In the diagram, △ABC∼△DEF. The area of △ABC is 12 square inches. Find the area of △DEF

Answer:

A)

Step-by-step explanation:

it is clearly reduced so you can eliminate the middle two options as answers;

reduction is always going to be a value less than 1 because a value greater than 1 would not be a reduction

Answer:

The median of Group A is greater than the median of Group B.

Step-by-step explanation:

Given

[tex]\begin{array}{cccccccccc}{Group\ A} & 4.5 & 4.8 & 4.6 & 5.0 & 4.8 & 4.4 & 4.7 & 5.2 & 3.9 \ \\ {Group\ B} & 5.5 & 4.9 & 4.0 & 4.2 & 4.8 & 4.1 & 3.5 & 4.6 & 4.3 \ \end{array}[/tex]

Required

Which of the options is true

(a) Group A complete in less time

To do this, we calculate the average of both using:

[tex]\bar x = \frac{\sum x}{n}[/tex]

Where

[tex]n = 9[/tex]

So, we have:

[tex]\bar x_A = \frac{4.5 + 4.8 + 4.6 + 5.0 + 4.8 + 4.4 + 4.7 + 5.2 + 3.9}{9}[/tex]

[tex]\bar x_A = \frac{41.9}{9}[/tex]

[tex]\bar x_A = 4.66[/tex]

[tex]\bar x_B =\frac{5.5 + 4.9 + 4.0 + 4.2 + 4.8 + 4.1 + 3.5 + 4.6 + 4.3}{9}[/tex]

[tex]\bar x_B =\frac{39.9}{9}[/tex]

[tex]\bar x_B =4.43[/tex]

The average time of Group A is higher than that of B, this means that Group A spend more time, on average.

(b) Group A has a greater median

First, we sort the given data in ascending order

[tex]\begin{array}{cccccccccc}{Group\ A} & 3.9 & 4.4 & 4.5 & 4.6 & 4.7 & 4.8 & 4.8 & 5.0 & 5.2 \ \\ {Group\ B} & 3.5 & 4.0 & 4.1 & 4.2 & 4.3 & 4.6 & 4.8 & 4.9 & 5.5 \ \end{array}[/tex]

The median is then calculated using:

[tex]Median = \frac{n + 1}{2}th[/tex]

This gives:

[tex]Median = \frac{9 + 1}{2}th[/tex]

[tex]Median = \frac{10}{2}th[/tex]

[tex]Median = 5th[/tex]

The median is the fifth item for both groups.

So, we have:

[tex]A =4.7[/tex]

[tex]B =4.3[/tex]

4.7 is greater than 4.3

Hence, (b) is true

Since (b) is true and only one option is correct, then (c) and (d) are incorrect

Answer:

b

Step-by-step explanation:

Answer:

the period is the to top points of the highest points on top of the crests

The period of function is,

P = 5

Since, In order to find the period of a graph in general, first, find the period of the parent function, and divide that by the absolute value of the coefficient of the independent variable.

Here, Graph of function is shown.

Hence, The period of function is,

P = 10/2

P = 5

Because there is two wave are shown.

Therefore, The period of function is,

P = 5

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The solutions of the nonlinear system of equations are the points (x₁, y₁) = (- 2, 10) and (x₂, y₂) = (3, 5).

We find in this place a non-linear system formed by a quadratic equation and a linear equation, which can be solved by algebra properties. The complete procedure is shown below:

y = 2 · x² - 3 · x - 4     (1)

y + x = 8                     (2)

By (2) in (1):

2 · x² - 3 · x - 4 + x = 8

2 · x² - 2 · x - 12 = 0

2 · (x² - x - 6) = 0

2 · (x - 3) · (x + 2) = 0

x = 3 ∨ x = - 2

y = 8 - 3 ∨ y = 8 - (- 2)

y = 5 ∨ y = 10

The solutions of the nonlinear system of equations are the points (x₁, y₁) = (- 2, 10) and (x₂, y₂) = (3, 5).

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Answer:

C.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is c 16/100

Answer:

6.71

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2

6^2+3^2=c^2

36+9=c^2

45=c^2

6.71=c

Answer:

17.99

Step-by-step explanation:

Trig Ratios:

Sin = Opposite over Hypotenuse

Cos = Adjacent over Hypotenuse

Tan = Opposite over Tangent

We can use trig ratio sine as we are given an angle ( 40° )and the hypotenuse (28) and we need to find its opposite side (w)

Recall that sin = opposite over hypotenuse

That being said we want to create an equation to solve for w

[tex]sin(40)=\frac{w}{28}[/tex]

Now we solve for w

Step 1 multiply each side by 28

[tex]\frac{w}{28} *28=w\\sin(40)*28=28sin(20) = 17.99[/tex]

we're left with w = 17.99

Answer:

470

Step-by-step explanation:

there are several surface areas.

1. the 4 side walls of the big block = 4*12*7 = 336

2. top and bottom of the big block = 2* 7*7 = 98

3. subtract the small rectangular area from the top area covered by the small block = 2*7 = 14

4. the 3 (visible) side walls of the small block on top =

3* 2*7 = 42

5. the small top and bottom areas of the small block =

2* 2*2 = 8

so, 1.+2.-3.+4.+5. = 470

Answer:

1. make both equal, so...

-14/24 + 9/24

=-5/24

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

According to Order of Operations, you always do exponents first

Answer:

#5 - C

#7 - A

Step-by-step explanation:

If two items are similar, it means that the angles and figure itself have not changed, just the size. The two objects are prototional to each other.

In order to find the length of one side, we have to find what the size difference is, if that makes sense. We have to figure out the number that the smaller size is multiplied by in order to get the bigger number (or the other way around).

#5:

Side LK and side DE are preportional. We can divide 35 by 10 to figure out the proportion size. 35/10=3.5. Then we can take that and use it to find the other side. MK and FD are proportional. We can now take 22 and multiply it by 3.5 to get the new side length. 22x3.5=77

#7:

Same thing. 12/8=1.5, which is the proportional size change. We can now take the already exisiting number and multiply it. 5x1.5=7.5

Could you please express this question better, I don't seem to understand the objective.

Step-by-step explanation:

1. 3.6 x 10^-1

2. 3.1 x 10^6

3. 5.3 x 10^-6

4. 4.2 x 10^-1

Answer:

C.)  3.6 + (6 - 4)

Step-by-step explanation:

Answer:

a) 12/52 = 3/14

b) 26/52 = 1/2

c) 4/52 = 1/13

d) 13/52 = 1/4

e) 8/52 = 2/13

Step-by-step explanation:

a) there are 12 face cards and 52 in the deck

b) half the cards are red, the other half black

c) one queen in each of four suits

d) the deck is broken up into 4 equal suits (hearts, diamonds, spades, clubs) so there are 13 of each.

e) like the answer in part C, there is one of each card in each of the four suits. that gives us four aces and four tens.

Answer:

B

Step-by-step explanation:

To evaluate g(7) substitute x = 7 into g(x) , that is

g(7) = [tex]\frac{7}{8}[/tex] × 7 - [tex]\frac{1}{2}[/tex]

      = [tex]\frac{49}{8}[/tex] - [tex]\frac{4}{8}[/tex]

      = [tex]\frac{45}{8}[/tex] → B

Answer:

False. It's 3 times.

Step-by-step explanation:

Answer: 3,052.08

Step-by-step explanation: 4/3 * pi * 18/2

Answer:

So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2 2 × 3 × 5. The actual prime factors of 60 are 2, 3, and 5.

Answer:

The Prime Factorization is:

2 x 2 x 3 x 5

In Exponential Form:

2^2 x 3^1 x 5^1

Answer:

♿⚠️⛔☢☣⬆️↗️➡️↘️⬇️↙️⤵️⤴️↪↩↔️↕️↖️⬅️

Answer:

6%

Step-by-step explanation:

[tex]\frac{531}{8850} *\frac{x}{100} \\531*100= 5310053100/8850= 6%[/tex]

Step-by-step explanation:

You need to times it, so 150 x 30, and then whatever it is, thata the answer

Answer:

6c = b

Step-by-step explanation:

6 cups of flour for each batch of bread, so 6c;

b is the batch of bread.

So basically,

6c = b

Answer:

A=lw+l(w

2)2+h2+w(l

2)2+h2Step-by-step explanation:

Answer:

40

Step-by-step explanation:

well I need the 3rd number but right now the answer is 40

Answer:

A

Step-by-step explanation:

Answer:

$120.29

Step-by-step explanation:

first you add the normal prices of what sally bought, then add 6.5% of the price she paid.

22.5(2) + 55 + 12.95 = 112.95

6.5          x

-----  =    -----

100     112.95

6.5(112.95)  = 100x

734.175/100 = 100x/100

7.35 ≅ x

112.95 + 7.35 = 120.30

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Answer:

1) 20/45= 4/9=4:9

2) 3:8:5

3) 10:7