solve similar triangles

Answer:

(A)[tex]420$ cm^3[/tex]

Step-by-step explanation:

Volume of the solid box [tex]= 10*6*15=900$ cm^3[/tex]

Since the box tube is constructed out of 1 cm thick metal, we subtract 1cm on both sides of the width and height.

See the attached diagram for illustration.

However, the depth of the box remains unchanged, therefore:

Internal Volume of the box[tex]=8*4*15=480$ cm^3[/tex]

Volume of metal used = Volume of Solid Box - Internal Volume

=900-480

=[tex]420$ cm^3[/tex]

The correct option is A.

Answer:

Complementary angles are two angles that add up to 90° in total measurement.

Example:

Angle 1 is 34°. It's complement would be 56°.

[tex]90 -34=56[/tex]

Brainilest Appreciated.

Answers

1.9 hours

Step-by-step explanation:

14 plus 3 = 17

32 divide by 17 = 1.9 hours

1 hour 0.9 multiply by 60

1.9= 1 hour 54 minutes

Answer: 75 students

Step-by-step explanation:

Skyler goes to a school that has 100 students in it. She asks 40 random students if they like the new 8.30 am start to the day and 30 of them say no they don't like it. This shows that: 30/40 = 3/4 of the students don't like it.

Since the school has 100 students, the number of students that doesn't like the 8.30 a.m start will be:

= 3/4 of 100

= 3/4 × 100

= 3 × 25

= 75

Answer:

The top two are 3 and 4

The bottom two are 6

Step-by-step explanation:

hope it works out

Answer:

y > 4

Step-by-step explanation:

2 (5y-4)>32

Divide each side by 2

2/2 (5y-4)>32/2

5y-4 > 16

Add 4 to each side

5y-4+4 > 16+4

5y > 20

Divide each side by 5

5y/5 > 20/5

y > 4

Step-by-step explanation:

2 (5y - 4) > 32

10y - 8 > 32 (by expanding)

10y> 32 + 8

10y> 40

Y > 40/10

Y=4

Hope this helps..

Answer:

2880

Step-by-step explanation:

The base is made up of two triangles and a square, if that makes sense. Finding the area of a triangle is (base x height)/2.  

The base of the tiny triangle is 4 because there is 8 inches extra to the 10 inch square. 10 x 4 = 40.

Now we have a 10 by 10 square: 10 x 10 = 100.

So, the area of the trapezoid is 140. There are two trapezoids in this prism, so both bases are 280.

The surface area of the sides are solved by 12 x 50 = 600. Together, the sides equal 1200.

The top is solved by 10 x 50 = 500.

The bottom is solved by 18 x 50 = 900.

Add them all together: 280 + 1200 + 500 + 900 = 2,880

Answer:

5/25

Step-by-step explanation:

Probability would be that you randomly select 5 cards so the selection goes above the fraction and the total amout of cards goes below.

Answer:

3243 / 10829 ≈ 0.2995

Step-by-step explanation:

There are 52 cards in a deck.  5 cards are selected, so the number of possible combinations is ₅₂C₅.

Of the 5 cards selected, 1 is a Jack and 4 are non-Jacks.

There are 4 Jacks in a deck.  The number of ways of choosing 1 Jack from 4 is ₄C₁.

There are 48 non-Jacks in a deck.  The number of ways of choosing 4 non-Jacks from 48 is ₄₈C₄.

So the probability is:

P = ₄C₁ ₄₈C₄ / ₅₂C₅

P = 4 × 194580 / 2598960

P = 778320 / 2598960

P = 3243 / 10829

P ≈ 0.2995

Answer:

Step-by-step explanation:

Susan started her homework at = 1:59 pm

She took time = 96 mins

Time at which she had volleyball practice = 4:00 pm

So, time between her starting of homework and starting of volleyball is given by

1:59 pm to 4:00 pm = 2 hrs and 1 mins

2 hr 1 min = 120 mins + 1 min = 121 mins

But she took 96 mins to do her homework, so

Out of 121 mins, 96 mins she took for homework

Remaining time = 121 mins - 96 mins = 25 mins

Therefore, time Susan had between finishing her homework and the beginning of volleyball practice is 25 mins

Answer:

It means line which is chioce 3 or C.

Step-by-step explanation:

Answer:line DC

Step-by-step explanation:because of the line with an arrow on each side. This demonstrates that DC is an entire line

So the right answer is 7.

Look at the attached picture

Hope it will help you...

Good luck on your assignment

~Pragya

Step-by-step explanation:

there's the solution ...i hope you can read

Answer:

2; 2; 0; 1; Isosceles and Obtuse

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

9 x 3 x 3 is 81

Answer:

18

Step-by-step explanation:

Area=3x3=9 units

9+9=18

Answer:

5 (4 x + 5)

That is the answer

5 is a factor if 20 and 25 and 4x + 5 cannot be furthor be simplified.

Answer:

97.5%

Step-by-step explanation:

Solution:-

- Denote a random variable,

           X: Scores of all juniors in a school district centralized test.

- The random variable ( X ) follows normal distribution with the corresponding parameters:

                         X ~ Norm ( μ , σ^2 )

Where,     μ = Mean score

                σ = standard deviation of scores secured

- The given parameters for the normal distribution are:

                        X ~ Norm ( 74 , 8^2 )

- To draw a Normal curve we need to draw a bell shaped curve and annotate the following descriptions:

      Mean ( μ ) : The vertical center-line that bifurcates the normal curve

      1st standard deviation ( μ ± σ ) : First small division to the left and right about the mean ( μ ). [ 74 - 8 , 74 + 8 ] = [ 66 , 82 ]

      2nd standard deviation ( μ ± 2σ ) : Second small division to the left and right about the mean ( μ ). [ 74 - 16 , 74 + 16 ] = [ 58 , 90 ]

      3rd standard deviation ( μ ± 3σ ) : Third small division to the left and right about the mean ( μ ) - tailed. [ 74 - 24 , 74 + 24 ] = [ 50 , 98 ]

- Mark the associated percentage of scores that lies between 1st, 2nd and 3rd standard deviations from the mean ( μ ). Apply the Empirical rule of statistics. Which states:

    p (  μ - σ  ,  μ + σ ) = p ( 66 , 82 ) = 67 %

    p (  μ - 2σ  ,  μ + 2σ ) = p ( 58 , 90 ) = 95 %

    p (  μ - 3σ  ,  μ + 3σ ) = p ( 50 , 98 ) = 99.7 %

- See the attachment for the complete diagram.

- To determine the percentage of students who scored no more than 90 on the test.

- Employ the use of standardizing the required probability by using the following relation:

          p ( X < x ) = p ( Z < [ (x - μ) / σ ] )

          p ( X < 90 ) = p ( Z < [ (90 - 74) / 8 ] )

                             = p ( Z < [ (90 - 74) / 8 ] )

                             = p ( Z < 2 )

- We will employ the use of Empirical rule of second deviation ( μ ± 2σ ) to evaluate the required percentage:

       p (  μ - 2σ  < X <  μ + 2σ ) = p ( 58 , 90 ) = 95 %

       1 - p ( 58 < X < 90 ) = 1 - 0.95 = 0.05

       p ( X > μ + 2σ ) = p ( X > 90 ) = [ 1 - p ( 58 < X < 90 ) ] / 2

                                                      = [ 1 - 0.95 ] / 2

                                                      = 0.05 / 2

                                                      = 0.025

Hence,

     p ( X < 90 ) = p ( Z < 2 ) = 1 - p ( X > 90 )

                                            = 1 - 0.025

     Answer                          = 0.975 ( 97.5 )%        

Answer:

x>-1

Step-by-step explanation:

Part (a)

Answer: 42

-------------

Work Shown:

The angle ABC is 90 degrees since AB and BC are perpendicular. The two segments form a right angle. Therefore, the three pieces of the angle must add to 90

24+x+24 = 90

x+48 = 90

x+48-48 = 90-48 ... subtracting 48 from both sides

x = 42

=======================================

Part (b), subpart (i)

Angle q is congruent to the 135 degree angle because they are vertical angles.

Vertical angles are opposite angles formed by the X shape when two lines cross, and vertical angles are always the same measure.

=======================================

Part (b), subpart (ii)

Answer: 225

-------------

Reasoning:

The four angles p,q,r and the 135 all add to 360, so,

p+q+r+135 = 360

subtract 135 from both sides so we isolate the "p+q+r" and that leads to

p+q+r+135 = 360

p+q+r+135-135 = 360-135

p+q+r = 225

Answer:

Scale factor = [tex]\frac{4}{9}[/tex]

Perimeter ratio = 4 : 9

Surface area ratio = 16 : 81

Volume ratio = 64 : 729

Step-by-step explanation:

Volume ratio = [tex]\frac{\text{volume of small prism}}{\text{Volume of large prism}}[/tex]

                      = [tex]\frac{128}{1458}[/tex]

                      = [tex]\frac{64}{729}[/tex]

                      = 64 : 729

Scale factor = [tex]\sqrt[3]{\frac{\text{volume of small prism}}{\text{Volume of large prism}}}[/tex]

                    = [tex]\sqrt[3]{\frac{64}{729}}[/tex]

                    = [tex]\frac{4}{9}[/tex]

Perimeter ratio = Scale factor

                         = [tex]\frac{4}{9}[/tex]

                         = 4 : 9

Surface area ratio = (Scale factor)²

                              = [tex](\frac{4}{9})^{2}[/tex]

                              = [tex]\frac{16}{81}[/tex]

                              = 16 : 81

Answer:Scale factor = 4/9

Perimeter ratio = 4 : 9

Surface area ratio = 16 : 81

Volume ratio = 64 : 729

Step-by-step explanation:

Answer:

28/21

Step-by-step explanation:

tan= opposite/adjacent

Answer:

[tex]\frac{15}{32}[/tex] cups of bread flour.

Step-by-step explanation:

Multiply 3 [tex]\frac{3}{4}[/tex] by [tex]\frac{1}{8}[/tex]

[tex]\frac{1}{8} * 3 \frac{3}{4} = \frac{1}{8} *\frac{15}{4} =\frac{15}{32}[/tex]

Answer:

120 ways

Step-by-step explanation:

Here, we want to calculate the number of ways in which the ribbons can be awarded.

There are 6 competitors and there should only be one first position. What this means is that there are 6 possible ways to become first and 6 possible ways to clinch the gold ribbon.

Now, looking at the second position, since one person already claimed the first, there would be only 5 of the competitors jostling for the second position. This means that the number of ways they can claim the blue ribbon is 5 ways

For the fourth position, there are only 4 competitors wanting to claim the red ribbon. This is because we already have winners for the first and second position.

The number of ways this can be done is thus 4 ways

Now the total number of ways the ribbons can be awarded would be 6 * 5 * 4 = 120 ways

Answer:

12 cm

Step-by-step explanation:

tan B = opposite side / adjacent side

Tan B = AC / BC

.75 = 9 / BC

Multiply each side by BC

BC (.75) = 9

Divide each side by .75

BC = 9/.75

BC =12

Answer:

Use the degree and the leading coefficient to determine the behavior.

Rises to the left and falls to the right

Step-by-step explanation:

Answer:

128 my answer needs to be long so im just gonna span a little

Step-by-step explanation:

i think 120 degrees

to get vertical position

Answer:

Daniel can make 12 outfits

Step-by-step explanation:

3*2*2=12

Answer:0.5 Pound

Step-by-step explanation:

Given

Natalia bought [tex]\frac{3}{4}[/tex] of a pound  of flour to bake cookies

She used [tex]\frac{2}{3}[/tex] of it

i.e. She use [tex]\frac{2}{3}\ of\ \frac{3}{4}\ \text{Pound}[/tex]

[tex]=\frac{2}{3}\times \frac{3}{4}[/tex]

[tex]=\frac{1}{2}\ \text{Pound}[/tex]

So she used [tex]\frac{1}{2}\ \text{Pound}[/tex] of flour.

Answer:

I think it is a 160o Angle

Step-by-step explanation: