when a number divides another number exactly the smaller number is called

The probability of getting 2 tails is option (b) 37.5%

The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.

Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:

P(htt) = 1/2 × 1/2 × 1/2 = 1/8

P(tht) = 1/2 × 1/2 × 1/2 = 1/8

P(tth) = 1/2 × 1/2 × 1/2 = 1/8

So, the probability of getting 2 tails is:

P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8

= 0.375

0.375 multiplied by 100% gives:

P(2 tails) = 37.5%

Therefore, the correct option is (b) 37.5%

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Answer:

To three decimal places, The process capability index is 0.167

Step-by-step explanation:

We have to find the process capability index,

Upper specification = 16.5 ounces,

Lowe specification = 15.5 ounces

Mean = 16.0 ounces

Standard Deviation = S = 1 ounce

process capability index = (upper specification - lower specification)/6S

process capability index = (16.5 - 15.5)/6(1)

= 1/6

Process capability index = 1/6 = 0.16666667

To 3 decimal places, we get,

Process capability index = 0.167

The correct answer, in minutes, is:  " 16 \(\frac{1}{3}\) minutes ".
_____

[Note:  This is the same value as " 16 minutes and 20 seconds."].
_____

Step-by-step explanation:

Convert 980 sec to "minutes".

Note the exact conversion:
  60 sec = 1 minute.

 
So: Given the values in this question:
  60 sec / 1 minute = "x  minutes/ 980 sec" ;

that is:

 " \(\frac{980 sec}{1} *\frac{1 min}{60 sec}\)  " ;
The units: "sec" ["seconds"] cancel out to: " 1 " ;

 since: " [sec / sec = 1 ] ;   and we can simplify and rewrite:

   " \(\frac{980 min}{60} = \frac{980}{60}\) min."

 →  Now, cancel out the last numerical value of "zero"
                  (in both the numerator and the denominator);  that is: to simplify the expression further—by dividing each side by "10" ;

              to get:  " \(\frac{98}{6}\) min."

Then: divide the numerator by the denominator:
        "[ 98 ÷ 6 = 16 \(\frac{1}{3}\) minutes ] ; — which is our answer.

Note: "1/3" of:  "1 minute"  = (1/3)*(60 seconds) = 20 seconds.

So;  "16 1/3" minutes = 16 minutes and 20 seconds".

_____
The correct answer, in minutes, is:  " 16 \(\frac{1}{3}\) minutes ".
  [Note:  This is the same value as " 16 minutes and 20 seconds."].
_____
Hope this answer and explanation is helpful to you!
Best of luck to you!

_____

Answer:

X=108

Step-by-step explanation:

ASSUMING ITS A HEXAGON the sixth angle would be 108 degrees. You get this by adding all the five angles which give you 612. You then subract 612 from 720. Because 720 is the whole measure of  a hexagon. and then when you subtract you get 108.n

Answer:

Below:

Step-by-step explanation:

The answer is "B" -44.

Hope it helps...

It's Ms-Muska

Answer:

e=15.33

t=17.88

Step-by-step explanation:

e/9.1=9.6/5.7

cross multiply

5.7e=87.36

e=15.33

t/9.1=11.2/5.7

cross multiply

5.7t=101.92

t=17.88

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

The mathematics curriculum involves examining numbers, the equation the environment we live in, structures, and both actual and hypothetical locations. A function is a variable representation of the relationship between the quantities of intake and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, when combined, provide unique outputs for each input.

Here,

Given :

mass of a population of duckweed is 500g

=>  function m(t)= 500x³^t/45

So,

=> t = 45 hours

Since it is given that the mass of the population of the duckweed triples every 45 hours

it is clear that the time taken for the duckweed to grow a mass triple the original size will be 45 hours .

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

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Answer:

XDDDDDDDDDDDDDDDDDDDDDDDDD

Step-by-step explanation:

The correct detection rate is the probability that if you have D, the test will say that you have D. Given that you test positive for D, the probability that you actually have it is 16.67%.

The probability that you actually have the disease (D) given that you tested positive is 0.1667 (16.67%). This can be calculated by multiplying the prevalence of the disease (P[D] = 0.001) by the correct detection rate of the test (1) and dividing it by the sum of the prevalence of the disease and the false positive rate of the test (0.001 + 0.005 = 0.006):

P[D | positive] = (P[D] × correct detection rate) / (P[D] + false positive rate)

P[D | positive] = (0.001 × 1) / (0.001 + 0.005)

P[D | positive] = 0.1667

P[D | positive] = 16.67%

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The complete question is:

The following problem was given to 60 students and doctors at the famous Hevardi Medical School (HMS): Assume there exists a test to detect a disease, say D, whose prevalence is 0.001, that is, the probability, P[D], that a person picked at random is suffering from D. is 0.001. The test has a false positive rate of 0.005 and a correct detection rate of 1. The correct detection rate is the probability that if you have D, the test will say that you have D. Given that you test positive for D, what is the probability that you actually have it?

beep bop boop bleep bloop i is bored lol

The probability of randomly selecting a gold medalist from the US is0.019

First, the probability of winning a gold medal is given by the quotient between the number of gold medals and the total number of medals.

