Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A. y=--x-5 B. y=+*+1 y=-x-8 O c. D. 11 v==x+3 4 ​

Answer:

[tex]40\sqrt3\ m[/tex]

Step-by-step explanation:

Given that,

The height of the tower, h = 40 m

The angle of elevation is 30°

We need to find the distance between the tower and the point. Let the distance is x. Using trigonometry,

[tex]\tan(30)=\dfrac{h}{x}\\\\\dfrac{1}{\sqrt3}=\dfrac{40}{x}\\\\x=40\sqrt3\ m[/tex]

So, the distance between the tower and the point is equal to [tex]40\sqrt3\ m[/tex].

Answer:

a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].

b) There are 2975 bacteria after 3 hours.

c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.

d) A population of 10,000 will be reached after 4.072 hours.

Step-by-step explanation:

a) The population growth of the bacteria culture is described by this ordinary differential equation:

[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)

Where:

[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].

[tex]P[/tex] - Population of the bacteria culture, no unit.

[tex]t[/tex] - Time, in hours.

The solution of this differential equation is:

[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)

Where:

[tex]P_{o}[/tex] - Initial population, no unit.

[tex]P(t)[/tex] - Current population, no unit.

If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:

[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]

[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]

[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]

[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]

[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]

[tex]k\approx 1.131\,\frac{1}{h}[/tex]

Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].

b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:

[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]

[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]

[tex]P(3) \approx 2975.508[/tex]

There are 2975 bacteria after 3 hours.

c) The rate of growth of the population is represented by (1):

[tex]\frac{dP}{dt} = k\cdot P[/tex]

If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:

[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]

[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]

The rate of growth after 3 hours is about 3365.3 bacteria per hour.

d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:

[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]

[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]

[tex]100 = e^{1.131\cdot t}[/tex]

[tex]\ln 100 = 1.131\cdot t[/tex]

[tex]t = \frac{\ln 100}{1.131}[/tex]

[tex]t \approx 4.072\,h[/tex]

A population of 10,000 will be reached after 4.072 hours.

Answer:

a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

Sample size of 100 > 30, which means that we use the Central Limit Theorem, and thus, the sampling distribution is approximately normal, following a diagonal line, and since the standard deviation of the population is not know, we use the t-procedure. Thus, the correct answer is given by option a.

Answer:

B

Step-by-step explanation:

(6)^1/2 × (8)^1/2

6^1/2 × 2 (2)^1/2

4 (3)^1/2

Answer:

c

Step-by-step explanation:

C is the correct answer

Answer:

Step-by-step explanation:

50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.

Answer:

200 kids and 500 adults

Step-by-step explanation:

x+y=700

7x+10y=6,400

(200,500)

kids=200

adults=500

Answer:

$1.50

Step-by-step explanation:

so its

4.5 ÷ 3

which

1.5

Answer:

Kindly check the attached picture

Step-by-step explanation:

The solution to the problem has been explicitly solved in the picture attached below :

We need to find a number that makes the denominator a perfect cube in other to simplify the expression which is 25/25.

Kindly check the attached picture for detailed explanation

Answer:

Could you please question correctly??

Step-by-step explanation:

Total Students:450

Oranges:250

Apples:280

Dislike:40

like:280-250+40

Answer

i dont see the question sorry

Answer:

Im sorry but why is this a question? Like what school gives this out

Answer:

B)7

Step-by-step explanation:

2-(-8)=10

10+(-3)=7

Answer:

$191

Step-by-step explanation:

Find how much she will be paying over the 24 months:

34(24)

= 816

Add the down payment to this:

816 + 70

= 886

Find the difference between this and 695:

886 - 695

= 191

So, the difference will be $191 more

Answer:

The point estimate for the number of pieces per package is of 18.72.

Step-by-step explanation:

Point estimate of a population mean:

The mean of the sample gives an estimate for the population mean.

They find that the sample mean number of pieces is 18.72.

This means that the point estimate for the number of pieces per package is of 18.72.

