What is 341/1000 in words

Answer:

Area of the floor of the classroom is 72 inch².

Step-by-step explanation:

We are given the dimensions of the rectangular floor as,

Length = 36 feet and Width = 32 feet

Since, the scale drawing have the length = 9 inches

This gives, the ratio of the actual length to the scale drawing length = [tex]\frac{36}{9}[/tex]

Thus, we have,

[tex]\frac{36}{9}=\frac{32}{x}[/tex], where x is the width in the scale drawing.

So, on solving,

[tex]x=\frac{32\times 9}{36}[/tex] i.e. x= 8 inches

Since, Area of the rectangle= Length × Width

Thus, area of the rectangular floor = 9 × 8 = 72 inch².

Thus, the area of the floor of the classroom is 72 inch².

The area of the floor of the scale drawing and the scale factor are 72 in² and 1/4 respectively

The scale factor = 9 / 36 = 1/4

The length of the model canbe calculated thus :

Model width = 32 × 1/4 = 8 inches

The Area of a rectangle can be calculated using the relation :

Area of floor = 8 inches × 9 inches = 72 inch²

Therefore, the area of the floor of the scale drawing is 72 in²

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Answer:

(x + 6)(x + 8)

Step-by-step explanation:

Multiply x^2 by 48.

48 * x^2 = [tex]48x^2[/tex]

Factor 48.

Find two factors which add to 14.

6 and 8.

Check

6 * 8 = 48

6 + 8 =14

Add x by 6

Add x by 8

Answer

(x + 6)(x + 8)

The factors of the given trinomial are (x+6) & (x+8)

If an algebraic expression has three non-zero terms or monomials, then it is called trinomial.

Example : [tex]x^{2} +x+1[/tex] , where [tex]x^{2} , x, 1[/tex] are three non-zero terms or monomials.

Given trinomial is [tex]x^{2} +14x+48[/tex]

First, we have to factorise 48 & find two factors whose addition is 14.

The factors are 6 & 8, since 6×8=48 & 6+8=14

Rewrite the terms : [tex]x^{2} +6x+8x+48[/tex]

Regroup terms into two proportional parts : [tex](x^{2} +6x)+(8x+48)[/tex]

Taking common from both parts : [tex]x(x+6)+8(x+6)[/tex]

Factor the expression : [tex](x+6)(x+8)[/tex]

∴ The factors are (x+6) & (x+8).

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ABOUT SLOPE INTERCEPT FORM:

You have to get y by itself:

5x + 8y = 16

-5x          -5x

8y = -5x + 15

8             8

y = -5/8x + 15/8

OR

I you wants to simplify 15/8, it's this:

y = -5/8x +1.875

HI!!! Really really sorry if I'm incorrect...

The area of the rectangle is 60 units²

Since from the graph, we have the vertices of the rectangle at (-1,1), (8, -2), (-3, -5) and (6, -8).

The pair (-1, 1) and (8, -2) represent the coordinates for the length of the rectangle while the pair (-1, 1) and (-3, -5) represent the coordinates for the width of the rectangle.

So, we find the length of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₂, y₂)

So, the length, L = √[(x₂ - x₁)² + (y₂ - y₁)²] where  (x₁, y₁) = (-1, 1) and (x₂, y₂) = (8, -2)

So, L = √[(x₂ - x₁)² + (y₂ - y₁)²]

L = √[(8 - (-1))² + (-2 - 1)²]

L = √[(8 + 1))² + (-3)²]

L = √[(9)² + (-3)²]

L = √[81 + 9]

L = √90

L = 3√10 units

Also, we find the width of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₃, y₃)

So, the width, W = √[(x₃ - x₁)² + (y₃ - y₁)²] where  (x₁, y₁) = (-1, 1) and (x₃, y₃) = (-3, -5)

So, W = √[(x₃ - x₁)² + (y₃ - y₁)²]

W = √[(-3 - (-1))² + (-5 - 1)²]

W = √[(-3 + 1))² + (-6)²]

W = √[(-2)² + (-6)²]

W = √[4 + 36]

W = √40

W = 2√10 units

Since the area of a rectangle A = LW, we have

A = 3√10 units × 2√10 units

A = 3 × 2 × √10 × √10 units²

A = 3 × 2 × 10 units²

A = 60 units²

So, the area of the rectangle is 60 units²

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The area of the rectangle is 60 units².