The number of medals is:

gold = 48 + 90 + 107 + 114 + 397 = 756

There are 1,019 silver ones

There are 782 bronze ones

Then the total number is 756 + 1019 + 782 = 2,557

Then the probability for the gold medal is:

P = 756/2,557

And the probability that the gold medalist is from the US is given by the quotient between the number won by the US (48) and the total number of gold ones (756)

So we get.

Q = 48/756

The joint probability is given by the product of the two:

p = (756/2,557 )*(48/756) = 48/2,557 = 0.019

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Answer:

Adam and buford

Step-by-step explanation:

Answer:

adam and buford

Step-by-step explanation:

In this case, the constant of proportionality is the speed at which you walk, which is 2.5 miles per hour.

Identifying the constant of proportionality is an important skill in 7th grade math. To do this, you need to look for a verbal description of the proportional relationship. This might be something like "If you buy 2 bags of chips, the cost is $4. If you buy 4 bags of chips, the cost is $8." In this example, the constant of proportionality is the cost per bag of chips, which is $2.

To find the constant of proportionality, you need to divide the second quantity by the first quantity. In the example above, you would divide the cost by the number of bags of chips. This gives you the cost per bag, which is the constant of proportionality.

Practice identifying the constant of proportionality by looking for relationships that involve two quantities that are proportional to each other. Keep in mind that the constant of proportionality is always the same, no matter what the quantities are. So, if you see a relationship like "If you walk 5 miles, it takes you 2 hours. If you walk 10 miles, it takes you 4 hours," the constant of proportionality is still the same, even though the quantities are different. In this case, the constant of proportionality is the speed at which you walk, which is 2.5 miles per hour.

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Thus, the cost of each balcony tickets and general admission floor tickets are 24 and 55.

Equations linear in two variables: It is a mathematical formula with the notation ax+by+c=0. X and Y are variables, whereas a, b, and c are real numbers. It is possible to state that a and b do not equal zero. When the same integer is added towards both sides, multiplied by the same number, or divided by the same number, a linear equation can be solved. X and Y stand for two-variable linear equations.

For the given query:

Let 'x' be the price of each balcony tickets.

Let 'y' be the price of each floor tickets.

Then, system of linear equation are:

27x + 82y = 3453 ...eq1

90x + 93y = 7182 ..eq2

Using substitution method:

27x + 82y = 3453

x = (3453 - 82y)/27  ...Put in eq 2

90( (3453 - 82y)/27 ) + 93y = 7182

10/3 *(3453 - 82y)) + 93y = 7182

10 *(3453 - 82y)) + 279y = 21546

34530 - 820y + 279y = 21546

541y = 12984

y = 24

Now,

x = (3453 - 82y)/27

x = (3453 - 82(24))/27

x = 55

Thus, the cost of each balcony tickets and general admission floor tickets are 24 and 55.

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The amount of money would be $1115.45 the zoo makes selling the waste that day.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

They charge farmers $5 per pound for the daily feces from the elephants. If an elephant's daily waste production is at or below the 10th percentile for the distribution of waste which is given in the question.

To determine the amount of money would the zoo make selling the waste that day.

P(z ≤ z₀) = 0.1

z₀ = -1.28

⇒z₀ =(x₀ -μ ) / σ

Substitute the values and solve for x₀,

⇒ -1.28 =(x₀ -250 ) / 21

⇒x₀ = (-1.28)×21 - 250

⇒x₀ = 223.09

So the amount of money would be as :

⇒ 223.09 × 5

⇒ 1115.45

Therefore, the amount of money would be $1115.45 the zoo makes selling the waste that day.

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Answer:

there are two incorrect 2 and 3

Step-by-step explanation:

After 10 years, the account will have approximately $379,315.92, given a deposit of $63,377 at an annual interest rate of 17.00% compounded quarterly.

To calculate the future value of the account after 10 years, we can use the formula for compound interest: A = P * (1 + r/n)^(nt), where A is the future value, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount (P) is $63,377, the annual interest rate (r) is 17.00% (or 0.17 as a decimal), the interest is compounded quarterly (n = 4), and the time period (t) is 10 years.

Plugging these values into the formula, we get A = 63377 * (1 + 0.17/4)^(4*10). Evaluating this expression, we find that A is approximately $379,315.92.

Therefore, after 10 years, the account will have approximately $379,315.92.

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SOLUTION

Draw the diagram

a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side.

Hence

SInce AC=30, Then

Thus, from the median properties of a triangle, AB = 15

Answer:

1+2=90° .so complementary angle

Answer:

You can use y − y1 = m(x − x1) and get 2-y= 1/6(9-3) so y = 1

Step-by-step explanation:

Since the speed limit is about  62.14 miles per hour, the correct options would be A, B, and C, which are, respectively, 55, 60 and 62,1 miles per hour.

To solve the problem, we need to convert the speed limit from kilometers per hour to miles per hour and then compare it to the given speeds.

100/1.61 = 62.14

So, the speeds that are less than or equal to the speed limit of 100 kilometers per hour are:

The speed of 63 miles per hour and 65.4 miles per hour is greater than the speed limit of 62.14 miles per hour, so it is not less than or equal to the speed limit. Options A, B and C are correct.

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Answer:

220 ft

Step-by-step explanation:

Given that:

Length of each curtain = 48 inches

Number of curtains required for Abby's curtain company = 55

Fabric of curtains is sold by the fabric store foot by foot.

Unit for conversion:

1 inch = \(\frac{1}{12}\) foot

To find:

The fabric (in feet) needed by Abby.

Solution:

First of all, let us convert the length of each curtain (which is given in inches) to feet.

As per given hint:

1 inch = \(\frac{1}{12}\) foot

48 inches = \(\frac{1}{12}\) \(\times\) 48 ft = 4 ft

So, length of one curtain is 4 ft.

Now, number of curtains required are 55.

Therefore, total length of curtains required can be found by multiplying the number of curtains with the length of one curtain.

Total length of curtain required = 55 \(\times\) 4 = 220 ft

The final solution in terms of the inverse Laplace transforms:

\(ƒ(t) = L^{-1}[F(s)]\)

We have,

To solve the given ordinary differential equation (ODE) using Laplace transform, we'll follow these steps:

Step 1: Take the Laplace transform of both sides of the equation.

Step 2: Solve for the Laplace transform of the function ƒ(t).

Step 3: Take the inverse Laplace transform to obtain the solution in the time domain.

Let's go through these steps:

Step 1: Taking the Laplace transform of the ODE, we have:

L[f"(t)] + 6L[f'(t)] + 13L[f(t)] = 48L[t - 5]

Step 2: Applying the Laplace transform properties and using the initial conditions, we get:

\(s^2F(s) - sf(0) - f'(0) + 6(sF(s) - f(0)) + 13F(s) = 48(e^{-5s}/s)\)

Simplifying, we have:

\(s^2F(s) + 6sF(s) + 13F(s) - s(0) - 0 + 6sF(s) - 6(0) + 13F(s) = 48(e^{-5s}/s)\)

Combining like terms, we obtain:

\((s^2 + 6s + 13)F(s) = 48(e^{-5s}/s)\)

Step 3: Solving for F(s), we have:

\(F(s) = 48(e^{-5s}/s) / (s^2 + 6s + 13)\)

To find the inverse Laplace transform of F(s), we can use partial fraction decomposition, but the expression involves complex roots.

Therefore,

The final solution in terms of the inverse Laplace transforms:

\(ƒ(t) = L^{-1}[F(s)]\)

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Answer:

2+4=6

20+40=60

200+400=600

2,000+4,000=6,000

Step-by-step explanation:

Answer:

Y-8

Step-by-step explanation:

Any point on the upper triangle ABC, for example point B, is translated 8 units down the y axis, appearing on the lower triangle A'B'C'

The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of amount $50 and a 25% markup on the selling price.

$50 / 0.25 = $200

To calculate the cost of the Nike baseball gloves with a markup of 25% and a margin of $50, use the following formula:

Cost = (Price + Markup) / (1 + Markup Percentage)

Cost = ($50 + $50) / (1 + 0.25)

Cost = $100 / 1.25

Cost = $80

Therefore, the manager can afford to pay amount $80 for each baseball glove.

The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of $50 and a 25% markup on the selling price.

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Answer= \(50cm^{2}\)

Each equation should be matched to the situation it represents as follows;

"Leilah has not yet studied 600 of her 2400 flashcards. She studies 40 new cards each day." ⇒ 2400 - 40x = 600

"Stetson rents studio space for $600 a month for music lessons. He charges his students $40 per hour and earned a profit of $2400 this month." ⇒ 40x - 600 = 2400

"A kit contains 600 letter tiles and 40 number tiles. Each tile has the same mass, and the kit has a total mass of 2400 g." ⇒ (600 + 40)x = 2400.

In this scenario and exercise, the independent variable (domain or input value) would be represented by the variable x, and then each of the situations described by the word sentence (problem) would be translated into an algebraic equation or linear function as follows;

Since Leilah studies 40 new cards per day, but hasn't studied 600 of her 2400 flashcards yet, a linear function to model or represent this situation is given by;

2400 - 40x = 600

The rent for Stetson's studio space is $600 per month and he charges his students $40 each hour while earning a profit of $2400 this month, a linear function to model or represent this situation is given by;

40x - 600 = 2400

Since this kit with a total mass of 2400rams contains 600 letter tiles and 40 number tiles, and each of the tiles have the same mass, the required linear function is given by;

(600 + 40)x = 2400.

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