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2 years ago

Simplify the following expression:-5[(x^3 + 1)(x + 4)]

Mathematics

1 answer:

lisov135 [29]2 years ago

8 0

Answer:

$-5x^{4} -20x^{3} -5x-20$

Step-by-step explanation:

$-5[(x^{3} +1)(x+4)]$

Use the FOIL method for the last two groups.

$-5(x^{4} +4x^{3} +x+4)$

Now, distribute the -5 into each term.

$-5x^{4} -20x^{3} -5x-20$

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If an intravenous solution containing 123 mg of a drug substance in each 250-mL bottle is to be administered at the rate of 200

12345 [234]

Answer:

24.39mL of the solution would be given per hour.

Step-by-step explanation:

This problem can be solved by direct rule of three, in which there are a direct relationship between the measures, which means that the rule of three is a cross multiplication.

The first step to solve this problem is to see how many mg of the solution is administered per hour.

Each minute, 200 ug are administered. 1mg has 1000ug, so

1mg - 1000 ug

xmg - 200 ug

$1000x = 200$

$x = \frac{200}{1000}$

$x = 0.2mg$

In each minute, 0.2 mg are administered. Each hour has 60 minutes. How many mg are administered in 60 minutes?

1 minute - 0.2 mg

60 minutes - x mg

$x = 60*0.2$

$x = 12mg$

In an hour, 12 mg of the drug is administered. In 250 mL, there is 123 mg of the drug. How many ml are there in 12 mg of the drug.

123mg - 250mL

12 mg - xmL

$123x = 250*12$

$x = \frac{250*12}{123}$

$x = 24.39$ mL

24.39mL of the solution would be given per hour.

7 0

1 year ago

Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need a

saveliy_v [14]

Answer:

Sofia will order 7 more rolls of sushi (84 pieces) and pay $56

Step-by-step explanation:

They need at least 100 pieces of sushi

Sofia had ordered and paid for 24 pieces of sushi already

Sushi comes in rolls

Each roll=12 pieces at $8

R=additional rolls that Sofia orders

Additional sushi= Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

Each roll has 12 pieces

76/12=6.33

Sofia has to order in rolls

So, she will order 7 more rolls of sushi of 12 pieces each

12*7=84 pieces

Recall, that they needed at least 100 pieces, so the number of pieces could be more than 100

If Sofia orders 84 pieces + the already ordered 24 pieces

Total pieces=108 pieces

She has paid for 24 pieces (3 rolls) at $8 per roll

7 rolls=$8*7

=$56

7 0

1 year ago

Read 2 more answers

The aquarium at Sea Critters Depot contains 140 fish. Eighty of these fish are green swordtails (44 female and 36 male) and 60 a

maxonik [38]

Given that:

Total number of fish = 140

Fish are green swordtails female = 44

Fish are green swordtails male = 36

Fish are orange swordtails female = 36

Fish are orange swordtails male = 24

Solution:

A. We have to find the probability that the selected fish is a green swordtail.

$\text{P(green swordtail)}=\dfrac{\text{Total green swordtail fish}}{\text{Total fish}}$

$\text{P(green swordtail)}=\dfrac{80}{140}$

$\text{P(green swordtail)}=\dfrac{4}{7}$

Therefore, the probability that the selected fish is a green swordtail is $\dfrac{4}{7}.$

B. We have to find the probability that the selected fish is male.

$\text{P(Male fish)}=\dfrac{\text{Total male fish}}{\text{Total fish}}$

$\text{P(Male fish)}=\dfrac{36+24}{140}$

$\text{P(Male fish)}=\dfrac{60}{140}$

$\text{P(Male fish)}=\dfrac{3}{7}$

Therefore, the probability that the selected fish is a male, is $\dfrac{3}{7}.$

C. We have to find the probability that the selected fish is a male green swordtail.

$\text{P(Male green swordtail)}=\dfrac{\text{Total male green swordtail fish}}{\text{Total fish}}$

$\text{P(Male green swordtail)}=\dfrac{36}{140}$

$\text{P(Male green swordtail)}=\dfrac{9}{35}$

Therefore, probability that the selected fish is a male green swordtail is $\dfrac{9}{35}.$

We have to find the probability that the selected fish is either a male or a green swordtail.

$\text{P(Male or green swordtail)}=\dfrac{\text{Total male or green swordtail fish}}{\text{Total fish}}$

$\text{P(Male or green swordtail)}=\dfrac{44+36+24}{140}$

$\text{P(Male or green swordtail)}=\dfrac{96}{140}$

$\text{P(Male or green swordtail)}=\dfrac{24}{35}$

Therefore, the probability the selected fish is either a male or a green swordtail is $\dfrac{24}{35}.$

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2 years ago

In a large city, 46% of adults support the local football team building a new stadium. If a poll is taken from a random sample o

Sveta_85 [38]

Answer: 0.46, 0.056, the distribution is approximately normal

Step-by-step explanation: The shape is approximately normal since the expected number of successes equals 36.8 and the expected number of failures equals 43.2 are both larger than 10

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2 years ago

Naomi and her children went into a bakery where they sell donuts for $1.25 each and cookies for $0.75 each. Naomi has $15 to spe

LiRa [457]

Answer:

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1 year ago

Simplify the following expression:-5[(x^3 + 1)(x + 4)]​

Simplify the following expression:-5[(x^3 + 1)(x + 4)]