To find the area of a rectangle, you need to multiply its length by its width.

Since from the graph, we have the vertices of the rectangle at (-1,1), (8, -2), (-3, -5) and (6, -8).

The pair (-1, 1) and (8, -2) represent the coordinates for the length of the rectangle while the pair (-1, 1) and (-3, -5) represent the coordinates for the width of the rectangle.

So, we find the length of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₂, y₂)

So, the length, L = √[(x₂ - x₁)² + (y₂ - y₁)²] where  (x₁, y₁) = (-1, 1) and (x₂, y₂) = (8, -2)

So, L = √[(x₂ - x₁)² + (y₂ - y₁)²]

L = √[(8 - (-1))² + (-2 - 1)²]

L = √[(8 + 1))² + (-3)²]

L = √[(9)² + (-3)²]

L = √[81 + 9]

L = √90

L = 3√10 units

Also, we find the width of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₃, y₃)

So, the width, W = √[(x₃ - x₁)² + (y₃ - y₁)²] where  (x₁, y₁) = (-1, 1) and (x₃, y₃) = (-3, -5)

So, W = √[(x₃ - x₁)² + (y₃ - y₁)²]

W = √[(-3 - (-1))² + (-5 - 1)²]

W = √[(-3 + 1))² + (-6)²]

W = √[(-2)² + (-6)²]

W = √[4 + 36]

W = √40

W = 2√10 units

Since the area of a rectangle A = LW, we have

A = 3√10 units × 2√10 units

A = 3 × 2 × √10 × √10 units²

A = 3 × 2 × 10 units²

A = 60 units²

So the area of the rectangle is 60 units².

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Answer:

y = -8

Step-by-step explanation:

The domain is the x values so x=-3

y = x-5

Substituting x=-3

y = -3-5

y=-8

Step-by-step explanation:

[tex]\sf \longmapsto{y = - 5 + - 3} \\ \\ \sf \longmapsto{y = - 5 + - 3 = \red{ - 8}} \\ \\ \sf \longmapsto \boxed{ \sf\: y = - 8}[/tex]

Answer:

[tex] b \le -6 [/tex]

Step-by-step explanation:

[tex] -1.2b - 5.3 \ge 1.9 [/tex]

Add 5.3 to both sides of the inequality.

[tex] -1.2b - 5.3 + 5.3 \ge 1.9 + 5.3 [/tex]

[tex] -1.2b \ge 7.2 [/tex]

Divide both sides by -1.2. When you multiply or divide both sides of an inequality by a negative number, the inequality sign changes direction. In this case, the "greater than or equal to" sign changes to a "less than or equal to" sign.

[tex] \dfrac{-1.2b}{-1.2} \le \dfrac{7.2}{-1.2} [/tex]

[tex] b \le -6 [/tex]

The solution set of the given inequality is {-6, -7, -8, -9, -10,......}.

The given inequality is -1.2b-5.3≥1.9.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The solution of given inequality can be solved as follows:

Add 5.3 to both side of the inequality, we get

-1.2b-5.3+5.3≥1.9+5.3

⇒ -1.2b≥7.2

Divide -1.2 to both side of the inequality, we get

-1.2b/(-1.2) ≤ 7.2/(-1.2)

⇒ b ≤ -6

So, solution set = {-6, -7, -8, -9, -10,......}

Therefore, the solution set of the given inequality is {-6, -7, -8, -9, -10,......}.

