What is 4/24 x 2/3 =

Simplied

Answer:

It's a 19 percent increase.

Step-by-step explanation:

Divide 97/120, then multiply it by 100. After that, you can subtract the answer by 100. The answer will be negative, so make it positive.

Answer:

= 70f - 9g

Step-by-step explanation:

1. Remove parentheses

2. Multiply the numbers

3. Multiply the numbers

Answer:

-1

Step-by-step explanation:

Answer: The fraction that makes up Democrats or Republicans is 49/50.

Step-by-step explanation: There are 100 senators in total. We have 46/100 representing the Democrats, and 13/25 representing the Republicans. The number representing the Republicans can be made into an equivalent fraction of the other simply by multiplying both numerator and denominator by 4 (in order to make the denominator the same, that is 100). Hence the fraction of Republicans is 52/100, while the rest are Independents. The independents are

Ind = 100 - (46/100 + 52/100)

Ind = 100 - 98/100

Ind = 2/100

{Total = 46/100 + 52/100 + 2/100}

{Total = 100/100}

However, the fraction of all senators that are Democrats or Republicans is derived as follows;

Dems = 46/100

Reps = 52/100

Total fraction = 46/100 + 52/100

Total fraction = 98/100

Total fraction = 49/50

Final answer:

To find the fraction of senators who are Democrat or Republican, we add the fractions representing Democrats and Republicans. The fraction is $rac{49}{50}$.

Explanation:

To find the fraction of senators who are Democrat or Republican, we need to add the fractions representing Democrats and Republicans. The fraction of senators who are Democrats is $rac{46}{100}$, and the fraction of senators who are Republicans is $rac{13}{25}$.

To add these fractions, we need a common denominator. The least common multiple of 100 and 25 is 100, so we can rewrite the fractions with denominators of 100. $rac{46}{100}$ is equivalent to $rac{46}{100}  imes  rac{1}{1}$, and $rac{13}{25}$ is equivalent to $rac{13}{25}  imes  rac{4}{4}$ (since $25  imes 4 = 100$).

Now we can add the fractions: $rac{46}{100} +  rac{13}{25} =  rac{46}{100} +  rac{52}{100} =  rac{98}{100}$.

So, $rac{98}{100}$ of the senators are Democrat or Republican, which simplifies to $rac{49}{50}$.

Answer:

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Step-by-step explanation:

We can find the slope of the line using

m = (y2-y1)/(x2-x1)

    = (-2 - -10)/(-1 - -1)

     = (-2+10)/(-1+1)

     = 8/0

When we have a 0 in the denominator the slope is undefined

Calculating the volume of a cylinder the radius is squared,

If the radius was 8 when 8 is squared you get 64

If the radius is multiplied by 1/2 the radius would become 4, 4 squared is 16

16 / 64 = 1/4

The volume would be 1/4 the original volume, so it would be 4 times smaller.

Final answer:

Halving the diameter of a cylinder makes its volume four times smaller, because the volume depends on the square of the radius, and reducing the diameter by half means the radius is also halved.

Explanation:

When the diameter of a cylinder is multiplied by 1/2, the radius of the cylinder is also reduced to half its original size. To understand the impact on the volume, we examine the volume formula for a cylinder: V = (pi = 3.1416) times r^2 times h, where V is the volume, r is the radius, and h is the height. If both the diameter and radius are reduced by half, the volume of the cylinder will be reduced by a factor of 1/2^2 for the radius squared part of the formula.

Volume is directly proportional to the square of the radius, so taking the original volume formula V =
times (original radius)^2 times h and then applying the radius reduction, we get the new volume V' =
times (1/2 times original radius)^2 times h = 1/4 times original volume. Therefore, the volume of the cylinder becomes four times smaller when the diameter (and thus radius) is halved.

Step-by-step explanation:

if a = 10

a² = 10²= 100

Hope it will help :)

Answer:

a^2 = 100

a * 2 = 20

Step-by-step explanation:

If a = 10 , than a2 =

a^2 = 100 because 10 ^2 = 10 * 10 = 100

a * 2 = 10 * 2 = 20

Answer:

120

Step-by-step explanation:

you multiply base times height of the rectangle to get 96 then you do 1/2 bh for the triangle to get 24 and then you add them to get 120

The area of the irregular polygon is 120ft^2

We are given that;

The figure with triangle on top and rectangular base

Height of triangle=4ft

Base* height= 12*8

Now,

Area of triangle= 1/2 * base * height

=1/2 * 12 * 4

=24

Area of rectangle= 12 * 8

=96

Total area= 24+96

=120

Therefore, by the given polygon answer will be 120ft^2.

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Answer:

m = -7

Step-by-step explanation:

1) expand: 2/9m-16/9=2/3m+4/3

2) add 16/9 to both sides:

2/9m-16/9+16/9=2/3m+4/3+16/9

3) simplify: 2/9m=28/9+2/3m

4) subtract 2/3 m from both sides:

2/9m-2/3m= 28/9+2/3m-2/3m

5) simplify: -4/9m=28/9

6) m=-7

Brad average typing rate in words per minute is 21

1260 divided by 60 = 21

(In case you meant 30 minutes)

1260 divided by 30 = 42

Answer:

x = 6/5

y = -14/5

Step-by-step explanation:

y = x -4

y - x = -4

y = 6x -10

y - 6x = -10

y - x = -4

y - 6x = -10

_________--

5x = 6

x = 6/5

y - x = -4 | ×6 |

y - 6x = -10 | ×1 |

6y - 6x = -24

y - 6x = -10

__________--

5y = -14

y = -14/5

Answer:

16 pi or approximately 50.24

Step-by-step explanation:

The area of a circle is given by

A = pi r^2 where r is the radius

r = d/2 where d is the diameter

r = 8/2 =4

So plugging into the equation for the area

A = pi (4)^2

A = 16pi

Using 3.14 as an approximation for pi

A = 16*3.14 =50.24

Based on the diagram shown above, the area of the shaded region rounded to the nearest hundredth is 1.34 square meter.

In Mathematics and Euclidean Geometry, the area of a square can be calculated by using this formula;

A = [tex]s^2[/tex]

Where:

By substituting the given side lengths into the formula, we have;

Area of square, A = 2.5 × 2.5

Area of square, A = 6.25 square meters.

In Mathematics and Geometry, the area of a circle can be calculated by using this formula:

Area of circle = π[tex]r^2[/tex]

Where:

r represents the radius of a circle.

By substituting, we have;

Radius of circle = diameter/2 = 2.5/2

Radius of circle = 1.25 m.

Area of circle = π × [tex]1.25^2[/tex]

Area of circle ≈ 4.91 square meters.

Area of the shaded region = Area of square - Area of circle

Area of the shaded region = 6.25 - 4.91

Area of the shaded region = 1.34 square meter.

The area of the shaded region is Area = 1.34 [tex]m^2[/tex].

To find the area of the shaded region (the area outside the circle but inside the square), we need to calculate the area of the square and the area of the circle, then subtract the area of the circle from the area of the square.

Given:

Side length of the square [tex]\(s = 2.5\)[/tex] meters

Use [tex]\( \pi = 3.14 \)[/tex]

1. Calculate the area of the square:

[tex]\[ \text{Area of the square} = s^2 = 2.5^2 = 6.25 \text{ square meters} \][/tex]

2. Calculate the radius of the circle:

Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square.

[tex]\[ \text{Diameter of the circle} = 2.5 \text{ meters} \][/tex]

[tex]\[ \text{Radius of the circle} = \frac{2.5}{2} = 1.25 \text{ meters} \][/tex]

3. Calculate the area of the circle:

[tex]\[ \text{Area of the circle} = \pi r^2 = 3.14 \times (1.25)^2 \][/tex]

[tex]\[ \text{Area of the circle} = 3.14 \times 1.5625 = 4.90625 \text{ square meters} \][/tex]

4. Calculate the area of the shaded region:

[tex]\[ \text{Area of the shaded region} = \text{Area of the square} - \text{Area of the circle} \][/tex]

[tex]\[ \text{Area of the shaded region} = 6.25 - 4.90625 = 1.34375 \text{ square meters} \][/tex]

Rounded to the nearest hundredth:

[tex]\[\text{Area of the shaded region} \approx 1.34 \text{ square meters}\][/tex]

The complete question is:

Calculate the area of the shaded region. Use 3.14 for pi. Round your answer to the nearest hundredth if necessary.

Area = ____ [tex]m^2[/tex].

The side length, s, of the resulting polyhedron is (20√3)/3 cm.

To find the value of s, the side length of the resulting polyhedron, we can analyze the original cube's corners and the pyramids that Donatello slices off. Each corner of the cube contributes one-eighth of a pyramid to the polyhedron. These pyramids are similar, and their base is an equilateral triangle with side length s/2, and the height is s/2.

Considering one of these pyramids, we can use the Pythagorean theorem to find its slant height (the side length of the original cube):

(s/2)^2 + (s/2)^2 + (s/2)^2 = 10^2

Simplifying:

3/4 * s^2 = 100

Now, solve for s:

s^2 = (4/3) * 100

s^2 = 400/3

s = √(400/3)

s = 20/√3

To rationalize the denominator, multiply by (√3/√3):

s = (20/√3) * (√3/√3)

s = (20√3)/3

So, the side length s of the resulting polyhedron is (20√3)/3 cm.

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The side length of the resulting polyhedron after slicing off corner pyramids is  [tex]\( \frac{10}{3} \).[/tex]

Of course, here's the solution in LaTeX:

To find the side length ( s ), we can break down the process step by step:

1. Start with a cube of side length ( 10 ).

2. Slice off a pyramid from each corner.

Since all the edges of the resulting polyhedron have the same length, let's find the side length of the pyramid. Consider one of the corner pyramids:

- It has a square base, with side length ( x , which is also equal to the side length of the cube.

- It has four congruent triangular faces.

If we draw a cross-section through the pyramid and the cube, we'll see that the cross-section of the pyramid is an isosceles right triangle with legs of length ( x ).

Given this, we can use Pythagoras' theorem to find the height of the pyramid. The hypotenuse of the right triangle is ( x ), and the legs are each  x ). So, we have:

[tex]\[ x^2 = x^2 + x^2 + h^2 \][/tex]

Solving for \( h \), the height of the pyramid, we get:

[tex]\[ h = \sqrt{x^2 - x^2} = \sqrt{x^2 - \left(\frac{x}{\sqrt{2}}\right)^2} \]\[ h = \sqrt{x^2 - \frac{x^2}{2}} = \sqrt{\frac{x^2}{2}} = \frac{x}{\sqrt{2}} \][/tex]

Now, we know that the height of the pyramid is [tex]\( \frac{x}{\sqrt{2}} \).[/tex]

When we remove the corner pyramid, the remaining shape is a pentagonal pyramid with a square base. This means the side length of the square base of the remaining polyhedron is [tex]\( 10 - 2x \).[/tex]

The height of this pentagonal pyramid is the same as the height of the corner pyramid, which is  [tex]\( \frac{x}{\sqrt{2}} \).[/tex]

So, we can set up an equation for the height of the remaining pyramid:

[tex]\[ 10 - 2x = \sqrt{2} \cdot \frac{x}{\sqrt{2}} \]\[ 10 - 2x = x \][/tex]

Solving for \( x \):

[tex]\[ 10 = 3x \]\[ x = \frac{10}{3} \][/tex]

So, the side length  [tex]\( s \) of the polyhedron after slicing off the corner pyramids is \( \boxed{\frac{10}{3}} \).[/tex]

Answer:

= 5 (-2y+3) / -y+3

Step-by-step explanation:

If you need more help, you can look at this website called "symbolab".

Answer:

Sum of the interior angles of a regular polygon is given by = (n-2)180°

where n is the no. of sides.

In the above figure, n= 10

Therefore, sum of the interior angles = (10-2)×180°

= 8×180°

= 1440°

Measure of each angle = 1440/10= 144°

Therefore, 10x+4=144

=> 10x= 140

=> x= 14

For the given figure the value of x is 14

Given  a regular polygon

A regular polygon is a polygon which has all sides equal and each side  subtends equal interior angle at the center.

According to the figure

We are given a regular polygon with 10 sides

The angle subtended  at the center is given as

(10x + 4)°

[tex]\rm The\; Sum \; of \; Interior\; angles = \bold {(n-2) \times 180\textdegree} ......(1) \\Where n = Number \; of \; sides \;of\; a \;polygon[/tex]

The Sum of interior angles =  ( 10-2) [tex]\times 180\textdegree[/tex]= 1440°

So the angle subtended by one side at the center is given as follows

1440°/ 10 = 144°

Since the angle subtended at the center = 144° = (10x + 4)°

so by solving this we can get

140 = 10x

x = 14  

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Answer:

its 4xy and 12x

( options B and C)

hope that helped :)

Answer:

its 4xy and 12x

Step-by-step explanation:

Answer:

8x(2x - 1)

Step-by-step explanation:

Step 1: Write expression

16x² - 8x

Step 2: Find GCF

We can factor and 8 out of both terms and also an x out of both terms.

GCF = 8x

Step 3: Factor

8x(2x - 1)

To factor the expression [tex]16x^2[/tex] - 8x, the greatest common factor is 8x, resulting in the factored expression 8x(2x - 1).

To factor the expression [tex]16x^2[/tex] - 8x by taking out the greatest common factor (GCF), we first identify the largest factor that divides both coefficients. Here, 8 is the GCF of 16 and 8, and since both terms also include a factor of x, the GCF is 8x. We then divide each term by 8x to find the factored expression:

[tex]16x^2[/tex] ÷ 8x = 2x

-8x ÷ 8x = -1

So, the expression factored by its greatest common factor is 8x(2x - 1).

Answer:

16 ^3/4 = 8

Step-by-step explanation:

distribute the exponential fraction.

Answer:

a = -2  b = 6  c = -3

x = -6 +- sq root (6^2 -4 * -2 *-3) / 2 * -2

x1 = [-6 + sq root (36 - 24)] / -4

x1 = [-6 + sq root (36 - 24)] / -4

x1 = (-6 + sq root (12) ) / -4

x1 = (-6 + 3.4641016151 ) / -4

x1 = -2.5358983849  / -4

x1 = 0.6339745962

x2 = (-6 - sq root (12) ) / -4

x2 = (-6 - sq root (12) ) / -4

x2= (-6 - 3.4641016151 ) / -4

x2 = - 9.4641016151 / -4

x2 = 2.3660254038

Step-by-step explanation:

Answer:

2 2/5

Step-by-step explanation:

-1 3/5 ÷ -2/3

First change the mixed number to an improper fraction

1 3/5 = (5*1 +3)/5 = 8/5

-8/5 ÷ -2/3

Copy dot flip

-8/5 * -3/2

Multiply the numerators then the denominators

24/10

Dividing the top and bottom by 2

12/5

Changing this back to a mixed number

10/5 +2/5

2 + 2/5

2 2/5

Pls mark Brainliest.

Answer:

12/5 or 2 2/5 is the answer.

Step-by-step explanation:

-1 3/5 divided by -2/3.

First, we must turn the mixed fraction into an improper fraction so we are able to perform operations without the hassle of an extra whole.

-1 3/5 = -8/5

Now let's divide. Division is the same as multiplying the dividend by the reciprocal of the divisor. The divisor is the latter, or the number we are dividing the other number by, i.e. -2/3.

The reciprocal of -2/3 is -3/2.

Now let's multiply.

-8/5 * -3/2 = 24/10, which simplifies into 12/5.

12/5 or 2 2/5 is the answer.

Answer:

result if 3 would be 3 I think I hope it helps have a good day

Answer:

7/11

Step-by-step explanation:

Answer:

18.9 miles

Step-by-step explanation:

11.90 + 7.9 = 18.9

Answer:

r=7

Step-by-step explanation:

-30=12-6r

We move all terms to the left:

-30-(12-6r)=0

We add all the numbers together, and all the variables

-(-6r+12)-30=0

We get rid of parentheses

6r-12-30=0

We add all the numbers together, and all the variables

6r-42=0

We move all terms containing r to the left, all other terms to the right

6r=42

r=42/6

r=7

Answer:

-3 = r OR r = -3

Step-by-step explanation:

-30 = 12 - 6r

30+12 = -18   12+12 = (cancels out left with just 6r)

-18/6r = -3

-3 = r

Hope this helped :)

Answer:

The required vector parametric equation is given as:

r(t) = <3cost, 3sint>

For 0 ≤ t ≤ 2π

Step-by-step explanation:

Given that

f(x, y) = <2y, -sin(y)>

Since C is a cirlce centered at the origin (0, 0), with radius r = 3, it takes the form

(x - 0)² + (y - 0)² = r²

Which is

x² + y² = 9

Because

cos²β + sin²β = 1

and we want to find a vector parametric equations r(t) for the circle C that starts at the point (3, 0), we can write

x = 3cosβ

y = 3sinβ

So that

x² + y² = 3²cos²β + 3²sin²β

= 9(cos²β + sin²β) = 9

That is

x² + y² = 9

The vector parametric equation r(t) is therefore given as

r(t) = <x(t), y(t)>

= <3cost, 3sint>

For 0 ≤ t ≤ 2π

The vector parametric equation for the circle C that starts at the point (3,0) and travels around the circle once counterclockwise for 0≤t≤2π is:

[tex]r(t) = <3cost, 3sint>[/tex]

We have

[tex]f(x, y) = <2y, -sin(y)>[/tex]

As C is a circle centered at the origin (0, 0), with radius r = 3,

So, equation is:

[tex](x - 0)^2 + (y - 0)^2 = r^2[/tex]

[tex]x^2+ y^2 = 9[/tex]

 As, cos²β + sin²β = 1

 Take ,

x = 3cosβ

y = 3sinβ

Then

[tex]x^2 + y^2 = 3^2cos^2\beta + 3^2sin^2\beta\\= 9(cos^2\beta + sin^2\beta) \\= 9\\x^2 + y^2 = 9[/tex]

The vector parametric equation r(t) is therefore given as

[tex]r(t) = <x(t), y(t)>[/tex]

[tex]= <3cost, 3sint>[/tex]

For 0 ≤ t ≤ 2π

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