A chemist wants to mix a 22% acid solution with a 36% acid solution to get 28 L of a 26% acid solution. How many liters of the 22% solution and how many liters of the 36% solution should be mixed?

Answer with Step-by-step explanation:

We are given that twos sets

[tex]S_1[/tex]={a+bx:[tex]a,b\in R[/tex]}=All polynomials which can expressed as  a linear combination of 1 and x.

[tex]S_2[/tex]={ax+b(2+x):[tex]a,b\in R[/tex]}=All polynomials which can be expressed as   a linear combination of x and 2+x.

We have to prove that given two sets are same.

[tex]S_2[/tex]={ax+2b+bx}={(a+b)x+2b}={cx+d}

[tex]S_2[/tex]={cx+d}=All polynomials which can be expressed as  a linear combination of 1 and x.

Because a+b=c=Constant

2b= Constant=d

Hence, the two sets are same .

slope-intercept formula y=mx+b

Answer:

Ben must make at least 14 deliveries to reach his goal.

Step-by-step explanation:

The problem states that Ben earns $9 per hour and $6 for each delivery he makes. So his daily earnings can be modeled by the following function.

[tex]E(h,d) = 9h + 6d[/tex],

in which h is the number of hours he works and d is the number of deliveries he makes.

He wants to earn more than $155 in an 8 hour work day.What is the least number of deliveries he must make to reach his goal?

This question asks what is the value of d, when E = $156 and h = 8. So:

[tex]E(h,d) = 9h + 6d[/tex]

[tex]156 = 9*8 + 6d[/tex]

[tex]156 = 72 + 6d[/tex]

[tex]6d = 84[/tex]

[tex]d = \frac{84}{6}[/tex]

d = 14

Ben must make at least 14 deliveries to reach his goal.

Answer:

0.0559

Step-by-step explanation:

Cant prove it but its right

To test the claim that more than 65% homeowners in Omaha possess a lawnmower, a one-tailed test of proportion was performed. After calculating a test statistic (z =1.52), it was determined that the P-value is 0.064, suggesting there is a 6.4% probability that a sample proportion this high could happen by chance given the null hypothesis is true.

In this question, you're asked to calculate the P-value for a test of the claim that the proportion of homeowners with lawn mowers in Omaha is higher than 65%. The proportion from the sample size of Omaha is given as 340/497 = 0.68 or 68%. To test this claim, you would employ a one-tailed test of proportion. The null hypothesis (H0) is that the proportion is equal to 65%, while the alternative hypothesis (Ha) is that the proportion is greater than 65%.

To determine the P-value, you need to first calculate the test statistic (z) using the formula: z = (p - P) / sqrt [(P(1 - P)) / n], where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting into the formula, z = (0.683 - 0.65) / sqrt [(0.65 * 0.35) / 497] = 1.52. The P-value is the probability of getting a z-score that is greater than or equal to 1.52.

Using a standard normal distribution table, or an online z-score calculator, you can find that P(Z > 1.52) = 0.064 (approximately). This is the P-value for the test, which indicates that if the null hypothesis is true, there is a 6.4% probability that a sample proportion this high could occur by chance.

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Answer:

Taking into account the information presented in the image attached for this food.  

Naturally sugar are

2 g

Step-by-step explanation:

Information presented regarding to the composition of this food is attached.

One serving has a weight of 55 g.

Total carbohydrates in one serving are 37 g. This value includes fiber and sugars.

If we detail sugars, it has 12 g of total sugars (St), where 10 g are added sugars (Sa) and all the rest Natural sugars (Sn).

Expressing sugars as an equation

St = Sa + Sn

Isolating Sn value

Sn = St - Sa

Sn = 12 g - 10 g  

Sn = 2 g

Finally, Natural sugars (Sn) is 2 g.  

All 22 grams of total sugars per serving in the food are naturally occurring, as the label specifies there are 0g of added sugars.

