from operating activities using the indirect method, we start with net income and adjust for changes in working capital.

Net Income = $50,000

Changes in Working Capital:

1. Accounts Receivable increased by $30,000, so we subtract $30,000.

2. Inventory decreased by $20,000, so we add $20,000.

3. Amounts Payable increased by $4,000, so we add $4,000.

4. Salaries Payable decreased by $1,000, so we subtract $1,000.

Now, let's calculate the cash flow from operating activities:

Cash flow from operating activities = Net Income + Changes in Working Capital

= $50,000 - $30,000 + $20,000 + $4,000 - $1,000

= $50,000 - $7,000

= $43,000

So, the amount of cash flow from continuing operating activities under the indirect method is $43,000.

Answer:

As we can see in the picture, we already knew 4 out of 6 sides of the figure so we need to find the other sides.

So the first missing side (the one near the 3 m one) should be:

7 - 4 = 3 (m)

The second missing side (the one near the 4m one) should be:

6 - 3 = 3 (m)

Now that we know all of the side lengths of the figure, the perimeter of the figure will be:

7 + 3 + 3 + 3 + 4 + 6 = 26 (m)

Answer:

1/10

Step-by-step explanation:

When Maggie gives a grape treat to her brother, there are 2 grape treats out of 5 total treats.

When Maggie selects another treat, there is 1 grape treat out of 4 treats left.

So the probability that both happen is:

2/5 × 1/4

1/10

Answer:

3m-3n

Step-by-step explanation:

We want to simplify the expression;

2m - [n - (m - 2n)].

We expand the parenthesis to obtain;

2m - (n - m + 2n)

2m - ( - m + 3n)

Expand further to get;

2m +m -3n

Combine the first two terms;

3m-3n

Final answer:

To find the total fraction of the lawn mowed by Melvin before his first break, one would add the additional 3/10 to the already mowed fraction represented by the shaded model.

Explanation:

The student's question is about calculating the fraction of the lawn that will be mowed by Melvin before he takes his first break. Initially, the question does not specify what fraction of the lawn is already mowed, but indicates that Melvin will mow an additional 3/10 of the lawn. Assuming that the shaded model represents the fraction already mowed (let's say x), the total fraction mowed before Melvin's first break would be x + 3/10. Without the specific value of the initially mowed fraction, we cannot provide the exact answer; however, generally, the operation would involve adding the given fraction to Melvin's progress before he mows the additional 3/10.

Answer:

See the attached photo for the calculations and answers

Step-by-step explanation:

The calculations and explanations are shown in the 3 attached photos below.

The answer to the given question will be a) P(flush) = 0.0019 b) P(one pair) = 0.4225 c) P( two pairs) = 0.475 d) P(three of a kind) = 0.211 e) P(four of a kind) = 0.00024

What is probability?

It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.

The probability of being dealt a flush:

For a suit there are 4 choices and 13C₅ choices for a card in that suit

Probability of flush = 4.( 13C₅)/52C₅

Probability of flush = 0.0019

The probability of being dealt one pair:

There are 13 possible values of a, 4C₂ choice for suit of a, 12C₃ value for b, c, d and 4 choices each for choosing the suit of b, c, d.

P(one pair) = (13.4C₂.12C₃.4.4.4)/52C₅

P(one pair) = 0.4225

The probability of being dealt two pairs:

There are 13C₂ possibility for the value of a and b, 4C₂ choices for suits of both a and b and 44 possibilities for c from the remaining cards.

P(2 pairs) = (13C₂.4C₂.4C₂.44)/(52C₅) = 0.475

The probability of being dealt three of a kind:

There are 13 possibilities for the value of a and 4C₃ choices for the suits of a, 12C₂ possibilities for both b and c and 4 choices of suits for both b and c.

P( three of a kind) = (13.4C₃.12C₂.4.4)/52C₅ = 0.211

The probability of being dealt four of a kind:

There are 13 possibilities of a and 4C₄ values for the suit of a and 48 choices of b from the remaining cards.

P(four of a kind) = (13.4C₄.48)/52C₅ = 0.00024

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Answer:

$84.70

Step-by-step explanation:

Using the formula, B = 70(1+0.1)^2 = 70*1.21 = 84.7.

Answer:

8(2p − q)(4p² + 2pq + q²)

Step-by-step explanation:

You would use the difference of cubes to factor this polynomial.

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

Answer:

7.1 miles

Step-by-step explanation:

Consider right triangle HospitalSchoolSupermarket. In this triangle:

The shortest road from the main entrance of the supermarket to the highway that connects the school and hospital will be the height drawn from the point Supermarket to the hypotenuse HospitalSchool.

Let the length of this road be x mi and the distance from School to point A be y mi. Use twice the Pythagorean theorem for right triangles Supermarket SchoolA and SupermarketHospitalA:

[tex]\left\{\begin{array}{l}x^2+y^2=8.82^2\\ \\x^2+(14.7-y)^2=11.76^2\end{array}\right.[/tex]

Subtract from the second equation the first one:

[tex]x^2+(14.7-y)^2-x^2-y^2=11.76^2-8.82^2\\ \\14.7^2-2\cdot 14.7y+y^2-y^2=11.76^2-8.82^2\\ \\-29.4y=11.76^2-8.82^2-14.7^2\\ \\29.4y=155.5848\\ \\y\approx5.24\ mi[/tex]

Thus,

[tex]x^2=8.82^2-5.24^2=50.3348\\ \\x\approx 7.1\ mi.[/tex]

The answer is 30.

if 7=a and 2(a+8)

all you need to do is replace a with 7

so the formula would then be 2(7+8)

next you would solve in the parentheses.

2(15)

and 2(15) is the same as 2 x 15

so the answer would be 30

Answer: E. 30

Step-by-step explanation:

Cause a=7 and the equation is 2 (a+8) and it the same as 2 × (7+8) which if you use PEMDAS it's 2 × 15 =30

Answer:

1/2

Step-by-step explanation:

The ratio of corresponding side lengths of the dilation are 1/2 those of the original, so the scale factor is 1/2.

___

For example, A'C'/AC = 9/18 = 1/2.