A basketball court is 94 feet by 50 feet. Eight fans ca
fit next to each other in a 3 ft. by 3 ft. area. How
many kids would you estimate can fit side by side
over the entire floor?

In other words, you'll use the SAS similarity property with 3/2 as the scale factor

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Explanation:

Choice A is not correct because we don't have enough info about all three pairs of sides.

Instead we'll go with SAS similarity. This is the idea where we'll use two pairs of sides to see if they are in the same proportion, and we'll also use the included angle between the two sides. The angles ABE and DBC are congruent as they are vertical angles. So that's where the "A" comes from in "SAS".

As for the S terms, we divide the corresponding sides like so

DB/AB = 9/6 = 3/2

BC/BE = 1.5/1 = 15/10 = 3/2

The scale factor as a fraction is 3/2, which converts to the decimal form 1.5

This says that triangle DBC has sides that are 3/2 = 1.5 times longer than corresponding sides in triangle ABE.

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If you're curious how the sides correspond, then look at the ordering of ABE and DBC. The order is important when it comes to similar triangles.

AB and DB are the first two letters of ABE and DBC respectively. So we have AB pair up with DB.

Similarly, BE and BC pair up because they are the last two letters of ABE and DBC respectively.

We divide sides of DBC over sides of ABE to get the scale factor from ABE to DBC. The scale factor must be some result larger than 1 do indicate an enlargement is going on.

Answer:

A) $48,720  B) $97,440

Step-by-step explanation:

A)

185 of 4000 = 720

12 months per year

4000 times 12 + 720

48000 + 720 = $48,720

B) 48,720 times 2 = $97,440

*wow she has a bunch of dough*

Answer:

[tex]A(L) = 4L - L^2[/tex]

Step-by-step explanation:

Given

Perimeter = 8m

Required

Determine its area as a function of length

Represent Length and Width with L and W, respectively;

Perimeter (P) is calculated as thus;

[tex]P = 2(L + W)[/tex]

Substitute 8 for P

[tex]8 = 2(L + W)[/tex]

Divide both sides by 2

[tex]4 = L + W[/tex]

Make W the subject of formula

[tex]W = 4 - L[/tex]

Area (A) of a rectangle is calculated as thus:

[tex]A = L * W[/tex]

Substitute 4 - L for W

[tex]A = L * (4 - L)[/tex]

Open bracket

[tex]A = 4L - L^2[/tex]

Represent as a function

[tex]A(L) = 4L - L^2[/tex]

Area of rectangle in terms of length L is

[tex]A(L)= 4L-L^2[/tex]

Given :

A rectangle has perimeter 8 m. Express the area A of the rectangle as a function of the length, L, of one of its sides

We know that the perimeter of rectangle formula is

[tex]perimeter = 2(length)+2(width )[/tex]

perimeter is 8m

Let the length of rectangle is L

[tex]P=2L+2W\\8=2(L+W)\\4=L+W\\W=4-L[/tex]

so width is 4-L

Now we use area formula

Area of rectangle = length times width

[tex]A=L(W)\\A=L(4-L)\\A= 4L-L^2[/tex]

Area of rectangle in terms of length L is

[tex]A= 4L-L^2[/tex]

Learn more : brainly.com/question/5085323

Answer:

Step-by-step explanation:

7.05 p.m we can call it as 19.05

and 1.00 p.m means 13.00

so time  from 19.05 to 24.00 is = 24.00-19.05= 4.55 hr

from 24.00 to 13.00 is = 13.00 hr

so total hr is 4.55 + 13.00= 17.55 hr

Answer:

0.049.

Step-by-step explanation:

The number after the 9 is 4 so 9 remains.

Answer:

0 => -⅘ => 1.5 => 3 => -4 => [tex]-\frac{11}{2} (-5.5)[/tex]

Step-by-step explanation:

The greater the absolute value of a slope, the steeper the slope. By absolute value, we mean the non-negative value of tthe .

To arrange the slope values, from the least steep to the steepest, ignore the negative sign in any of the slope values.

Thus, in the order from the least steep to the steepest, we have:

0 => -⅘ => 1.5 => 3 => -4 => [tex]-\frac{11}{2} (-5.5)[/tex]

The greater the absolute value of the slope, the greater the vertical movement. The greater the vertical movement, the steeper the slope.

A slope value of 0 connotes a horizontal line.

Answer:

4255 students choose Drama

4995 students choose Other

3700 students choose Comedy

Step-by-step explanation:

18500 x _% =

Ex: 18500 x 23% = 4255.

Answer:

3m +7n  +5т

Step-by-step explanation:

6m +7n +5т — Зm

Combine like terms

3m +7n  +5т

Answer:

Pero cuando una magnitud crece y la otra disminuye proporcionalmente, se le llama proporcionalidad Inversa. Dos magnitudes son inversamente proporcionales si al multiplicar (o dividir) una de ellas por un número, la otra queda dividida (o multiplicada) por el mismo número.

Or, But when one magnitude increases and the other decreases proportionally, it is called Inverse proportionality . Two quantities are inversely proportional if when multiplying (or dividing) one of them by a number, the other is divided (or multiplied) by the same number.

Answer:

9

Step-by-step explanation:

Answer:

T = Z + pr

Z + T = pr

Z/r + T/r = p

Answer:

p = Z/r + T/r

Answer:

The answer is below

Step-by-step explanation:

International system of unit (SI unit) are standard units which are universally accepted. There are 7 basic SI units which are meter (m), second (s), kilogram (kg), mole (mol), ampere (A), candela (cd) and kelvin (K).

The SI unit of flow rate is the m³/s.

The conversions needed are:

1 minute = 60 seconds,

1 cm³ = 1 ml = 0.001 ml,

1000000 cm³ = 1 m³,

1 L = 0.001 m³

We have to convert 5.0 liters of blood per minute. to m³/s. Therefore:

[tex]5\ L/minute=\frac{5\ L*0.001\ m^3}{1\ min*60\ s}=8.33*10^{-5} \ m^3/s[/tex]

Answer:

66

Step-by-step explanation:

To find the range, find the difference between the smallest and largest values

The largest value is 193 and the smallest is 127

193 - 127

= 66

The range of Roger's score after he bowled 7 games last weekend is 66

Given scores:

155, 165, 138, 172, 127, 193 , 142

The highest score is 193

Lowest score is 127

Range = Highest score - Lowest score

= 193 - 127

= 66

Therefore, the range of Roger's score after he bowled 7 games last weekend is 66

Read More:

https://brainly.com/question/19411341

Answer:

e(as in variable)=1/7x+2, e(as in euler)=2.388326

Step-by-step explanation:

2.718282

7

+181−179

=2.388326

Answer: Hi!

Since this is a right triangle, we already know that one angle is 90 degrees. Since the angles of a triangle all add up to 180 degrees, and the two unknown angles will be equal, all we have to do is subtract 90 from 180 and then divide the difference by 2!

180 - 90 = 90

90 ÷ 2 = 45

The two missing angles are each 45 degrees.

(x = 45 and y = 45)

Make sure to put the degrees sign after your answers!

Hope this helps!

Answer:

45 degrees.

Step-by-step explanation:

All of the angles in a triangle is 180 degrees.

Knowing that we subtract 90 degrees, the right angle from 180 degrees.

180-90=90

Since both the angles are equal,

90/2=45

Hope this helps :)

Have a great day!

Answer: 162°

Step-by-step explanation:

Using exterior angle methods,

sum total of exterior angle of polygon =  ³⁶⁰/ₙ , where n is the size of the polygon.                                                 =   ³⁶⁰/₂₀

One exterior angle                               =  18°.

Now the interior angle                          = 180° - 18° ( angle on a straight line )

Therefore, the measure of the interior angle = 162°.

Not , Other methods can still be applied.

Answer:

We have a circular track that is 1 meter wide, which would mean that the diameter is equal to 1 meter.

First, we want to define this problem as a one dimensional problem. The position 0 is in the doorway, the bedroom is the positive axis, and the hallway is the negative side.

P(t) = R*cos(c*t) + R*sin(c*t).

Where R is the amplitude, in the case of the circular motion, R is equal to the radius.

If the diameter is 1m, the radius is 1m/2 = 0.5m

The equation now is:

P(t) = 0.5m*cos(c*t) + 0.5m*sin(c*t).

We also know that for t = 0s, the train is as far into the bedroom as it can, the maximum position is P = 0.5m

Then  we have:

P(0s) = 0.5m*1 + 0.5*0 = 0.5m

And we also know that the period is t = 2seconds.

The period for the sine and cosine functions is 2*pi, then:

c*2s = 2*pi

c =pi/s

The function now is:

P(t) = 0.5m*cos(t*pi/s) + 0.5m*sin(t*pi/s)

When this function is positive, this means that the train is inside her bedroom, when the function is negative, the train is outside the bedroom, when P(t) = 0, the train is in the doorway.

Answer:

24.78%

Step-by-step explanation:

Initial price = $230

Final price = $287

change in price = final price - initial price

= 287 - 230

= $57

Percent change

= (change in price / initial price) x 100%

= (57 / 230) x 100%

= 24.78%

Answer:

Her return is  [tex]R = 0.10[/tex]

Step-by-step explanation:

From the question we are told that

   The number of shares purchased is [tex]n = 100 \ shares[/tex]

    The  cost price  of each share is  [tex]x = \$ 20[/tex]

    The limit order is    [tex]y = \$ 33[/tex]

    The first  market price for each share is  [tex]k = \$ 23[/tex]

    The second   market price for each share is [tex]u = \$ 26[/tex]

     The  third market price for each share is  [tex]w = \$ 22[/tex]

Generally the  limit order would  not be  executed given that it is higher than the market opening and  closing price.