To determine the grams of naturally occurring sugar in a serving of food, we need to examine the nutritional information provided.

According to the label, it includes 0g added sugars, which implies that all of the sugars listed are naturally occurring.

Therefore, if there are 22g total sugars in one serving of the food, and none of these are added sugars, then all 22 grams can be attributed to naturally occurring sugars.

Answer:

Protein

Step-by-step explanation:

According to U.S. Food and Drug Administration (FDA) information, the current scientific evidence indicates that protein intake is not a matter of public concern, this is why the FDA does not request to add a % Daily Value on the Nutrition Facts panel, unless if the product is made for protein such as 'high protein' products or if this food is meant for use by childrend under 4 years old.

Answer:Protein

Step-by-step explanation: took quiz :)

Answer:

The cost is $9.70 per kilogram.

Step-by-step explanation:

This can be solved by a rule of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In this problem, the measures are the weight of the cheese and the price. As the weight increases, so does the price. It means that this is a direct rule of three.

Solution:

The problem states that cheese costs $4.40 per pound. Each kg has 2.2 pounds. How many kg are there in 1 pound. So:

1 pound - xkg

2.2 pound - 1 kg

[tex]2.2x = 1[/tex]

[tex]x = \frac{1}{2.2}[/tex]

[tex]x = 0.45[/tex]kg

Since cheese costs $4.40 per pound, and each pound has 0.45kg, cheese costs $4.40 per 0.45kg. How much does is cost for 1kg?

$4.40 - 0.45kg

$x - 1kg

[tex]0.45x = 4.40[/tex]

[tex]x = \frac{4.40}{0.45}[/tex]

[tex]x = 9.70[/tex]

The cost is $9.70 per kilogram.

"The cost per kilogram of cheese is approximately $2.00.

To find the cost per kilogram, we need to convert the cost from dollars per pound to dollars per kilogram using the conversion factor between pounds and kilograms. Given that 1 kilogram is equal to 2.2 pounds, we can set up the following conversion:

Cost per pound of cheese = $4.40

Conversion factor = 2.2 pounds/kilogram

Now, to find the cost per kilogram, we divide the cost per pound by the conversion factor:

Cost per kilogram = Cost per pound / Conversion factor

Cost per kilogram = $4.40 / 2.2 pounds/kilogram

Performing the division, we get:

Cost per kilogram ≈ $2.00

Answer: (A) 30%

Step-by-step explanation:

Given : The probability that a bird will lay an egg =0.75

The probability that the egg will hatch  =0.50

Now, the probability that the egg will lay an egg and hatch = [tex]0.75\times0.50[/tex]

Also,The probability that the chick will be eaten by a snake before it fledges =0.20

Then, the probability that the chick will not  be eaten by a snake before it fledges : 1-0.20=0.80

Now, the probability that a parent will have progeny that survive to adulthood will be :-

[tex]0.75\times0.50\times0.80=0.30=30\%[/tex]

Hence, the probability that a parent will have progeny that survive to adulthood =  30%

[tex]y=\displaystyle\sum_{n\ge0}a_nx^n=a_0+\sum_{n\ge1}a_nx^n[/tex]

[tex]y'=\displaystyle\sum_{n\ge0}(n+1)a_{n+1}x^n=a_1+\sum_{n\ge0}(n+1)a_{n+1}x^n[/tex]

[tex]y''=\displaystyle\sum_{n\ge0}(n+1)(n+2)a_{n+2}x^n[/tex]

Notice that [tex]y(0)=-3=a_0[/tex], and [tex]y'(0)=2=a_1[/tex].

Substitute these series into the ODE:

[tex](x-1)y''-xy'+y=0[/tex]

[tex]\displaystyle\sum_{n\ge0}(n+1)(n+2)a_{n+2}x^{n+1}-\sum_{n\ge0}(n+1)(n+2)a_{n+2}x^n-\sum_{n\ge0}(n+1)a_{n+1}x^{n+1}+\sum_{n\ge0}a_nx^n=0[/tex]

Shift the indices to get each series to include a [tex]x^n[/tex] term.

