Finding the Constant of Proportionality from a Graph

Answer:

C. 1365

Step-by-step explanation:

The expression nCr can be written with the simple equation:

n! / ((n-r)! * r!)

So to evaluate 15C4:

15! / ((15-4)! * 4!)

= 1365

So 15C4 = 1365

Cheers.

Answer:

1365

Step-by-step explanation:

15!/4!(15-4)!

1365

Answer:

Step-by-step explanation:

Area of the basket ball court = Length * Breadth (since it is rectangular in nature)

Area of the basket ball court = 94 feet * 50 feet

Area of the basket ball court = 4700ft²

Area of the space covered by 8 kids = 3ft * 3ft = 9ft²

To know the number of kids that would fit the entire floor, we will use the expression;

Number of kids in the floor = 8*Area of the basket ball court /Area of the space covered by 8 kids = 8*4700/9

= 8*4700/9

= 8*522.22

≈ 4,178 kids

Hence approximately 4,178 kids can fit side by side  over the entire floor

Answer:

7

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Answer: x=-3

Step-by-step explanation:

move -9 over to -12 and the 9 becomes positive and then add -12+9 and your answer will be negative

Answer: (a). 0.2% (b). 0.4%

Step-by-step explanation:

This is quite straightforward, so let us follow this carefully.

(a) let us consider the expression that was given in the question;

(8.47 + 0.06)1/3 from the binomial expression,

⇒  (x + ∆x)n = xn + nxn-1∆x

So using the stated formula above

(8.47 + 0.06)1/3 = (8.47)1/3+ 1/3(8.47)1-(1/3) (0.06) = 2.038 + 1/3(8.47)(2/3) (0.06)

= 2.038 + 0.005

This gives us the algebric value as x = 2.038

Also, the uncertainity is ∆x = 0.005

Let us calculate the percentage of relative uncertainity;

Relative uncertainity percent is given thus;

⇒ (∆x / x) * 100

= (0.005 / 2.038) * 100 = 0.2%

We have that the relative uncertainity percent is 0.2%

(b). Also we will consider the expression;

log(6.56 + 0.05)

Let us apply the binomial expression to this;

log(6.56 + 0.05) = log(6.56) + ((0.05)2 / 6.56) = 0.817 + 0.003

This makes the algebric value of x = 0.817

and the uncertainity is  ∆x = 0.003

Therefore the Relative uncertainity percent is = (∆x / x) * 100

= (0.003 / 0.817) * 100 = 0.4%

We have the relative uncertainity percent as 0.4%

cheers I hope this helped !!

☺ Hi ☺

Find the value of 4!.

• Let's find the value of 4! :

[tex]4! = 4 × 3 × 2 × 1 = {24}[/tex]

Answer:

a^2=b^2+c^2.

a^2=10^2+17^2.

a^2=100+289.

a^2=389.

a=√389.

a=19.72~20cm.

Answer:0.222222

Step-by-step explanation:

DIVIDE 2 BY 9

Answer: .18

Step-by-step explanation:

Answer:

49 or 7^2

Step-by-step explanation:

9 x 5 + 4

=> 45 + 4

=> 49 or 7^2

Answer: 49

Step-by-step explanation: Multiply 9 and 5. Then add 4. Use PEMDAS.

9 × 5 = 45

45 + 4 = 49

Answer:

Step-by-step explanation:

[tex]a.\\sin \theta =\frac{12}{13}\\\theta=sin ^{-1}(\frac{12}{13}) \approx 67^\circ\\b.\\cos75=\frac{x}{13}\\x=13 cos ~75 \approx 7.5 ~ft[/tex]

it forms a right angled triangle.

ladder=hypotenuse.

side of house=perpendicular.

from the base of house to the foot of ladder on the ground=base

Answer:

See Explanation

Step-by-step explanation:

[tex] \overline{CB} ||\overline {ED}... (GIVEN) \\

\& BD\:\&\: CE \: are \: transversals\\

\angle CBF\cong \angle EDF.. (alternate \: \angle 's) \\

\overline{CB} \cong \overline {ED}..... (GIVEN) \\

\angle BCF \cong \angle FED.. (alternate \: \angle 's) \\

\therefore \triangle CBF \cong \triangle EDF.. (By \: ASA\: Postulate) [/tex]

Answer:  see proof below

Step-by-step explanation:

   Statement                     Reason

1. CB || ED                       1. Given

2. ∠E ≅ ∠C                     2. Alternate Interior Angle Postulate

3. ∠D ≅ ∠B                     3. Alternate Interior Angle Postulate

4. CB ≅ ED                     4. Given

5. ΔCBF ≅ ΔEDF            5. ASA Congruency Theorem

Answer:

252* warmer

Step-by-step explanation:

130 -(-122) = 130 + 122 = 252

Answer:

vertical angles

Step-by-step explanation:

Opposite angles that are congruent are known as vertical angles.

Answer:

Just two

Step-by-step explanation:

Glorias teacher asks her to draw a triangle with 90 degree angle and a 42 degree angle.

The presence of 90 degrees indicates that it's a right angle triangle.

The remaining angle= 180-90-42

The remaining angle= 48 degrees

Due to the presence of 90 degrees, the angle 42 and 48 degrees will interchange two times only to form only two unique triangles.

the answer is:

A. -16

Hi there! Hopefully this helps!

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

[tex]17 = r + 10[/tex]

Swap sides so that all variable terms are on the left hand side.

[tex]r + 10 = 17[/tex]

Subtract 10 from both sides.

[tex]r = 17 - 10[/tex]

Answer:

40

Step-by-step explanation:

4 is in "Ten's place".

So, the number is multiplied with 10.

