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3 years ago

A store was selling lawn mowers for $69. The repair

Mathematics

2 answers:

ale4655 [162]3 years ago

8 0

Answer: he is right

Step-by-step explanation:

Natali5045456 [20]3 years ago

5 0

Answer:

$84.87

Step-by-step explanation:

The mover costs $69

23% of 69 is $15.87

add the two together to get $84.87

(or just multiply 69 by 1.23)

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A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

Kaylis [27]

Answer:

A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

$P(t) = 400e^{kt}$ .

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

$\frac{90}{4} = e^{4k}$ .

Taking logarithm

$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

$P(t) = 400e^{0.7783t}$ .

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

$t = \frac{\ln 75}{0.7783} \approx 5.55$ .

So, after 5.55 hours the population of bacteria will reach 30000.

6 0

3 years ago

De la población de adultos en estados unidos, 36% tiene una alergia. una muestra de 1200 adultos seleccionados al azar resultó e

densk [106]

Answer:

sorry I cant understand your question

4 0

3 years ago

A triangle has two side of length 3 and 7. The third side of this triangle must not be shorter than (blank) or longer than (blan

Marina86 [1]

Answer:

The sum of two side lengths of a triangle must be greater than the length of the third.

So, if two side lengths are 3 and 7, the length of the third side must be less than 10 units.

However, it cannot be shorter than 4 units, as 3 + 4 = 7.

So your answer is: The third side of this triangle must not be shorter than 4 or longer than 10

Let me know if this helps!

5 0

3 years ago

Health insurance benefits vary by the size of the company. The sample data below show the number of companies providing health i

telo118 [61]

Answer:

Step-by-step explanation:

a. The hypothesis of testing are

Null Hypothesis, H0: The health insurance coverage is independent of the size of the company.

Alternative hypothesis, H1: The health insurance coverage is not independent of the size of the company

The test statistics is calculated as

X² = ∑(Ei - Oi)² ≅X²(r-1)(c-1)

i Ei

where Oi's are the observed values and Ei's are the expected values,

E= row total × column total

total

The expected values are

Sizeof the Company

Health Insurance Small Medium Large Total

Yes 42 63 84 189

No 8 12 16 36

Total 50 75 100 225

Therefore, the test statistics is

X² =∑ (Ei -Oi)² =6.94 ≅ x²₂

i Ei

The critical value is found to be 5.99. Since test statistics > critical value, we reject H0 and conclude that the health insurance coverage is not independent of the size of the company.

The associated p-value is 0.031 (<0.05).

b. Percentage of employees lacking health insurance coverage is

Small 14/50 x 100 = 28%

Medium 10/75 x 100 = 13%

Large 12/100 x 100 = 12%

Hence depending on the above percentage, we can support the claim that the employees of small companies are more likely to lack health insurance coverage.

8 0

3 years ago

Hello… please help What is a parabola in mathematics?

Airida [17]

A parabola in mathematics is basically plane curve which is mirror-symmetrical and is approximately U-shaped. A point and a line in a U shape.

Example below:

4 0

3 years ago