[tex]\displaystyle\sum_{n\ge1}n(n+1)a_{n+1}x^n-\sum_{n\ge0}(n+1)(n+2)a_{n+2}x^n-\sum_{n\ge1}na_nx^n+\sum_{n\ge0}a_nx^n=0[/tex]

Remove the first term from both series starting at [tex]n=0[/tex] to get all the series starting on the same index [tex]n=1[/tex]:

[tex]\displaystyle-2a_2+a_0+\sum_{n\ge1}n(n+1)a_{n+1}x^n-\sum_{n\ge1}(n+1)(n+2)a_{n+2}x^n-\sum_{n\ge1}na_nx^n+\sum_{n\ge1}a_nx^n=0[/tex]

[tex]\displaystyle-2a_2+a_0+\sum_{n\ge1}\bigg[n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-(n-1)a_n\bigg]x^n=0[/tex]

The coefficients are given recursively by

[tex]\begin{cases}a_0=-3\\a_1=2\\\\a_n=\dfrac{(n-2)(n-1)a_{n-1}-(n-3)a_{n-2}}{n(n-1)}&\text{for }n>1\end{cases}[/tex]

Let's see if we can find a pattern to these coefficients.

[tex]a_2=\dfrac{a_0}2=-\dfrac32=-\dfrac3{2!}[/tex]

[tex]a_3=\dfrac{2a_2}{3\cdot2}=-\dfrac12=-\dfrac3{3!}[/tex]

[tex]a_4=\dfrac{2\cdot3a_3-a_2}{4\cdot3}=-\dfrac18=-\dfrac3{4!}[/tex]

[tex]a_5=\dfrac{3\cdot4a_4-2a_3}{5\cdot4}=-\dfrac1{40}=-\dfrac3{5!}[/tex]

[tex]a_6=\dfrac{4\cdot5a_5-3a_4}{6\cdot5}=-\dfrac1{240}=-\dfrac3{6!}[/tex]

and so on, suggesting that

[tex]a_n=-\dfrac3{n!}[/tex]

which is also consistent with [tex]a_0=3[/tex]. However,

[tex]a_1=2\neq-\dfrac3{1!}=-3[/tex]

but we can adjust for this easily:

[tex]y(x)=-3+2x-\dfrac3{2!}x^2-\dfrac3{3!}x^3-\dfrac3{4!}x^4+\cdots[/tex]

[tex]y(x)=5x-3-3x-\dfrac3{2!}x^2-\dfrac3{3!}x^3-\dfrac3{4!}x^4+\cdots[/tex]

Now all the terms following [tex]5x[/tex] resemble an exponential series:

[tex]y(x)=5x-3\displaystyle\sum_{n\ge0}\frac{x^n}{n!}[/tex]

[tex]\implies\boxed{y(x)=5x-3e^x}[/tex]

The given differential equation is a second-order homogeneous differential equation. The power series method may not straightforwardly work for this equation due to the x dependence in the coefficients. Even using advanced techniques like the Frobenius method, the solution cannot be expressed as an elementary function.

The given differential equation (x − 1)y'' - xy' + y = 0 is an example of a second order homogeneous differential equation. To solve the equation using the power series method, let's assume a solution of the form y = ∑(from n=0 to ∞) c_n*x^n. Substituting this into the equation and comparing coefficients, we can find a relationship for the c_n's and thus the power series representation of the solution.

However, for this particular differential equation, the power series method is not straightforward because of the x dependence in the coefficients of y'' and y'. Therefore, the standard power series approach would not work, and we would need more advanced techniques like the Frobenius method which allows for non-constant coefficients.