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When adding like terms, they simply add together:

6y + 3y = 9y

The rule of adding two powers are as follows:

[tex]x^{a} + x^{b} = x^{a+b}[/tex]

So:

[tex]y^{4}  + y^{4} = y^{4 + 4} = y^{8}[/tex]

So 6y⁴ + 3y⁴ = 9y⁸

Answer:

Moira's solution is..... incorrect

6y4+3y4 is the same as...... (6*y^4) + (3*y^4)

9y8 is the same as...... 9y*y*y*y*y*y*y*y

6y4+3y4 simplifies to..... 9y^4

[tex]\frac{2}{7}y + 5 = -9\ /\cdot7\\2y+35=-63\\2y=-63-35\\2y=-98\ /:2\\y=-49\\ \\ \\\frac{2}{7}\cdot(-49)+5=-14+5=-9[/tex]

Answer:

She poured 3 pints

Step-by-step explanation:

I’m pretty sure you can first do 10% at a time which you can round to 13 which is 3 so 3 plus 3 then add tax

Hi There!

Step-by-step explanation:

20% = 0.2

6.25% = 0.0625

Discount: 12.99 * 0.20 = $2.598

Sale Price: 12.99 - 2.598 = $10.392

Tax: 10.392 * 0.0625 = 0.6495

Price After Tax: 10.392 - 0.6495 = 9.7425

Round: 9.7425 = 9.74

Answer:

$9.74

Hope This Helps :)

Answer:

Correct choice is D (In a whole pepperoni pizza are 660 calories, in  in a whole ham and pineapple pizza are 580 calories).

Step-by-step explanation:

Let x calories be the number of calories a whole pepperoni pizza contains and y calories be the number of calories a whole ham and pineapple pizza contains.

1. If half a pepperoni pizza plus three fourths of a ham and pineapple pizza contains 765 calories, then

[tex]\dfrac{1}{2}x+\dfrac{3}{4}y=765.[/tex]

2. If 1/4 of a pepperoni pizza plus a whole ham and pineapple pizza contains 745 calories. then

[tex]\dfrac{1}{4}x+y=745.[/tex]

3. Multiply each equation by 4 and get a system of two equations:

[tex]\left\{\begin{array}{l}2x+3y=3060\\x+4y=2980\end{array}\right.[/tex]

From the second equation [tex]x=2980-4y[/tex], then

[tex]2(2980-4y)+3y=3060,\\ \\5960-8y+3y=3060,\\ \\-8y+3y=3060-5960,\\ \\-5y=-2900,\\ \\y=580.[/tex]

Then

[tex]x=2980-4\cdot 580=2980-2320=660.[/tex]

The whole pepperoni pizza contains 660 calories and the whole ham and pineapple pizza contains 580 calories. These values are obtained using a system of two equations obtained from the given statements.

Let's denote 'P' as the calories in a whole pepperoni pizza, and 'H' as the calories in a whole ham and pineapple pizza. We can then interpret the problem as two equations based on the given information.

First equation (from the first sentence in the question): 0.5P + 0.75H = 765.

Second equation (from the second sentence in the question): 0.25P + H = 745.

Now we just need to solve this system of equations. Multiply the second equation by two to match the 'P' terms in both equations: 0.5P + 2H = 1490.

Subtract the first equation from this new equation: 0.5P + 2H - (0.5P + 0.75H)= 1490 - 765. This simplifies to: 1.25H = 725, meaning H = 580 calories.

We can then substitute H = 580 into the first original equation to solve for P: 0.5P + 0.75*580 = 765. Solving this gives P = 660 calories.

So, a whole pepperoni pizza contains 660 calories, and a whole ham and pineapple pizza contains 580 calories. This corresponds to the option d) in the given list.

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Answer:

$11535.60 will be in his account when he is 40 years old

Step-by-step explanation:

Jackson deposited $5,000 at 3.8% interest, compounded continuously, when he was 18 years old

Time period is from 18 years to 40 years

t= 40 - 18 = 22

For compounding continuously we use formula

[tex]A= Pe^{rt}[/tex]

P = initial amount deposited = 5000

r= rate of interest = 3.8% = 0.038

t= time period = 22 years

now plug in all the values and find out A final amount

[tex]A= 5000e^{0.038*22}[/tex]

[tex]A= 5000e^{0.836}[/tex]

A= 11535.60

Answer:

Option A is correct.

d = 50t shows the relationship between d and t

Step-by-step explanation:

Point slope form: For a point [tex](x_1, y_1)[/tex] and a slope m, the equation of the line can be written as

[tex]y-y_1=m(x-x_1)[/tex] ......[1], where m is the slope of the line.

Here, d represents the total distance ( in miles) and t represents the time (in hours).

From the given table:

Consider any two points (1, 50) and (2, 100).

Calculate slope:

Slope(m) =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

               = [tex]\frac{100-50}{2-1}=\frac{50}{1} =50[/tex]

⇒[tex]m= 50[/tex]

Now, by point slope intercept form:

Substitute  m= 50 and (1, 50) in [1]

we have;

[tex]y -50 = 50(x-1)[/tex]

Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]

y -50 = 50x -50

Add both sides 50 we get;

y -50+ 50= 50x -50 + 50

Simplify:

[tex]y =50x[/tex]

∵y = d represents the distance and x = t represents the time;

then, our equation become:

[tex]d = 50t[/tex]

The equation representing the relationship between the distance covered (d) and time (t) in the given situation is d = 50t. This signifies that the distance covered is equal to 50 times the time.

In the given data, we observe that the total distance (d) travelled by the car in an hour is always 50 miles. This means that every hour, the car covers a distance of 50 miles.

Therefore, the relationship between the distance covered (d) and time (t) can represent this situation is d = 50t.

This signifies that 'd', the distance covered, is equal to 50 times 't', the time in hours. For example, when t=1 hour, d = 50*1 = 50 miles. Similarly, when t=2 hours, d = 50*2 = 100 miles. This continues accordingly.

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Answer:

The answer is C (4,-3)

Step-by-step explanation:

When you reflect over the x axis that means you flip the image to the opposite side over the x (horizontal) line. So if the first line is (4,3) then the reflection is (4,-3)

Answer:

c is the answer

Step-by-step explanation:

(3,-1) and (4,2)

find the slope y2-y1 over x2-x1

so 2 and -1 is 2+1 = 3 and

4-3 = 1

so 3/1 = 3 so it is c

Answer:

30b

Step-by-step explanation:

-6(-5) is 30.

Answer:

$497.80

Step-by-step explanation:

First, you want to find half of 10.48. This should be 5.24.

So, add 10.48 and 5.24. This gives you 15.72.

Now, you want to multiply that by 5, since 5 hours were overtime.

This gives you 78.60.

Lastly, you want to multiply 10.48 by 40.

This gives you 419.20

Now, add 78.60 and 419.20 together, giving you your answer of $497.80

Sara got $497.80 for the week.

Answer:

x = ± 1/8

Step-by-step explanation:

64 x^2 =1

Divide each side by 64

64 x^2/64 = 1/64

x^2 = 1/64

Take the square root of each side, remembering to take the positive and negative.

sqrt(x^2) = ±sqrt(1/64)

x = ±sqrt(1)/ sqrt(64)

x = ± 1/8

1. The direction of the vector [tex]\theta[/tex] relative to the positive x-axis satisfies

[tex]\tan\theta=\dfrac35\implies\theta\approx30^\circ[/tex]

2. A vector with magnitude [tex]\|\mathbf v\|[/tex] and direction [tex]\theta[/tex] has component form

[tex]\mathbf v=\langle\|\mathbf v\|\cos\theta,\|\mathbf v\|\sin\theta\rangle[/tex]

We have [tex]\|\mathbf v\|=5[/tex], but "angle of 60 degrees with the negative x-axis" is a bit ambiguous. I would take it to mean "60 degrees counterclockwise relative to the negative x-axis", so that the direction is [tex]\theta=240^\circ[/tex]. Then

[tex]\mathbf v=\langle5\cos240^\circ,4\sin240^\circ\rangle\approx\langle-2.5,-4.3\rangle[/tex]

But this doesn't match any of the options, so more likely it means the angle is 60 degrees clockwise relative to the negative x-axis, in which case [tex]\theta=120^\circ[/tex] and we'd get