  Considering Rebecca's initial investment of $ 20 per share, her return is mathematically evaluated as

         [tex]R = \frac{w + d - x}{x}[/tex]

Here d stands for the dividend but since we are told that the stock did not pay any dividend

        [tex]R = \frac{22 + 0 - 20}{20}[/tex]

         [tex]R = 0.10[/tex]

Answer:

£837.5

Step-by-step explanation:

If she has 50 m² and it costs £16.75 for every m² of concrete, 50 × 16.75 = £837.5.

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

Explanation:

If sin(x) = 3/5, then cos(x) = 4/5 through the use of the trig identity

sin^2(x) + cos^2(x) = 1

This is assuming that x is in quadrant Q1.

Plug those values into the identity below and simplify.

sin(2x) = 2*sin(x)*cos(x)

sin(2x) = 2*(3/5)*(4/5)

sin(2x) = 24/25

Answer:

24/25

Step-by-step explanation:

Trig functions relate the angle of a triangle with the sides of that triangle (right triangle)

sin(x)= 3/5 (opposite/ hypotenuse) (25=9-x^2, using pythag. theorem, remaining side= 4)

now, cos(x)= 4/5

now, the double angle identity states:

sin2x= 2sinxcosx

so,

sin2x= 2 * (3/5) * (4/5) =

24/25

Answer:

12 arrangements with 5 lilies and 3 daisies

Step-by-step explanation:

Answer:

The answer is A

Its A.

Reasoning: Because I Took The Test

Step-by-step explanation:

After you find the sums for each set, make a list, counting the number of ways a sum can occur.

You'll notice that for Set A, sums of 5, 6, 7, 8, and 9 all appear 4 times.  So they have equal probabilities.  In Set B, a sum of 7 appears 6 times.  Sums smaller or larger than 7 are less common.

When we look at the data, we see that were more sums of 7 than any other sum.  So this data was probably from Set B.

Answer:

Proportions have not changed significantly ( B )

Step-by-step explanation:

GIVEN DATA :

Test statistic = 4.99

significance level = 1% = 0.01

k ( number of groups ) = 3

will we use the chi-squared test to determine the degree of freedom

which is : k-1 = 3 - 1 = 2

looking at the chi-square table to determine the critical value of the test

at significance level = 0.01 and degree of freedom = 2 the critical value = 9.21

Comparing the test value ( 4.99 ) and the critical value ( 9.21 ) it can seen  that the test value < critical value  which is a condition for not rejecting null hypothesis of the test.

therefore we won't reject the null hypothesis

Answer:

the answer is 14.08

Step-by-step explanation:

Question:

Suppose we want to choose 5 objects, without replacement, from 16 distinct objects.

A) How many ways can this be done, if the order of the choices is relevant?

B) How many ways can this be done, if the order of the choices is not relevant?

Answer:

A. 4368 ways

B. 524160 ways

Step-by-step explanation:

Given

[tex]Objects = 16[/tex]

[tex]Selection = 5[/tex]

Required

A & B

Solving (A)

Because the order of choice is irrelevant, this implies combination and it is calculated as follows;

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

Where n = 16 and r = 5

[tex]^{16}C_5 = \frac{16!}{(16-5)!5!}[/tex]

[tex]^{16}C_5 = \frac{16!}{11!5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12 * 11!}{11!5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12}{5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12}{5 * 4 * 3 * 2 * 1}[/tex]

[tex]^{16}C_5 = \frac{524160}{120}[/tex]

[tex]^{16}C_5 = 4368\ ways[/tex]

Solving (B)

Because the order of choice is relevant, this implies permutation and it is calculated as follows;

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

Where n = 16 and r = 5

[tex]^{16}P_5 = \frac{16!}{(16-5)!}[/tex]

[tex]^{16}P_5 = \frac{16!}{11!}[/tex]

[tex]^{16}P_5 = \frac{16 * 15 * 14 * 13 * 12 * 11!}{11!}[/tex]

[tex]^{16}P_5 = 16 * 15 * 14 * 13 * 12[/tex]

[tex]^{16}P_5 = 524160\ ways[/tex]

Answer:

5/8 of a gallon

Step-by-step explanation:

since a cup is 1/16 of a gallon and were asked what part of a gallon is 10 cups so what were going to do is....

(1/16)*10= 10/16 = 5/8

Answer:

-8.

Step-by-step explanation:

y = 8 - 2x.

x = 8.

y = 8 - 2(8)

= 8 - 16

= -8.

Hope this helps!