A company has determined that it must increase production of a certain line of goods by 112 times last years production. The new output will be 2885 items. What was last year's output?

Answer:

The second one:

L∪J={i,j,k,l,m,n,o}

Step-by-step explanation:

The union is the elements listed in either set.

So since l,m,n, and o are elements of set L, they will also be elements of whatever it is "unioned" with.

Since i,j,k,l and m are elements of set J, they will also be elements of whatever it is "unioned" with.

When you write the union, just be sure to include each element that occurs in either set once.

So the union of L and J is {i,j,k,l,m,n,o}.

The answer is the second one.

The intersection would actually be that upside down U thing, the ∩ symbol. The intersection of two sets is a list of elements that both sets include.  So here the intersection would just consist of the elements l amd m.

The union of L and J is {i,j,k,l,m,n,o}. The correct option is the second option - L∪J = {i,j,k,l,m,n,o}

From the question, we are to determine the union of the sets

The union of two given sets is the smallest set which contains all the elements of both sets.

The given sets are

L= {l,m,n,o}

J= {i,j,k,l,m}

We are to determine the union of L and J, that is, L∪J

L∪J will be the set that contains all the elements of both L and J

Therefore

L∪J = {i,j,k,l,m,n,o}

Hence, the union of L and J is {i,j,k,l,m,n,o}. The correct option is the second option - L∪J = {i,j,k,l,m,n,o}

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Answer:

Her adjusted body weight is 78.26kg = 78.3kg, rounded to the nearest tenth.

Step-by-step explanation:

To find the Adjusted Body Weight(AjBW), first we have to consider the Ideal Body Weight(IBW).

We have the following formulas:

[tex]IBW = 45.5kg + 2.3kg*i[/tex], in which i is the number of inches that the woman has above 5 feet.

[tex]AjBW = IBW + 0.4*(ABW - IBW)[/tex], in which [tex]ABW[/tex] is her Actual Body Weight

So, in this problem:

Each pound has 0.45kg. So her weight is [tex]ABW = 220*0.45 = 99.8[/tex]kg.

The woman is 8 inches above 5 feet, so [tex]i = 8[/tex].

[tex]IBW = 45.5 + 2.3*8[/tex]

[tex]IBW = 63.9[/tex]kg

Her ideal body weight is 63.9kg. Her adjusted body weight is:

[tex]AjBW = IBW + 0.4*(ABW - IBW)[/tex]

[tex]AjBW = 63.9 + 0.4*(99.8-63.9)[/tex]

[tex]AjBw = 78.26[/tex]kg

Her adjusted body weight is 78.26kg = 78.3kg.

recall your d = rt, distance = rate * time.

A = first plane

B = second plane

the assumption is that they both start off from the same point at the same time in opposite directions.

at some time say "t" hours, plane A will be some distance, hmmm say "d" miles, since we know they'll both be 4000 miles apart, then plane B will be "4000 - d" miles at that time, since both took off at the same time, then plane A as well as plane B have both been travelling "t" hours.

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{plane A}&d&400&t\\ \textit{plane B}&4000-d&600&t \end{array}\qquad \qquad \begin{cases} \boxed{d}=400t\\\\ 4000-d=600t \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 2nd equation}}{4000-\boxed{400t}=600t}\implies 4000=1000t\implies \cfrac{4000}{1000}=t\implies 4=t[/tex]

Answer:

600 ml

Step-by-step explanation:

Given,

240 ml of milk provides about 8 grams of protein,

That is, the ratio of grams of protein provided and milk = [tex]\frac{8}{240}[/tex]

Let x be the quantity of milk in ml that provides 20 grams of protein,

So, the ratio of grams of protein provided and milk = [tex]\frac{20}{x}[/tex]

[tex]\implies \frac{8}{240}=\frac{20}{x}[/tex]

By cross multiplication,

8x = 4800

Divide both sides by 8,

x = [tex]\frac{4800}{8}[/tex] = 600

Hence, 600 ml milk should be needed to provide 20 grams of protein.

To obtain 20 grams of protein, you would need to get 600 ml of milk.

To find out how much milk you should get to obtain 20 grams of protein, we can use a proportion:

240 ml of milk provides 8 grams of protein

x ml of milk provides 20 grams of protein

To solve for x, we can set up the following proportion:

240/8 = x/20

Cross multiplying, we get:

8x = 240 * 20

x = (240 * 20)/8

Therefore, you would need to get 600 ml of milk to obtain 20 grams of protein.

Answer:  p = -0.004n + 8

Step-by-step explanation:

Consider the number of shirts & the price as an x,y - coordinate

4000 shirts at $32  -->  (4000, 32)

5000 shirts at $28  --> (5000, 28)

Use the slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{28-32}{5000-4000}\quad =\dfrac{-4}{1000}\quad =-0.004[/tex]

Next, use the Point-Slope formula (replace x with n & replace y with p):

[tex]y-y_1=m(x-x_1)\implies p-p_1=m(n-n_1)\\\\\\p-28=-0.004(n-5000)\\\\p-28=-.004n-20\\\\\large\boxed{p=-0.004n+8}[/tex]

Answer:

Percentage of total net sales = 91.17%

The percentage of cost of merchandise sold = 44.11 %

Percentage of First year expenses = 41.17 %

Percentage of Overall profit = 5.88 %

Step-by-step explanation:

Given:

Gross sales= $204,000

Customer returns and allowances = $18,000

Cost of the merchandise they sold = $90,000

overall profit before taxes = $12,000

Now,

The Net sales = Gross sales - sales returns  

or

The net sales = $204,000 - $18,000 = $186,000

Thus,

Percentage of total net sales = [tex]\frac{\textup{Net sales}}{\textup{Gross sales}}\times100[/tex]

or

Percentage of total net sales = [tex]\frac{186,000}{204000}\times100[/tex]

or

Percentage of total net sales = 91.17%

Now,

The percentage of cost of merchandise sold = [tex]\frac{\textup{cost of the merchandise sold }}{\textup{Gross sales}}\times100[/tex]

or

The percentage of cost of merchandise sold = [tex]\frac{\textup{90,000}}{\textup{204,000}}\times100[/tex]

or

The percentage of cost of merchandise sold = 44.11 %

And,

Percentage of First year expenses = [tex]\frac{\textup{Expenses}}{\textup{Gross sales}}\times100[/tex]

or

Percentage of First year expenses = [tex]\frac{\textup{84000}}{\textup{204000}}\times100[/tex]

or

Percentage of First year expenses = 41.17 %

also,

Percentage of Overall profit = [tex]\frac{\textup{Overall profit}}{\textup{Gross sales}}\times100[/tex]

or

Percentage of Overall profit = [tex]\frac{\textup{12,000}}{\textup{204,000}}\times100[/tex]

or

Percentage of Overall profit = 5.88 %

The correct representation are as follows:

Part (a): [tex]\boxed{m\cdot a=}[/tex]

Part (b): [tex]\boxed{2*\left(\text{cos}(2\cdot \theta)\right)-1=}[/tex]

Part (c): [tex]\boxed{a*\left(\text{sin}(x)\right)+15=}[/tex]

Part (d): [tex]\boxed{\sqrt{\dfrac{2\cdot g\cdot \triangle y}{m}}=}[/tex]

Part (e): [tex]\boxed{N_{0}\cdot e^{-(\lambda\cdot t)}}[/tex]

Further explanation:

in the question it is given that while writing any mathematical expression the symbol to be used for multiplication is [tex]\cdot\text{ dot}[/tex].

For example: [tex](2\times 3)[/tex] is incorrect and [tex](2\cdot 3)[/tex] is correct.

If a mathematical expression is to be written in its explicit form then the symbol [tex]*\text{ aestrick}[/tex] is used.

Part (a):

The expression given in part (a) is as follows:

[tex]ma=[/tex]

The correct representation of the above expression is as follows:

[tex]\boxed{m\cdot a=}[/tex]

For multiplication [tex]\cdot\text{ dot}[/tex] symbol is used.

Part (b):

The expression given in part (b) is as follows:

[tex]2\text{cos}(2\theta)-1=[/tex]

The correct representation of the above expression is as follows:

[tex]\boxed{2*\left(\text{cos}(2\cdot \theta)\right)-1=}[/tex]

For multiplication [tex]\cdot\text{ dot}[/tex] symbol is used.

Part (c):

The expression given in part (c) is as follows:

[tex]a\text{sin}(x)+15=[/tex]

The correct representation of the above expression is as follows:

[tex]\boxed{a*\left(\text{sin}(x)\right)+15=}[/tex]

Part (d):

The expression given in part (d) is as follows:

[tex]\sqrt{{2g\triangle y/m}=[/tex]

The correct representation of the above expression is as follows:

[tex]\boxed{\sqrt{\dfrac{2\cdot g\cdot \triangle y}{m}}=}[/tex]

For multiplication [tex]\cdot\text{ dot}[/tex] symbol is used.

Part (e):

The expression given in part (e) is as follows:

[tex]N_{0}e^{-\lambda t}[/tex]

The correct representation of the above expression is as follows:

[tex]\boxed{N_{0}\cdot e^{-(\lambda\cdot t)}}[/tex]

For multiplication [tex]\cdot\text{ dot}[/tex] symbol is used.

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Answer details:

Grade: College

Subject: Mathematics

Chapter: NA

Keywords: Expression, representation, ma, cdot, aestrick, wcos(2theta)-1, asin(x)+15, sqraureroot(2gdeltay/m), N0e-lamda t, lowercase greek, multiplication dot.

Basically, here we want to just rewrite all the multiplications using the * symbol, which represents multiplication in most common programmation languages and math calculators.

We usually do not use it when a scalar multiplies a variable, like in:

2x

but just to be complete, let's also use it as 2*x.

for example, the first expression we get is:

ma = m*a

b) Completing the others is trivial, we just need to identify where we have multiplications and add the correspondent symbol there.

[tex]2cos^2(\theta) - 1 = 2*cos^2(\theta) - 1[/tex]

c) asin(x)+15 =

Note that while "Asin(x)" is a function, I assume that here we have "a times sin(x)", so we will write:

[tex]asin(x) + 15 = a*sin(x) + 15[/tex]

D)  (√(2gΔy)/m)

Here we have the term "Δy", this is not a multiplication, this means a "difference in the value of y", so we will leave it as it is.

[tex]\frac{\sqrt{2g\Delta y} }{m} = \frac{\sqrt{2*g*\Delta y} }{m}[/tex]

E)  N0e−λt,

Here N0 is a term in itself, and actually should be written as N₀, so this is not N times zero.