Unfortunately, even with the Frobenius method, the solution isn't an elementary function, meaning the solution cannot be expressed in terms of a finite combination of basic arithmetic operations, exponentials, logarithms, constants, and solutions to algebraic equations.

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The given sequence is convergent with a limit of -3/2, while the series is divergent since its terms do not approach zero

The sequence in question is An = [6*n/(-4*n + 9)]. To find out if this sequence is convergent or divergent, we need to take the limit as n approaches infinity. As n approaches infinity, the 'n' in the numerator and the 'n' in the denominator will dominate, making the sequence asymptotically equivalent to -6/4 = -3/2. Thus, the sequence is convergent, and its limit is -3/2.

On the other hand, the series ∑n=1[infinity]( An ) is the sum of the terms in the sequence. We can see that as n approaches infinity, the terms of this series do not approach zero, which is a necessary condition for a series to be convergent (using the nth term test). Therefore, the series is divergent.

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Answer:

59 coins

Step-by-step explanation:

The number of coins in Anthony's collection is 294

Using the parameters given for our Calculation;

Total number of coins now :

Six times as many coins can be calculated thus :

Therefore, the number of coins in Anthony's collection is 294

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Answer:

[tex]CV=\frac{0.1252}{1.57}=0.07975[/tex]

[tex]CV=\frac{0.1317}{1.72}=0.07657[/tex]

The relative variability is almost equal in both samples a slight greater variability can be noticed in the first sample.

Step-by-step explanation:

The coefficient of variation of a sample is defined as the ratio between the mean standard deviation and the sample mean. And it represents the percentage relation of the variation of the data with respect to the average.

[tex]CV=\frac{S}{\bar X}[/tex]

In the case of the first sample you have:

[tex]CV=\frac{0.1252}{1.57}=0.07975[/tex]

In the case of the second sample you have:

[tex]CV=\frac{0.1317}{1.72}=0.07657[/tex]

The relative variability is almost equal in both samples a slight greater variability can be noticed in the first sample.

Answer: There are 3.36 ounces of ground almonds in 1 cup.

Step-by-step explanation:

Since we have given that

1 pint = 0.42 pounds

As we know that

1 cup = 0.5 pints

1 pound = 16 ounces

So, We need to find the number of ounces.

As 1 pint = 0.42 pounds = 0.42 × 16 = 6.72 ounces

0.5 pints is given by

[tex]6.72\times 0.5\\\\=3.36\ ounces[/tex]

Hence, there are 3.36 ounces of ground almonds in 1 cup.

To find out how many ounces are in one cup of ground almonds if 1 pint (2 cups) weighs 0.42 pounds, you divide 0.42 pounds by 2 to get the weight per cup, then multiply by 16 to convert pounds to ounces, resulting in 3.36 ounces per cup.

The question involves converting weight measurements from one unit to another, specifically from pounds to ounces. To do this, you use the conversion factor of 16, because there are 16 ounces in 1 pound. Applying this to the recipe question:

1 pint of ground almonds weighs 0.42 pounds. Since 1 pint equals 2 cups, this weight corresponds to 2 cups of ground almonds.

To find out how many ounces 1 cup of ground almonds weighs, first divide the total weight by the number of cups:

0.42 pounds ÷ 2 cups = 0.21 pounds per cup.

Then, convert pounds to ounces:

0.21 pounds × 16 ounces/pound = 3.36 ounces.

So, for the recipe, you should use 3.36 ounces of ground almonds.

Answer:  10

Step-by-step explanation:

The formula to find the sample size is given by :-

[tex]n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2[/tex]

Given : Significance level : [tex]\alpha=1-0.99=0.1[/tex]

Critical z-value=[tex]z_{\alpha/2}=2.576[/tex]

Margin of error : E=5

Standard deviation : [tex]\sigma=6[/tex]

Now, the required sample size will be :_

[tex]n=(\dfrac{(2.576)\ 6}{5})^2=9.55551744\approx10[/tex]

Hence, the final sample required to be of 10 .

