A snack bar weighs 61g, and 10% of the weight is apple. How many
grams of apple are in the snack bar?

Answer:

[tex]90^{\circ}[/tex]. In other words, these two vectors are perpendicular (orthogonal) to one another.

Step-by-step explanation:

Let [tex]\|a\|[/tex] and [tex]\|b\|[/tex] denote the magnitudes of vector [tex]a[/tex] and vector [tex]b[/tex]. The dot product between these two vectors is represented as [tex]a^{T}\, b[/tex].  Let [tex]\theta[/tex] denote the angle between the two vectors. The cosine of this angle would be equal to:

[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|}\end{aligned}[/tex].

The dot product between vector [tex]a = \langle 1,\, 2\rangle[/tex] and [tex]b = \langle 1,\, -1/2\rangle[/tex] is:

[tex]\begin{aligned}a^{T}\, b &= {\begin{bmatrix}1 \\ 2\end{bmatrix}}^{T}\, \begin{bmatrix}1 \\ -1/2\end{bmatrix} \\ &= 1 \times 1 + 2 \times \left(-\frac{1}{2}\right) \\ &= 0\end{aligned}[/tex].

The magnitudes of the two vectors are:

[tex]\begin{aligned}\| a \| &= \sqrt{1^{2} + 2^{2}} \\ &= 5\end{aligned}[/tex].

[tex]\begin{aligned}\| b \| &= \sqrt{1^{2} + \left(-\frac{1}{2}\right)^{2}} \\ &= \frac{1}{2}\, \sqrt{5}\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|} \\ &= \frac{0}{5 \times (\sqrt{5} / 2)} \\ &= 0\end{aligned}[/tex].

Among all angles between [tex]0^{\circ}[/tex] and [tex]180^{\circ}[/tex], the only angle with a cosine of [tex]0[/tex] is [tex]90^{\circ}[/tex]. Therefore, the angle between vector [tex]a[/tex] and vector [tex]b[/tex] must be [tex]90^{\circ}\![/tex]. Hence, these two vectors are perpendicular to one another.

Answer:   i think it will take 48 hours

Step-by-step explanation:

here's how to get 48 so basically 450-400-2= 48

now if you end up doing 400 - 450 then you will get -50 if you do 400-450-2 you will get a -52 so you want to make sure you do the biggest number first and then do the smaller numbers to get 48 like 450 - 400 - 2 and then you will have 48

i hope this helps!

Answer:

  442 ft²

Step-by-step explanation:

The amount of insulation needed is the amount that covers the area of the side walls and the ceiling. The area of the side walls is the product of the perimeter and height. The area of the ceiling is the product of length and width.

__

Lateral area = Ph = 2(L+W)h = 2(15 ft +8 ft)(7 ft) = 322 ft²

Ceiling area = LW = (15 ft)(8 ft) = 120 ft²

__

Insulation needed = lateral area + ceiling area = 322 ft² +120 ft²

Insulation needed = 442 ft²

Answer: C. 6t

Step-by-step explanation:

T is unknown, but because you are only asked for the equation to figure out the total,  you simply multiply the 6 chairs per t, or table together, 6t

Answer:

Asher should be 61

Step-by-step explanation:

Answer:

Maybe 8

Step-by-step explanation:

because its the same side

Answer:

f(x)-2x+4

Step-by-step explanation:

f(x)-g(x)

f(x)-g(x)=f(x)-(2x-4)

f(x)-(2x-4) remove parentheses for addition or subtraction

f(x)-2x+4

Answer:

2/125 or 0.016

Step-by-step explanation:

0.1= 1/10

1/10^3 × 2^-4

2 × 1/5^3

2 × 1/125

2/125

Answer:

The answer should be 3 :)

Step-by-step explanation:

Pick a point on f(x) and count up until you hit the g(x) point :)

When i did this, i got 3 :)

Have an amazing day!!

Please rate and mark brainliest!!

[tex]\dfrac 6p = x+a\\\\\implies \dfrac 6p \times\dfrac 16 = (x+a) \times\dfrac 16 ~~~~~~;\left[\text{Multiply both sides by}~ \dfrac 16 \right]\\\\\implies \dfrac 1p = \dfrac{x+a}6\\\\\implies p= \dfrac{6}{x+a}~~~~~~~~~~~~~~~~~~~~;[\text{Cross multiply}][/tex]

Answer:

depends mostly it'll b 180 degress

Step-by-step explanation:

Answer:

it is .925 which is very close to 9/10 so C would be correct

Step-by-step explanation:

Answer:

0.925 so I would pick option C.

Answer:

total mass is equal to

450g+840g+366g+1kg

=1626g+1000g

=2626g

mass is in kg so it is 2.626kg

Answer:

1/3 or 33%

Step-by-step explanation:

You can first do: 50/150

Which is 5/15 simplified

And do the quick math:

1/3 or 33%

Answer:

100°

Step-by-step explanation:

the total of all angles around O on one side of AD is 180° (as that would represent a half-circle).

and the sum of the arc angles AB + BC + CD covers the whole 180°.

so, we have

180 = 55 + BC + 25

180 = 80 + BC

BC = 100°

The semi-annual net cash flow that the company must achieve in order for the purchase to be made is $5041.

Maximum amount that can be invested = $32348.

Less: Present value of salvage value = $5927

Present value of cash inflow = $32348 - $5927 = $26421.

Net cash flow will be:

= $26421 / PV factor

= $26421/5.242

= $5041

In conclusion, the correct option is $5041.

Learn more about cash flow on:

https://brainly.com/question/735261

Answer:

the equivalent expression is 1.1(1.3)^4 ×(1.3)^x

Answer:

d

Step-by-step explanation:

i took the test

The price of the pen and the erasers Raphael and his friend bought are GHC 3 and GHC 1 respectively.

let

x = price of pen

y = price of erasers

The equation

8x + 9y = 33

5x + 6y = 21

48x + 54y = 198

45x + 54y = 189

48x - 45x = 198 - 189

3x = 9

x = 9/3

x = 3

substitute into (1)

8x + 9y = 33

8(3) + 9y = 33

24 + 9y = 33

9y = 33 - 24

9y = 9

y = 9/9

y = 1

How to solve simultaneous equation:

https://brainly.com/question/16863577

Answer:

940

Step-by-step explanation:

To find the original price of something that been discount do the following:

Or we can do the following:

We shall consider the original price as x; hence the discount can be considered as (x−263.20). We can write the equation:

x · 72/100=x - 263.20

x · 18/25 = x - 263.20

Multiply both sides by 25

18x = 25(x - 263.20)

Open the brackets.

18x = 25x-6580

Add 6580 to each side.

6580 +18x = 25x

Subtract 18x from each side.

6580 = 7x

Subtract 7x from each side.

x = 940

Check Answer:

940 * 72% = 676.80

940 - 676.80=263.20

Hence, the regular price is 940.

~lenvy~

Step-by-step explanation:

The sale price ( The marked price ) :- $263.20

Discount :- 72%

Discount :- marked 100 ,Discount 72 ,Seliing ( Regular ) 28

Regular price :- 263.20 × 28 / 100

$ 73.69

Answer:

A

Step-by-step explanation:

because -98.4 is the opposite of 98.4 and 98.4 is it's absolute value

Answer:

12x−9y−12z

Step-by-step explanation:

1. 16x−12y−3z−4x−(−3y)−9z

2. Combine 16x and −4x to get: (12x−12y−3z+3y−9z)

3. Combine −12y and 3y to get: (12x−9y−3z−9z)

4. Combine −3z and −9z to get: (12x−9y−12z)

Answer: 12x−9y−12z Step-by-step

explanation: 1. 16x−12y−3z−4x−(−3y)−9z 2. Combine 16x and −4x to get: (12x−12y−3z+3y−9z)3. Combine −12y and 3y to get: (12x−9y−3z−9z) 4. Combine −3z and −9z to get: (12x−9y−12z)

Answer:

See below.

Step-by-step explanation:

e=12c+6

e=12(1)+6

e=12+6

e=18

e=12(2)+6

e=24+6

e=30

e=12(3)+6

e=36+6

e=42

e=12(4)+6

e=48+6

e=54

-hope it helps

2a means = 2 x a

if a = 4

3 x (2 x 4 + 6) = 3 x (8 + 6) = 3 x 14 = 42

Answer:

Step-by-step explanation:

[tex]=5\displaystyle\int_{0}^{\pi/6}dx\displaystyle\int_{0}^{2}x\sec^2(xy)dy\\=5\displaystyle\int_{0}^{\pi/6}dx\displaystyle\int_{0}^{2}\sec^2(xy)d(xy)\\=5\displaystyle\int_{0}^{\pi/6}dx\tan(xy)|_{y=0}^{y=2}[/tex]

[tex]=5\displaystyle\int_{0}^{\pi/6}\tan(2x)dx\\=-\frac{5}{2}\ln\cos(2x)|_{0}^{\pi/6}\\=-\frac{5}{2}[\ln\cos(\pi/3) - \ln\cos(0)]\\[/tex]

[tex]=-\frac{5}{2}\ln{\frac{1}{2}[/tex]

Answer:

63

Step-by-step explanation:

This is a cyclic quadrilateral, meaning that its opposite angles are supplementary. So, x=180-117=63.

Answer: binomial

Step-by-step explanation: it has 2 terms

Answer:

85cm^3

Step-by-step explanation:

Volume = Base Area * Height

17*5=85