So we will get:

[tex]N_0e -\lambda t = N_0*e - \lambda*t[/tex]

If instead of that, the right part was an exponent (I can't tell because of how you wrote it) we would get:

[tex]N_0e^{ -\lambda t} = N_0*e^{ - \lambda*t}[/tex]

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To find when Ima Neworker's rate will exceed 12 units per hour, given a learning curve rate of 65%, we analyze the improvement in production rate from the initial 2 units per hour up to the target, using the learning curve concept.

The question relates to the concept of a learning curve, which represents how new workers or processes improve in efficiency as experience is gained. Ima Neworker can produce her first unit in 30 minutes (which is half an hour), so when she starts, her production rate is 2 units per hour. The question asks how many units will be produced before her production rate exceeds 12 units per hour, given a learning curve rate of 65%. This means that each time the cumulative production doubles, the time taken to produce each unit falls to 65% of the previous time.

Since the initial production rate is 2 units per hour, we want to know how many units she has to produce before her production rate exceeds 12 units per hour. 12 units per hour is 6 times faster than her initial rate, and we can reference a learning curve table or use the formula to calculate the necessary doubling periods required to achieve this.

To determine when Ima Neworker's production rate exceeds 12 units per hour, we use a 65% learning curve. By calculations, production time per unit drops below 5 minutes per unit between producing 8 and 16 units, indicating she exceeds the rate at around 12 units. Thus, she will need to produce approximately 12 units before reaching this threshold.

Calculating Production Using a Learning Curve

Ima Neworker requires 30 minutes to produce her first unit, which translates to 2 units per hour initially. The learning curve rate of 65% indicates that with each doubling of previously produced units, the time required to produce another unit will be 65% of the time it took for the previous set.

Step-by-Step Calculation

We need to produce units such that Ima's production rate exceeds 12 units per hour, meaning she should produce a unit in less than 1/12 hours (5 minutes).

Thus, Ima will need to produce more than 8 but fewer than 16 units. By interpolation, it will be close to 12 units when her rate exceeds 12 units per hour.

Answer:  60

Step-by-step explanation:

5 shorts × 4 shorts × 3 socks = 60 different uniforms

To find the surface area of the resulting surface when rotating the arc of a parabola about the y-axis, you can integrate using either x or y as the variable. Both methods yield the same result.

The question asks for the area of the surface created by rotating the arc of the parabola y = 3x^2 from (5, 75) to (10, 300) about the y-axis.

There are two different solutions provided, both utilizing different methods of integration.

The first solution uses the given equation y = 3x^2 and integrates with respect to x, while the second solution uses the equation x = y^(1/3) and integrates with respect to y.

Both solutions arrive at the same answer to find the surface area.

Answer:

Step-by-step explanation:

First, observe that:

[tex](n+1)^2(2(n+1)^2-1)=(n^2+2n+1)(2n^2+4n+1)=2n^4+8n^3+11n^2+6n+1[/tex]

We will prove by mathematical induction that, for every natural,  

[tex]1^3+3^3+5^3+......(2n-1)^3=n^2(2n^2-1)[/tex]

We will prove our base case (when n=1) to be true.

Base case:

[tex]1^3+3^3+5^3+......(2n-1)^3=1=n^2(2n^2-1)[/tex]

Inductive hypothesis:  

Given a natural n,  

[tex]1^3+3^3+5^3+......(2n-1)^3=n^2(2n^2-1)[/tex]

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

[tex]1^3+3^3+5^3+......(2(n+1)-1)^3=1^3+3^3+5^3+......(2n+1)^3=\\=n^2(2n^2-1)+(2n+1)^3=2n^4-n^2+8n^3+12n^2+6n+1=2n^4+8n^3+11n^2+6n+1[/tex]

Then, by the observation made at the beginning of this proof, we have that

[tex]1^3+3^3+5^3+......(2(n+1)-1)^3=(n+1)^2(2(n+1)^2-1[/tex]

With this we have proved our statement to be true for n+1.  

In conlusion, for every natural n

,

[tex]1^3+3^3+5^3+......(2n-1)^3=n^2(2n^2-1)[/tex]

b)

Observe that [tex]3\mid (n^3-n+3) \iff 3\mid (n^3-n) \iff 3\mid n(n^2-1)[/tex]

Then,

Therefore, for every [tex]n\in \mathbb{N}), 3\mid (n^3-n+3)[/tex]  

c)

We will prove by mathematical induction that, for every natural n>3,

[tex](n-1)^2<2n^2.[tex]

We will prove our base case (when n=4) to be true.

Base case:

[tex](n-1)^2=(4-1)^2=9<32=2*4^2=2n^2 [/tex]

Inductive hypothesis:  

Given a natural n>4,  

[tex](n-1)^2<2n^2.[tex]

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

[tex]((n+1)-1)^2=((n-1)+1)^2=(n-1)^2+2(n-1)+1<2n^2+2(n-1)+1=2n^2+2n- 1<2n^2+2n+1 =2(n+1)^2.[tex]

With this we have proved our statement to be true for n+1.    

In conclusion, for every natural n>3,

[tex](n-1)^2<2n^2.[tex]

Answer:

a)109 of the surveyed households only own a hand gun and do not support the ban on hand guns.

b)328 of the surveyed households do not own a gun and support the ban on hand guns

c )112 of the surveyed households do not own a gun and do not support the ban on handguns.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents those who own a hand gun.

