A tortoise and hare are competing in a race. The function f and g are such that f(t) represents the tortoise's distance from the finish line (in meters) t seconds after the start of the race and g (t) represents the hare's distance from the finish line (in meters) t seconds after the start of the race.
If we want to compute the number of seconds needed for the hare to finish the race, which of the following procedures should be used?
A. Solve g(t)=0 for the value of t.
B. Solve g(t)=1000 for the value of t.
C. Evaluate g(0).
D. Solve f(t)=g(t) for the value of t.
E. Evaluate g(1000).

Answer:

1. a) $24, b) $36, c) $48

2. a) $18, b) $27, c) $36

3. a) $1.64, b) $2.46, c) $3.28

5. a) $30, b) $50, c) $70

6. a) $4.05, b) $6.75, c) $10.80

7. a) $14.85, b) $24.75, c) $39.60

Explanations:

Whatever we multiply the item by, we multiply the cost by. If we double the number of socks, we double the price. If we triple the number of socks, we triple the price.

1. a) 3 costs $12, and 3 x 2 = 6, so we do the same to the price: $12 x 2 = $24

b) 3 times 3 is 9, so 3 x 12 gives you that cost, $36

c) 3 x 4 = 12, so 12 x 4 = $48

2. a) 3 pairs is $9, and we need 6 pairs. 3 x 2 = 6, so we also multiply the price x 2 = $18

b) 3 x 3 = 9 pairs, multiply the cost times 3 as well. 9 x 3 = $27

c) 3 x 4 = 12, multiply the cost x 4. 9 x 4 = 36

3. 4 apples cost $0.82

a) 4 x 2 = 8 apples, $0.82 x 2 = $1.64

b) 4 x 3 = 12 apples, $0.82 x 3 = $2.46

c) 4 x 4 = 16 apples, $0.82 x 4 = $3.28

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The concept is the same for all the other questions as well. Please comment below if you need a different explanation to understand this. :)

Answer:

Step-by-step explanation:

5.

3x-1 = 4x+13

-1=x+13

12=x

3(12)-1

36-1

Answer: 35

Second 5.

I'm not completely sure what this is referring to (please tell me if there is another part for this because there isn't any numbers such as <1 shown on the picture.)

6.

90+40+x=180

130+x=180

50=x

Answer: 50

7.

x+71=90

x=19

Answer: 19

Answer:  x - 4  without the absolute value bars surrounding it

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Explanation:

If x is larger than 4, then x-4 is positive. For example, if x = 5, then

x-4 = 5-4 = 1

So for cases when x > 4, the |x-4| and x-4 are the same identical expression. Try out more values of x to compare the two outputs. I recommend making a table with 3 columns. You'll have x in column 1, then |x-4| in column 2, and x-4 in column 3. You should find that the outputs for columns 2 and 3 are identical when x is larger than 4.

It's only when x < 4 is when |x-4| and x-4 differ. Instead we would say |x-4| = -(x-4). But we aren't focused on this case.

In short, when x > 4, we simply drop the absolute value bars to get the answer  x - 4

Answer: =

Step-by-step explanation: just took the test

We will see that both angles are actually the same one (but in different units) so the symbol that we need to use is the equal symbol.

Here we have two angles, one in degrees and  the other in radians, we want to compare them. To do it, we will need to write both of the angles in the same units.

The angles are:

pi/3 rads

60°

First, remember that:

pi rads = 180°

1 rad = (180°/pi)

With this, we can change the units of the first angle to get:

pi/3 rads = pi/3*(180°/pi) = 180°/3 = 60°

So both angles are actually the same angle, then the symbol that correctly compares them is the equal symbol.

pi/3 rads = 60°

If you want to learn more about angles, you can read:

https://brainly.com/question/17972372

Step-by-step explanation:

Problem #1

alright, so it would be 7 1/4-6 3/8=7/8

we can check by adding:

6 3/8+7/8=7 1/4.

Problem #2

we can do the same for this one!

