1 point
Jayden is making a chain from construction paper from red and green paper links. The
pattern of the links is red, red, green, green, green. If there are 30 links all together, how
many are red and green?

Pascal's triangle is a way of organizing the coefficients in the binomial expansion, [tex](a+b)^n[/tex]:

n = 0   =>  1

n = 1    =>  1   1

n = 2   =>  1   2   1

n = 3   =>  1   3   3   1

n = 4   =>  1   4   6   4   1

and so on, where each row starts and ends with a 1, and the numbers in the middle are obtained by adding together the two numbers directly above and to the left. These coefficients are then mulitplied by descending powers of a and descending powers of b (or vice versa, because the pattern is symmetric), starting with 0 and going up to n.

In this case, we have

[tex](x+4)^3=1\cdot x^3\cdot4^0+3\cdot x^2\cdot4^1+3\cdot x^1\cdot4^2+1\cdot x^0\cdot4^3[/tex]

Notice how the powers of x and 4 always sum to n = 3.

Simplifying, we get

[tex](x+4)^3=x^3+12x^2+48x+64[/tex]

so that

a = 1

b = 3

c = 12

d = 2

e = 48

f = 1

g = 64

Answer:

63 dimes

Step-by-step explanation:

Set up a system of equations where d is the number of dimes and q is the number of quarters:

d + q = 106

0.1d + 0.25q = 17.05

Solve by elimination by multiplying the top equation by -0.25 to eliminate q:

-0.25d - 0.25q = -26.5

0.1d + 0.25q = 17.05

Add together and solve for d:

-0.15d = -9.45

d = 63

So, there were 63 dimes in the piggy bank

Answer:

25°

Step-by-step explanation:

[tex]55 \degree = \frac{1}{2} \bigg \{(100 \degree + 35 \degree) - x \bigg \} \\ 55 \degree \times 2 = 135 \degree - x \\ 110 \degree = 135 \degree - x \\ x = 135 \degree - 110 \degree \\ \huge \red{ \boxed{ x = 25 \degree}}[/tex]

Answer:

Step-by-step explanation:

Answer:

It's point W!!!

Step-by-step explanation:

Have a great day :)

I think that the answer is 21.2 .I can't say it with confidence but still maybe it will help you

Answer:

The bowl's diameter is 35.8 cm

Step-by-step explanation:

Recall that 1 liter = 1000 cubic cm ad have in mind that in order to get a diameter in cm, we would need to write the volume of the bowl in cubic cm.

if 6 liters is 1/4 of the bowl, then 4 times 6 liters must fill the bowl. That is: the volume of the sphere is 24 liters.

24 liters in cubic cm is: 24000 cubic cm

now, we need to use the formula for the volume of a sphere of radius R:

[tex]Vol=\frac{4}{3} \pi\,R^3\\24000=\frac{4}{3} \pi\,R^3\\R^3=\frac{24000\,(3)}{4\,\pi} \\R=\sqrt[3]{\frac{24000\,(3)}{4\,\pi} } \\R\approx 17.894\,\,cm[/tex]

therefore, the diameter of the bowl is twice this radius value:

[tex]Diameter\approx 17.894\,* 2=35.788\,\,cm[/tex]

this value rounded to 3 significant figures is: 35.8 cm

Answer:

Following are the answer to this question:

Step-by-step explanation:

According to Eucharistic algorithm:

[tex]gcd(un+1,un) = gcd (un+1-un, un)[/tex]  

                        [tex]= gcd (un , un-1)[/tex]

so many recursions following  

It was the first two the Fibonacci 1,1 numbers  

[tex]gcd(un+1, un) = gcd(1,1) = 1 \\\\ from 1 =1 \text{and euclidean principle} \\\\?gcd (un+1,un ) = 1[/tex]

Answer:

11 years

Step-by-step explanation:

t=time

1700+50t=600+150t

The reason we have this equation is because they both have the same time and based on the initial numbers that they have equating the two will give you the exact year and number of students of both school.