-The set B represents those who own a rifle

-The set C represents those who support the ban of handguns.

-D represents those who do not own a gun and do not support the ban on hand guns.

We have that:

[tex]A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)[/tex]

In which [tex]a[/tex] are those that only own a hand gun, [tex]A \cap B[/tex] are those who own both a handgun and a rifle, [tex]A \cap C[/tex] are those who own a hand gun and support the ban on handguns, and [tex]A \cap B \cap C[/tex] are those who own both a hand gun and a rifle, and also support the ban on hand guns.

By the same logic, we have:

[tex]B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)[/tex]

In which [tex]b[/tex] are those who only own a rifle, and [tex]B \cap C[/tex] are those who own a rifle and support the ban on handguns.

[tex]C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)[/tex]

In which [tex]c[/tex] are those who support the ban on hand guns and do not own any handguns.

This diagram has the following subsets:

[tex]a,b,c,D(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)[/tex]

There were 1000 households surveyed, so:

[tex]a + b + c + D + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1000[/tex]

We start finding the values from the intersection of three sets.

Solution:

48 own both a hand gun and a rifle and also support the ban on hand guns.

[tex]A \cap B \cap C = 48[/tex]

70 own a hand gun and support the ban on hand guns:

[tex](A \cap C) + (A \cap B \cap C) = 70[/tex]

[tex]A \cap C = 70 - 48[/tex]

[tex]A \cap C = 22[/tex]

206 own a rifle but no hand gun and do not support the ban on hand guns.

[tex]b = 206[/tex].

136 own both a hand gun and a rifle:

[tex](A \cap B) + (A \cap B \cap C) = 136[/tex]

[tex]A \cap B = 136 - 48[/tex]

[tex]A \cap B = 88[/tex]

493 supported the ban on hand guns.

[tex]C = 493[/tex]

437 own a rifle:

[tex]B = 437[/tex]

267 own a hand gun:

[tex]A = 267[/tex]

a) How many of the surveyed households only own a hand gun and do not support the ban on hand guns?

This is the value of [tex]a[/tex], that we can find from the following equation:

[tex]A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)[/tex]

[tex]267 = a + 88 + 22 + 48[/tex]

[tex]a = 267 - 158[/tex]

[tex]a = 109[/tex]

109 of the surveyed households only own a hand gun and do not support the ban on hand guns.

b) How many of the surveyed households do not own a gun and support the ban on hand guns?

This is the value of [tex]c[/tex], that we can find from the following equation:

[tex]C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)[/tex]

[tex]493 = c + 22 + (B \cap C) + 48[/tex]

Here, we also have to find [tex]B \cap C[/tex], that are those who own a rifle and support the ban on hand guns. We can find this from the following equation:

[tex]B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)[/tex]

[tex]437 = 206 + (B \cap C) + 88 + 48[/tex]

[tex]B \cap C = 437 - 342[/tex]

[tex]B \cap C = 95[/tex]

So

[tex]493 = c + 22 + (B \cap C) + 48[/tex]

[tex]493 = c + 22 + 95 + 48[/tex]

[tex]c = 493 - 165[/tex]

[tex]c = 328[/tex]

328 of the surveyed households do not own a gun and support the ban on hand guns.

a) How many of the surveyed households  do not own a gun and do not support the ban on hand guns?

This is the value of d, that can be found from the following equation:

[tex]a + b + c + D + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1000[/tex]

[tex]109 + 206 + 328 + D + 88 + 22 + 95 + 40 = 1000[/tex]

[tex]D = 1000 - 888[/tex]

[tex]D = 112[/tex]

112 of the surveyed households do not own a gun and do not support the ban on handguns.

I like guns but im christian

Answer:

Step-by-step explanation:

You already have the answer.

1 [at] = 760 [mmHg]

1 [at] = 14,7 [psi]

1500 [mmHg] * 1 [at] / 760 [mmHg] * 14,7 [psi] / 1 [at] = 29.0 [psi]

Answer:

a) There are 11 balls left in the bag.

b) 4 of the balls in the bag are red.

c) 3 brown, 2 green, 2 white.

d) [tex]P = \frac{2}{11}[/tex]

e) The probability that the first ball is red and the second is green is:

[tex]\frac{5}{66}[/tex]

The probability that both balls are red is:

[tex]\frac{5}{33}[/tex]

f) The probability that both balls are green is:

[tex]\frac{1}{66}[/tex]

g) The probability that the first ball is brown and the second is white is:

[tex]\frac{1}{22}[/tex]

The probability that the first ball is brown and the second is white is:

[tex]\frac{1}{22}[/tex]

They are the same probabilities.

Step-by-step explanation:

There are 12 balls in the bag

5 red

3 brown

2 green

2 white

If you draw a red ball and put it aside:

a) How many balls are left in the bag?

There were 12 balls in the bag, and one was put aside.

So, there are 11 balls left in the bag.

b) How many of the balls in the bag are red?

There were 5 red balls in the bag, and one was put aside.

So, there are 4 red balls in the bag.

c) How many are brown? Green? White?

The ball put aside was red, so we still have the same number of the balls of the other colors.

3 brown, 2 green, 2 white.

d) Draw a second ball from the bag. What is the probability that it is green?

There are 11 balls in the bag, 2 of which are green. So the probability that the second ball is green is:

[tex]P = \frac{2}{11}[/tex]

Now put both balls back in the bag and draw two balls without replacing them.

e) What is the probability that the first ball is red and the second ball is green (without replacement)?

[tex]P = P_{1}*P_{2}[/tex]

[tex]P_{1}[/tex] is the probability that the first ball is red. There are 12 balls, 5 of which are red. So:

[tex]P_{1} = \frac{5}{12}[/tex]

Since there are no replacements, now there are 11 balls in the bag, 2 of which are green. So:

[tex]P_{2} = \frac{2}{11}[/tex]

The probability that the first ball is red and the second is green is:

[tex]P = P_{1}*P_{2} = \frac{5}{12}*\frac{2}{11} = \frac{5}{66}[/tex]

What is the probability that the first ball is red and the second ball is also red (without replacement)?

[tex]P = P_{1}*P_{2}[/tex]

[tex]P_{1}[/tex] is the probability that the first ball is red. There are 12 balls, 5 of which are red. So:

[tex]P_{1} = \frac{5}{12}[/tex]

Since there are no replacements, now there are 11 balls in the bag, 4 of which are red. So:

[tex]P_{2} = \frac{4}{11}[/tex]

The probability that both balls are red is:

[tex]P = P_{1}*P_{2} = \frac{5}{12}*\frac{4}{11} = \frac{5}{33}[/tex]

f) What is the probability that the first ball is green and the second ball is also green (without replacement)?

[tex]P = P_{1}*P_{2}[/tex]

[tex]P_{1}[/tex] is the probability that the first ball is green. There are 12 balls, 2 of which are green. So:

[tex]P_{1} = \frac{2}{12}[/tex]

Since there are no replacements, now there are 11 balls in the bag, 1 of which is green. So:

[tex]P_{2} = \frac{1}{11}[/tex]

The probability that both balls are green is:

[tex]P = P_{1}*P_{2} = \frac{2}{12}*\frac{1}{11} = \frac{1}{66}[/tex]

g) What is the probability that the first ball is brown and the second ball is white (without replacement)?

[tex]P = P_{1}*P_{2}[/tex]

[tex]P_{1}[/tex] is the probability that the first ball is brown. There are 12 balls, 3 of which are brown. So:

[tex]P_{1} = \frac{3}{12}[/tex]

Since there are no replacements, now there are 11 balls in the bag, 2 of which are white. So

[tex]P_{2} = \frac{2}{11}[/tex]

The probability that the first ball is brown and the second is white is:

[tex]P = P_{1}*P_{2} = \frac{3}{12}*\frac{2}{11} = \frac{1}{22}[/tex]

Would this be different than the probability that the first ball is white and the second ball is brown?

[tex]P = P_{1}*P_{2}[/tex]

[tex]P_{1}[/tex] is the probability that the first ball is white. There are 12 balls, 2 of which are brown. So:

[tex]P_{1} = \frac{2}{12}[/tex]

Since there are no replacements, now there are 11 balls in the bag, 3 of which are brown. So

[tex]P_{2} = \frac{3}{11}[/tex]

The probability that the first ball is brown and the second is white is:

[tex]P = P_{1}*P_{2} = \frac{2}{12}*\frac{3}{11} = \frac{1}{22}[/tex]

They are the same probabilities.

Answer:

The angle is 28.

Step-by-step explanation:

If we consider the system below (were "A"is the angle):  

A   +  [(x/2)-14] = 90       (complement)

A   +   x   = 180                 (suplement)

We can isolate "X=180 - A"  and apply this in the first equation. This way we are able to have only one variable, and w'll see that A=28.

Answer:

A) find its center  = (3, 2)

B) find the radius of the circle = √104

C) find the equation of the circle = x² + y² - 6x - 4y -91 = 0

Step-by-step explanation:

A)- The center must be the mid-points of (-2, 1) and (8, 3).

So, using the equation of mid-point,

[tex]h=\frac{x_{1}+x_{2}}{2}  and  k=\frac{y_{1}+y_{2}}{2}[/tex]

Here, (x₁, y₁) = (-2, 1) and (x₂, y₂) = (8, 3)

Putting these value in above equation. We get,

h = 3 and k = 2

Thus, Center = (h, k) = (3, 2)

B)- For finding the radius we have to find the distance between center and any of the end point.

Thus using Distance Formula,

[tex]Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

[tex]Radius =\sqrt{(8+2)^{2}+(3-1)^{2}}[/tex]

⇒ Radius = √104 = 2√26

C)- The equation of circle is determined by formula:

[tex](x-h)^{2}+(y - k)^{2} = r^{2}[/tex]

where (h, k ) is center of circle and

r is the radius of circle.

⇒ (x - 3)² + (y - 2)² = 104

⇒ x² + y² - 6x - 4y -91 = 0

which is the required equation of the circle.

To measure tartar emetic for the prescription, keep in mind the sensitivity of your balance and the acceptable weighing error. Tartar emetic of 15mg should be weighed as accurately as the balance allows and if the measurement falls within the acceptable error range, it can be dissolved in cherry syrup for uniform distribution.

The tartar emetic dose required by the prescription is 0.015 g. However, you're using a balance with a sensitivity of 4 mg (milligrams). Similar to procure the accurate tartar emetic measurement, you must take into account the balance's sensitivity and the acceptable weighing error of 5%.

