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kramer
3 years ago
10

Marcus and Cody both leave the park at the same time, but in opposite directions. If Cody travels 6 mph faster than Marcus and a

fter 4 hours they are 64 miles apart, how fast is each traveling? Solve using Rare times time = Distance.
Mathematics
1 answer:
Evgesh-ka [11]3 years ago
6 0

Answer: Marcus travels at 5mph and Cody travels at 11mph


Step-by-step explanation:

x = Marcus

x + 6 = Cody


4(x + x + 6) = 64

4x + 4x + 24 = 64

8x + 24 = 64

8x = 40

40/8 = 5

5 + 6 = 11

Marcus = 5 Cody = 11


4*5 + 11*4 = 64

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If you travel at a rate of 45 mph how many minutes will you will it take you to travel 1 mile
stiks02 [169]
It'd take you<span>, 1 minute and 33 secounds.
45 miles = 60 minutes
1 mile = 60/45 = 4/3 = 1.33 minutes </span>
7 0
3 years ago
You have 10 cookies and want to give 1/2 of them to a friend how many do you give to your friend
pogonyaev
1/2 of 10 is 5 so the answer you are looking for is 5 cookies
5 0
3 years ago
Read 2 more answers
Bacteria of species A and species B are kept in a single environment, where they are fed two nutrients. Each day the environment
DiKsa [7]

Answer:

We require 4,550 of species A and 1,460 of species B that can coexist in the environment so that all the nutrients are consumed each day

Step-by-step explanation:

Let n₁ be the population of A required and n₂ be the population of B required.

Now we require 2 units of the first nutrient for species A and one unit of the first nutrient for species B. The total nutrients required by species A is 2n₁ and that by species B is 1n₂ = n₂. So, the total nutrients required by both species A and B is 2n₁ + n₂. Since this equals the quantity of the first nutrient which is 10,560, then  2n₁ + n₂ = 10,560 (1)

Now we require 5 units of the second nutrient for species A and 6 units of the second nutrient for species B. The total nutrients required by species A is 5n₁ and that by species B is 6n₂. So, the total nutrients required by both species A and B is 5n₁ + 6n₂. Since this equals the quantity of the first nutrient which is 31,510, then  5n₁ + 6n₂ = 31,510 (2).

So, we have two simultaneous equations which we would solve to find the populations of A and B which satisfy both equations.

2n₁ + n₂ = 10,560  (1)

5n₁ + 6n₂ = 31,510 (2)

From (1) n₂ = 10,560 - 2n₁ (3)

Substituting equation (3) into (2), we have

5n₁ + 6(10,560 - 2n₁) = 31,510

expanding the brackets, we have

5n₁ + 63,360 - 12n₁ = 31,510

collecting like terms, we have

5n₁ - 12n₁ = 31,510 - 63,360

simplifying, we have

- 7n₁ = -31,850

dividing both sides by -7, we have

n₁ = -31,850/-7

n₁ = 4,550

Substituting n₁ = 4,550 into (3), we have

n₂ = 10,560 - 2(4,550)

n₂ = 10,560 - 9,100

n₂ = 1,460

So, we require 4,550 of species A and 1,460 of species B that can coexist in the environment so that all the nutrients are consumed each day

3 0
2 years ago
Calculate a critical z-score for a left-tailed, right-tailed, or two-tailed test.
muminat

Answer:

a. Z = -1.175.

b. Z = 1.34.

c. |Z| = 2.054.

d. |Z| = 1.28.

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. The critical z-score for a left-tailed test at a 12% significance level

Left-tailed test: The region of interest is the 12th percentile or below.

Thus, the critical z-score is Z with a p-value of 0.12, so Z = -1.175.

b. The critical z-score for a right-tailed test at a 9% significance level

Right-tailed test: The region of interest is the 100 - 9 = 91th percentile and above.

Thus, the critical z-score is Z with a p-value of 0.91, so Z = 1.34.

c. The critical z-score for a two-sided test at a 4% significance level is 1.75.

Two-tailed test: The region of interest is between the 4/2 = 2th percentile and the 100 - (4/2) = 98th percentile.

Thus, the critical z-score is |Z| with a p-value of 0.02 or 0.98, so |Z| = 2.054.

d. The critical z-score for a two-sided test at a 20% significance level is 0.85.

Region of interest is between the 20/2 = 10th percentile and the 100 - (20/2) = 90th percentile.

Thus, the critical z-score is |Z| with a p-value of 0.1 or 0.9, so |Z| = 1.28.

4 0
3 years ago
Wilson is 6 years older than Mary. Wilson's age is 10 years less than five times Mary's age. The equations below model the relat
Neko [114]

Answer:

Wilson is 6 older than mary

w=6+m

wilson is 10 less than 5 times mary

w=-10+5m

w=5m-10

so now we set them eqal to each other since both equal w

m+6=w=5m-10

m+6=5m-10

minus m both sides

6=4m-10

add 10 to both sides

16=4m

divide both sides by 4

4=m

sub back

w=m+6

w=4+6

w=10

wilson=10

mary=4

the correct method is math

3 0
3 years ago
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