8 1/4-7 3/8=7/8

to check:

7/8+7 3/8=8 1/4

Answer:

Let's solve for x.

y=12x

Step 1: Flip the equation.

12x=y

Step 2: Divide both sides by 12.

12x /12 = y /12

x= 1 /12 y

Answer:  x= 1 /12 y

Step-by-step explanation: Hope this helps :D

Answer:

Step-by-step explanation:

(number of sides-2)*180 = (6-2)*180 = 720°

a= 720/6= 120°

lines form 180° angles

b= 180-120= 60°

sum of angles in a triangle is 180, and the angles are ≡

c=180/3 = 60°

c and d are supplementary angles (they add to 180)

d= 180-60 = 120°

d ≡ e+e because are vertical angles

e= 120/2 = 60°

sum of angles in a triangle is 180

f= 180 -90-60 = 30°

(number of sides-2)*180 = (5-2)*180 = 540°

g= 540/5= 108°

9514 1404 393

Answer:

  y = 9

Step-by-step explanation:

Corresponding parts of the proportion have the same ratios. We notice that 33 is 3 times 11, so 27 is 3 times y.

  y = 27/3 = 9

Using the exponential notation, the correct expression which represents 5 × 5 × 5 × 5 is 5⁴

Given tha expression :

Number of 5's = 4

The number of 5's can be used as the power of the base, since the base is common.

Base = 5

Hence,

5 × 5 × 5 × 5 = 5⁴

Learn more : https://brainly.com/question/25629067

Answer:

The answer is B and BTW AMC STOCKS ARE RISING

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

The confidence interval will be "41.04, 43.81".

Step-by-step explanation:

Given that,

Sample size,

n = 10

Sample total,

423.5

Sample mean,

[tex]\bar X =\frac{423.5}{10}[/tex]

   [tex]=42.35[/tex]

Sample variance,

[tex]s = \sqrt{4.5894}[/tex]

  [tex]=2.1423[/tex]

[tex]df=n-1[/tex]

   [tex]=9[/tex]

[tex]t^*=18331[/tex]

Now,

The margin of error will be:

⇒ [tex]E=\frac{s\times t^*}{\sqrt{n} }[/tex]

       [tex]=\frac{2.1423\times 1.8331}{\sqrt{9} }[/tex]

       [tex]=\frac{3.928}{3 }[/tex]

       [tex]=1.309[/tex]

hence,

The 90% confidence level will be:

= [tex](\bar X-E),(\bar X+E)[/tex]

By substituting the values, we get

= [tex](42.35-1.309),(42.35+1.309)[/tex]

= [tex](41.04),(43.81)[/tex]

Answer: 3 were blue

Step-by-step explanation:

Blue  + Red  =   18....so.....

B  +  5B  =  18

6B  =  18

B   =18 /   6    =    3  blue

Answer:

I'm pretty sure its C

Step-by-step explanation:

Move the point P two steps right. The original coordinates of P were (2,5)  moving the point 2 units right increases the X value (X,Y) by 2 units, making it (4, 5)

Answer:

[tex]\frac{s}{s-4}[/tex]

Step-by-step explanation:

Given

[tex]\frac{s^2+6s}{s^2+10s+24}[/tex] ÷ [tex]\frac{s-4}{s+4}[/tex] ( factor and simplify fraction on left )

= [tex]\frac{s(s+6)}{(s+4)(s+6)}[/tex] ÷ [tex]\frac{s-4}{s+4}[/tex] ← cancel (s + 6) on numerator/ denominator

Leave first fraction, change division to multiplication, turn second fraction upside down

= [tex]\frac{s}{s+4}[/tex] × [tex]\frac{s+4}{s-4}[/tex] ← cancel (x + 4) on numerator/ denominator

= [tex]\frac{s}{s-4}[/tex]

Answer:

B

Step-by-step explanation:

Depreciates 14% per year so 100% - 14% is 86% or 0.86. Formula is (principal)(rate)^ years

Answer:

1515

Step-by-step explanation:

Answer:

$75.5

Step-by-step explanation:

The first step is to calculate the percentage decrease

= 100-18

= 82%

Therefore the original cost of the shirt before the discount can be calculated as follows

= 82/100 × x = 61.91

= 82x/100= 61.91

Cross multiply

82x= 100×61.91

82x= 6191

x = 6191/82

= 75.5

Hencd the original cost of the shirt is $75.5

Answer:

75.50

Step-by-step explanation:

Answer:

A

you fist have to gather your resources

Answer:

i guess D

because it is most important to understand the problem before going to any further step or conclusions.

