The diameter of a circle is 4 cm. Which equation can be used to find its circumference
A: C = pi x 44
B: C = pi x 2
C: C = 16 x pi
D: C = pi x 4

Jake ran 0.534 km in all, if he ran 145 meters before lunch and 389 meters after lunch.

Step-by-step explanation:

The given is,

                  Jake ran 145 meters before lunch.

                  389 meters after lunch.

Step:1

        Total distance ran by Jake,

           Total distance = Jake run before lunch + Jake run after lunch...(1)

        Where,

                    Jake run before lunch = 145 meters

                       Jake run after lunch = 389 meters

        Equation (1) becomes,

                    Total distance = 145 + 389

                                             = 534

                    Total distance = 534 meters

Step:2

        1 kilometer = 1000 meters

        Total distance ran by Jake = 534 meters

                                                     = [tex]\frac{534}{1000}[/tex] kilometers

                                                     = 0.534

      Total distance ran by Jake  = 0.534 km

Result:

         Jake ran 0.534 km in all, if he ran 145 meters before lunch and 389 meters after lunch.

Answer:

0.534

Step-by-step explanation:

I did the work

Answer:

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

Step-by-step explanation:

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

Answer:

sin D= 12/15

sin E= 9/15

cos D=9/15

Step-by-step explanation:

Use SOH CAH TOA

Sine= opposite/hypotenuse

Cosine= adjacent/hypotenuse

Tangent= opposite/adjacent

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]

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: 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:

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:

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

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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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.

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:

= 70f - 9g

Step-by-step explanation:

1. Remove parentheses

2. Multiply the numbers

3. Multiply the numbers

Answer:

-1

Step-by-step explanation:

Answer:

18.9 miles

Step-by-step explanation:

11.90 + 7.9 = 18.9

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:

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:

Car would have traveled [tex]1.283[/tex] miles more with the extra time

Step-by-step explanation:

Given

Speed of the car - [tex]70[/tex] miles per hour

Speed of car in miles per second

[tex]\frac{70}{60* 60}[/tex]

[tex]= 0.0194[/tex] miles per second

Time wasted in talking instead of travelling

[tex]66[/tex] seconds and [tex]513[/tex] milliseconds

Total time wasted in seconds

[tex]66 + \frac{513}{1000} \\66 + 0.513[/tex]

[tex]66.153[/tex] seconds

Distance that would have been traveled in this time instead of talking

[tex]0.0194[/tex] miles per second [tex]* 66.153[/tex] seconds

[tex]= 0.0194 * 66.153[/tex] miles

[tex]= 1.283[/tex] miles

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

Answer:

The correct answer is 24.

Step-by-step explanation:

Jose wants to have an average mean of 25 points per game in his 6 basket ball matches.

Total points Jose plans to achieve in 6 games is 25 × 6 = 150.

Points score by him in the first five matches are 28, 24, 26, 27 and 21.

Total points in 5 matches is 126.

Thus the points he need to score in his next game to have an average mean of 25 is given by 150 - 126 = 24.

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:

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:

its 4xy and 12x

( options B and C)

hope that helped :)

Answer:

its 4xy and 12x

Step-by-step explanation:

Answer:

6 different groups of toy animals

Step-by-step explanation:

In this question, we are to calculate the number of different groups of toy animals Michael can take.

Since we are selecting, this is clearly a COMBINATION question. Now from the question, we are trying to select 5 toy animals from a group of 6 different animals to fit in the bag

The number of ways we can do this is  6C5 ways

Mathematically, if we have to select a number of r items from a group of n items, the number of ways this can be done is;

nCr = n!/(n-r)!r!

Using the case in the question, we have; 6!/5!(6-5)! = 6!/5!1! = 720/120 = 6 groups

Answer:

6 different groups of toy animals

Step-by-step explanation:

The question above can be solved by applying the Combination technique

Combination technique uses the formula:

nCk = n! /k!(n-k)!

Where in the question above:

n = 6

k = 5

Therefore we have , 6C5

= 6! / 5! (6-5)!

= 6!/ 5!(1!)

6! = 6×5×4×3×2×1

5! = 5×4×3×2×1

Hence,

= (6×5×4×3×2×1) / (5×4×3×2×1)(1)

= 6

Hence, Michael can take 6 different groups of toy animals with him on his vacation.

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

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