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3 years ago

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There are 4 lunch choices in a school cafeteria: Salad, Pizza, Spaghetti, and Sub Sandwiches. The percentage of students that ch

ose salad is 15%. If 45 students chose salad, what is the total number of students that ate lunch

2 answers:

andrew-mc [135]3 years ago

5 0

Answer:

The total number of students that ate lunch are 300 .

Step-by-step explanation:

Formula

$Percentage = \frac{Part\ value\times 100}{Total\ value}$

As given

There are 4 lunch choices in a school cafeteria: Salad, Pizza, Spaghetti, and Sub Sandwiches.

The percentage of students that chose salad is 15%.

If 45 students chose salad.

Here

Percentage = 15%

Part value = 45

Put in the formula

$15 = \frac{45\times 100}{Total\ value}$

$Total\ value= \frac{4500}{15}$

$Total\ value= 300$

Therefore the total number of students that ate lunch are 300 .

11Alexandr11 [23.1K]3 years ago

5 0

45/x / 15/100 = 4500 divided by 15x = 300

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Answer:

Part A:

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Part B:

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It is not possible for Eric to have spent exactly 35 minutes playing basketball

Step-by-step explanation:

The total time Eric plays basketball and volleyball = 95 minutes

The time duration Eric plays basket ball = x

The time duration Eric plays volleyball = y

Part A:

The pair of relationships between the number of minutes Eric plays basketball (x) and the number of minutes he plays volleyball (y) are;

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(2) x = y + 25

Part B:

By substituting the value of x in equation (2) into equation (1), we have;

x + y = (y + 25) + y = 95

2·y + 25 = 95

2·y = 95 - 25 = 70

y = 70/2 = 35 minutes

Therefore, Eric spends 35 minutes playing volleyball every day

Part C:

It is not possible for Eric to have spent only 35 minutes playing basketball because, given that he plays basketball for 25 minutes longer than he plays volley, the number of minutes he spends playing volleyball will then be given as follows;

x = y + 25

35 = y + 25

y = 35 - 25 = 10 minutes

The total time = x + y = 10 + 35 = 45 minutes ≠ 95 minutes.

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Answer:

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Uninhibited growth can be modeled by exponential functions other than A(t) =Upper A 0 e Superscript kt. For example, if an i

laila [671]

The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than $A(t)=A_{0}e^{kt}$ . for example, if an initial population P₀ requires n units of time to triple, then the function $P(t)=P_{0}(3)^{\frac{t}{n} }$ models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form $P(t)=P_{0}(3)^{\frac{t}{n} }$ that models the population.

b) What will the population be in 47 days?

c) When wil the population reach 750?

d) Express the model from part (a) in the form $A(t)=A_{0}e^{kt}$ .

Answer: a) $P(t)=50(3)^{\frac{t}{30} }$

b) P(t) = 280 insects

c) t = 74 days

d) $A(t)=50e^{0.037t}$

Step-by-step explanation:

a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

$P(t)=50(3)^{\frac{t}{30} }$

b) In t = 47 days:

$P(t)=50(3)^{\frac{t}{30} }$

$P(47)=50(3)^{\frac{47}{30} }$

$P(47)=50(3)^{1.567}$

P(47) = 280

In 47 days, population of insects will be 280

c) P(t) = 750

$750=50(3)^{\frac{t}{30} }$

$\frac{750}{50}=(3)^{\frac{t}{30} }$

$(3)^{\frac{t}{n} }=15$

Using the property <u>Power</u> <u>Rule</u> of logarithm:

$log(3)^{\frac{t}{30} }=log15$

$\frac{t}{30}log(3)=log15$

$t=\frac{log15}{log3} .30$

t = 74

To reach a population of 750 insects, it will take 74 days

d) To express the population growth into the described form, determine the constant k, using the following:

A(t) = 3A₀ and t = 30

$A(t)=A_{0}e^{kt}$

$3A_{0}=A_{0}e^{30k}$

$3=e^{30k}$

Use Power Rule again:

$ln3=ln(e^{30k})$

$ln3=30k$

$k=\frac{ln3}{30}$

k = 0.037

Equation for exponential growth will be:

$A(t)=50e^{0.037t}$

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3 years ago