Answer:

437

Step-by-step explanation:

21850/100 * 2 = 437

Answer:

the actual hourly percent increase is 6.823 %

Step-by-step explanation:

Given that data in the question;

rate chemical decomposes increasing continuously at 6.6 %,

r = 6.6% = 0.066

actual hourly percent increase = ?

Now,

hourly percent increase = ( [tex]e^r[/tex] - 1 ) × 100%

we substitute

hourly percent increase = ( [tex]e^{0.066[/tex] - 1 ) × 100%

hourly percent increase = ( 1.06823 - 1 ) × 100%

hourly percent increase = 0.06823 × 100%

hourly percent increase = 6.823 %

Therefore, the actual hourly percent increase is 6.823 %

Answer:

Step-by-step explanation:

The raked portion is 5/12 plus 4/9, or (applying the LCD, 36),

20/36 + 24/36.

The sum of these two fractions is 44/36, or 1/9.

1/9 of the yard remains to be raked.

Answer:

$23.25

Step-by-step explanation:

12+11.25

Answer:

candy bars = a

cupcakes = b

a=1.5$

b=2.25$

Step-by-step explanation:

candy bars = a

cupcakes = b

1)5a+2b = 12

2)3a + 3b = 11.25

We can understand

3a + 3b = 3(a+b)= 11.25

a+b = 11.25÷3 = 3.75

from No.2 equation.

than we do

(5a+2b) - 2(a+b)

and we got 3a

so

12 - 7.5 = 4.5 = 3a

a=1.5$

b=2.25$

Answer:

61 seconds

Step-by-step explanation:

Answer:

23 seconds

Step-by-step explanation:

The slowest time is 23 second and the fastest time is 61 seconds

The time before the bar is the tens place and each time after the bar is the ones place

Answer:

30 More minutes

Step-by-step explanation:

3/4 of an hour is 45

1/4 is 15

45-15 is 30

Answer:

1 hour

Step-by-step explanation:

Answer:

C=6.6666666666666666666666666

Answer:

[tex]D.\frac{2}{6}[/tex]

Step-by-step explanation:

√15 = 3.87298334621

11/25 = 11 ÷ 25 = 0.44

3/20 = 3 ÷ 20 = 0.15

2/6 = 2 ÷ 6 = 0.33333333333

Answer:

Answer = A.)10

Step-by-step explanation:

The median for test A is 30 and the median for test B is 40. So you take the bigger number and subtract it by the smaller number to get the difference. 40-30 = 10

Answer:

40.84 to nearest hundredth.

Step-by-step explanation:

C = pi * d

= pi * 13

= 40.8407

Answer:

V=326.725636 or V=104[tex]\pi[/tex]

Step-by-step explanation:

V=[tex]\pi[/tex][tex]r^{2}[/tex]h

V=[tex]\pi[/tex][tex]2^{2}[/tex](26)

V=[tex]\pi[/tex]4(26)

V=326.725636

Answer:

The null hypothesis should be [tex]H_0: \mu = 12[/tex]

The alternate hypothesis should be [tex]H_1: \mu \neq 12[/tex]

Step-by-step explanation:

You wondered if the sugar content in energy drinks is really the same as labeled in the products. The disclosure on Red Bull 12 oz.

At the null hypothesis, we test if the sugar content is the same labeled, that is:

[tex]H_0: \mu = 12[/tex]

At the alternate hypothesis, we test if the sugar context is different from the labeled, that is, different of 12.

[tex]H_1: \mu \neq 12[/tex]

Answer:

− 1.  ¯3

Step-by-step explanation: