Andrew and Katherine rode their bikes and met at a park.
Andrew’s house was 8 miles from the park, Katherine’s house was 5 miles from
the park. They each left their house at the same time and Andrew arrived 10
minutes after Katherine arrived. Katherine’s average speed was 2 mph slower
than Andrew’s average speed. {hint: UNITS matter!}
a. Write an equation to represent this data.
b. What was Andrew’s average speed?

A function assigns the value of each element of one set to the other specific element of another set. The number of centenarians in the country in 2013 is 9.4175×10⁴⁵.

A function assigns the value of each element of one set to the other specific element of another set.

The exponential function that can be used to project the number of centenarians in a certain country is [tex]H(t) = 80,030.83(1.0481)^t[/tex].

Now, the number of centenarians in the country in 2013 is,

[tex]H(t) = 80,030.83(1.0481)^t\\\\H(2013) = 80,030.83(1.0481)^{2013}\\\\H(2013) = 9.4175 \times 10^{45}[/tex]

Also, the number of centenarians in the country in 2038 is,

[tex]H(t) = 80,030.83(1.0481)^t\\\\H(2038) = 80,030.83(1.0481)^{2038}\\\\H(2038) = 3.048 \times 10^{46}[/tex]

Hence, the number of centenarians in the country in 2013 is 9.4175×10⁴⁵.

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Answer:

I'm not too sure but I think It's 34

Step-by-step explanation:

Rusty in that particular area of math

Write tan in terms of sin and cos.

[tex]\displaystyle \lim_{t\to0}\frac{\tan(6t)}{\sin(2t)} = \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)}[/tex]

Recall that

[tex]\displaystyle \lim_{x\to0}\frac{\sin(x)}x = 1[/tex]

Rewrite and expand the given limand as the product

[tex]\displaystyle \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)} = \lim_{t\to0} \frac{\sin(6t)}{6t} \times \frac{2t}{\sin(2t)} \times \frac{6t}{2t\cos(6t)} \\\\ = \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right)[/tex]

Then using the known limit above, it follows that

[tex]\displaystyle \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right) = 1 \times 1 \times \frac3{\cos(0)} = \boxed{3}[/tex]

Answer:

Hi. Here is your answer:

1/6

Step-by-step explanation:

this is because 1/6 is equal to 5/30 of your answer.

here is proof.

which school do you go to?

Hope this helps

Brainliest please

Have a great day

Please fully rate!

The probability that the first lands on [tex]6[/tex] and the second lands on an odd number is [tex]\frac{1}{12}[/tex]

Since The probability of rolling a [tex]6[/tex] should be [tex]\frac{1}{6}[/tex] because there are [tex]6[/tex] total numbers.

Now The probability of rolling an odd number is [tex]\frac{1}{2}[/tex], since there are an equal number of odd and even numbers on a die.

Now the final probability should be

[tex]=\frac{1}{6}*\frac{1}{2}[/tex]

[tex]=\frac{1}{12}[/tex]

Therefore, The probability that the first lands on [tex]6[/tex] and the second lands on an odd number is [tex]\frac{1}{12}[/tex]

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The correct answer is option C which is nine more than two-fifths of the number is nine.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, expansion and division.

The given expression is:-

( 2 / 5) x  +  9 = 9

The expression can be written in the words nine more than two-fifths of the number is nine.

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The sin function can be model as N(t) = 0.5sin(πt/6) + 1.5 if the attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

The attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.

We know the sine function is:

y = Asin(w + c) + s

Here:

A is amplitude

w is angular velocity,

s is vertical Displacement,

c = phase angle

A = (2000000 - 1000000) /2 =  500,000

w = 2π/T  

T = 12

w = 2π/12 = π/6

s = (1000000 +2000000) /2 = 3,000,000/2 = 1,500,000

500,000sin(π/6 + 0) + 1500000

500000sin(π/6)+1500000

or

0.5sin(πt/6) + 1.5

Thus, the sin function can be model as N(t) = 0.5sin(πt/6) + 1.5 if the attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.

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Sam’s operating expenses for last year given the gross profit and the net income is  $33,345.

Operating expense is the expense that a company incurs in the course of running its business. It is determined by subtracting net income from gross profit.

Operating expense =  gross profit - net income

$105,355 -  $72,010 = $33,345

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Answer:

B

Step-by-step explanation:

Answer:

v=13117.69 m3

Step-by-step explanation:

Hope this helps.

Answer:

The answer is 803.84

Step-by-step explanation:

Carry on learning i hope this helps..

A function, c(x), that models the water used by the car wash on a shorter day is C(x) = 4x³ + 7x² − 14x - 6

Given:

The amount of water used in normal days:

The amount of decrease in water used is modeled by the equation;

To find the function C(x), we would have to subtract eq(ii) from eq(i)

5x³ +9x²-14x +9

-  x³+2x² +15

= C(x) 4x³+7x²-14x-6

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Answer:

Below in bold.

Step-by-step explanation:

109, 94, 87, 103, 89, 112, 98, 115, 99

First arrange them in ascending order.

87 89 94 98 99 103 109 112 115

The median is the middle value:

= 99.

The lower quartile

= (89+94) / 2

= 183/2

= 91.5.

Answer:

13x+50=641.50, where x is the about of hours Luke worked. (x=45,5[h])

Answer:

11.86

Step-by-step explanation:

Answer:

43 + 7i

Step-by-step explanation:

Given: (1 + 5i)(3 - 8i)

To find: Multiplication and simplification

Solution:

i=[tex]\sqrt{-1}[/tex],

Now, we simply open the brackets as follows:

(1 + 5i)(3 - 8i)

1(3 - 8i) + 5i (3 - 8i)

3 - 8i + 15i - 40[tex]i^{2}[/tex]

3 + 7i - 40[tex]i^{2}[/tex] - (i)

[tex]i^{2}[/tex] = i * i

[tex]i^{2}[/tex] = [tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex]

[tex]i^{2}[/tex] = -1

Now, put  [tex]i^{2}[/tex] = -1 into the equation (i)

we get

⇒ 3 + 7i -40(-1)

⇒ 3 + 7i + 40

⇒ 43 + 7i

∴ Final Answer : 43 + 7i

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Here we go ~

what we need to know here is that :

[tex]\qquad \sf  \dashrightarrow \:i \cdot i = - 1[/tex]

Now, let's proceed accordingly ~

[tex]\qquad \sf  \dashrightarrow \:(1 + 5i) \cdot(3 - 8i)[/tex]

[tex]\qquad \sf  \dashrightarrow \:(1 \cdot3) - (1 \sdot8i) + (5i \cdot3) - (5i \cdot8i)[/tex]

[tex]\qquad \sf  \dashrightarrow \:3 - 8i + 15i - ( - 1)(40)[/tex]

[tex]\qquad \sf  \dashrightarrow \:3 + 7i - ( - 40)[/tex]

[tex]\qquad \sf  \dashrightarrow \:3 + 40 + 7i[/tex]

[tex]\qquad \sf  \dashrightarrow \:43 + 7i[/tex]

Check the picture below.

[tex]~~~~~~\textit{initial velocity in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&19.6\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&24.5\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-4.9t^2+19.6t+24.5\hspace{5em}\stackrel{\textit{when it hits the ground}}{0=-4.9t^2+19.6t+24.5}[/tex]

Answer:

A

Step-by-step explanation:

Answer:1,024

Step-by-step explanation:

    We will use the formula hint it gives:

[tex]\displaystyle {1^{st}\;term} * \text{common ratio}\,^{(\text{desired term -1})}[/tex]

[tex]-1 * -4^{6-1}[/tex]

[tex]-1 * -4^{5}[/tex]

[tex]-1*-1,024[/tex]

[tex]1,024[/tex]

    The 6th term in the sequence is 1,024.

Answer:

I don't see your questions.

Egypt. Africa. America

Answer:

BC≈8,38

Step-by-step explanation:

AB=a

BC=c

CA=b

a²+b²=c²

3.3²+7.7²=c²

√70,18=√c²

c≈8,38

The number of edges of a polyhedron with 4 faces and 4 vertices will be 6.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Using Euler's formula, the number of the edges does a polyhedron with 4 faces and 4 vertices have

We know the formula for the edges of the polyhedron will be

F + V = E + 2

The number of faces, vertices, and edges of a polyhedron are denoted by the letters F, V, and E.

Then we have

4 + 4 = E + 2

     E = 8 - 2

     E = 6

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Answer:

23

Add positive 14 and 9 to get 23

14 + 9 = 23

-14 + 23 = 9

Answer:

C=12

Step-by-step explanation:

The interior angle of a polygon is 360.

So just add them all up.

(3c-29)+(127)+(c+43)+(c+43)+(2c+36)+(c+44)=360

Combine like terms

8c+264=360

Simplify

8c=96 .  Divide both sides by 8

C=12

Answer:

Step-by-step explanation:

Answer:

Kindly read through

Step-by-step explanation:

All have been solved step by step

Answer:

Step-by-step explanation:

The volume of the empty space is 30.49 cubic inches if the sphere with a 2-inch radius is packed in a cube so that all sided touch.

It is defined as three-dimensional geometry that has six square faces and eight vertices.

We have a sphere with a 2-inch radius is packed in a cube so that all sided touch.

The volume of the sphere = (4πr³)/3 = (4π(2)³)/3 = 33.51 cubic inches

The side length of the cube = 4 inches

Because diameter of the sphere is 4 inches and all sided touch to the cube face.

Volume of the cube = 4³ = 64

The volume of the empty space = 64- 33.51 = 30.49 cubic inches

Thus, the volume of the empty space is 30.49 cubic inches if the sphere with a 2-inch radius is packed in a cube so that all sided touch.

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Answer:

if im not wrong all answers are 7

Step-by-step explanation:

if you add all the numbers u get 49 and if u divide by 7 cuz u have seven numbers. you should get 7 thats you mean. then for median if u put them from least to greatest ur middle number would still be seven and then your mode would be seven since seven shows up the most.

Answer:

A: Isosceles (two sides the same)

B: Equilateral (all sides the same)

C: Scalene (all sides different)

Step-by-step explanation:

Answer:

1 and 1/12

hope this helped

Step-by-step explanation:

distance = 400m

time taken = 1 min 35 sec = 95 sec

average speed = 400m / 95 sec = 4=2105 m/ sec

Answer:

4.21 m / sec.

Step-by-step explanation:

1 min 35 sec.

= 60 + 35

= 95 sec.

So average speed = 400/95

= 4.21 m / sec.