The solution to the equation x3 = 125 is: 5 -5 ±5

Answer:

A 6 Packages of buns and 5 packages of wieners.

Step-by-step explanation:

Because if you multiply 6x10 you get 60 and if you multiply 5x12 you get 60 exactly 1 wieners per bun

Let

ATQ

[tex]\\ \sf \longmapsto Area=Length\times Width[/tex]

[tex]\\ \sf \longmapsto x(x+3)=28[/tex]

[tex]\\ \sf \longmapsto x^2+3x=28[/tex]

[tex]\\ \sf \longmapsto x^2+3x-28=0[/tex]

[tex]\\ \sf \longmapsto x^2+7x-4x-28=0[/tex]

[tex]\\ \sf \longmapsto x(x+7)-4(x+7)=0[/tex]

[tex]\\ \sf \longmapsto (x-4)(x+7)=0[/tex]

[tex]\\ \sf \longmapsto x=4\:or\:x=-7[/tex]

[tex]\\ \sf \longmapsto Width=4units[/tex]

[tex]\\ \sf \longmapsto Length=4+3=7units[/tex]

Answer:

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, [tex]A(10) = 0.7278A(0)[/tex]. We use this to find k.

[tex]A(t) = A(0)e^{-kt}[/tex]

[tex]0.7278A(0) = A(0)e^{-10k}[/tex]

[tex]e^{-10k} = 0.7278[/tex]

[tex]\ln{e^{-10k}} = \ln{0.7278}[/tex]

[tex]-10k = \ln{0.7278}[/tex]

[tex]k = -\frac{\ln{0.7278}}{10}[/tex]

[tex]k = 0.03177289938 [/tex]

Then

[tex]A(t) = A(0)e^{-0.03177289938t}[/tex]

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?

We have to find find A(5), as a function of A(0). So

[tex]A(5) = A(0)e^{-0.03177289938*5}[/tex]

[tex]A(5) = 0.8531[/tex]

The decay factor is:

1 - 0.8531 = 0.1469

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Answer:

hope this help you

sorry if it is mistake

Answer:

D ) none of these .. i think this help you

9514 1404 393

Answer:

  (e) f′(x)=2xg(x)+x²g′(x)

Step-by-step explanation:

The product rule applies.

  (uv)' = u'v +uv'

__

Here, we have u=x² and v=g(x). Then u'=2x and v'=g'(x).

  f(x) = x²·g(x)

  f'(x) = 2x·g(x) +x²·g'(x)

Answers:

The boxplot is shown below.

=========================================

Explanation:

What your teacher wants is the five number summary.

This consists of:

Given in that exact order.

The given data set is  { 8, 19, 11, 20, 2, 14, 17, 9, 15}

This sorts to  {2, 8, 9, 11, 14, 15, 17, 19, 20}

From this sorted set, we see that 2 is the smallest item. So this is the min value. This is data point 1.

The max is the largest item, which in this case is 20, so this value goes in the box for data point 5.

---------------------

Count out the number of values in the sorted set. You should count out n = 9 items.

Because n is odd, this means the median is in slot n/2 = 9/2 = 4.5 = 5

The value in the 5th slot is 14 which is the median (data point 3).

-----------------------

Once you determine the median, break the sorted set up like so

L = {2, 8, 9, 11}

U = {15, 17, 19, 20}

L is the lower set of values smaller than the median

U is the upper set of values larger than the median

The median itself is not part of set L and not part of set U either. It's ignored entirely from this point on.

From here, we find the middle values of L and U

You should find that the middle value of L is (8+9)/2 = 17/2 = 8.5 which is the value of Q1 (data point 2)

And also, the middle value of set U is (17+19)/2 = 36/2 = 18 which is the value of Q3 (data point 4)

-----------------------

To wrap everything up, we have this five number summary

These will determine the features of the boxplot as shown below.

In this case, there are no outliers.

Answer:

1/4 cup each

Step-by-step explanation:

Take the amount of ice cream and divide by 3

3/4÷ 3

Copy dot flip

3/4 * 1/3

Rewriting

3/3 * 1/4

1/4 cup each

Answer:

Pvalue

Step-by-step explanation:

The Pvalue measure which takes up a value in the range 0 - 1 is a statistical measure used on hypothesis testing to measure the likelihood of obtaining result atleast as extreme as the outcome of the statistical hypothesis test, The Pvalue is used in hypothesis testing to make a case for the alternative hypothesis, which involves being compared with the α - value.

Lower p values favors the adoption of alternative depending on how extreme th α-value is. The Pvalue is dependent on the value if the test statistic.

