Fiona ran 6 laps around a track each lap was 500 meters how far did Fiona run? Circle all that apply
A. 30 kilometers
B. 3 kilometers
C. 3,000 meters
D. 300 meters

Let the time taken by 2nd computer be = x

Time taken by first computer = 60 seconds

Total time taken by both = 40 seconds

So, equation becomes:

[tex]\frac{1}{60}+\frac{1}{x}=\frac{1}{40}[/tex]

[tex]\frac{-1}{x}=\frac{1}{60}-\frac{1}{40}[/tex]

Solving this we get,

x=120 seconds

Hence, the 2nd computer will take 120 seconds to finish a search alone.

It would take the second computer 120 seconds to finish the same search

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the rate of the first computer and y represent the rate of the second computer.

Two computers working together can finish a search in 40 seconds. Hence:

It takes one of the computer 60 seconds, hence:

40/x + 2/3 = 1

x = 120 seconds

Therefore it would take the second computer 120 seconds to finish the same search

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Answer:

The change in the lateral surface area is approximate [tex]6.32\ m^{2}[/tex]

Step-by-step explanation:

we know that

The lateral surface area of the cone is equal to

[tex]LA=\pi r l[/tex]

where

r is the radius of the base

l is the slant height

Part 1

we have

[tex]r=10\ m, h=6\ m[/tex]

Calculate the slant height l (applying the Pythagoras Theorem)

[tex]l^{2}=r^{2}+h^{2}[/tex]

substitute the values

[tex]l^{2}=10^{2}+6^{2}[/tex]

[tex]l^{2}=136[/tex]

[tex]l=\sqrt{136}\ m[/tex]

Find the lateral area of the cone

[tex]LA=\pi (10)(\sqrt{136})[/tex]

[tex]LA=10\pi \sqrt{136}\ m^{2}[/tex]

Part 2

we have

[tex]r=9.9\ m, h=6\ m[/tex]

Calculate the slant height l (applying the Pythagoras Theorem)

[tex]l^{2}=r^{2}+h^{2}[/tex]

substitute the values

[tex]l^{2}=9.9^{2}+6^{2}[/tex]

[tex]l^{2}=134.01[/tex]

[tex]l=\sqrt{134.01}\ m[/tex]

Find the lateral area of the cone

[tex]LA=\pi (9.9)(\sqrt{134.01})[/tex]

[tex]LA=9.9\pi \sqrt{134.01}\ m^{2}[/tex]

Part 3

Find  the change in the lateral surface area

[tex]10\pi \sqrt{136}-9.9\pi \sqrt{134.01}[/tex]

assume [tex]\pi =3.14[/tex]

[tex]10(3.14)\sqrt{136}-9.9(3.14)\sqrt{134.01}=6.32\ m^{2}[/tex]

To approximate the change in the lateral surface area of a right circular cone with a fixed height of 6m, we can use the formula √A = 2πrL, where A is the cross-sectional area, r is the radius, and L is the slant height. By calculating the slant height for both radii and using the formula, we find that the change in the lateral surface area is 15.36m².

To approximate the change in the lateral surface area of a cone, we can use the formula √A = 2πrL, where A is the cross-sectional area, r is the radius, and L is the slant height. In this case, the height (h) is fixed at 6m. So, we need to find the slant height for both radii, using the formula L = √(r² + h²).

Step 1: Find the slant height for the first radius, r1 = 10m:

L1 = √(10² + 6²) = √136 = 11.66m

Step 2: Find the slant height for the second radius, r2 = 9.9m:

L2 = √(9.9² + 6²) = √135.20 = 11.61m

Step 3: Calculate the change in the lateral surface area, using the formula √A1 - √A2:

√A1 = 2π x 10m x 11.66m = 732.94m²

√A2 = 2π x 9.9m x 11.61m = 717.58m²

Change in Lateral Surface Area = √A1 - √A2 = 732.94m² - 717.58m² = 15.36m²

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Answer:

[tex]\large\boxed{A=480\ m^2}[/tex]

Step-by-step explanation:

The formula of an area of a kite:

[tex]A=\dfrac{d_1d_2}{2}[/tex]

d₁, d₂ - diagonal

Look at the picture.

Use the Pythagorean theorem.

[tex]x^2+5^2=13^2[/tex]

[tex]x^2+25=169[/tex]               subtract 25 from both sides

[tex]x^2=144\to x=\sqrt{144}\\\\x=12\ m[/tex]

Therefore d₁ = (2)(12 m) = 24 m.

[tex]y^2+12^2=37^2[/tex]

[tex]y^2+144=1369[/tex]         subtract 144 from both sides

[tex]y^2=1225\to y=\sqrt{1225}\\\\y=35\ m[/tex]

Therefore d₂ = 5 + 35 = 40 m.