(n+4) +7 remove the parenthesis

n+4+7 add the same number answer is n +11

Step-by-step explanation:

For each case we have the next step by step solution.

Answer: Our required probability is [tex]\dfrac{11}{20}[/tex]

Step-by-step explanation:

Since we have given that

Number of red marbles = 8

Number of blue marbles = 2

Number of yellow marbles = 7

Number of green marbles = 3

So, Total number of marbles = 8 + 2 + 7 + 3 = 20

So, Probability for selecting a red marble and then selecting a green marbles is given by

P(red) + P(green) is equal to

[tex]\dfrac{8}{20}+\dfrac{3}{20}\\\\=\dfrac{8+3}{20}\\\\=\dfrac{11}{20}[/tex]

Hence, our required probability is [tex]\dfrac{11}{20}[/tex]

Answer: [tex]8.76\%[/tex]

Step-by-step explanation:

The formula to find the final amount after getting simple interest :

[tex]A=P(1+rt)[/tex], where P is the principal amount , r is rate of interest ( in decimal )and t is time(years).

Given : Justin deposited $2,000 into an account 5 years ago.

i.e. P = $2,000 and  t= 5 years

He has just withdrawn $2,876.

i.e. we assume that A = $2876

Now, Put all the values in the formula , we get

[tex](2876)=(2000)(1+r(5))\\\\\Rightarrow\ 1+5r=\dfrac{2876}{2000}\\\\\Rightarrow\ 1+5r=1.438\\\\\Righhtarrow\ 5r=0.438\\\\\Rightarrow\ r=\dfrac{0.438}{5}=0.0876[/tex]

In percent, [tex]r=0.0876\times100=8.76\%[/tex]

hence, He earned [tex]8.76\%[/tex] of interest on account.

Answer:

Step-by-step explanation:

The given information can be tabulated as follows:

                          Graphics G     Printing P            Total

X                                      3                 2                    5

Y                                      1                  1                      2

Available                       21                19

We have the constraints as

[tex]3x+y\leq 21\\2x+y\leq 19\\x\leq 2\\y\leq 15[/tex]

Thus we have solutions as

[tex]0\leq x\leq 2\\0\leq y\leq 15[/tex]

Answer:

There is a 35.7% probability that this deal will not materialize.

Step-by-step explanation:

This problem can be solved by a simple system of equations.

-I am going to say that x is the probability that this deal materializes and y is the probability that this deal does not materialize.

The sum of all probabilities is always 100%. So

[tex]1) x + y = 100[/tex].

Bob, the proprietor of Midland Lumber, believes that the odds in favor of a business deal going through are 9 to 5.

Mathematically, this means that:

[tex]2) \frac{x}{y} = \frac{9}{5}[/tex]

We want to find the value of y. So, we can write x as a function of y in equation 2), and replace it in equation 1).

Solution:

[tex]\frac{x}{y} = \frac{9}{5}[/tex]

[tex]x = \frac{9y}{5}[/tex]

[tex]x + y = 100[/tex]

[tex]\frac{9y}{5} + y = 100[/tex]

[tex]\frac{14y}{5} = 100[/tex]

[tex]14y = 500[/tex]

[tex]y = \frac{500}{14}[/tex]

[tex]y = 35.7[/tex]

There is a 35.7% probability that this deal will not materialize.

Answer: P means "This statement is false"

then, P is a "function" of some statement,

if i write P( 3> 1932) this could be read as:

3>1932, this statement is false.

You could see that 3> 1932 is false, so P( 3>1932) is true.

Then you could se P(x) at something that is false if x is true, and true if x is false, so p is a negation.

Answer:

One proof can be as follows:

Step-by-step explanation:

We have that [tex]g.c.d(a,b)=1[/tex] and [tex]a=cp, b=dq[/tex] for some integers [tex]p, q[/tex], since [tex]c[/tex] divides [tex]a[/tex] and [tex]d[/tex] divides [tex]b[/tex].  By the Bezout identity two numbers [tex]a,b[/tex] are relatively primes if and only if there exists integers [tex]x,y[/tex] such that

[tex]ax+by=1[/tex]

Then, we can write

[tex]1=ax+by=(cp)x+(dq)y=c(px)+d(qy)=cx'+dy'[/tex]

Then [tex]c[/tex] and [tex]d[/tex] are relatively primes, that is to say,

[tex]g.c.d(c,d)=1[/tex]

Answer: There is increase of 4.255 in the amount of carbon in the atmosphere.

Step-by-step explanation:

Since we have given that

Concentration of carbon in Earth's atmosphere in 1800 = 280 ppm

Concentration of carbon in Earth's atmosphere in 2015 = 399 ppm

We need to find the percentage increase in the amount of carbon in the atmosphere.

So, Difference = 399-280 = 119 ppm

so, percentage increase in the amount of carbon is given by

[tex]\dfrac{Difference}{Original}\times 100\\\\=\dfrac{119}{280}\times 100\\\\=\dfrac{11900}{280}\\\\=42.5\%[/tex]

Hence, there is increase of 4.255 in the amount of carbon in the atmosphere.

Answer:

[tex]1\,\,cm/min[/tex]

Step-by-step explanation:

Let V be the volume of cube and x be it's side .

We know that volume of cube is [tex]\left ( side \right )^{3}[/tex] i.e., [tex]x^3[/tex]

Given :

[tex]\frac{\mathrm{d} V}{\mathrm{d} t}=1200\,\,cm^3/min[/tex]

[tex]x=20\,\,cm[/tex]

To find : [tex]\frac{\mathrm{d} x}{\mathrm{d} t}[/tex]

Solution :

Consider equation [tex]V=x^3[/tex]

On differentiating both sides with respect to t , we get

[tex]\frac{\mathrm{d} V}{\mathrm{d} t}=3x^2\left ( \frac{\mathrm{d} x}{\mathrm{d} t} \right )\\1200=3(20)^2\left ( \frac{\mathrm{d} x}{\mathrm{d} t} \right )\\\frac{\mathrm{d} x}{\mathrm{d} t} =\frac{1200}{3(20)^2}=\frac{1200}{3\times 400}=\frac{1200}{1200}=1\,\,cm/min[/tex]

So,

Length of the side is increasing at the rate of [tex]1\,\,cm/min[/tex]

Step-by-step explanation:

We want to show that

[tex]=A \setminus (B \cup C) = (A\setminus B) \cap (A\setminus C)[/tex]

To prove it we just use the definition of [tex]X\setminus Y = X \cap Y^c[/tex]

So, we start from the left hand side:

[tex]=A \setminus (B \cup C) = A \cap (B \cup C)^c[/tex] (by definition)

[tex]=A \cap (B^c \cap C^c)[/tex] (by DeMorgan's laws)

[tex]=A \cap B^c \cap C^c[/tex] (since intersection is associative)

[tex]=A \cap B^c \cap A \cap C^c[/tex] (since intersecting once or twice A doesn't make any difference)

[tex]=(A \cap B^c) \cap (A \cap C^c)[/tex] (since again intersection is associative)

[tex]=(A\setminus B) \cap (A \setminus C)[/tex] (by definition)

And so we have reached our right hand side.

Answer:

There are 100 milligrams of metoclopramide HCl in each milliliter of the prescription

Step-by-step explanation:

When the prescription says Purified water qs ad 100 mL means that if we were to make this, we should add the quantities given and then, fill it up with water until we have 100 mL of solution, being the key words qs ad, meaning sufficient quantity to get the amount of mixture given.

Then, knowing there is 10 grams of metoclopramide HCl per 100 mL of prescription, that means there is (1 gram = 1000 milligrams) 10000 milligrams of metoclopramide HCl per 100 mL of prescription. That is a concentration given in a mass/volume way.

Knowing the concentration, we can calculate it per mL instead of per 100 mL

[tex]Concentration_{metoclopramide HCL}= \frac{10000mg}{100mL} =100 \frac{mg}{mL}[/tex]

Answer: 0.0011

Step-by-step explanation:

By using the standard normal distribution table , the probability that Z is to the left of 3.05 is [tex]P(z<3.05)= 0.9989[/tex]

We know that the probability that Z is to the right of z is given by :-

[tex]P(Z>z)=1-P(Z<z)[/tex]

Similarly,  the probability that Z is to the right of 3.05 will be :-

[tex]P(Z>3.05)=1-P(Z<3.05)=1-0.9989=0.0011[/tex]

Hence, the probability that Z is to the right of 3.05 = 0.0011

Answer:

The man had a displacement of 12.88 m southeastward

Step-by-step explanation:

The path of man forms a right triangle. The first two magnitudes given in the problem form the legs and the displacement that we must calculate forms the hypotenuse of the triangle. To do this we will use the equation of the pythagorean theorem.

H = magnitude of displacement

[tex]H^2 = \sqrt{L_1^2 + L_2^2} = \sqrt{6.70^2 + 11.0^2} = \sqrt{165.89}   =12.88 m[/tex]

using the graphic method, we will realize that the displacement is oriented towards the southeast

Answer:

See explanation below.

Step-by-step explanation:

The prime numbers are bold:

1  2  3 4  5 6  7  8  9  10  11 12  13  14  15  16  17

18  19  20  21  22  23  24  25  26  27  28  29  30  31

a) We can see that as we go higher, twin primes seem less frequent but even considering that, there is an infinite number of twin primes. If you go high enough you will still eventually find a prime that is separated from the next prime number by just one composite number.

b) I think it's interesting the amount of time that has been devoted to prove this conjecture and the amount of mathematicians who have been involved in this. One of the most interesting facts was that in 2004 a purported proof (by R. F. Arenstorf) of the conjecture was published but a serious error was found on it so the conjecture remains open.

Answer:

160 lbs = 72.57kg

Step-by-step explanation:

This can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

Each lb has 0.45kg. How many kg are there in 160lbs. So:

1lb - 0.45kg

160 lbs - xkg

[tex]x = 0.45*160[/tex]

[tex]x = 72.57[/tex] kg

160 lbs = 72.57kg

Answer:

b.

917 sheet sets.

Step-by-step explanation:

We are asked to find the total number of sheet sets received by linens department.

To find the total number of sheet sets received by linens department, we will add the number of dozens of each sheet.

[tex]\text{Total number of sheet sets received in dozens}=19\frac{1}{2}+33\frac{2}{3}+23\frac{1}{4}[/tex]

[tex]\text{Total number of sheet sets received in dozens}=\frac{39}{2}+\frac{101}{3}+\frac{93}{4}[/tex]

Make common denominator:

[tex]\text{Total number of sheet sets received in dozens}=\frac{39*6}{2*6}+\frac{101*4}{3*4}+\frac{93*3}{4*3}[/tex]

[tex]\text{Total number of sheet sets received in dozens}=\frac{234}{12}+\frac{404}{12}+\frac{279}{12}[/tex]

[tex]\text{Total number of sheet sets received in dozens}=\frac{234+404+279}{12}[/tex]

[tex]\text{Total number of sheet sets received in dozens}=\frac{917}{12}[/tex]

To find the number of sheets, we will multiply number of dozens of sheets by 12 as 1 dozen equals 12.

[tex]\text{Total number of sheet sets received}=\frac{917}{12}\times 12[/tex]

[tex]\text{Total number of sheet sets received}=917[/tex]

Therefore, the total number of sheet sets received is 917.