Answer:

a) 615

b) 715

c) 344

Step-by-step explanation:

According to the Question,

Z = (x - mean)/standard deviation

Now,

For x = 4171,  Z = (4171 - 3311)/860 = 1  

Next, multiply that by the sample size of 732.

Z = (1581 - 3311)/860 = -2    

Z1 = (3311 - 3311)/860 = 0

Z2 = (5031 - 3311)/860= 2  

P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772

  approximately 47% fall between 0 and 1 standard deviation, so take 0.47 times 732 ⇒ 732×0.47 = 344.

Answer: [tex]7\sqrt{42}[/tex]

Step-by-step explanation:

42 students divided equally into 7 groups means 42 divided by 7, and [tex]7\sqrt{42}[/tex] is the only choice that shows that.

7√42. is the expressions would represent a class of 42 students divided equally into 7 groups

A division is a process of splitting a specific amount into equal parts.

Given,

A class of forty two Forty two students divided equally into 7 groups.

Forty two students divided equally into seven groups means forty two divided by seven, and

this can be done by using 7√42.

42 students divided equally into 7 groups means forty two divided by seven

Hence  7√42. is the expressions would represent a class of 42 students divided equally into 7 groups

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ2

Answer:

B

O 50° is the mZACB out of the options

Answer:

the answer is false

Step-by-step explanation:

comment if you want explanation

Answer:

True

Step-by-step explanation:

When using the formulas to find the surface area, both have equal surface area

Answer:

D. Critical value =± 0.707; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.

Step-by-step explanation:

Given that :

Correlation Coefficient, r = 0.693

The sample size, n = 8

The degree of freedom used for linear correlation :

df = n - 2

df = 8 - 2 = 6

Using a critical value calculator for correlation Coefficient at α = 0.05

The critical value obtained is : 0.707

The test statistic :

T = r / √(1 - r²) / (n - 2)

T = 0.693 / √(1 - 0.693²) / (8 - 2)

T = 0.693 / 0.2943215

T = 2.354

Since ;

Test statistic < Critical value ; we fail to reject the null and conclude that there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.

Answer:

7.5 dm

Step-by-step explanation:

Plus mo baka tama ako

9514 1404 393

Answer:

Step-by-step explanation:

Each image point has its signs reversed from the pre-image point.

  (x, y) ⇒ (-x, -y) . . . . describes the rotation

Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.

Answer:

3rd and 2nd option

Step-by-step explanation:

Answer: Let the number be x

3-2x is the equation.

Answer:

0.18431525 = 18.4%

Step-by-step explanation:

General Formula :

total trials Cn⋅p(success)^n⋅p(fail)^total−n

1198144* (.0218)^3 * (1-.0218)^191

Answer:

A

Step-by-step explanation:

Number of suitcases on a plane is discrete because you can only have an integer amount. You can't have a fraction of a suitcase on a plane.

Answer:

For the Broadway actors acting in their first role on Broadway, mean: 0.184, Standard Deviation: 0.063.

For the proportion of smokers, mean = 0.167, standard deviation = 0.068

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers.

This means that [tex]p = 0.184, n = 38[/tex]

What are the mean and standard deviation for the sampling distribution of p^?

Mean:

[tex]\mu = p = 0.184[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.184*0.816}{38}} = 0.063[/tex]

Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.

This means that [tex]n = 30, p = 0.167[/tex]

What is the mean and the standard deviation of the sampling distribution of p^ ?

Mean:

[tex]\mu = p = 0.167[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.167*0.833}{30}} = 0.068[/tex]

urdxvjok NCAA earth bno

Answer:

It would take Al 7.5 days to build the grill alone.

Step-by-step explanation:

Since Tim and Al are bricklayers, and Tim can construct an outdoor grill in 5 days, and if Al helps Tim, they can build it in only 3 days, to determine how long would it take Al to build the grill alone should be done the following calculation:

1/5 + X = 1/3

0.20 + X = 0.333

X = 0.333 - 0.20

X = 0.1333333

X = 1 / 7.5

Therefore it would take Al 7.5 days to build the grill alone.

Answer:

The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].

Step-by-step explanation:

Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.

Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].