Substitute:

[tex]A=\dfrac{(24)(40)}{2}=(24)(20)=480\ m^2[/tex]

4. You total the songs to find out how many possibilities all together = 20

Then how many of those are rap songs = 5

So the probability of getting rap songs is 5/20 or (simplified) 1/4

Explanation of sandwich combinations using a tree diagram and computation of the probability for Joel's first song being rap.

Tree Diagram for David's Sandwich Combinations:

Probability for Joel's Jumble:

Answer:

C

Step-by-step explanation:

C is the most logical answer

Answer:

Answer x  = 8

Step-by-step explanation:

(5x + 4) + (8x - 18)= 90      The two angles must be complementary for this to work. Remove the brackets

5x + 4 + 8x - 18 = 90          Collect like terms

13x - 14 = 90                        Add 14 to both sides

13x = 104                              Divide by 13  

x = 8 Answer

Check

Sin(8*8 - 18) = sin(64 - 18) = sin(46) = 0.7193

Cos(5*8 + 4) = cos(44) = 0.7193

This problem is very interesting. Thanks for posting.

Answer: second option.

Step-by-step explanation:

Let's represent the slant height of the figure with: [tex]l[/tex]

Then, to find the value of the slant height you must apply the Pythagorean Theorem, where:

[tex]l[/tex] is the hypotenuse and the other legs are 12 units and 5 units ([tex]\frac{10units}{2}=5units[/tex])

Therefore, you obtain that the slant height of the figure is the shown below:

[tex]l=\sqrt{(5units)^2+(12units)^2}\\l=13units[/tex]

Answer:

The correct answer is Slant height =13 units

Step-by-step explanation:

From the figure we can see a square pyramid

Points to remember

Hypotenuse² = Base² + Height²

To find the slant height

Fro figure we can see a right angles triangle with,

Base = 10/2 = 5 units  and Height = 12 units

We have to find Hypotenuse (Slant height)

Hypotenuse² = Base² + Height²

Slant height² = 5² + 12² = 25 + 144 = 169

Slant height = √169 = 13 units

Therefore the slant height = 13 units

Answer:

78.09

Step-by-step explanation:

Answer:

1.78.09

2. 2755.59

Step-by-step explanation:

you go to the whome insurance company for auto insurance the charge $525.00 as a base rate for six months of insurance for your vehicle they offer a 15% discount for safe driver habits and a 10% discount for an excellent credit rating of 5% for a good rating the increase the rate by 5% and 10% respectively for a fair or poor credit rating you have a fair credit rating and qualify for the safe driver discount how much do the insurance cost you per month?

Insurance is more like a protection against any risk associated with vehicles, assets, buildings and lives.

the charge form the insurer is $525 with a 15% discount means

525 * 0.85 = 446.25    

or525-(525*15%)

aand increment in rate after 6 months

446.25 * 1.05 = 468.56  or  

446.25+446.25+5%

468.56 / 6 =

78.09

2. if the cost of the vehicle is 17000

a discount of 10%b for an excellent credit rating equals

17000*.90

$15300+1.05

16065

therefore per month he is going to pay 16065/6

$2677.5

add answer +78.09=2755.59

Answer:

The probability would be 97.8%

Step-by-step explanation:

In order to find that, lets look at the amount of standard deviations away the amount given is. Since the number is 30 away from the mean, and the standard deviation is 15, we can find the total number of deviations it is away.

30/15 = 2

Now that we have that, we can look at the probability curve for standard deviations. Outside of 2 standard deviations above is only a 2.2% likelihood. Since that is the case, we can find the amount that would be under that as 100% minus the amount we just found.

100% - 2.2% = 97.8%

Answer:

NO SOLUTION.

Step-by-step explanation:

4x - y    =  -5

12x - 3y  = 15

Multiply the first equation by 3:

12x - 3y = -15

Note that the left side of this equation is the same as the left side of the second one, but the right sides are different.  The left side cannot be equal to 2 different values. Therefore there  is NO SOLUTION.

Note if we subtract the last 2 equations we get:

0 = 30  which is, of course, absurd.

➷ If a line is parallel to the line, then the slope will remain the same

Now, you just need to substitute the values of that coordinate into the equation

1/2 = -1/2(3) + c

Simplify:

1/2 = -1.5 + c

Add 1.5 to both sides

c = 2

Therefore, the equation of the line would be:

y = -1/2x + 2

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x + 3 is in this form

with m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes, hence

slope of parallel line = - [tex]\frac{1}{2}[/tex], thus

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (3, [tex]\frac{1}{2}[/tex]) into the partial equation

[tex]\frac{1}{2}[/tex] = - [tex]\frac{3}{2}[/tex] + c ⇒ c = 2

y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of parallel line

To find the coordinate of K', we first rotate point a (-7,-2) 270 degrees clockwise. Then, we shift the resulting coordinates 3 units down. The coordinate of K' is (-7, -5).

To find the coordinate of K', we first need to rotate point a (-7,-2) 270 degrees clockwise. To do this, we can use the rotation matrix:

[cos(theta)  -sin(theta)] [x]
[sin(theta)  cos(theta)]  [y]

Plugging in the values, we get:

[cos(270)  -sin(270)] [-7]
[sin(270)  cos(270)]  [-2]

Simplifying, we have:

[-0 -1] [-7]
[1  0]]  [-2]

Multiplying, we get:

[0 -7]
[1  0]]

Now, we shift the resulting coordinates 3 units down. Adding -3 to the y-coordinate, the coordinate of K' is (-7, -5).

Answer:

5.545

Step-by-step explanation:

This problem can be easily solved by using the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

in this case, the formula can be applied in the following way

a^2 = b^2  + c^2  - 2*b*c*cos(α)

Where

a,b,c are each of the sides of the triangle,

α is the angle between sides b and c

(See attached picture)

If we use the formula we get

a^2 = (9)^2 + (6)^2 - 2*(9)(6)*cos(37°)

a^2 = 81 + 36 - 86.2526

a^2 = 30.747

a = sqrt(30.747)

a = 5.545

Answer:

a.30.4 units²

Step-by-step explanation:

Using the triangle attached, we can find the angle at C which is 180-(22+105)=53°

Then we use the sine rule to find the value of side c.

14/sin105=c/sin53

c=(14/sin105)× sin53

c=11.575

We can now use the sine formula to find the area of the triangle. A=(1/2)absin∅

A= (1/2)×14×11.575sin22

A=30.4

Answer:

30.4

Step-by-step explanation:

Correct on edg2020

Answer:

Step-by-step explanation:

5 out of 8 because there are four one spaces and one pink space so that equals 5 and there are a total of 8 spaces to hit

Answer:

5/8.

Step-by-step explanation:

There are a total of 8 sectors of which 4 are 1 and 1 is pink.

So Prob (hitting a 1) = 4/8 = 1/2.

Prob (hitting a pink) = 1 /8.

So the probability of hitting a pink or a 1 = 1/2 + 1/8

= 5/8.

Answer: Option D.

Step-by-step explanation:

To solve this exercise you must keep on mind the Angle at the Center Theorem.

According to the  Angle at the Center Theorem, an inscribed angle is half of the central angle.

Therefore, given in the inscribed angle m∠BAC=35°, you can calculate the central angle m∠EFD as following:

[tex]BAC=\frac{EFD}{2}[/tex]

- Solve for EFD.

[tex]EFD=2*BAC[/tex]

- When you substitute values. you obtain:

[tex]EFD=2(35\°)\\EFD=70\°[/tex]

Answer:

Option B. ∠EFD = 35°

Step-by-step explanation:

In a circle F, it has been given mED = mDB = mBC

We have to find the measure of ∠EFD

We should always remember the inscribed angle theorem which states that the measure of an inscribed angle is always half the measure of intercepted arc.

m(arc BC) = 2×∠CAB = 2×35 = 70°

Now it has been given in the question

mED = mBC

Therefore m(arc ED) = 70°

Again applying the same theorem

m(arc ED) = 2×∠EFD

70° = 2×∠EFD

m∠EFD = [tex]\frac{70}{2}=35[/tex]

Option B. 35° is the answer.

Answer:

[tex]\large\boxed{A=46x\ m^2}[/tex]

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

b₁, b₂ - bases

h - height

We have

b₁ = 12m , b₂ = 6.4 m, h = 5x m.

Substitute:

[tex]A=\dfrac{12+6.4}{2}\cdot5x=\dfrac{18.4}{2}\cdot5x=9.2\cdot5x=46x[/tex]

The correct option is a) [tex]\large\boxed{A=46x\ m^2}[/tex]

The formula of an area of a trapezoid:

[tex]A=(b_1+b_2)/(2)\cdot h[/tex]

b₁, b₂ - bases

h - height

We have

b₁ = 12m , b₂ = 6.4 m, h = 5x m.

Substitute:

[tex]A=(12+6.4)/(2)\cdot5x=(18.4)/(2)\cdot5x=9.2\cdot5x=46x[/tex]

Answer:

12

Step-by-step explanation:

Let's calculate how many possible outfits does Tobias has.

Hats: 2, Shirts: 3, Pants: 2

If he's picking everything at random blindly from his closet, he could pick any of the hats, any of the shirts and any of the pants.  That makes a total of:

2 x 3 x 2 = 12 possible combinations.  

That doesn't mean the arrangement will look pretty :-)

Tobias has 12 possible outfit combinations from his closet. This is calculated by multiplying the choices he has for each item of clothing: 2 hats, 3 shirts, and 2 pairs of pants.

In this mathematics problem, Tobias has 2 hats, 3 shirts, and 2 pairs of pants. In such problems, an easy rule to remember is that for independent choices you multiply your options. So, for his hats, he has 2 options. For shirts, he has 3 options and for pants, he has 2 options. To find the total number of outfit combinations, just multiply these options: 2 (hats) * 3 (shirts) * 2 (pants) = 12 possible outfit combinations. Therefore, Tobias can mix and match his clothing items to make 12 different outfits.

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A is the answer to that question

the operation functions are shown as question marks, please replace accordingly

Answer:

d. does not exist

Step-by-step explanation:

The given limits are;

[tex]\lim_{x \to 4} f(x) =5[/tex], [tex]\lim_{x \to 4} g(x) =0[/tex] and [tex]\lim_{x \to 4} h(x) =-2[/tex]

We want to find

[tex]\lim_{x \to 4} \frac{f}{g}(x)= \lim_{x \to 4} \frac{f(x)}{g(x)}[/tex]

By the properties of limits, we have;

[tex]\lim_{x \to 4} \frac{f}{g}(x)= \frac{\lim_{x \to 4} f(x)}{\lim_{x \to 4} g(x)}[/tex]

This gives us;

[tex]\lim_{x \to 4} \frac{f}{g}(x)= \frac{5}{0}[/tex]

Division by zero is not possible. Therefore the limit does not exist.

The amount of fluid used in 4 days will be 18 ounces

Since each of them use 1 1/2 cups and they are 3

so the collective amount in 1 day will be

3 * 1 1/2 = 9/2

Now

The amount in 4 days will be

4 * 9/2 = 18

Therefore they will collectively use 18 ounces in 4 days

Answer:

There are 46 seats in row 10

Step-by-step explanation:

In order to find that we need to write this as an equation. We know that 6 is the constant and 4 is the coefficient for the variable. This would give us the equation:

y = 4x + 6

And this satisfies the equation for row 1, since when we put in the row number for x, it gives us the correct number of seats.

y = 4x + 6

y = 4(1) + 6

y = 4 + 6

y = 10

Now we can use that equation for any row. Let's use it for row 10

y = 4x + 6

y = 4(10) + 6

y = 40 + 6

y = 46

The parabola's line of symmetry is the x-axis.

y = 1/4p x²

Replace  x  with  −  x  and  y  with  − y  to check if there is x-axis, y-axis , or origin symmetry.  

Symmetric with respect to the y-axis

Answer:

1/3

Step-by-step explanation:

you go up 1 and down 3

Answer:

1/3

Step-by-step explanation:

The way to find slop is find the RISE/RUN between the two points.

Answer:

  [tex]\dfrac{z_1}{z_2}=\dfrac{1}{2}\,\text{cis}\,\dfrac{7\pi}{12}[/tex]

Step-by-step explanation:

The quotient of complex numbers is the quotient of their magnitudes at the difference of their angles.

  [tex]\dfrac{z_1}{z_2}=\dfrac{\text{cis}\,\dfrac{2\pi}{3}}{2\,\text{cis}\,\dfrac{\pi}{12}}=\dfrac{1}{2}\,\text{cis}\left(\dfrac{2\pi}{3}-\dfrac{\pi}{12}\right)\\\\\bf{\dfrac{z_1}{z_2}=\dfrac{1}{2}\,\text{cis}\,\dfrac{7\pi}{12}}[/tex]

Answer: 48°

Step-by-step explanation: The Answer is 48° this is because a triangle is equal to 180° and to find the missing side, add the two sides you do know and subtract them from 180 and you will get 48°

Have an awesome day,

Eric

Answer:

[tex]15\pi\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of the cone is equal to

[tex]LA=\pi rl[/tex]

where

r is the radius of the base

l is the slant height

we have

[tex]r=3\ cm[/tex]

Applying the Pythagoras Theorem find the slant height

[tex]l^{2}=3^{2} +4^{2}\\ \\l^{2}=25\\ \\l=5\ cm[/tex]

substitute in the formula

[tex]LA=\pi (3)(5)=15\pi\ cm^{2}[/tex]

Answer: 6

Step-by-step explanation: The formula to solve this is 2x + 8 = x + 14

First, you need to subtract x from each side:

X + 8 = 14

Next, subtract 8 from each side:

X = 6

Final answer:

To find the original number, we can solve the equation 2x + 8 = 14 + x.

Explanation:

To solve this problem, let's represent the original number as 'x'.

If you double the number, it becomes 2x. If you then add 8 to it, the equation becomes: 2x + 8 = 14 + x.

To isolate 'x' on one side of the equation, we subtract 'x' from both sides: 2x - x = 14 - 8.

This simplifies to: x = 6.

So, the original number is 6.