Two buses leave towns 520 kilometers apart at the same time and travel toward each other. One bus travels 16 km/h slower than the other. If they meet in 2 hours, what is the rate of each bus?

Answer:

there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

Step-by-step explanation:

Given the data in the question;

Let S(t) represent the amount sea ice around the North Pole in millions of square meters at a given time t,

t is the number of months since January.

Now, we use a cosine curve to model this scenario

Vertical shift will be;

D = ( 6 + 14 ) / 2 = 20 / 2

D = 10

Next is the Amplitude;

|A| = ( 6 - 14 ) / 2

|A| = 4

Now, the horizontal stretch factor will be;

B = 2π / 12

B = π/6

Hence;

S(t) = 4cos( π/6 × t ) + 10 ----------- let this be equation 1

Now we find when there will be less than 9 million square meters of sea ice;

S(t) = 9

so we have

9 = 4cos( π/6 × (t-2) ) + 10

9 - 10 = 4cos( π/6 × (t-2) )

-1 = 4cos( π/6 × (t-2) )

-1/4 = cos( π/6 × (t-2) )

so we have;

cos⁻¹( -1/4 ) = π/6 × (t₁-2)  -------- let this be equation 2

2π - cos⁻¹( -1/4 ) = π/6 × (t₂-2)  -------- let this be equation 3

so we solve equation 2 and 3

we have'

t₁ - t₂ = 6/π × ( 2π - cos⁻¹( -1/4 ) - cos⁻¹( -1/4 ) )

t₁ - t₂ = 6/π × ( 2π - 2cos⁻¹( -1/4 )  

t₁ - t₂ = 6/π × ( π - cos⁻¹( -1/4 )  

t₁ - t₂ = 6/π × ( π - 104.4775 )

t₁ - t₂ = 6/π × ( π - 104.4775 )  

t₁ - t₂ = 5.035

therefore, there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

Answer:

see below

Step-by-step explanation:   6  5  17  43

Volume of a sphere = 121.5 π mm³   Find r

Vol Sphere = (4π r³) / 3     solve for r

Vol Sphere × 3 = (4π r³)

(Vol Sphere × 3) / 4π = r³

∛((Vol Sphere × 3) / 4π)  = r

∛((121.5 π mm³× 3) / 4π)  = r         the pi terms cancel

∛((121.5  mm³× 3) / 4)  = r

∛((364.5  mm³) / 4)  = r

∛((91.125  mm³) )  = r

       4.5   =  r

Answer:

The solution set to the absolute value is:

[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]

Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].

Step-by-step explanation:

From Mathematics, we know that absolute values are defined by the following characteristics:

1) For [tex]x \ge 0[/tex], [tex]|x| = x[/tex]

2) For [tex]x < 0[/tex], [tex]|x| = - x[/tex]

Then, if [tex]|x| = x[/tex], then the solution set to the absolute value is:

[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]

Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].

Answer:

Perimeter: 18.28

Area: 22.28

Step-by-step explanation:

1. Approach

An easy method that can be used to solve the given problem is the partition the given figure into two smaller figures. One can divide this figure into a square and a semi-circle. After doing so, one can find the area of the semi-circle and the area of the square. Finally, one can add the two area together to find the final total area. To find the perimeter of the figure, one can add the lengths of three of the sides of the square and then one can add half of the circumference of the circle to the result. The final value will be the perimeter of the entire figure.

2. Find the circumference of the semi-circle

The circumference of a circle is the two-dimensional distance around the outer edge of a circle, in essence the length of the arc around a circle. The formula to find the circumference of a circle is as follows,

C = 2(pi)r

Since a semi-circle is half of a circle, the formula to find its circumference is the following,

C = (pi)

Where (pi) is the numerical value (3.1415) and (r) is the radius of the circle. By its definition, the radius of a circle is the distance from a point on the circle to the center of the circle. This value will always be half of the diameter, that is the distance from one end of the circle to the other, passing through the center of the circle. The radius of a circle is always half of the diameter, thus the radius of this semi-circle is (2). Substitute this into the formula and solve for the circumference;

C = (pi)r

C = (pi)2

C ~ 6.28

3. Find the area of the semi-circle

The formula to find the area of a circle is as follows,

A = (\pi)(r^2)

As explained earlier, a semi-circle is half of a circle, therefore, divide this formula by (2) to find the formula for the area of a semi-circle

A = ((pi)r^2)/(2)

The radius of this circle is (2), substitute this into the formula and solve for the area of a semi-circle;

A = ((pi)r^2)/(2)

A = ((pi)(2^2))/(2)

A = (pi)2

A = 6.28

4. Find the area and perimeter of the square,

The perimeter of a figure is the two-dimensional distance around the figure. Since the semi-circle is attached to one of the sides of a square, one only needs to add three sides of the square to find the perimeter of the square;

P = 4+4+4

P = 12

The area of a square can be found by multiplying the length by the width of the square.

A = l*w

Substitute,

A = 4*4

A=16

5. Find the area and the perimeter of the figure,

To find the perimeter of the figure, add the value of the circumference to the vlalue of the perimeter of the square;

A = C+P

A = 6.28+12

A = 18.28

To find the area of the figure, add the value of the area of the circle to the area of the square;

A = 6.28+16

A = 22.28

Answer: b) f(m)

Step-by-step explanation:

Answer:

(My answers are not rounded!)

Problem A:

Area: 285 cm^2

Perimeter: 70 cm

Problem B:

Area: 30 m^2

Perimeter: 30 m

Problem C:

Area: 28 m^2

Perimeter: 24 m

Problem D:

Lateral Area: 150 in^2

2 (l + w) h

= 2 (11 + 4) 5

= 2(15)5

= 30(5)

= 150

Surface Area: 238 in^2

2 (lw + hl + hw)

2 (11 x 4 + 11 x 5 + 5 x 4)

= 2 ( 44 + 55 + 20)

= 2 (119)

= 238

Volume: 220 in^3

Length x width x height (rectangular prism)

use formula: 11 x 5 x 4 = 220

Problem E:

Area: 379.94 m^2

Formula: πr^2 (circle)

3.14(11^2)

= 3.14(121)

= 379.94

Circumference: 69.08 m

Formula: 2πr

= 2(3.14)11

= 6.28(11)

=69.08

Problem F:

Area: 49 m^2

length x width

7 x 7 = 49

Perimeter: 28 m

2 (l + w)

= 2 (7 + 7)

= 2(14)

= 28

Problem G:

Area: 1,056 cm^2

length x width

48 x 22 = 1,056

Perimeter: 140 cm

2 (l + w)

2 (48 + 22)

2(70)

=140

Problem H:

Lateral Area: 94.2 in^2

2πrh

= 2(3.14) x 1.5(10)

= 6.28 x 15

= 94.2

Surface Area: 108.33 in^2

2πrh+2πr2

=2(3.14) 1.5(10) + 2(3.14) 1.5^2

= 108.33

Volume: 70.65 in^3

πr2h

= 3.14(1.5^2) 10

= 3.14(2.25) 10

= (7.065) 10

= 70.65

Option B, The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times

Step-by-step explanation:

The distribution of apple candies can be represented as normal curve and hence the sample proportion for this is true and can be drawn.

The rest other cases do not represent a normal distribution and hence it will not be easy to plot curve for these samples.

hence, option B is correct

Answer:

4

Step-by-step explanation:

Based on your math expression:

7-15 = -8

-2*(-8) = 16

16 / 4 = 4

Answer:

4

Step-by-step explanation:

-2(7-15)

=-14+30

=16÷4

=4

Answer:

253.5 ft³

Step-by-step explanation:

Volume of a pyramid = [tex] \frac{1}{3} [/tex]× base area × height

Volume of a prism = base area × height

Volume of the pyramid

= [tex] \frac{1}{3} [/tex]× (6×6.5÷2) × 9

= [tex] \frac{1}{3} [/tex]× 19.5 × 9

= 58.5 ft³

Volume of the prism

= (6×6.5÷2) × 10

= 195 ft³

Volume of the solid

= 58.5 + 195

= 253.5 ft³

Answer:

A

Step-by-step explanation:

the base is 19.5 feet squared

(6 * 6.5 / 2)

multiplied by 10 gives you 195 feet cubed for the lower solid

19.5 * 9 / 3

gives you 58.5 feet cubed for the upper solid

just add both volumes together

Answer:

b. The speed of the car is an explanatory variable

Step-by-step explanation:

In the scenario above, the variable which the researcher intends to measure is the a distance covered by a car using the speed information available. The measured variable is the dependent variable as it outcome depends on the variable with which it is being measured, this is called the independent or explanatory variable.

Therefore, car speed is the explanatory or independent variable

Distance is the dependent, response or measured variable.

Answer:

[tex]\frac{3}{17}, \\0.176, \\18\%[/tex]

Step-by-step explanation:

The area a total of 4+3+6+5=18 balls, consisting of:

After a green ball is selected (implied that it is not replaced or put back), there will be 17 balls total, consisting of:

Therefore, the probability of drawing another green one is:

[tex]\boxed{\frac{3}{17}=0.176=18\%}[/tex]

Answer:

If I understand this right I think it would be 8 and 6?

Step-by-step explanation:

Sorry if this is wrong I'm really bad at math, please tell me if this is right.

Answer:

I searched the q and this is what I found

Step-by-step explanation:

Explanation: Number greater than 4 are 5 and 6 . So required probability is 26=13.

Answer:

the answer is in  

Step-by-step explanation:

Answer:

285 mi

Step-by-step explanation:

We can see that for every gallon, Josh drives 30 more miles. This means that he will drive 30*9.5 mi.

30*9.5 = 285

Step-by-step explanation:

15 may be

HOPE IT HELP U ...

Answer:

A. $15 is the mode.

Step-by-step explanation:

In order to answer this question, we need to know the definition of mode. "The mode of a set of numbers is the number that occurs the most" Since out of the four numbers, the one that appears the most is $15, then $15 is the mode.

Answer:

12 and 12.5

Step-by-step explanation:

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2*x+2*3=x-4

2x+6=x-4

2x-x=-4-6

x=-10

Answer:

[tex]x = - 10[/tex]

Step-by-step explanation:

Let's solve:

[tex]2(x+3)=x−4[/tex]

Step 1: Simplify both sides of the equation.

[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]

Step 2: Subtract x from both sides.

[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]

Step 3: Subtract 6 from both sides.

[tex]x+6−6=−4−6 \\ x=−10[/tex]

Answer:

[tex]\text{D. }464\:\mathrm{ft^2}[/tex]

Step-by-step explanation:

The surface area of the prism consists of four rectangles and two trapezoids. The sum of the areas of these polygons will give the total surface area of the prism:

Rectangle 1 (top base): [tex]12\cdot 14=168[/tex]

Rectangle 2 (bottom base): [tex]6\cdot 14 = 84[/tex]

Trapezoids 1 and 2 (lateral): [tex]2\cdot 9 \cdot 4=72[/tex]

Rectangles 3 and 4 (lateral): [tex]2\cdot 14\cdot 5=140[/tex]

Thus the total surface area is equal to

[tex]168+84+72+140=\boxed{\text{D. }464\:\mathrm{ft^2}}[/tex]

Answer:

C

Step-by-step explanation:  

 pedometers are devices that count the steps you take throughout the day. Seeing your daily step count can give you an idea of how active you are in a given day and give motivating feedback to help you achieve a daily step goal.

Answer:c i just took the test

Step-by-step explanation:

The mean of 43,69,48,37,85,57,95,102 is 67

Answer:

8h+(-5.9d)-17+4d-3.4h

8h-5.9d-17+4d-3.4h

group the like terms

8h-3.4h+4d-5.9d-17

4.6h-1.9d-17

Step-by-step explanation:

Answer:

It's 4 miles East from the store.

Step-by-step explanation:

6 miles east - 2 miles west = 4 miles East

Displacement for north and south should cancel out since they are equal to each other.

Answer:

The nth term of this sequence is [tex]a_{n} = -2n + 2[/tex]

Step-by-step explanation:

In this sequence we keep adding -2 on to get the next term. This sequence is called an arithmetic sequence, a sequence that uses addition to keep increasing.

The formula for the nth term of an arithmetic sequence is

[tex]a_{n} = d[/tex] · [tex]n + a_{1} - d[/tex]

[tex]a_{1}[/tex] stands for the first term in the sequence, and [tex]d[/tex] stands for the difference between each number in the sequence.

[tex]a_{1} = 0[/tex] and [tex]d[/tex] = -2, so :

[tex]a_{n} = -2[/tex] · [tex]n + 0 - (-2)\\[/tex]

[tex]a_{n} = -2n + 2[/tex]

Therefore, to find the nth term in this sequence you would use the formula

[tex]a_{n} = -2n + 2[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

Modern graphing calculators have a derivative function available, so using a calculator to find the next value of x is pretty simple.

The Newton's Method iterator for finding the next approximation to the root (x') is ...

  x' = x -f(x)/f'(x) . . . . . where f'(x) is the derivative of f(x).

The attachment shows the first 3 iterations (4 approximations). We observe that the starting point is pretty far from the root, and on the wrong side of some wiggles in the function, so convergence is pretty slow.

The desired approximations are shown above and in the table below.

__

Additional comment

To 12 significant figures, the only real root is −1.10305899649. When the calculator can interactively produce a next guess, you can type the next guess value into the iterator function even as it is showing you the next value. This lets you find the best-precision result as fast as you can type it.

For a calculator like a TI-84, the iterator function can make repeated use of "Ans" as an argument. It usually doesn't take more than 3 or 4 iterations to get a best-precision result, since the number of good decimal places is about doubled on each iteration. (Of course, you have to start with a better approximation than the one given in this problem.)

Answer:

A

Step-by-step explanation:

36*12*6+12*24*3=3456

Answer:

3456

Step-by-step explanation:

36*12*6 + 24*12*3

just add up the two volumes