[tex]\mathbf v=\langle5\cos120^\circ,4\sin120^\circ\rangle\approx\langle-2.5,4.3\rangle[/tex]

3. Same as question 2, but now we're using [tex]\mathbf i,\mathbf j[/tex] notation. The vector has magnitude [tex]\|\mathbf v\|=14[/tex] and its direction is [tex]\theta=-30^\circ[/tex]. So the vector is

[tex]\mathbf v=14\cos(-30^\circ)\,\mathbf i+14\sin(-30^\circ)\,\mathbf j=12.1\,\mathbf i-7\,\mathbf j[/tex]

4. The velocity of the plane relative to the air, [tex]\mathbf v_{P/A}[/tex] is 175 mph at 40 degrees above the positive x-axis. The velocity of the air relative to the ground, [tex]\mathbf v_{A/G}[/tex], is 35 mph at 60 degrees above the positive x-axis. We want to know the velocity of the plane relative to the ground, [tex]\mathbf v_{P/G}[/tex].

We use the relationship

[tex]\mathbf v_{P/G}=\mathbf v_{P/A}+\mathbf v_{A/G}[/tex]

Translating the known vectors into component form, we have

[tex]\mathbf v_{P/G}=\langle145\cos40^\circ,145\sin40^\circ\rangle+\langle35\cos60^\circ,35\sin60^\circ\rangle\approx\langle152,143\rangle[/tex]

This vector has magnitude and direction

[tex]\|\mathbf v_{P/G}\|\approx\sqrt{152^2+143^2}\approx208\,\mathrm{mph}[/tex]

[tex]\tan\theta\approx\dfrac{143}{152}\implies\theta\approx43^\circ[/tex]

(or 43 degrees NE)

Answer: #3 is v=12.1i-7j

got it right on my test

#4 is C 208 mph and 43 northeast

Step-by-step explanation:

Answer:

158

Step-by-step explanation:

Simplify the following:

2×5×3 + 2×5×8 + 2×3×8

5×3 = 15:

2×15 + 2×5×8 + 2×3×8

5×8 = 40:

2×15 + 2×40 + 2×3×8

3×8 = 24:

2×15 + 2×40 + 2×24

2×15 = 30:

30 + 2×40 + 2×24

2×40 = 80:

30 + 80 + 2×24

2×24 = 48:

30 + 80 + 48

| 8 | 0

| 4 | 8

+ | 3 | 0

1 | 5 | 8:

Answer:  158

Kaylee is using the formula for the surface area of a rectangular prism. She calculates it as 2(5×3) + 2(5×8) + 2(3×8), which adds up to 158 square inches, representing the total surface area of the prism.

Kaylee is calculating the surface area of a rectangular prism using a mathematical formula. The formula comprises three terms, each representing the area of a pair of opposite faces. Let's break down the calculation:

When Kaylee calculates these areas and adds them together, she gets:

2(5×3) + 2(5×8) + 2(3×8) = 2(15) + 2(40) + 2(24) = 30 + 80 + 48 = 158 square inches.

Thus, the total surface area of the rectangular prism is 158 square inches.

Final answer:

The equation given to calculate the distance between the trains is D = |262.5 - 120T|. To find the values of T for which D = 50, substitute 50 for D in the equation and solve for T. By solving the equations, we find that T is approximately 1.8 and 2.6.

Explanation:

The equation given to calculate the distance between the trains is D = |262.5 - 120T|, where T is the time after Train B departs. To find the values of T for which D = 50, substitute 50 for D in the equation and solve for T.

50 = |262.5 - 120T|

To remove the absolute value, we can split the equation into two cases:

Solving these equations will give us the values of T for which D = 50.

By solving both equations, we find that T is approximately 1.8 and 2.6, so the answer is A) 1.8 and 2.6.

Answer: Variant A

Step-by-step explanation:

Answer:

The correct answer is B) x equals quantity of 2 plus or minus 2i square root of 2 all over 3.