0.015 g is equal to 15 mg. Our balance's lowest measurement is 4 mg, which is less than the 15 mg we need to weight accurately. When considering the acceptable weighing error of 5%, the actual amount of tartar emetic measured could range from 14.25 mg to 15.75 mg (15 mg ± 5%).

To solve with the stipulated constraints, you need to carefully weigh out the tartar emetic as close as the balance will allow, and if it does not reach the desired measurement but falls within the acceptable error range, you can dissolve it in the cherry syrup for uniform distribution within the medication. Always remember to mix well and be precise with measurements to ensure the correct strength of medicine.

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Calculate the acceptable error range for the weight of tartar emetic, then weigh it out on a balance with the specified sensitivity. Once within the error range, dissolve the tartar emetic in the cherry syrup.

The question asks how to obtain the correct quantity of tartar emetic given the equipment and accepted weighing error. To do this, first you must calculate the acceptable error range by multiplying the desired weight of the tartar emetic (0.015 g) by 5%, which yields an acceptable error of 0.00075 g. Since your balance has a sensitivity of 4 mg (0.004 g), it can accurately measure out this quantity. Then you would weigh out the tartar emetic on the balance until you are within this error range.

It's important to note that tartar emetic is fully soluble in water and so cherry syrup, which is water-based, can be used as the solvent for tartar emetic. After weighing, dissolve the tartar emetic into the cherry syrup before moving on to measure out the other ingredients for the prescription.

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Answer:

Step-by-step explanation:

Given that the three orders are independent of each other.

X - no of ships not shipped on time

X is binomial with p = 0.05 and q = 0.95, n = 3

a)  the probability that all are shipped on time=[tex]0.95^3 =0.854[/tex]

b) the probability that exactly one is not shipped ontime

=P(X=1) =[tex]3C1(0.05)(0.95)^2 = 0.135[/tex]

c) the probability that two or more orders are notshipped on time

[tex]= P(X=2)+P(x=3)\\= 1-P(x=0)-P(x=1)\\=1-0.854-0.135\\=0.011[/tex]

Final answer:

The probabilities for the shipping orders, assuming independence, are calculated: all on time is 0.857, exactly one not on time is 0.135, and two or more not on time is 0.008.

Explanation:

The probability that a customer's order is not shipped on time is 0.05. Since the orders are independent events, we can calculate the following:

Probability that all are shipped on time: Since the orders are independent, the probability of all orders shipped on time is the product of their individual probabilities: (1-0.05)3 = (0.95)3 = 0.857.

Probability that exactly one is not shipped on time: There are three scenarios where exactly one order can be not shipped on time (NSO for not shipped, SO for shipped): NSO-SO-SO, SO-NSO-SO, SO-SO-NSO. The probability for each scenario is 0.05 * 0.95 * 0.95. Since there are three such scenarios, multiply by 3: 3 * (0.05 * 0.95 * 0.95) = 0.135.

Probability that two or more orders are not shipped on time: The probability of at least one order being shipped on time is 1 minus the probability of none being shipped on time, which is 1 - (0.05)3. From this, we subtract the probability of all being shipped on time and the probability of exactly one not being shipped on time to get our answer: 1 - (0.95)3 - (3 * 0.05 * 0.95 * 0.95) = 0.008.

Answer:  30

Step-by-step explanation:

The combination of n things taking r at a time is given by :-

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Given : At a restaurant a menu has 5 salads and 6 entrees.

Then, the number of ways you can order a dinner that contains 1 salad and 1 entree will be :_

[tex]^5C_1\times ^6C_1\\\\=5\times6=30[/tex]

Hence, the number of ways you can order a dinner that contains 1 salad and 1 entree = 30

Answer:

Option C.

Step-by-step explanation:

Negative 5 represents (-5)

Square root of negative 44 is [tex]\sqrt{(-44)}[/tex]

By the statement "negative 5 minus the square root of negative 44." will be

(-5) - [tex]\sqrt{(-44)}[/tex]

= -5 -[tex]\sqrt{(-1)(44)}[/tex]

= [tex]-5-\sqrt{(-1)(4\times11)}[/tex]

= [tex]-5-2\sqrt{11(-1)}[/tex]

= [tex]-5-2(\sqrt{11} )[\sqrt{(-1)} ][/tex]

= [tex]-5-2i\sqrt{11}[since\sqrt{(-1)=i}][/tex]

Option c will be the answer.

Answer:

R is reflexive

R is not symmetric

R is transitive

Step-by-step explanation:

R is reflexive.

To show this, we have to verify that for any pair of integers [tex](x_1,x_2)[/tex]

[tex](x_1,x_2)R(x_1,x_2)[/tex].

But this is obvious because

[tex]x_1=x_1[/tex] and [tex]x_2\leq x_2[/tex].

R is not symmetric.

To show it, we need to find two pairs [tex](x_1,x_2)[/tex] and [tex](y_1,y_2)[/tex] such that

[tex](x_1,x_2)R(y_1,y_2)[/tex]

but [tex](y_1,y_2) \not \mathrel{R} (x_1,x_2)[/tex]

For example (1,1) and (1,2).

[tex](1,1)R(1,2)[/tex] for 1=1 and [tex]1\leq 2[/tex] but  

[tex](1,2) \not \mathrel{R} (1,1)[/tex] because [tex]2\not \leq 1[/tex]

Finally, R is transitive.

