Phil, Melissa, Noah, and olivia saw a tall tree that cast a shadow 34 feet long. They observed at the same time that a 5-foot-tall person cast a shadow that was 8.5 feet long. How tall is the tree?

Answer:

(a) 120 choices

(b) 110 choices

Step-by-step explanation:

The number of ways in which we can select k element from a group n elements is given by:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:

[tex]10C7=\frac{10!}{7!(10-7)!}=120[/tex]

Then each student have 120 possible choices.

On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:

1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:

[tex](5C3)(5C4)=\frac{5!}{3!(5-3)!}*\frac{5!}{4!(5-4)!}=50[/tex]

2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:

[tex](5C4)(5C3)=\frac{5!}{4!(5-4)!}*\frac{5!}{3!(5-3)!}=50[/tex]

3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:

[tex](5C5)(5C2)=\frac{5!}{5!(5-5)!}*\frac{5!}{2!(5-2)!}=10[/tex]

So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:

50 + 50 + 10 = 110

Answer:

Given the equation 8 + 3y = 2·(x+5)

slope=2/3

y- intercept= (0, 2/3) or y= 2/3.

x-intercept=  (-1, 0) or x = -1.

Step-by-step explanation:

Given 8 + 3y = 2·(x+5) ⇒ 8 + 3y = 2x + 10 ⇒ 3y = 2x + 10 -8 ⇒ 3y = 2x + 2

⇒ y = (2/3)x + 2/3.

Here slope = 2/3 and y-intercept = 2/3.

To find x-intercept, we have to calculate the value of "x" when y =0.

⇒ 0 = (2/3)x + 2/3 ⇒ 0 - 2/3 = (2/3)x ⇒ -2/3 = (2/3)x ⇒ (-2/3)/(2/3)= x

⇒ x =-1.

Answer:here's ur answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=3(y-b)

or x=3y-3b

3y=x+3b

[tex]y=\frac{x+3b}{3}[/tex]

Answer:

.

Step-by-step explanation:

The problem states:

f(p) is the average number of days a house stays on the market before being sold for price p in $1,000s

So we know:

p is the price in $1000s and

f(p) is the number of days before its sold for p

This means f(275) would be the number of days before its sold for 275,000 (since p is in $1000s).

The answer is:

f(275) represents the average number of days houses stay on the market before being sold for $275,000.

The statement "f(275) represents the average number of days houses stay on the market before being sold for $275,000" best describes the meaning of f(275).

Given,

Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s.

In the given function f(p), the variable p represents the price of a house in thousands of dollars ($1,000s), and f(p) represents the average number of days a house stays on the market before being sold for that price.

Therefore, when you evaluate f(275), it tells you the average number of days houses stay on the market before being sold for $275,000.

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Answer:

(on Edge)  1. "The equation of the scenario is p = 55 - 0.5w"

2. "The values of p must be any whole number 45 to 55"

BTW i got number 1 from this user https://brainly.com/profile/Alyssamarie03-2838077

Answer:

The answer to your question is: I agree with you, the first option

Step-by-step explanation:

• (0,1) U (1,infinity)  This is the right answer because there are 2 invervals in which the graph decreases, and these intervals are listed in this option.

•(-infinity,-1)U(-1,0)  This option is wrong because from (-∞ , -1) the graph grows up and also from (-1, 0).

•(-infinity,-1)  The graph grows up, this option is incorrect

. (1,infinity) The graph decreases but the option is incomplete.

The correct option is A which is the function decreasing over the interval (0,1) U(1, infinity).

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Check all the options:-

Therefore, the correct option is A which is the function decreasing over the interval (0,1) U(1, infinity).

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Answer:

8

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$906.25\\ P=\textit{original amount deposited}\\ r=rate\to 6.25\%\to \frac{6.25}{100}\dotfill &0.0625\\ t=years\dotfill &1 \end{cases} \\\\\\ 906.25=P(0.0625)(1)\implies 906.25=0.0625P\implies \cfrac{906.25}{0.0625}=P \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 14500=P~\hfill[/tex]

The volume of a cylinder is changing at a rate of 256π cm³/min when the height of the cylinder is 12 cm, the radius is 4 cm, the circumference of the cylinder is increasing at a rate of π4 cm/min, and the height of the cylinder is increasing four times faster than the radius.

The primary equation you need for this problem is the volume of a cylinder, which is V = πr²h. Given the height h of the cylinder is increasing four times faster than the radius r, if we use dh/dt for the rate of change of the height and dr/dt for the rate of change of the radius, we have dh/dt = 4dr/dt.