Answer:

50%

Step-by-step explanation:

There are a total of 5 + 5 = 10 socks

Knee high socks = 5

=> 5/10 = the probability of getting knee high socks

=> 1/2

=> 50%

Answer:

1/2

Step-by-step explanation:

5 pairs of knee high socks and 5 pairs of crew socks= 10 pairs of socks

P ( knee high) = number of knee high/ total

                       = 5/10 = 1/2

Answer:

A. 23.6

Step-by-step explanation:

Let the dotted line be y

Then

and

So

Correct answer is A. 23.6

Answer:

23.6

Step-by-step explanation:

Answer:

f^-1(x) = 1/5 x

Step-by-step explanation:

y = 5x

Exchange x and y to find the inverse

x = 5y

Solve for y

1/5x = y

The inverse is 1/5x

Answer:

[tex]\Large \boxed{f^{-1}(x)=\frac{x}{5} }[/tex]

Step-by-step explanation:

f(x) = 5x

Replace f(x) with y.

y = 5x

Switch variables.

x = 5y

Divide both sides by 5.

[tex]\frac{x}{5} =y[/tex]

Answer:

Number of steps per floor= 18 steps

Step-by-step explanation:

he counted 252 steps. Emilio lives on the 14th floor.

The number of steps between the ground floor and the fourteenth floor.

Let's bear in mind that there 14 floors .

Number of steps per floor= total steps/floor

Number of steps per floor= 252/14

Number of steps per floor= 18 steps

Answer:

Its an integer number

Step-by-step explanation:

hope this helps✨

Answer:

8/11

Step-by-step explanation:

3 mechanics and 8 electricians = 11 employees total

if one selected at random the possibility of the employee to be an electrician is 8/11

Start by finding the slope of the line.

m = y2 - y1 / x2 - x1

m = 5 - 2/1 - 0 ⇒ 3/1 ⇒ 3.

So the slope of the line is 3.

This can be used with either one of our two points

to write the equation of the line in point-slope form.

So let's go with the point (0, 2).

Point-slope form is written y - y1 = m(x - x1).

Since we are using the point (0, 2), y - y1 would be y - 2.

"m" would be 3 and x1 would be 0.

So we have y - 2 = 3(x - 0).

Answer:

120

Step-by-step explanation:

Answer:

DCE and BCA

Step-by-step explanation:

Vertical angles are angles which lie directly opposite each other on intersecting lines. Because of this they are equal, and share the same vertex. Out of these pairs, only DCE and BCA are vertical angles because they lie opposite to each other on the lines FJ and IM, and share a vertex of point C.

Hope this helped!

Answer:

Step-by-step explanation:

We observe that the values in the top row are sequential, and that the values in the bottom row have a common difference of 32. That means the sequence is an arithmetic sequence.

__

The values in the table form an arithmetic sequence. The term values are shown in the bottom row, and the term numbers are shown in the top row. This sequence is associated with a linear function. The domain of the function is the set of time values: greater than or equal to zero.

__

Comment on the function

This function seems to be the linear function ...

  distance = 32×time - 16

It seems a little odd that the distance associated with time zero is negative. We usually think of distance as a positive value, whereas displacement can be a signed value.

As a rule, time is measured as positive from some reference point (the start of motion, for example). Here, we have no reason to believe that the function is intended to be defined for negative time values.

Answer:

arithmetic

bottom

top

linear

≥ 0

Step-by-step explanation:

Answer:

volume = 4/3

Step-by-step explanation:

volume of the solid can be calculated using the given data :

x = 0,

y = z^2,

z = 0,   z = 2-x-y

attached below is the detailed solution and a free hand sketch of the boundaries of the solid

Answer:

3x+4=72-x (congruent triangle side are equal)

3x+x=72-4

4x=68

X=68/4

therefore,X=17 ans

Answer:

x = 17

Step-by-step explanation:

[tex]\because\triangle IJK \cong \triangle PQR.....(given)\\\therefore \angle I \cong \angle P....(cact)\\\therefore m\angle I = m\angle P\\\therefore 3x+4 = 72-x\\\therefore 3x+x = 72-4\\\therefore 4x = 68\\\therefore x = \frac{68}{4}\\\therefore x = 17[/tex]

Answer:

Hey there!

It's easier to graph a function in slope intercept form:

y+6=-3(x+5)

y+6=-3x-15

y=-3x-21

So, the slope is -3, and the y intercept is -21.

I'll attach a graph of the function down below

Let me know if this helps :)

Answer:

A. -4

Step-by-step explanation:

F(-1) means we must plug the number "-1" in for each x.

F(x) = x^2 + 3x - 2

F(-1) = (-1)^2 + 3(-1) - 2

= 1 - 3 - 2

= -4

Answer:

first answer

(x+1)(x+2)/2

Step-by-step explanation:

flip the second term and multiply

(x²-4x-5)/(x-2) * (x²-4)/(2x-10)

(x-5)(x+1)/(x-2) * (x+2)(x-2)/2(x-5)  

(x+1)(x+2)/2

Answer: 0.001 kilometer in 1 meter

Step-by-step explanation:

1 kilometer = 1000 meter

so there are 0.001 kilometer in 1 meter

Answer:

51.96 mm² approximately

Step-by-step explanation:

the first thing you should know is that the area of a rectangle is base*height sin of (

the included angle i.e

Arectangle= bh sin90° since all angles of a rectangle are equal then the included angle is 90°

Arectangle= bh sin90° since sin90 is 1 we simply use the equation bh because multiplying bh by one is bh. bearing this in mind , the area of the parallelogram can be calculated as:

Aparallelogram= bh sin of sin of the included angle

Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°

Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866

Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866Aparallelogram=51.96 mm² approximately

Answer: 1.6 hours.

Step-by-step explanation:

Ok, the speed of the bats is 99mph.

Here we can think this situation as a circle where the radius is growing at a speed of 99mph.

We assume that the initial radius is r = 0, and we can write the equation of the radius as a linear equation that depends on the time t.

r(t) = 99mi/h*t

First, let's find the radius that we need:

The area of a circle is:

A = ´pi*r^2

If we want A = 80,000 mi^2 we have:

80,000 mi^2 = 3.14*r^2

r = √(80,000 mi^2/3.14) = 159.6 mi

So the radius must be 159.6 miles.

Now, we know that the speed at which the radius increases is 99miles per hour, and we also know that:

Distance = Speed*Time.

in this case:

Distance = 159.6 mi

Speed = 99mi/h

Time = is the thing we want to find.

159.6mi = 99mi/h*T

T = 159.6mi/99mi/h = 1.6 hours.

The third quartile, or the value at which 75% of all days the stock is below, is $14.3325.

Used the formula that states,

the range of the distribution by subtracting the minimum value from the maximum value:

Range = Max value - Min value = $15.17 - $11.82 = $3.35

Given that the stock value follows a uniform distribution from $11.82 to $15.17.

Hence,

Range = $15.17 - $11.82

= $3.35

Now, the uniform distribution is symmetric, and the median (50th percentile) is the midpoint of the range,

Median = (Min value + Max value) / 2

= ($11.82 + $15.17) / 2

= $13.495

Hence, the third quartile (75th percentile);

75th percentile = Median + (0.25 × Range)

= $13.495 + (0.25 × $3.35)

= $13.495 + $0.8375

= $14.3325

To learn more about the third quartile visit:

https://brainly.com/question/9180614

#SPJ12

Answer: 121

Step-by-step explanation:

If 2^x = 5, what is the value of 2³^×

This can also be re arranged in the form

(2^x)³ - 4

Since 2^x = 5, we now substitute for the value in the expression above.

5³ - 4

= 125 - 4

= 121.