A building that is 150 ft tall casts a shadow of 20 feet long.
At the same time a tree casts a shadow of 2 ft. How tall is
the tree?

a. 15

b. 20

c. 25

d. 30

Answer:10/7 and mixed number form is 1 3/7

The other answer is just wrong.

There are 9•9•8 = 648 distinct 3-digit codes. The first digit can be any numeral from 1-9, the next digit can be any from 0-9 minus the one used in the first position, and the last digit can be any from 0-9 minus both the numerals used in the first two positions.

But that doesn't even account for the divisibility constraint.

Let the code be [tex]abc[/tex]. We can expand this as

[tex]100a + 10b + c[/tex]

In order for this to be divisible by 4, we observe that

[tex]100a + 8b + 2b + c = 4 (25a + 2b) + (2b+c)[/tex]

so we only need [tex]2b+c[/tex] to be divisible by 4.

The last digit must be even, so there are only 5 choices for the last digit. I list the possibilities and outcomes below. For some integer [tex]k[/tex], we need

[tex]c=0 \implies 2b=4k \implies b=2k[/tex]

[tex]c=2 \implies 2b+2=4k \implies b = 2k-1[/tex]

[tex]c=4 \implies 2b+4 = 4k \implies b = 2(k-1)[/tex]

[tex]c=6 \implies 2b+6 = 4k \implies b = 2k-3[/tex]

[tex]c=8 \implies 2b+8=4k \implies b = 2(k-2)[/tex]

Ignoring [tex]a[/tex] for the moment, in the cases of [tex]c\in\{0,4,8\}[/tex], [tex]b[/tex] is also even. This leaves 3 choices for [tex]c[/tex] and 2 choices for [tex]b[/tex].

Likewise, in the cases of [tex]c\in\{2,6\}[/tex], [tex]b[/tex] is odd. This leaves 2 choices for [tex]c[/tex] and 5 choices for [tex]b[/tex].

Now taking into account the choice for [tex]a[/tex], we have the following decision tree.

• If [tex]a\in\{2,6\}[/tex] and [tex]c\in\{0,4,8\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{a,c\}[/tex] - a total of 2•3•3 = 18 codes.

• If [tex]a\in\{4,8\}[/tex] and [tex]c\in\{0,4,8\}\setminus\{a\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{a,c\}[/tex] - a total of 2•2•3 = 12 codes.

• If [tex]a\in\{2,6\}[/tex] and [tex]c\in\{2,6\}\setminus\{a\}[/tex], then [tex]b\in\{1,3,5,7,9\}\setminus\{a,c\}[/tex] - a total of 2•1•5 = 10 codes.

• If [tex]a\in\{4,8\}[/tex] and [tex]c \in\{2,6\}[/tex], then [tex]b\in\{1,3,5,7,9\}[/tex] - a total of 2•2•5 = 20 codes.

• If [tex]a\in\{1,3,5,7,9\}[/tex] and [tex]c\in\{0,4,8\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{c\}[/tex] - a total of 5•3•4 = 60 codes.

• If [tex]a\in\{1,3,5,7,9\}[/tex] and [tex]c\in\{2,6\}[/tex], then [tex]b\in\{1,3,5,7,9\}\setminus\{a\}[/tex] - a total of 5•2•4 = 40 codes.

Hence there are a total of 18 + 12 + 10 + 20 + 60 + 40 = 160 codes.

Answer:

I believe he sells each bar for .75 cents

Answer:

D

Step-by-step explanation:

this would simplify, in slope-intercept form, as y= 15x - 66

The value of x in the function r(x) = x - 3/x-4 is equal is 3.

To solve this problem, all that is required from us is simply substitute the values and solve for the value of x.

Data;

A function from a set A to a set B assigns to each element of A exactly one element of B. The set A is usually the domain of the function while the set B is the codomain of the function.

Given that the function R(x) is

[tex]R(x) = \frac{x-3}{x-4}[/tex]

And also, R(x) is equal to 0.