Answer:

a. L{t} = 1/s² b. L{1} = 1/s

Step-by-step explanation:

Here is the complete question

The The Laplace Transform of a function ft), which is defined for all t2 0, is denoted by Lf(t)) and is defined by the improper integral Lf))s)J" e-st . f(C)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of s as a fixed constant) 1. Find Lft) (hint: remember integration by parts) A. None of these. B. O C. D. 1 E. F. -s2 2. Find L(1) A. 1 B. None of these. C. 1 D.-s E. 0

Solution

a. L{t}

L{t} = ∫₀⁰⁰[tex]e^{-st}t[/tex]

Integrating by parts  ∫udv/dt = uv - ∫vdu/dt where u = t and dv/dt = [tex]e^{-st}[/tex] and v = [tex]\frac{e^{-st}}{-s}[/tex] and du/dt = dt/dt = 1

So, ∫₀⁰⁰udv/dt = uv - ∫₀⁰⁰vdu/dt w

So,  ∫₀⁰⁰[tex]e^{-st}t[/tex] =  [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ -  ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]

∫₀⁰⁰[tex]e^{-st}t[/tex] =  [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ -  ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]

= -1/s(∞exp(-∞s) - 0 × exp(-0s)) + [tex]\frac{1}{s}[/tex] [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰

= -1/s[(∞exp(-∞) - 0 × exp(0)] - 1/s²[exp(-∞s) - exp(-0s)]

= -1/s[(∞ × 0 - 0 × 1] - 1/s²[exp(-∞) - exp(-0)]

= -1/s[(0 - 0] - 1/s²[0 - 1]

= -1/s[(0] - 1/s²[- 1]

= 0 + 1/s²

= 1/s²

L{t} = 1/s²

b. L{1}

L{1} = ∫₀⁰⁰[tex]e^{-st}1[/tex]

= [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰

= -1/s[exp(-∞s) - exp(-0s)]

= -1/s[exp(-∞) - exp(-0)]

= -1/s[0 - 1]

= -1/s(-1)

= 1/s

L{1} = 1/s

Answer:

D) y = 2x + 1

Step-by-step explanation:

Answer:[tex]n=\frac{58}{31}[/tex]

Step-by-step explanation:

[tex]124n=232\\\frac{124n}{124}=\frac{232}{124}\\n=\frac{232}{124}=\frac{58}{31}[/tex]

The value of n is 18.75. To find the value of n, we need to solve the equation: 124n = 232 five

Let's first convert "232 five" into a numerical value:

"232 five" means 2325 (since five is in the units place).

Now, the equation becomes:

124n = 2325

To solve for n, divide both sides of the equation by 124:

n = 2325 / 124

Now, perform the division:

n = 18.75

So, the value of n is 18.75.

To know more about equation:

https://brainly.com/question/10724260

#SPJ2

Answer:

Step-by-step explanation:

1500(1.055)^7= 2182.02

Answer:

Step-by-step explanation:

The steps and their reasons for the equation 8(y - 3) = - 40 are given below.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

8(y - 3) = - 40

            Steps                                               Reason

       8(y - 3) = - 40                                          Given

       8y - 24 = - 40                                Distributive property

8y - 24 + 24 = - 24 + 24                 Addition Property of Equality

               8y = - 16                                      Simplifying

          8y / 8 = - 16/8                       Division property of equality

                  y = - 2                                       Simplifying

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The mean and the variance are:

[tex]\mu = \frac{nk}{N}[/tex]

[tex]\sigma^2 = \frac{nk(N-k)(N-n)}{N^2(N-1)}[/tex]

We have that:

5 + 7 = 12 rocks, which means that [tex]N = 12[/tex]

9 are chosen, which means that [tex]n = 9[/tex]

7 are granite, which means that [tex]k = 7[/tex]

Question a:

[tex]E(X) = \mu = \frac{9\times7}{12} = 5.25[/tex]

[tex]Var(X) = \sigma^2 = \frac{9\times7(12-7)(12-9)}{12^2(12-1)} = 0.5966[/tex]

Thus:

[tex]E(X) = 5.25, Var(X) = 0.5966[/tex]

Question b:

Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:

[tex]P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,12,9,7) = \frac{C_{7,4}*C_{5,5}}{C_{12,9}} = 0.1591[/tex]

[tex]P(X = 5) = h(5,12,9,7) = \frac{C_{7,5}*C_{5,4}}{C_{12,9}} = 0.4773[/tex]

[tex]P(X = 6) = h(6,12,9,7) = \frac{C_{7,6}*C_{5,3}}{C_{12,9}} = 0.3181[/tex]

Thus

[tex]P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.1591 + 0.4773 + 0.3181 = 0.9545[/tex]

So P(X < 6) = 0.9545.