If we take 3 pairs of integers [tex](x_1,x_2), (y_1,y_2)[/tex] and [tex](z_1,z_2)[/tex]

Such that

[tex](x_1,x_2)R(y_1,y_2)[/tex] and [tex](y_1,y_2)R(z_1,z_2)[/tex] then

[tex]x_1=y_1[/tex] and [tex]x_2\leq y_2[/tex]

[tex]y_1=z_1[/tex] and [tex]y_2\leq z_2[/tex]

But then,

[tex]x_1=z_1[/tex] and [tex]x_2\leq z_2[/tex]

So  

[tex](x_1,x_2)R(z_1,z_2)[/tex].

The mean cost of repair is $391.75. The median cost of repair is $419.50. There is no mode for the repair costs.

To compute the mean, median, and mode cost of repair, we first need to list the repair costs in numerical order:

The mean is calculated by finding the average of the repair costs, which is the sum of the costs divided by the total number of costs. In this case, the mean is $(249 + 403 + 436 + 479)/4 = $391.75.

The median is the middle value of the data set once it is ordered. In this case, the median is $419.50, which is the average of $403 and $436.

The mode is the value that appears most frequently in the data set. In this case, there is no mode because none of the repair costs occur more than once.

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The mean cost of repair is $391.75, while the median cost is $419.50. Since there are no repeated repair costs, there is no mode.

To determine the mean, median, and mode repair costs of the four cars, follow these steps:

Mean

The mean (average) cost of repair is calculated by summing all the repair costs and then dividing by the number of cars.

Sum of costs = $436 + $403 + $479 + $249 = $1567

Number of cars = 4

Mean = $1567 / 4 = $391.75

So, the mean cost of repair is $391.75.

Median

To find the median, list the repair costs in ascending order: $249, $403, $436, $479.

Since there are four data points (even number), the median is the average of the two middle numbers.

Median = ($403 + $436) / 2 = $839 / 2 = $419.50

So, the median cost of repair is $419.50.

Mode

The mode is the number that appears most frequently in a data set.

In this case, each cost appears only once; therefore, no mode exists.

Answer:

(a) 0.704

(b) 0.8475

Step-by-step explanation:

(a) Let 'A' be the event that you travel by car and late

Let 'B' be the event that you travel by bus and late

Let 'C' be the event that you travel by Bicycle and late

Then, P (A)  = 50% = [tex]\frac{50}{100}[/tex] = [tex]\frac{1}{2}[/tex]

         P (B)   = 20% = [tex]\frac{20}{100}[/tex] = [tex]\frac{1}{5}[/tex]

         P (C)   = 1%  = [tex]\frac{1}{100}[/tex]  = [tex]\frac{1}{100}[/tex]

A₁ = Student travels by car

B₁ = Student travels by bus

C₁ = Student travels by bicycle

Then according to teacher P(A₁) = [tex]\frac{1}{3}[/tex], P(B₁) = [tex]\frac{1}{3}[/tex], P(C₁) = [tex]\frac{1}{3}[/tex]

Now we have to find "Student is already late and traveled to school that day by car." which will be given as [tex]P(\frac{A}{L})[/tex]

where L : student is late

By using Bay's Theorem :

[tex]P(\frac{A}{L})[/tex]  = [tex]\frac{P(A)\times P(A_1)}{P(A)\times P(A_1)+P(B)\times P(B_1)+P(C)\times P(C_1)}[/tex]

= [tex]\frac{\frac{1}{2}\times \frac{1}{3}}{\frac{1}{2}\times \frac{1}{3}+\frac{1}{5}\times \frac{1}{3}+\frac{1}{100}\times \frac{1}{3}}[/tex]

= [tex]\frac{\frac{1}{6}}{\frac{1}{6}+\frac{1}{15}+\frac{1}{300}}[/tex]

= [tex]\frac{\frac{1}{6}}{\frac{50+20+1}{300}}[/tex]

= [tex]\frac{1}{6}\times \frac{300}{71}[/tex]

= [tex](\frac{50}{71})[/tex]

= 0.704

(b) Here P(A₁) = [tex](\frac{10}{100})[/tex]

              P(C₁) = [tex](\frac{90}{100})[/tex]

            [tex]P(\frac{A}{L})[/tex]  = We have to find and known student is late and traveled by car.

[tex]P(\frac{A}{L})[/tex] = [tex]\frac{P(A)\times P(A_1)}{P(A)\times P(A_1)+(P(C)\times P(C_1)}[/tex]

= [tex]\frac{\frac{1}{2}\times \frac{1}{10}}{\frac{1}{2}\times \frac{1}{10}+\frac{1}{100}\times \frac{9}{10}}[/tex]

= [tex]\frac{\frac{1}{20} }{\frac{1}{20}+\frac{9}{1000}}[/tex]

= [tex]\frac{\frac{1}{20}}{\frac{50+9}{1000}}[/tex]

= [tex]\frac{1}{20}\times \frac{1000}{59}[/tex]

= [tex](\frac{50}{59})[/tex]

= 0.8475

Answer:

The level of significance observed is 0.99154

Step-by-step explanation:

Assuming that in a sample of size 50 people stated that they do not like the snack (p = 17/50), you have:

Proportion in the null hypothesis [tex]\pi_0=0.5[/tex]

Sample size [tex]n=50[/tex]

Sample proportion [tex]p=17/50=0.34[/tex]

The expression for the calculated statistic is:

[tex] = \frac{(p - \pi_0)\sqrt{n}}{\sqrt{\pi_0(1-\pi_0)}}[/tex]

[tex]= \frac{(0.34 - 0.5)\sqrt{50}}{\sqrt{0.34(0.66)}} = -2,38833[/tex]

The level of significance observed is obtained from the value of the statistic calculated:

[tex]P(Z>Z_{calculated}) = 0.99154[/tex]

Answer:

See explanation

Step-by-step explanation:

During daytime in New York City, UberRUSH has a base fare of $3.00 plus $2.50 per mile.