Also, the rate at which the circumference of the cylinder is increasing is d(2πr)/dt=2πdr/dt = π4 cm/min. Hence we can set up an equation as 2πdr/dt = π4. Solving for dr/dt, we get dr/dt = 2 cm/min.

Substituting this into the previous equation, we find that dh/dt = 8 cm/min. Now, if we take the derivative of the volume equation with respect to time, we get dV/dt = πr²dh/dt + 2πrh*dr/dt.

With the values r = 4cm, h = 12cm, dr/dt = 2 cm/min, and dh/dt = 8 cm/min, replacing in the equation above gives us: dV/dt = π*4²*8 + 2π*4*12*2 = 256π cm³/min. So, the volume of the cylinder is changing at a rate of 256π cm³/min.

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Answer:

Step-by-step explanation:

The cost of the area of the deck is fixed, because the area is fixed. It will be ...

  ($12/ft²)×(100 ft²) = $1200

__

The cost of the railing is proportional to its length, so it will be minimized by minimizing the length of the railing. If the length of it is x feet parallel to the house, then the length of it perpendicular to the house (for a deck area of 100 ft²) is 100/x.

The total length of the railing is ...

  r = 2(100/x) + x

We can minimize this by setting its derivative with respect to x equal to zero:

  dr/dx = -200/x² +1 = 0

Multiplying by x² and adding 200, we get ...

  x² = 200

  x = √200 ≈ 14.142

So, the minimum railing cost will be had when the deck is 14.142 ft by 7.071 ft. That railing cost is about ...

  $9 × (200/√200 +√200) ≈ $254.56

__

We might imagine that dimensions near these values would have almost the same cost. Here are some other possibilities:

__

Then the total cost for a couple of possible deck sizes will be $1200 plus the railing cost, or ...

_____

Note on the solution process

It can be helpful to use a spreadsheet or graphing calculator to do the repetitive computation involved in finding suitable dimensions for the deck.

Answer:

5!!

Step-by-step explanation:

When writing the polynomial in standard form, we have:

5X⁴ - 2X + 1

The leading coefficient is 5, since it's part of the term with the highest degree.

Final answer:

The leading coefficient of the polynomial 1 - 2x + 5x⁴ in standard form is 5, as standard form requires terms to be in descending powers of x.

Explanation:

The question asks to identify the leading coefficient of a polynomial when written in standard form. The given polynomial is 1 - 2x + 5x⁴. The standard form of a polynomial requires the terms to be written in descending powers of x. Therefore, the standard form of the given polynomial is 5x⁴ - 2x + 1. The leading coefficient is the coefficient of the term with the highest power of x, which in this case is 5 for the term 5x⁴.

There are a total of 8 letters in student, with 6 different letters ( there are 2 s's and 2 t's).

First find the number of arrangements that can be made using 8 letters.

This is 8! which is:

8 x 7 x 6 x 5 x 4 3 x 2 x 1 = 40,320

Now there are 2 s's and 2 t's find the number of arrangements of those:

S = 2! = 2 x 1 = 2

T = 2! = 2 x 1 = 2

Now divide the total combinations by the product of the s and t's:

40,320 / (2*2)

= 40320 / 4

= 10,080

The answer is A. 10,080

Answer:

Step-by-step explanation:

We notice that the multiplier of the squared term in f(x) is 0.5; in g(x), it is -2, so is a factor of -4 times that in f(x).

If we scale f(x) by a factor of -4, we get ...

  -4f(x) = -2(x -2)² -12

In order for the squared quantity to be x+3, we have to add 5 to the value that is squared in f(x). That is, x -2 must become x +3. We have to replace x with (x+5) to do that, so ...

  (x+5) -2 = x +3

The replacement of x with x+5 amounts to a translation of 5 units to the left.

We note that the added constant after our scaling changes from +3 to -12. Instead, we want it to be -1, so we must add 11 to the scaled function. That translates it upward by 11 units.

The attached graph shows the scaled and translated function g(x):

  g(x) = -4f(x +5) +11

Answer:

  see below

Step-by-step explanation:

3. The answers in the image below are in "interval notation". In set notation, they might be ...

  increasing: {x∈ℝ: -2 < x < 0 ∪ 2 < x}

  decreasing: {x∈ℝ: 0 < x < 2}

  positive: {x∈ℝ: -4 ≤ x < 1.5 ∪ 3 < x}

  negative: {x∈ℝ: 1.5 < x < 3}

  domain: {x∈ℝ: x ≥ -4}

  range: {x∈ℝ: x ≥ -3}

  y-intercept: y ∈ {2}

  x-intercepts: x ∈ {1.5, 3}

  relative minimum: (x, y) ∈ {(2, -3)}

  relative maximum: (x, y) ∈ {(0, 2)}

__

4. Answers are in the image below.

The function is increasing where its slope is positive, decreasing where its slope is negative. Where the slope changes sign, there may be a point where the slope is 0 or undefined. The function is neither increasing nor decreasing there, so those points are not part of the intervals for increasing or decreasing.

The function is positive when it is above the x-axis, negative when it is below the x-axis. The function is neither positive nor negative where it is on the x-axis or where it is undefined.

The domain is the horizontal extent of the function. Any points where the function is undefined are excluded.

The range is the vertical extent of the function, all of the y-values where the function output is defined. Here, m(2) is not defined, so y=-7 is not an output at that point. However, y=7 is an output for m(-14 2/3). Likewise, m(9) does not have an output of 0, but m(3) does, so 0 is part of the range.

X- and y-intercepts are where the graph intersects the x- or y-axis, respectively. M(x) is undefined at (9, 0), so there is no x-intercept there.

A relative minimum is any point where the y-values increase on either side of the point. For m(x), the function is undefined at its relative minima, so it cannot be said to have any.

A relative maximum is any point where the y-value decreases on either side of the point. M(x) has one at the vertex of the parabolic segment.

Answer:

$7,000 at a rate of 7% and $21,000 at a rate of 14%.

Step-by-step explanation:

Let x be amount invested at 7% and y be amount invested at 14%.

We have been given that a women's professional organization made two small-business loans totaling $28,000. We can represent this information in an equation as:

[tex]x+y=28,000...(1)[/tex]

The interest earned at 7% in one year would be [tex]0.07x[/tex] and interest earned at 14% in one year would be [tex]0.14x[/tex].

We are also told that the organization received from these loans was $3,430. We can represent this information in an equation as:

[tex]0.07x+0.14y=3,430...(2)[/tex]

Form equation (1), we will get:

[tex]x=28,000-y[/tex]

Upon substituting this value in equation (2), we will get:

[tex]0.07(28,000-y)+0.14y=3,430[/tex]

[tex]1960-0.07y+0.14y=3,430[/tex]

[tex]1960+0.07y=3,430[/tex]

[tex]1960-1960+0.07y=3,430-1960[/tex]

[tex]0.07y=1470[/tex]

[tex]\frac{0.07y}{0.07}=\frac{1470}{0.07}[/tex]

[tex]y=21,000[/tex]

Therefore, an amount of $21,000 was invested at a rate of 14%.

[tex]x=28,000-y[/tex]

[tex]x=28,000-21,000[/tex]

[tex]x=7,000[/tex]

Therefore, an amount of $7,000 was invested at a rate of 14%.

Answer:

Probability 50%

Odds 5:5

Step-by-step explanation:

Probability is calculated as favorable cases divided by total cases.

While odds are calculated as favorable cases divided by (total cases - favorable cases)

Favorable cases (green) : 5

Total cases(green, red and blue): 10

Probability= 5/10 * 100%=50%

Odds = 5:(10-5) = 5:5

Answer:

it is 50%

Step-by-step explanation:

Answer:

13,18meters

Step-by-step explanation:

If the temple is in a height of 24 meters and to get there there are 91 steps, each step is 24 m / 91 = 26,37cm

The 50th step then is 26, 37cm. 50=13.18meters

Answer:

A. 52°

Step-by-step explanation:

All interior angles of ANY quadrilateral sum up to 360°; corresponding base angles sum up to 180°, therefore the m∠A is 52°.

I am joyous to assist you anytime.

Answer: a) critical value = 0.0853, b) we reject the null hypothesis.

Step-by-step explanation:

Since we have given that

z = -1.37

And the hypothesis are given below:

[tex]H_0:p=\dfrac{1}{4}=0.25\\\\H_1:p\neq 0.25[/tex]

Since α = 0.01

since critical value = 0.0853

As we can see that 0.853 < 0.25.

so, we reject the null hypothesis.

Hence, a) critical value = 0.0853, b) we reject the null hypothesis.

Answer:

9.271 inches.

Step-by-step explanation:

Let AC be the length of original line segment and point B divides it into two segments such that AB is longer and BC is smaller segment.

[tex]AB+BC=AC=15[/tex]

We can describe the golden ratio as:  

[tex]\frac{AB}{BC}=\frac{AC}{AB}=1.618[/tex]

[tex]\frac{AC}{AB}=1.618[/tex]

[tex]\frac{15}{AB}=1.618[/tex]

[tex]\frac{15}{1.618}=AB[/tex]

[tex]9.270704=AB[/tex]

[tex]AB=9.271[/tex]

We can verify our answer as:

[tex]AB+BC=15[/tex]

[tex]9.271+BC=15[/tex]

[tex]9.271-9.271+BC=15-9.271[/tex]

[tex]BC=5.729[/tex]

[tex]\frac{AB}{BC}=1.618[/tex]

[tex]\frac{9.271}{5.729}=1.618[/tex]

[tex]1.618=1.618[/tex]

Hence proved.

Therefore, the length of the longer side would be 9.271 inches.

Answer:

  $1,220,200

Step-by-step explanation:

The total of Mary's payments is ...

  $3695.20/mo × 30 yr × 12 mo/yr = $1,330,200

The difference between this repayment amount and the value of her loan is the interest she pays:

  $1,330,200 -110,000 = $1,220,200 . . . total interest paid

_____

Mary's effective interest rate is about 40.31% per year--exorbitant by any standard.

Answer:

What is it asking?

Step-by-step explanation:

Answer:

The answer to your question is EF = 12

Step-by-step explanation:

Data

DE = 6x

EF = 4x

DF = 30

Process

                DE    +    EF      = DF

               6x     +    4x       = 30

                           10x = 30

                            x = 30 / 10

                            x = 3

             6(3)    + 4 (3)     = 30

             18   +     12      = 30

                         30 = 30

DE = 6(3) = 18

EF = 4(3)  = 12

Answer:  0.1010052

Step-by-step explanation:

Given : Significance level : [tex]\alpha=0.01[/tex]

Alternative hypothesis : [tex]H_1:\ p\neq\dfrac{3}{4}[/tex]

The test statistic value : [tex]z=-1.64[/tex]

Since , the alternative hypothesis is two-tailed, so the test is a two-tailed test.

Using standard normal distribution table for z, we have

The P-value of two-tailed test will be :-

[tex]2P(z>|-1.64|)=2P(z>1.64)\\\\=2(1-P(z\leq1.64))\\\\=2(1-0.9494974)\\\\=0.1010052[/tex]

Hence, the P-value = 0.1010052

Answer:

The answer to your question is below:

Step-by-step explanation:

A number is divisible by 9 if the sum of all the individual digits is evenly divisible by 9.

7,625    example    7 + 6 + 2 +5 = 20  it's not divisible by 9

4,932                      4 + 9 + 3 + 2 = 19 it's not divisible by 9

9,180                                                18  it is divisible

2,969                                                26 it's not divisible by 9

9,180                                                18 it is divisible

4,932                                                18 it is divisible

2,969                                                26 it's not divisible by 9

Answer:

9180 is divisible by 9 .

Step-by-step explanation:

A number is divisible by 9 if the sum of all of it's digits is divisible by 9.

Here, for each of the given numbers, we will find sum of digits then check if the sum of digits is divisible by 9.

For 7,625  :    

 7 + 6 + 2 +5 = 20  ( not divisible by 9)

For 4,932 :                  

 4 + 9 + 3 + 2 = 19 (not divisible by 9)

For 9,180 :  

9+1+8 = 18              ( divisible by 9 )

For 2,969 :

2+9+6+9=26         (not divisible by 9)                                      

Answer:

c. {(1, a), (0, a), (2, c), (3, b)}

Step-by-step explanation:

Answer:

   12.94%

Step-by-step explanation:

r = 100(1/2)^(d/5) = 100((1/2)^(1/5))^d ≈ 100(.87055)^d

The daily decrease is 1 - 0.87055 = 0.12944 ≈ 12.94%

Answer:

2 .

length of ,XY= a-6

length of ,YZ =3a+11

total length of ,XZ =41

Since,Point X,Y,Z lies in same straight line XZ..

So,

XZ= XY+ YZ

41= a-6 + 3a+11

41= 4a +5

41-5 = 4a

36/4 = a

a= 9

putting value of a in lengths XY and XZ we get,

XY= 9-6

= 3

YZ = 3*9 + 11

=27 + 11

=38

Length of XY = 3

Length of YZ = 38

Answer of 3 and 4 are as similar of above solved examples..