Step-by-step explanation:

We are given the following quadratic equation:

[tex]-3x^2-4x-4 = 0[/tex]

Since, it cannot be factorized so we will use the quadratic formula:

x = [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

Substituting in the values of a, b and c in the above formula to get:

x = [tex]\frac{-(-4)+-\sqrt{(-4)^2}-4(-3)(-4) }{2(-3)}[/tex]

x = [tex]-\frac{2}{3} +i \frac{2\sqrt{2} }{3}[/tex], x = [tex]-\frac{2}{3} -i \frac{2\sqrt{2} }{3}[/tex]

Therefore, the correct answer option is B) x equals quantity of 2 plus or minus 2i square root of 2 all over 3.

Answer:

see below  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

1 milk = 1 3/4 cup of flour

1 flour = 3/7 cup of cocoa powder

4 cups of milk = 1 3/4 x 4 = 7/4 x 4/1 = 7 cups of flour

7 cups of flour = 7 x 3/7 =  7/1 x 3/7 = 3 cups of cocoa powder

Kenneth needs 3 cups of cocoa powder for the chocolate cakes he is making with 4 cups of milk.

To find out how many cups of cocoa powder Kenneth needs for his chocolate cakes, we should first determine how much flour is necessary for 4 cups of milk and then how much cocoa powder is needed for that amount of flour. Kenneth uses one and 3/4 cups of flour for each cup of milk. So for 4 cups of milk, he needs:

1 ¾ cups of flour/cup of milk x 4 cups of milk = 7 cups of flour

Next, for every cup of flour, Kenneth needs 3/7 cup of cocoa powder. Therefore, to find out the total cups of cocoa powder for 7 cups of flour, the calculation is:

3/7 cups of cocoa powder/cup of flour x 7 cups of flour = 3 cups of cocoa powder

So Kenneth needs a total of 3 cups of cocoa powder for his cakes.

Multiply by 2:

2=u-2

4=u or u=4.

Answer:

i is equal to the square root of -1, and -1 to any power equals -1

Step-by-step explanation:

[tex]i^18[/tex] must be equal to 1 because [tex]i^4[/tex] is equal to 1, and 18 is a multiple of 4.

The imaginary unit i is defined as the square root of -1. Therefore, by definition, [tex]i^2[/tex] = -1.

Now let's consider higher powers of i:

[tex]- i^3 = i^2 i = -1 i = -i[/tex]

[tex]- i^4 = i^2 = -1 = 1[/tex]

Notice that when we raise i to the fourth power, we get 1. This is a key observation because it means that the powers of i repeat every four powers. This is known as the cyclical nature of the powers of i.

Given that [tex]i^4 = 1[/tex], we can express any power of i that is a multiple of 4 as 1. This is because raising i to any multiple of 4 will result in an even number of -1 factors, which will always multiply to 1.

Now, let's consider [tex]i^18[/tex]:

- Since 18 is divisible by 4 (18 = 4 * 4.5), we can express [tex]i^18 as (i^4)^4.5[/tex].

- We know that [tex]i^4 = 1[/tex], so [tex](i^4)^4.5 = 1^4.5 = 1[/tex].

Therefore, [tex]i^18[/tex] = 1, not -1 as initially stated. The power of i cycles through -1, -i, 1, and i, repeating every four powers. Since 18 is a multiple of 4, i^18 lands on 1 in this cycle.

Answer:

c = (ab -d) /a

Step-by-step explanation:

a(b – c) = d  

Divide each side by a

a/a(b – c) = d  /a

b-c = d/a

Subtract b from each side

b-b-c = d/a -b

-c = d/a -b

Multiply by -1

-1*-c = -1(d/a -b)

c = -d/a +b

c = b - d/a

Get a common denominator

c = b*a/a -d/a

Combine over the common denominator

c = (ab -d) /a

Answer:

(-0.8)×4=(-3.2)

(-3.2)×4=(-12.8)

(-12.8)×4=(-51.2)

(-51.2)×4=(-204.8)

anser is -204.8

Step-by-step explanation: