Ms. Buback is competing in a race in which she both runs and rides a bike. She runs 5 kilometers in 0.5 hours and rides her bike 20 kilometers in 0.8 hours. At the rate given, how many kilometers can she bike in one hour?

Answer:

[tex]\underline{192}, 24, \underline{3}, \underline{\dfrac{3}{8}}, \dfrac{3}{64}[/tex]

[tex]\underline{\dfrac{1}8}, \dfrac{1}{4}, \dfrac{1}{2}, \underline{1}[/tex]

[tex]81, \underline{27, 9, 3, 1},\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given the Geometric sequences:

1. ___, 24, ___, ___, 3/64

2. ___, 1/4, 1/2, ___

3. 81, ___, ___, ___, ___, 1/3

To find:

The values in the blanks of the given geometric sequences.

Solution:

First of all, let us learn about the [tex]n^{th}[/tex] term of a geometric sequence.

[tex]a_n=ar^{n-1}[/tex]

Where [tex]a[/tex] is the first term and

[tex]r[/tex] is the common ratio by which each term varies from the previous term.

Considering the first sequence, we are given the second and fifth terms of the sequences.

Applying the above formula:

[tex]ar = 24\\ar^4 = \dfrac{3}{64}[/tex]

Solving the above equation:

[tex]r = \dfrac{1}{8}[/tex]

Therefore, the sequence is:

[tex]\underline{192}, 24, \underline{3}, \underline{\dfrac{3}{8}}, \dfrac{3}{64}[/tex]

Considering the second given sequence:

[tex]ar = \dfrac{1}{4}\\ar^2 = \dfrac{1}{2}\\\text{Solving the above equations}, r = 2[/tex]

Therefore, the sequence is:

[tex]\underline{\dfrac{1}8}, \dfrac{1}{4}, \dfrac{1}{2}, \underline{1}[/tex]

Considering the third sequence:

[tex]a = 81\\ar^5=\dfrac{1}{3}\\\Rightarrow r = 3[/tex]

Therefore, the sequence is:

[tex]81, \underline{27, 9, 3, 1},\dfrac{1}{3}[/tex]

Answer:

in the explanation

Step-by-step explanation:

In the number line, the left most number would be -200 as it's the lowest, the middle would be -150, as this number is in between the other two, and the right most would be 75, as it's the greatest.

Hope this helps!

Answer:

B

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

50%

Step-by-step explanation:

first the numerator is decreased by 75% so its 0.25. the denominator is decreased by 50% so its 0.5. Then, we will divide 0.25 and 0.5 which equals 0.5. to find %, do 0.5*100 which equals 50%

The fraction will decrease by 0.5 or 50%

Let the original fraction be a/b. If the numerator is decreased by 75%  and the denominator is decreased by 50%, the resulting faction will be:

0.25a/0.50b

Taking the ratio of the quotient of the result will give:

0.25a/0.50b  

= 25/100a * 100/50 b

= 25a/50b

= 0.5a/b

Hence the fraction will decrease by 0.5 or 50%

Learn more on percentages here: https://brainly.com/question/19247356

Answer:

1. 6x+10

2. 3x+[tex]\frac{1}{2}[/tex]/5

3. 2.5x-1.1

I'm not sure if I did it in the correct format. :(

Answer:

B:rate

Step-by-step explanation:

the formula distance= rate × time

Answer:

B

Step-by-step explanation:

The formula for distance is rate × time.

Flow and work don't make sense. Also, work is force × distance.

However, you were given rate is equal to distance/time (r=d/t) and were asked to find what distance would be:

in that case, we'll isolate d onto one side

here's the equation

r=d/t

multiply by t on both sides

rt=d, or rate × time equals distance

either way it's B

Hope this helps!

Answer:

the third option

Step-by-step explanation:

Answer:

56 batches

Step-by-step explanation:

224/4 = 56

Answer:

-8 × 3 = - 3 × ( 8)

or -21 = -21

Answer:

-21

Step-by-step explanation:

Answer:

37.5%

60%

75% and .75

Step-by-step explanation:

Answer: 3 2/4 & 9 13/15

Step-by-step explanation:

Answer:I think D I just got off of this sorry if I’m wrong

Step-by-step explanation:

Answer:

choose c beacuse it is closer to and is not false

Step-by-step explanation:

:D

Answer:

A or B

Step-by-step explanation:

sry if im wrong-happy new year!

Answer:

Yeah I think you're correct I got the same

Step-by-step explanation:

Answer:2 is equal to 18/1 which is 36 divided by 2

Step-by-step explanation:

Answer:

1 is 20/1 or 20 miles per hour

2 is 18/1 or 18 push ups per min

3 is 15/1 or 15 dollars per hour

4 is 50/1 or 50 km per hour

Step-by-step explanation:

divide the numerators by the denominators

Answer:

see below

Step-by-step explanation:

5x+5+4x=4-3x+6

Combine like terms

9x+5 = 10-3x

Add 3x to each side

9x+3x +5 = 10-3x+3x

12x+5 = 10

Subtract 5 from each side

12x+5-5 = 10-5

12x = 5

Divide each side by 12

12x/12 = 5/12

x=5/12

Answer:

Lets show that:

Use formula:

Multiply LHS by 2sinx/2sinx:

Now, we can easily find that:

Coming back to the original equation, we get:

y = 6x - 4

Substitute the given x values to solve for y.

x = 1:

y = 6(1) - 4

y = 6 - 4

y = 2

1 = 2

x = 3:

y = 6(3) - 4

y = 18 - 4

y = 14

3 = 14

x = 10:

y = 6(10) - 4

y = 60 - 4

y = 56

10 = 56

x                y

1                 2

3               14

10             56

Answer:

150

Step-by-step explanation:

A=B*H/2

A=15*20/2

A=300/2

A=150

Ignore the hypotenuse btw

Answer:

C - 150 mm²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Step-by-step explanation:

Step 1: Define Variables

Base b = 15 mm

Height h = 20 mm

Step 2: Find Area A

9514 1404 393

Answer:

  B

Step-by-step explanation:

At t=0, the value is ...

  C(0) = 50,000·(0.9^0) -2000 = 48,000

At t=20, the value is ...

  C(20) = 50,000(0.9^20) -2000 = 6079 -2000 = 4079

The only graph that matches these end points is B.

Answer:

The correct answer is Graph B depicted in the picture.

Step-by-step explanation:

I have taken the test on Plato and have answered correctly.

Answer:

cosjk = √55 i/3

tanjk = 8/√55 i

Step-by-step explanation:

Given

sin jk = 8/3

According to SOH CAH TOA

Sin theta = opposite/hypotenuse = 8/3

Opposite = 8

hypotenuse = 3

Get the adjacent using the pythagoras theorem

hyp² = opp²+adj²

adj² = hyp² - opp²

adj² = 3² - 8²

adj² = 9-64

adj² = -55

adj = √-55

adj = √55 i (i = √-1)

Get cosjk

cosjk = adj/hyp

cosjk = √55 i/3

Get tanjk

tanjk = opp/adj

tanjk = 8/√55 i

Answer:

x=17

Step-by-step explanation:

we know the sum of angles in atriangle is 180°

x +17 + 4x -34 +6x +10 = 180

x+4x+6x +17 -34 +10 = 180

11x -7 =180

11x = 180 +7

x = 187/11 = 17

Answer:

1176

hope this will help you

Answer:

Step-by-step explanation:

2L168      

2L84

2L42

3L21

7L7

2x2x2x3x7=168

2L196

2L98

7L49

7L7

2x2x7x7=196

Answer:

A. 13 + t = 17

Step-by-step explanation:

The top rectangle shows 13 and t, the 13 and t rectangle is the same size as the 17 rectangle so 13 + t = 17. It's not multiplication as there's no multiple's of 13 or t on the diagram.

*Answer**

To get the Greates Common Factor (GCF) of 1700 and 1938 we need to factor each value first and then we choose all the copies of factors and multiply them:

1700: 2 2 5 5 17

1938: 2 3 17 19

GCF: 2 17

The Greates Common Factor (GCF) is: 2 x 17 = 34

Answer:

8 percent loss

Step-by-step explanation:

The percentage loss is -8%.

Given that,

Based on the above information, the percentage loss should be

[tex]= \frac{\$4.60-\$5}{\$5}[/tex]

= -8%

Therefore we can conclude that the percentage loss should be -8%.

Learn more: brainly.com/question/2155156