[tex]R(x) = \frac{x-3}{x-4}\\ 0= \frac{x-3}{x-4} \\0(x-4) = x - 3\\0 = x- 3\\x = 3[/tex]

The value of x in the function is 3.

Learn more on functions here;

https://brainly.com/question/1214333

Answer:

30 pounds are left over after the bag filled

Step-by-step explanation:

145×3

= 435

now,

465-435

= 30

Answer:

21.98

Step-by-step explanation:

Formula for Circumference of a Circle:

C=2πr

1. We find r, which is basically the diameter divided by 2, aka half of the diameter:

d/2 = r

Fill in:

7/2 = r

r = 3.5

2. We fill in the Formula:

C = 2πr

C = 2(3.14)(3.5)

3. Multiply it all

3.14 x 3.5 = 10.99

10.99 x 2 = 21.98

Hence, the circumference of the circle is 21.98.

Answer:

-7

32

Step-by-step explanation:

a)9-16=-7

b)4-10=-6

2∆-6

36-4

32

Answer:

A

Step-by-step explanation:

No need. It’s simple.

B can’t be it because it uses multiplication.

C can’t be it because it makes no sense.

D also makes no sense.

Answer:1.03125

Step-by-step explanation:

The simulation of the medicine and the bowler hat are illustrations of probability

From the question,

From the simulation, 23 of the 30 randomly generated numbers show that the medicine is effective on at least two

So, the probability is:

p = 23/30

p = 0.767

Hence, the probability that the medicine is effective on at least two is 0.767

From the simulation, 0 of the 30 randomly generated numbers show that the medicine is effective on none

So, the probability is:

p = 0/30

p = 0

Hence, the probability that the medicine is effective on none is 0

The probability of hitting a headpin is:

p = 90%

The probability a bowler hits a headpin 4 out of 5 times is:

P(x) = nCx * p^x * (1 - p)^(n - x)

So, we have:

P(4) = 5C4 * (90%)^4 * (1 - 90%)^1

P(4) = 0.3281

Hence, the probability that the bowler hits a headpin 4 out of 5 times is 0.3281

Read more about probabilities at:

https://brainly.com/question/25870256

Frank would need two gallons of maroon painting and one gallon of white painting to paint all his room.

Area of the ceiling:

Assuming the floor has the same area, the total area for the floor and ceiling is 288 square feet.

Area of the door:

Total area in white 144 feet + 21 feet = 165 square feet

Total of gallons

1 gallon equals 400 square feet, which means only one gallon of white painting is required.

Area of one wall:

Considering 1 gallon equals 400 square feet, a total of 2 gallons would be required.

Note: This question is incomplete because the image of the room is missing; below I attach the missing section.

Learn more about area in: https://brainly.com/question/16151549

Step-by-step explanation:

again ?

out of the total of 70°, 30° are taken by the first angle.

so, that leaves 70 - 30 = 40° for the second angle.

q = 40°

is there still something unclear about this ? please let me know.

Answer:

Step-by-step explanation:

numbers are {3.46,3.47,3.48,3.49,3.50,3.51,3.52,3.53,3.54,3.55,3.56,3.57,3.58,3.59}

Answer:

Perimeter : 150

Area : 1,350

Answer:

4.2 or 21/5

Step-by-step explanation:

i used demos

Answer:

4 1/5

[tex]\frac{14 * 9}{3 * 10} = \frac{126}{30}~which~is~also~4\frac{1}{5}[/tex]

Answer:

A 67 inches is the correct answer

[tex]\text{Given that,}\\\\\text{Area of the rectangle,}~ A = 344 ~ in^2\\\\\text{Width of the rectangle,}~w = 16 ~ in\\\\\text{Length of the rectangle,}~ l=?\\\\~~~~~~A = l \times w \\\\\implies l= \dfrac{A}w =\dfrac{344}{16}=21.5 ~in\\\\\text{Perimeter of the rectangle} = 2(l+w) = 2(21.5+16)=75~ in[/tex]

Answer:

Problem 3: 51°

Problem 5: 5 feet

Step-by-step explanation:

Image 1:

We are asked to find the missing angle. First off, we know that the full semi-circle equals 180 degrees. knowing this, subtract the second angle from 180 to get the smaller angle.

180 - 129 = 51

The unkown angle is 51 degrees.

Image 2:

We are asked to find the missing side. Apply the numbers of the known sides to the Pythagorean Theorem.

a² + b² = c²

a² + 12² = 13²

a² + 144 = 169

a² = 25

a = 5

The missing side is 5 feet.

Answer:

Step-by-step explanation:

First we need to find the score of the incorrect answers and the questions that were not answered.

Score for the incorrect answers = 4*(-2) = -8

Score for the questions not answered = 6*(-1) = -6

Score for the questions answered correctly = 106 - [ (-8) + (-6) ]

                                                                       = 106 -[-14]

                                                                        = 106 + 14

                                                                        = 120

Number of questions answered correctly = total score for questions that were answered correctly ÷ score of 1 correct answer

= 120 ÷ 4

= 30

30 questions were answered correctly.

Answer:

y=-x-3

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

It's given that,

Now, according to formula ~

[tex]\qquad \sf  \dashrightarrow \: v = \pi {r}^{2}x[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = \frac{22}{7} \times {5}^{2} \times 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = \frac{22}{7} \times 25 \times 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = \frac{6600}{7} [/tex]

[tex]\qquad \sf  \dashrightarrow \:v \approx 942.86 \: \: unit {}^{3} [/tex]

The measure of the angle that is 57° in this 2-dimensional figure is the angle vertically opposite to the angle 57  (the angle formed at X)

From the given diagram, we have the following:

The two angles on the straight line are 123 degrees and 57 degrees.

<F + 57 = 180

<F = 180 - 57

<F = 123 degrees

Hence the measure of the angle that is 57° in this 2-dimensional figure is the angle vertically opposite to the angle 57  (the angle formed at X)

Learn more on lines and angles here: https://brainly.com/question/25770607

Answer:

One bucket of popcorn:  6$

One box of candy: $3.75

2 buckets of popcorn:  $12

3 boxes of candy:  $11.25

2 buckets of popcorn and 3 boxes of candy:  $23.25

Step-by-step explanation:

We can find the cost of one bucket of popcorn and one box of candy using a system of equations

[tex]4P + 6C=46.50\\P + C =9.75[/tex]

We can use the elimination method and thus multiply the second equation by -4:  

[tex]4P + 6C = 46.50\\-4(P+C=9.75)\\\\4P + 6C = 46.50\\-4P -4C=-39\\\\2C = 7.5\\\\C = 3.75[/tex]

We can plug C into the second equation to find P:

[tex]P + 3.75 = 9.75\\P = 6[/tex]

Thus, the cost of two buckets of popcorn is 6 * 2 = $12

And the cost of three boxes of candy is 3.75 * 3 = $11.25

And the cost of both two buckets of popcorn and three boxes of candy is (6*2) + (3*3.75) = 12 + 11.25 = $23.25

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's calculate the slope ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{3 - 4}{7 - ( - 2)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{ - 1}{9} [/tex]

That's the required slope, I hope it helps~

Answer:

One root ; x = 3

Step-by-step explanation:

( a ± b )² = a² ± 2ab + b²

~~~~~~~~~

y = x² - 6x + 9

x² - 6x + 9 = x² - 2(x)(3) + 3² = ( x - 3 )²

( x - 3 )² = 0 ⇒ x - 3 = 0 ⇒ x = 3

Answer:

x < 39

Step-by-step explanation:

x - 27 < 12

Add 27 to both sides.

x - 27 + 27 < 12 + 27

x < 39

[tex]\qquad\qquad\huge\underline{{\sf Answer☂}}[/tex]

Let's solve the inequality ~

[tex]\qquad \sf  \dashrightarrow \: x - 27 < 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: x < 12 + 27[/tex]

[tex]\qquad \sf  \dashrightarrow \: x < 39[/tex]