Question c:

5 of basaltic and 4 of granite: 0.1591 probability.

7 of granite is P(X = 7), in which

[tex]P(X = 7) = h(7,12,9,7) = \frac{C_{7,7}*C_{5,2}}{C_{12,9}} = 0.0455[/tex]

0.1591 + 0.0455 = 0.2046, thus:

P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.

A similar question is found at https://brainly.com/question/24008577

Step-by-step explanation:

Many factors would be used to assess the effectiveness of a human rights campaign, including the following:

Social Influence. Direct Interpersonal Reach. Participant Observation. Reputation. Volume of Search & Interest. Website Traffic.

National Research.

Answer:

1

Step-by-step explanation:

the maximum of f(X)=sin(X) is 1

Answer:

B) 1 unit to the left

Step-by-step explanation:

9514 1404 393

Answer:

  B)  K′ = (–2,2), L′ = (1,2), M′ = (1,–1), N′ = (–2,–1)

Step-by-step explanation:

Translation 2 units right adds 2 to the x-coordinate.

Translation 4 units upward adds 4 to the y-coordinate.

The translation can be represented by the relation ...

  (x, y) ⇒ (x +2, y +4)

__

You can choose the correct answer by looking at the translation of K.

  K(-4, -2) ⇒ K'(-4+2, -2+4) = K'(-2, 2) . . . . . matches choice B

Answer:

Step-by-step explanation:

(ii) right angle becuase perpendicular

iv) congruent because <b=<a (opp ang in isc.tria. is equal)

since ΔADC ≅ Δ BDC, AB=BD

Answer:

A

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan12° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{44}[/tex] ( multiply both sides by 44 )

44 × tan12° = AC , then

AC ≈ 9.35 ( to 2 dec. places )

Answer:

4 scoops of ice cream

Step-by-step explanation:

Plug in the total cost, number of scoops of nuts, and number of liquid toppings into the formula. Then, solve for s:

C = 0.50s + 0.35n + 0.25t

3.55 = 0.50s + 0.35(3) + 0.25(2)

3.55 = 0.50s + 1.05 + 0.5

3.55 = 0.50s + 1.55

2 = 0.50s

4 = s

So, the sundae had 4 scoops of ice cream.

Answer:

-6

Step-by-step explanation:

27-3/2x=36

53-3x=72

3x=-18

x=-6

Answer:

Hello,

Just using the theorem of Thalès,

Step-by-step explanation:

Let say h the hight of the building

[tex]\dfrac{h}{3} =\dfrac{42.75}{1.23}\\\\h=104.268296...\approx{104(m)}[/tex]

9514 1404 393

Answer:

  B B C C A A

Step-by-step explanation:

If we number the equations 1 to 6 left to right, then we have ...

Let W be the random variable representing your winnings from playing the game. Then

[tex]P(W=w)=\begin{cases}\text{prob. of rolling an even number}=\frac12&\text{if }w=\$0.50-\$1=-\$0.50\\\text{prob. of rolling a 1}=\frac16&\text{if }w=\$2-\$1=\$1\\\text{prob. of rolling 3 or 5}=\frac13&\text{if }w=\$1-\$1=\$0\\0&\text{otherwise}\end{cases}[/tex]

In short, you have a 1/6 chance of profiting from the game, and a 5/6 chance of losing money. So the odds of winning are (1/6)/(5/6) = 1/5 or 1 to 5.

Answer: No, there isn't equal opportunity

======================================================

Explanation:

Let's define the two events

From the table, we see that

P(B) = 340/500 = 0.68

meaning that there's a 68% chance of picking someone who got the class they wanted (i.e. 68% of the people got the class they wanted)

------------

Now let's assume that the person is on the honor roll. This means we only focus on the "honor roll" column. There are 125 people here that got the class they wanted out of 205 honor roll students total.

So,

P(B given A) = 125/205 = 0.609756

which rounds to 0.61

This says that if a person is on the honor roll, then they have roughly a 61% chance of getting the class they want.

The chances have gone down from 68% to 61% roughly.

------------

It appears that being on the honor roll does affect your chances of getting into the class you want.

Therefore, all students do not have the same equal opportunity.

We would need to have P(B) and P(A given B) to be the same exact value for true equal opportunity to happen.

All students do not have equal opportunity.

From the table, we have the following parameters:

The above means that:

The probability that a person is on honor roll call is:

p1 = 205/500

p1 = 0.41

The probability that a person got the math class requested

p2 = 340/500

p2 = 0.68

Both probabilities are not equal.

Hence, it is true that all students do not have equal opportunity.

Read more about probability at:

https://brainly.com/question/25870256