A. Let x be the number of miles Sergio uses the taxi, then he will pay $2.50x for x miles plus a base fare of $3.00. In total, the cost of using UberRUSH services during the day in New York City is

[tex]C=3.00+2.50x[/tex]

B. The rate of change for the cost of riding UberRUSH during the day in New York City is the slope of the line represented by linear function in part A. So, the rate of change is 2.5 and it shows the change in price per 1 mile driven.

C. The y-intercept is 3.00 (or simply 3) and it represents the initial cost (when 0 miles are driven)

D. The graph of the function is shown in attached diagram. The diagram shows the part of the line starting from point (0,3). This is because the number of miles driven cannot be negative.

Answer:

[tex]x=\frac{\pi}{4}[/tex] and [tex]x=-\frac{3\pi}{4}[/tex]

Step-by-step explanation:

We are given that sin x+cos x=cos 2x

We have to solve the given equation for [tex]0\leq x\leq 2\pi[/tex]

[tex] sin x+cos x=cos^2x-sin^2x[/tex]

Because [tex]cos 2x=cos^2-sin^2[/tex]

[tex] sinx+cos x=(sinx +cos x)(sinx-cos x)[/tex]

[tex] 1 =sin x-cos x[/tex]

[tex] sin x=cos x[/tex]

[tex]\frac{sinx }{cos x}=1[/tex]

[tex]tan x=1[/tex]

[tex]tan x=\frac{sinx}{cos x}[/tex]

[tex]tan x=tan\frac{\pi}{4}[/tex]

[tex]x=\frac{\pi}{4}[/tex]

Tan x is positive in I and III quadrant

In III quadrant angle[tex]\theta[/tex]  replace by [tex]\theta -\pi[/tex]

Therefore, [tex]tan x=tan (\frac{\pi}{4}-\pi)=tan\frac{\pi-4\pi}{4}=tan\frac{-3\pi}{4}[/tex]

[tex]x=-\frac{3\pi}{4}[/tex]

Answer:

3.045%.

Step-by-step explanation:

We are asked to find the corresponding effective interest rate for 3% per year compounded continuously.

We will use effective interest formula to solve our given problem.

[tex]r=e^i-1[/tex], where,

r = Effective interest rate,

e = Mathematical constant,

r = Interest rate in decimal form.

Let us convert given interest rate in decimal form.

[tex]3\%=\frac{3}{100}=0.03[/tex]

Substitute values:

[tex]r=e^{0.03}-1[/tex]

[tex]r=1.030454533953517-1[/tex]

[tex]r=0.030454533953517[/tex]

[tex]r\approx 0.03045[/tex]

Convert into percentage:

[tex]0.03045\times 100\%=3.045\%[/tex]

Therefore, the corresponding interest rate would be 3.045%.

Answer:

The required ratio is 9 : 61

Step-by-step explanation:

Given,

$72 for 488 photos,

That is, the price of 488 photos = 72 dollars,

So, the ratio of price of photos and number of photos = [tex]\frac{72}{488}[/tex]

∵ HCF(72, 488) = 8,

Thus, the ratio of price of photos and number of photos = [tex]\frac{72\div 8}{488\div 8}[/tex]

= [tex]\frac{9}{61}[/tex]

Answer:

[tex]a.\hspace{3} \frac{6}{38} = 0.15789474\\\\b.\hspace{3} \frac{45}{55} = 0.81818181\\\\c.\hspace{3} \frac{4}{28} = 0.14285714\\\\d.\hspace{3} \frac{35}{28} = 1.25\\\\e.\hspace{3} \frac{1030}{2030} = 0.50738916[/tex]

Step-by-step explanation:

Rational numbers, expressed as decimal numbers, are obtained from the operation of division between the integer of the numerator and the integer of the denominator. Then:

[tex]a.\hspace{3} \frac{6}{38} = 6\div38 = 0.15789474\\\\ b.\hspace{3} \frac{45}{55} = 45\div55 = 0.81818181\\\\c.\hspace{3} \frac{4}{28} = 4\div28 = 0.14285714\\\\ d.\hspace{3} \frac{35}{28} = 35\div28 = 1.25\\\\ e.\hspace{3} \frac{1030}{2030} = 1030\div2030 = 0.50738916[/tex]

The only way to get a term containing [tex]x^{25}[/tex] is to take 6 copies of 1, 1 copy of [tex]x[/tex], and 3 copies of [tex]x^8[/tex] (since 6+1+3=10, and 6*0+1*1+3*8=25). So this term has a coefficient of

[tex]\dfrac{10!}{6!1!3!}=840[/tex]