=> 4 x 10

=> 40

The value of 4 in 45 = 40

Answer: [tex]f(x)=-x[/tex]

Step-by-step explanation:

When f(-x)= -f(x), then it is known as an odd function.

i) [tex]f(x) = x^3 + 5x^2 + x[/tex]

Then, [tex]f(-x)=(-x)^3+5(-x)^2+(-x)=-x^3+5x^2-x\neq -x^3-5x^2-x[/tex]

i.e. [tex]f(-x)\neq-f(x)[/tex]

ii) [tex]f(x)=\sqrt{x}[/tex]

[tex]f(-x)=\sqrt{-x}\neq-\sqrt{x}[/tex]

i.e. [tex]f(-x)\neq-f(x)[/tex]

iii) [tex]f(x)=x^2+x[/tex]

[tex]f(-x)=(-x)^2+(-x)=x^2-x\neq-x^2-x[/tex]

i.e. [tex]f(-x)\neq-f(x)[/tex]

iv) [tex]f(x)=-x[/tex]

[tex]f(-x)=-(-x)=x[/tex]

[tex]-f(x)=-(-x)=x[/tex]

i.e. [tex]f(-x)=-f(x)[/tex]

Hence, f(x) is an odd function.

Answer:

D

Step-by-step explanation:

if you don't want to read

Answer:

Hey there!

Well first, don't feel bad, since trig is really hard, especially if you are just learning it.

If you've learned about SOH CAH TOA, you will see that TOA is the best identity to use here.

tangent 20=x/10

tangent 20 (10)=x

x=3.64

Let me know if you have any other trig questions, I'm always here to help :)

Answer:

15% above the trend.

Step-by-step explanation:

A time series represented by Y comprises of dataset observed over a particular period of time. Time series is handy in determining the future of a particular business.

In a multiplicative model, if the seasonal factor is 1.15 for a particular season, then we expect that the time series in that season would be

Y = T × C × S × 1

where;

Seasonal S = 1.15

As such Y would increase by 15% above the trend if all other things are being equal.

Answer:

Approximately 2 days.

Step-by-step explanation:

The frog can only jump 3 lily pads each day.

24 hours = 1 day

[tex]\frac{24}{3}[/tex] = 8 hours

Thus, it would take the frog 8 hours to cover a lily pad.

To get to the edge of the pond, the frog would jump through 6.5 lily pads (since he is at the middle of a lily pad at the center of the pond).

So that;

Total time required to get to the edge of the pond can be determined by;

6.5 × 8 hours = 52 hours

Number of days to get to the edge of the pond = [tex]\frac{52}{24}[/tex]

                                                                    = 2.2

It would take him approximately 2 days to get to the edge of the pond.

Answer:

−(−45)

I hope this helps.

Answer:

−(−45)

Step-by-step explanation:

Answer: ( -0.731,  0.682)

Step-by-step explanation:

The unit vector is defined as a vector that points in the same direction as our vector (137 degrees from the x-axis) and has a magnitude of 1.

Knowing the angle, is really simple to do it.

First, we know that for a radius R and an angle A, the rectangular coordinates can be written as:

x = R*cos(A)

y = R*sin(A)

And if we want that the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 137°

x = 1*cos(137°) = -0.731

y = 1*sin(137°) = 0.682

Then the unit vector is: ( -0.731,  0.682)

The unit vector is ( -0.731,  0.682)

[tex]x = R\times cos(A)\\\\y = R\times sin(A)[/tex]

And the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 137°

so,  

[tex]x = 1\times cos(137) = -0.731y = 1\times sin(137) = 0.682[/tex]

Then the unit vector is: ( -0.731,  0.682)

learn more: https://brainly.com/question/20492533?referrer=searchResults

Answer:

(0,-4) (5,0)

Step-by-step explanation:

4x-5y=20

First, we must put the equation into slope intercept form: y= mx+b

5y=4x-20=y=4/5x-4

The y intercept, by definition, is b. In this scenario, b is -4.

One ordered pair that works is (0,-4).

Also, we can find the ordered pair for the x intercept. By definition, the x intercept is the value of x when y equals zero. hence, we substitute 0 for y and then we can find an ordered pair that works and solve for x!:

Therefore, (5,0) works as well!

Answer:

Number of salsa batches produced = 18 batches

Step-by-step explanation:

Given:

1 red onion = 12 batch of salsa

Amount of red onion = one and half (1.5)

Find:

Number of salsa batches produced

Computation:

Number of salsa batches produced = 1.5 × 12

Number of salsa batches produced = 18 batches

Answer: b) 6.10%

Step-by-step explanation:

to find the probability for the other bag to contain exactly 4 balls at that time;  

is only possible if you have chosen a particular bag 10 times and other bag 6 times.

After that, once again at the 17th attempt

so the required probability =     ¹⁶c₁₀ × (1/2¹⁰ × (1/2)⁶ × (1/2)

= 0.610

CONVERT TO PERCENT

0.610 × 100

= 6.10%

Answer:

f(x) = -5 if -5 <= x <= -3

f(x) = -2 if -3 < x <= 2

f(x) = 5 if 2 < x <= 6

Step-by-step explanation:

This is a simple piece wise function. Notice there are three lines or "solutions" for y-values over a range of x-values. Also notice there are filled in and not filled in circles. If the circle is not filled in, then it is not a solution. If it is, then it is a solution.

So for this, -5 is the solution if the range of x is from -5 through -3 inclusive since it has filled in circles.

-2 is a solution if the range of x is from -3 exclusive through 2 inclusive since at -3 it's open circle and 2 is filled.

5 is a solution if the range of x is from 2 exclusive through 6 inclusive since 2 it's open circle and 6 is filled.

To right that in notation simply

f(x) = -5 if -5 <= x <= -3

f(x) = -2 if -3 < x <= 2

f(x) = 5 if 2 < x <= 6

Cheers.