a recipe requires 1/2 cup of flour for every batch of cookies. How many batches of cookies can be made with 4 1/2 cups of flour?

The angle of refraction is 15.6 deg.

We have given that An incident ray strikes a piece of diamond at an angle of 40. 5 degrees.

When a ray of light passes from medium 1 to medium 2, the refractive index of medium 2 with respect to 1 is the ratio of the absolute refractive index of medium 2 and medium 1

[tex]1n_{2}=\frac{^{n_{1}}}{n_{2}}[/tex]

When light passes from air into diamond, with the given values of refractive indices,

[tex]an_{d}=\frac{^{n_{d}}}{n_{a}}=\frac{2.42}{1.0003} =2.4193[/tex]

According to Snell's law,

[tex]an_{d}=\frac{^{sini}}{sin r}[/tex]

[tex]< br/ > sinr=an_{d}=\frac{^{sini}}{sin r}=\frac{sin(40.5)}{2.41930} =0.2684[/tex]

[tex]< br/ > r=arcsin(0.2684)=15.57 deg[/tex]

The angle of refraction is 15.6 deg

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Answer:

42 sq ft

Step-by-step explanation:

L x W x H

3 x 7 x 2

21 x 2

42 sq ft

Answer:

Tm = 6 - Ts

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

Answer:

1/16

Step-by-step explanation:

start with

3/10 times 5/24 and simplify till you get 1/2 times 1/8 which is 1/16

Answer:

0.0625 or 1/16

Step-by-step explanation:

1. Multiply fractions, a x b/c

When you a x b/c , you would do 0.3 x 5 /24, wich would be 1.5/24

0.3 x 5 = 1.5

2. Simplify 1.5/24.

Change 1.5 to 15/10

To get 15/10, you do 1.5 x 10 over 10, witch would be 15/10 , because 1.5 x 10 is 15.

3. Simplify 15/10

15/10, you can divided both by 5, witch would be 15/5 , 3 and 10 divided by 5 witch would gives you 2, hence 15/10 simplfies to 3/2

4. Divided 3/2 by 24 , which would give you 1/16

Answer:

y^12/5 aka the first option

Step-by-step explanation:

(9x^5y^16)/(45x^5y^4)

rules of exponents say youll do 5-5 because when dividing with exponents you subtract them

you get x^0 which is equal to 1 due to another rule of exponents

youll do 16-4 next and get 12 so y^12

now 9/45=5

the answer is (y^12)/5 (the first option)

Answer:

[tex]\sf x=2+\sqrt{6},\:x=2-\sqrt{6}[/tex]

Explanation:

[tex]\sf y = x^2 -4x[/tex]

given that y = 2

[tex]\sf x^2 -4x = 2[/tex]

[tex]\sf x^2 -4x -2 = 0[/tex]

using quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ \ when \ ax^2 + bx + c = 0[/tex]

[tex]\rightarrow \sf x_{1,\:2}=\dfrac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}[/tex]

[tex]\rightarrow \sf x_1=\dfrac{-\left(-4\right)+2\sqrt{6}}{2\cdot \:1},\:x_2=\dfrac{-\left(-4\right)-2\sqrt{6}}{2\cdot \:1}[/tex]

[tex]\rightarrow \sf x=2+\sqrt{6},\:x=2-\sqrt{6}[/tex]

in decimals:

[tex]\rightarrow \sf x=4.45 , \ -0.45[/tex]

The inequalities that must be true if m is greater-than-or-equal-to n are given as:

Only those operations are allowed which are sure to not modify the inequality between the expressions in the statement.

Some operations that are sure not to modify the inequalities are:

Addition, Subtraction, multiplication by positive real numbers, division by positive real numbers etc.

Example, if 5 > 2, then you can do whatever which keeps the term on the side of 5 bigger than the terms formed on side of 2.

Thus, 5 + 1  > 2 + 1 is correct, (it was addition of 1, a real number).

For the considered case, we're given that:

[tex]m \geq n[/tex]

Checking all the options sequentially, we get:

It must be true, since the multiplication is done by 2.1, which is > 0

It must be true since -4 is a real number, and addition or subtraction of any real number (if done on all the sides of the statement) doesn't change the inequality

From [tex]m \geq n[/tex], addition or subtraction is guaranteed to not change the inequality only if they are of same quantity on all the sides of the inequality. Thus, this inequality is not necessary to be true.
Example, if we take m = 5, n =3, then,

[tex]5 \geq 3[/tex] but [tex]5 - 3=0 \: \rm and \: 3 + 3= 6 \implies 5-3 < 3 + 3[/tex]

It must be true if given that [tex]m \geq n[/tex] since multiplication of equal positive real number on both the sides of  [tex]m \geq n[/tex] was done.

one-half of 6 = 3, thus, this inequality means [tex]3m \geq 9m[/tex]

Dividing both the sides by 3, we get:

[tex]m \geq 3n[/tex]

It is not  necessary to be true if  [tex]m \geq n[/tex]. Example

[tex]3 \geq 2\\but\\ 3 < 3 \times 2 = 6[/tex]

Thus, the inequalities that must be true if m is greater-than-or-equal-to n are given as:

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Answer:

C. 1200 yds

Step-by-step explanation:

Each cm equals 10 yards, so start by multiplying the 3cm and 8 cm by 10. Then all you do is insert those numbers into the equation for the area of a triangle which is 1/2BH

1/2*80*30=1200

Answer:

C. 1,200 yds

Step-by-step explanation:

To find the area of a triangle, you must use the triangle area formula, [tex]A = \frac{1}{2}(b*h)[/tex].

Since 1 cm = 10 yards, then 8 cm = 80 yards and 3 cm = 30 yards. You can use 80 yards as your base and 30 yards as your height to find the area:

[tex]A=\frac{1}{2} (80*30)[/tex]

[tex]A=\frac{1}{2} (2400)[/tex]

[tex]A=1200[/tex]

Therefore, the answer is C. 1,200 yards.

I hope this helps!

Answer:

Step-by-step explanation:

the square root of 12 is 3.4 so the answer is 3.4

The completely factored form of the Wen's polynomial, which has the four terms initial, is,

[tex](6x^2+7)(x-2)[/tex]

The factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.

Wen is factoring the polynomial, which has four terms.

[tex]6x^3 - 12x^2+ 7x - 14[/tex] '

Take out the greatest common factor from the equation and make separate groups as,

[tex]6x^2(x - 2)+ 7(x - 2)\\(x-2)(6x^2+7)[/tex]

Rearrange the above equation as,

[tex](6x^2+7)(x-2)[/tex]

Thus, the completely factored form of the Wen's polynomial, which has the four terms initial, is,

[tex](6x^2+7)(x-2)[/tex]

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Answer:

A

Step-by-step explanation:

Trust me

160 i believe. to find the area of a triangle act like its a square and divide in half. for squares multiply base by height.

take the area of each shape and add it up

The radius of the given circle with a central angle of 7π/10 and arc length of 33cm is 15cm.

It is given that

The central angle of the given circle = 7π/10 radians

Length of arc = 33cm

Arc length = central angle* radius

From the above formula

Radius = Arc length/Central Angle

Radius = [tex]\frac{33}{(7\pi)/10 }[/tex]

Radius = 15cm

Therefore, radius of the given circle is 15cm.

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Answer:

15 cm or B on egde

Step-by-step explanation:

Answer:

Step-by-step explanation:

When we say "y varies inversely as x", we mean that y is proportional to the inverse of x: y = k·(1/x). This relation is usually written ...

  y = k/x

It can be solved for the other values:

  xy = k . . . . multiply by x

  x = k/y . . . divide by y

If you are given the equation, the value of k can be read directly from it: it is the constant in the numerator.

__

  k = xy = 5·6 = 30; the equation is y = 30/x

  y = k/x = 36/4 = 9; the equation is y = 36/x

 k = 50 (read from the equation); x = k/y = 50/20 = 5/2

  k = 24 (read from the equation); y = k/x = 24/12 = 2

Answer:

If [tex]sin x = 0[/tex] we get [tex]2 (0) (\pm1) = 0[/tex] which is true. so we have a first set of solutions given by

[tex]x= 0; x = \pi[/tex];

Else, if [tex]sin x \ne 0[/tex] we can divide both sides by it and we get

[tex]2 cos x = \frac 1 {cos x} \rightarrow 2cos^2x =1 \rightarrow cos^2x =\frac12\\cos x= \pm \frac{\sqrt2}2[/tex]

Which gives us a second set of solutions given by [tex]x= \frac{\pi}4;x= \frac{3\pi}4; x= \frac{5\pi}4;x= \frac{7\pi}4[/tex];

We can group all solutions (doesn't matter, but it's more elegant!) by writing

[tex]x= k\frac{\pi}4; k\in \{0,1,3,4,5,7\}[/tex]

Rami's family will pay less if they use savings instead of credit.

Step-by-step explanation:

Took the test 8th grade K12

Step-by-step explanation:

formula for trapezoid or trapezium=h/2 × (a+b)

1.5/2 ×(2+7)

0.75 ×9

3.25msquare

Answer:

Step-by-step explanation:

First of all, you have to set up the equation

2x^2 + x -1 = 2               Subtract 2 from both sides

2x^2 + x - 1 - 2 = -2+2   Combine

2x^2 + x - 3 = 0             This factors.

(2x + 3)(x -1 ) = 0

Either

2x + 3 = 0                       Subtract 3 from both sides

2x = - 3                           Divide by 2

2x/2 = - 3/2                    

x = - 3/2                         which you already know

or

x - 1 = 0                          Add 1

x - 1 + 1 = 1

x = 1

the other answer is x = 1

Answer:

x = 80

Step-by-step explanation:

Because of the parallel lines and the transversal to the left,

x + 67 = 147

x = 80

Answer:

80°

Step-by-step explanation:

I have added some letters for ease.

wyzu is an interior angle. Therefore ∡wyz + ∡yzu = 180°

∡yzu + 147° = 180°

∡yzu = 180°-147

∡yzu = 33°

∡yzu + x° + 67° = 180° ( Supplementary Angle )

33° + x° + 67° = 180°

x° + 100° = 180°

x° = 180° - 100°

x° = 80°

Answer:

Income : £270

Expenditure:£204

profit: £66

The volume of the cylinder is [tex]\pi r^{2}h[/tex]

Volume = [tex]\pi 3^{2} * 4=113.097[/tex] cubic inches (approximated)

Hope that helped!

n/3-2 = 2

n/3 = 4

n = 12

The solution to the algebraic equation, n/3 - 2 = 2, is: n = 12.

If given an algebraic equation, such as n/3 - 2 = 2, to solve for n, you have to isolate n as shown below:

n/3 - 2 = 2

Add 4 to both sides of the equation

n/3 = 2 + 2

n/3 = 4

Multiply both sides by 3

n = (4)(2)

n = 12

Therefore, the solution to the algebraic equation, n/3 - 2 = 2, is: n = 12.

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Answer:

I believe the answer is D. which is $9.06

Step-by-step explanation:

Answer:1) 1/12 2)21/5 3) 9/25.

Step-by-step explanation:

5x1/12x5 is 5/60, which is 1/12. 4 2/3 is 14/3. 14x9/3x10 is 126/30, or 21/5. 36 percent is 36/100. Divide by 2. 18/50. Divide by two again, 9/25.

Answer:x=-1

add 1 to 3 to get 4, add 3 to -7 to get -4, divide both sides by -4

Answer:

[tex] \: [/tex]

Step-by-step explanation:

Given Equation,

[tex] \\ {\longrightarrow \qquad{ \sf{-3x+3=-7x-1}}}\\ \\ [/tex]

Adding 7x to both sides we get,

[tex]{\longrightarrow \qquad{ \sf{-3x+3 + 7x=-7x-1 + 7x}}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{4x+3=-1}}}\\ \\ [/tex]

Subracting -3 from sides we get,

[tex] \\ {\longrightarrow \qquad{ \sf{4x+3 - 3=-1 - 3}}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{4x=-4}}}\\ \\ [/tex]

Dividing both sides by 4 we get,

[tex] \\ {\longrightarrow \qquad{ \sf{ \frac{4x}{4} = \frac{ - 4}{4} }}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x=-1}}}\\ \\ [/tex]

Answer:

if it is area of triangle it would be 49

Step-by-step explanation: