[tex]\frac{-23}{30} + \frac{5}{48}[/tex]

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:

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

Answer:

j

Step-by-step explanation:

Answer:

200 words per minute

Step-by-step explanation:

1000:5

1000/5 reduced will give you your unit rate.

200 words/minute

If 1000 words were read in 5 minutes, each minute would be 1000 divided by 5 which is 200.

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:

Its an integer number

Step-by-step explanation:

hope this helps✨

Answer:

B. 0.09x

Step-by-step explanation:

x is the initial price.

0.09x is the 9% sales tax.

-30 is the instant rebate.

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:

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:

1.125 feet

Step-by-step explanation:

1 yard = 3 feet

3/4 yard = 2.25 feet

2.25 feet / 2 = 1.125 feet per frame

i hope this helps!

-TheBusinessMan

Answer:

The value for the test statistics = 3.48

Step-by-step explanation:

Given that:

population mean [tex]\mu[/tex] = 75

sample size n = 25

sample mean [tex]\overline x[/tex]= 78.48

standard deviation = 5

The value for the test statistics can be computed by using the formula:

[tex]z = \dfrac{\overline x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{78.48- 75}{\dfrac{5}{\sqrt{25}}}[/tex]

[tex]z = \dfrac{3.48}{\dfrac{5}{5}}[/tex]

z = 3.48

The value for the test statistics = 3.48

Answer:480

Step-by-step explanation:

To find volume u need to multiply height * width * length

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:

120

Step-by-step explanation:

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:

1/24

Step-by-step explanation:

1/3÷ 8

Copy dot flip

1/3 * 1/8

1/24

Answer:

1/24

Step-by-step explanation:

Answer:

well you put a plus sign, but im letting you know I did the division.

Step-by-step explanation:

The answer is 35 remainder 11.

Hope this helped

Answer:

It's point W!!!

Step-by-step explanation:

Have a great day :)

Answer:

c or b

Step-by-step explanation:

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:

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:

[tex]x^{-2}y^{-5}[/tex]

Step-by-step explanation:

The options are not given; however, the question can still be solved

Given

[tex]y^{-8}y^3x^0x^-2[/tex]

Required

Simplify

Start by rewriting the expression

[tex]y^{-8} * y^3 * x^0 * x^{-2}[/tex]

Apply the following laws of indices: [tex]a^x * a^y = a^{x+y}[/tex]

This gives:

[tex]y^{-8+3} * x^{0-2}[/tex]

Evaluate the exponents

[tex]y^{-5} * x^{-2}[/tex]

[tex]x^{-2}y^{-5}[/tex]

Hence, [tex]x^{-2}y^{-5}[/tex] is equivalent to [tex]y^{-8}y^3x^0x^-2[/tex]

Answer:

The answer is- (Drumroll)

Step-by-step explanation:

The answers are [tex]x^-2y^-5[/tex], and [tex]1/x^2y^5[/tex]

Answer:

Step-by-step explanation:

Given h(t) = t²+t+ 12 and k(t) = √t-1, we are to find k(k.h)(10)

k{h(t)} = k{ t²+t+ 12}

Since k(t)= √t-1, we will replace the variable t in the function with t²+t+ 12

k(h(t)) = √{(t²+t+ 12)-1}

k(h(t)) = √t²+t+12-1

k(h(t)) = √t²+t+11

Substituting t = 10 into the resulting function;

k(h(10)) =  √(10)²+(10)+11

k(h(10)) = √100+10+11

k(h(10)) = √121

k(h(10))= 11

hence the value of  (k compose h) (10) is 11

Answer:

B. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.

Step-by-step explanation:

non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa. From the example, Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent. So if Jon got a face card, he would not have eight of clubs

Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.

Given,

Statements .

Here,

Non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa.

For instance,

Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent.

So if Jon got a face card, he would not have eight of clubs .

Thus option B is correct statement .

Know more about mutually exclusive events,

https://brainly.com/question/28565577

#SPJ6

Answer:

see explanation

Step-by-step explanation:

Assuming you require the derivative of f(x) from first principles, then

f' (x) = [tex]lim_{h>0}[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]

       = [tex]lim_{h>0}[/tex] [tex]\frac{\frac{1}{(x+h)}-\frac{1}{x} }{h}[/tex]

       = [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-(x+h)}{x(x+h)} }{h}[/tex]

       = [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-x-h}{x(x+h)} }{h}[/tex]

        = [tex]lim_{h>0}[/tex] [tex]\frac{-h}{hx(x+h)}[/tex] ← cancel h on numerator/ denominator

        =  - [tex]\frac{1}{x^2}[/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:

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:

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:

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:

n = 10.286      aprox.

Step-by-step explanation:

n+4 + n/6 = 16

n/6 = 16 - 4 - n

n = 6(12-n)

n = 6*12 + 6*-n

n = 72 - 6n

n + 6n = 72

7n = 72

n = 72/7

n = 10.286       aprox.

verify:

10.286 + 4 + (10.286/6) = 16

14.286 + 1.714 = 16