Instructions for a chemical procedure state to mix salt, baking soda, and water in a 20:15:10 ratio by mass. How many grams of water would be required to make a mixture that contains 24 grams of baking soda?

Instructions For A Chemical Procedure State To Mix Salt, Baking Soda, And Water In A 20:15:10 Ratio By

Answers

Answer 1

Answer:

16 g of water.

Step-by-step explanation:

salt : baking soda : water =  20 : 15 : 10

If we have  24 g of baking soda that is 24/15 = 8/5 times of 15.

So by proportion the amount of water would be 10 * 8/5 = 16 grams.

Answer 2

The mass of water in the mixture is 16 gm

What is Ratio and Proportion ?

When a number is divisible by another number then they can be written in the form of ratio p :q , When two ratios are equal they are said to be in proportion.

It is given that

salt, baking soda, and water in a 20:15:10 ratio by mass are mixed

mixture contains 24 grams of baking soda

Mass of Water = ?

Baking Soda : Water = 15 : 10

Let the mass of water is x

then the ratio is 24 : x

As both these ratios are equal

15 : 10 = 24 : x

15 / 10 = 24 / x

x = 24 * 10 / 15

x = 16 gm

Therefore the mass of water in the mixture is 16 gm.

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Related Questions

Find the probability that Z is to the right of 3.05.

Answers

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

The physician orders an IV infusion of D5W 1000 ml to infuse over the next eight hours. The IV tubing that you are using delivers 10 gtt/ml. What is the correct rate of flow (drops per minute)? _gtt/min (rounded to the nearest drop)

Answers

Answer: 10gtt/ml means that in 10 drops there is a ml of the solution.

Now, you need 1000ml in 8 hours, and want to know the correct rate of flow in drops per minute.

first, 8 hours are 8*60 = 480 minutes.

then you need to infuse 1000ml in 480 minutes, so if you infuse at a constant rate, you need to infuse 1000/480 = 2.083 ml/min.

And we know that 10 drops are equivalent to 1 ml, then 2.083*10= 20.8 drops are equivalent a 2.083 ml, rounding it up, you get 21 drops for the dose.

So the correct rate of flow will be 21 drops per minute.

Final answer:

To find the correct rate of flow for an IV infusion, convert the time to minutes, divide the total volume by the total time to find the rate in ml/min, then multiply by the drip factor to convert to drops/min. Rounding to the nearest drop, we get 21 gtt/min.

Explanation:

To calculate the correct rate of flow for an IV infusion, we need to use the given information: the volume of the IV infusion (D5W 1000 ml), the time over which it must infuse (8 hours), and the IV tubing drip factor (10 gtt/ml).

First, convert the time from hours to minutes as we're interested in drops per minute: 8 hours * 60 minutes/hour = 480 minutes.

Next, we divide the total volume by the total time: 1000 ml / 480 minutes = ~2.08 ml/min. This is the rate in ml/min.

Finally, we multiply by the drip factor to get the rate in drops per minute: 2.08 ml/min * 10 gtt/ml = 20.8 gtt/min.

Rounding to the nearest drop gives us a rate of 21 gtt/min.

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Let p stand for "This statement is false." What can be said about the truth value of p. (Hint: Did we really assign a truth value to p? See Example 5 for a discussion of truth value assignment.)

Answers

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.


Calculate (a) the number of milligrams of metoclopramide HCl in each milliliter of the prescription:

Metoclopramide HCl 10 g

Methylparaben 50 mg

Propylparaben 20 mg

NaCl 800 mg

Purifed water qs ad 100 mL

Answers

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]

The system of equation, if a b are arbitrary numbers x+2y-3z- a 2x+4y-6z 2a+2 has (A) No solutions regardless of values of a and b (B) Infinitely many solutions regardless of values of a and b (C) a unique solution if a b-0 D) a unique solution regardless of values of a and b

Answers

Answer:

(A) No solutions regardless of values of a and b.

Step-by-step explanation:

Asumming that the system of equations is [tex]x+2y-3z=a\\ 2x+4y-6z=2a+2[/tex], the corresponding augmented matrix of the system is [tex]\left[\begin{array}{cccc}1&2&-3&a\\2&4&-6&2a+2\end{array}\right][/tex].

If two time the row 1 is subtracted to row 1, we get the following matrix

[tex]\left[\begin{array}{cccc}1&2&-3&a\\0&0&0&2a+2-2a\end{array}\right][/tex].

Then the system has no solutions regardless of values of a and b.

what is the answer of 2.8 plus 7.2

Answers

Answer:

10.022

Step-by-step explanation:

1. 49/9

2. 106/25

3. 10.022

4. When you add two rational numbers, each number can be written as a :

fraction

5. The sum of two fractions can always  be written as a : fraction

6. Therefore, the  sum of two rational numbers will always be : rational

A man in a maze makes three consecutive displacements. His first displacement is 6.70 m westward, and the second is 11.0 m northward. At the end of his third displacement he is back to where he started. Use the graphical method to find the magnitude and direction of his third displacement.

Answers

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

Consider a fair coin which when tossed results in either heads (H) or tails (T). If the coin is tossed TWO times 1. List all possible outcomes. (Order matters here. So, HT and TH are not the same outcome.) 2. Write the sample space. 3. List ALL possible events and compute the probability of each event, assuming that the probability of each possible outcome from part (a) is equal. (Keep in mind that there should be many more events than outcomes and not all events will have the same probability.)

Answers

Answer:

Sample space = {(T,T), (T,H), (HT), (HH)}

Step-by-step explanation:

We are given a fair coin which when tossed one times either gives heads(H) or tails(T).

Now, the same coin is tossed two times.

1) All the possible outcomes

Tails followed by tails

Rails followed by heads

Heads followed by a tail

Heads followed by heads

2) Sample space

{(T,T), (T,H), (HT), (HH)}

3) Formula:

[tex]Probability = \displaystyle\frac{\text{Favourable outcome}}{\text{Total number of outcome}}[/tex]

Using the above formula, we can compute the following probabilities.

Probability((T,T)) =[tex]\frac{1}{4}[/tex]

Probability((T,H)) =[tex]\frac{1}{4}[/tex]

Probability((H,T)) =[tex]\frac{1}{4}[/tex]

Probability((H, H)) =[tex]\frac{1}{4}[/tex]

Probability(Atleast one tails) = [tex]\frac{3}{4}[/tex]

Probability(Atleast one heads) = [tex]\frac{3}{4}[/tex]

Probability(Exactly one tails) = [tex]\frac{2}{4}[/tex]

Probability(Exactly one heads) = [tex]\frac{2}{4}[/tex]

Ben earns $9 per hour and $6 for each delivery 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?

Answers

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.

Find the lengths of the sides of the triangle PQR. P(2, −3, −4), Q(8, 0, 2), R(11, −6, −4) |PQ| = Incorrect: Your answer is incorrect. |QR| = |RP| = Is it a right triangle? Yes No Is it an isosceles triangle? Yes No

Answers

Answer:

the length PQ is 9 units,the length QR is 9 units,the length PR is 9.48 units,the triangle is not a right triangle,this is a isosceles triangle

Step-by-step explanation:

Hello, I think I can help you with this

If  you know two points, the distance between then its given by:

[tex]P1(x_{1},y_{1},z_{1} ) \\P2(x_{2},y_{2},z_{2})\\\\d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1}  )^{2}+(z_{2}-z_{1} )^{2} }[/tex]

Step 1

use the formula to find the length PQ

Let

P1=P=P(2, −3, −4)

P2=Q=Q(8, 0, 2)

[tex]d=\sqrt{(8-2)^{2} +(0-(-3))^{2}+(2-(-4))^{2}} \\ d=\sqrt{(6)^{2} +(3)^{2}+(6 )^{2}}} \\d=\sqrt{36+9+36}\\d=\sqrt{81} \\d=9\\[/tex]

the length PQ is 9 units

Step 2

use the formula to find the length QR

Let

P1=Q=Q(8, 0, 2)

P2=R= R(11, −6, −4)

[tex]d=\sqrt{(11-8)^{2} +(6-0))^{2}+(-4-2 )^{2}}  \\\\\\d=\sqrt{(3)^{2} +(6)^{2}+(-6 )^{2}}} \\d=\sqrt{9+36+36}\\d=\sqrt{81} \\d=9\\[/tex]

the length QR is 9 units

Step 3

use the formula to find the length PR

Let

P1=P(2, −3, −4)

P2=R= R(11, −6, −4)

[tex]d=\sqrt{(11-2)^{2} +(-6-(-3)))^{2}+(-4-4 )^{2}}  \\\\\\d=\sqrt{(9)^{2} +(-6+3)^{2}+(-4-(-4) )^{2}}} \\d=\sqrt{81+9+0}\\d=\sqrt{90} \\d=9.48\\[/tex]

the length PR is 9.48 units

Step 4

is it a right triangle?

you can check this by using:

[tex]side^{2} +side^{2}=hypotenuse ^{2}[/tex]

Let

side 1=side 2= 9

hypotenuse = 9.48

Put the values into the equation

[tex]9^{2} +9^{2} =9.48^{2}\\ 81+81=90\\162=90,false[/tex]

Hence, the triangle is not a right triangle

Step 5

is it an isosceles triangle?

In geometry, an isosceles triangle is a type of triangle that has two sides of equal length.

Now side PQ=QR, so this is a isosceles triangle

Have a great day

(7)-0, at the points x 71, 72, 73, 74, and 7.5 Use Euler's method with step size 0.1 to approximate the solution to the initial value pro oblemy - 2x+y The approximate solution to y'=2x-y?.y(7)=0, at the point x = 71 is (Round to five decimal places as needed.)

Answers

Answer:

2.68

Step-by-step explanation:

We are given that [tex]x_0=7,x_1=7.1,x_2=7.2,x_3=7.3,x_4=7.4,x_5=7.5[/tex]

h=0.1

y'=2x-y

y(7)=0,f(x,y)=2x-y

[tex]x_0=7,y_0=0[/tex]

We have to find the approximate solution to the initial problem at x=7.1

[tex]y_1=y_0+hf(x_0,y_0)[/tex]

Substitute the value then, we get

[tex]y_1=0+(0.1)(2(7)-0)=0+(0.1)(14)=1.4[/tex]

[tex]y_1=1.4[/tex]

[tex]x_1=x_0+h=7+0.1=7.1[/tex]

[tex]y_2=y_1+hf(x_1,y_1)[/tex]

Substitute the values then, we get

[tex]y_2=1.4+(0.1)(2(7.1)-1.4)=1.4+(0.1)(14.2-1.4)=1.4+(0.1)(12.8)=1.4+1.28[/tex]

[tex]y_2=1.4+1.28=2.68[/tex]

Hence, the approximation solution to the initial problem at x=7.1 is =2.68

Given:
An = [6 n/(-4 n + 9)]
For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise.

(a) The sequence {An }._________________
(b) The series ∑n=1[infinity]( An )________________

Answers

Final answer:

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

Explanation:

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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A group of friends goes out for single-scoop ice-cream cones. There are sugar cones, cake cones and waffle cones. But there are only five flavors of ice-cream left (peppermint, horehound, chocolate malt, gingerbread, and squirrel). How many cone/ice cream combinations can be ordered?

Answers

Answer: 15

Step-by-step explanation:

Given : The number of kinds of ice-cream cones ( sugar cones, cake cones and waffle cones)=3

The number of flavors of ice-creams =5

By using the fundamental principle of counting , we have

The number of possible cone/ice cream combinations can be ordered will be :-

[tex]5\times3=15[/tex]

Hence, the number of possible cone/ice cream combinations can be ordered =15

In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.3%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.

Joe $

Jill $

Answers

Answer:

Ans. Joe will have $720,862.28 and Jill will have $819,348.90 after 30 years.

Step-by-step explanation:

Hi, since the interest is compounded with each payment, the effective rate of Joe is exactly equal to its compounded rate, that is 9.3%, but in the case of Jill, this rate is compounded weekly, this means that we have to divide 9.3% by 52 (which are the weeks in a year) in order to obtain an effective rate, in our case, effective weekly.

On the other hand, the time for Joe is pretty straight forward, he saves for 30 years at an effective annual interest rate of 9.3%, but Jill saves for 30*52=1560 weeks, at a rate of 0.1788% effective weekly.

They both have to use the following formula in order to find how much money will they have after 30 years of savings.

[tex]FutureValue=\frac{A((1+r)^{n}-1) }{r}[/tex]

In the case of Joe, this should look like this

[tex]FutureValue=\frac{5,000((1+0.093)^{30}-1) }{0.093} =720,862.28[/tex]

In the case of Jill, this is how this should look like.

[tex]FutureValue=\frac{96.15((1+0.001788)^{1560}-1) }{0.001788} =819,348.90[/tex]

Best of luck.

Suppose you are planning to sample cat owners to determine the average number of cans of cat food they purchase monthly. The following standards have been set: a confidence level of 99 percent and an error of less than 5 units. Past research has indicated that the standard deviation should be 6 units. What is the final sample required?

Answers

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 .

1. Suppose that A , B and C are sets. Show that A \ (B U C) (A \ B) n (A \ C).

Answers

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.

Suppose that for some [tex]a,b,c[/tex] we have [tex]a+b+c = 1[/tex], [tex]ab+ac+bc = abc = -4[/tex]. What is [tex] a^3+b^3+c^3?[/tex]

Answers

Consider the cubic polynomial,

[tex](x+a)(x+b)(x+c)[/tex]

Expanding this gives

[tex]x^3+(a+b+c)x^2+(ab+ac+bc)x+abc=x^3+x^2-4x-4[/tex]

We can factor this by grouping,

[tex]x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x^2-4)(x+1)=(x-2)(x+2)(x+1)[/tex]

Then letting [tex]a=-2[/tex], [tex]b=2[/tex], and [tex]c=1[/tex] gives [tex]a^3+b^3+c^3=-8+8+1=\boxed1[/tex]

Cheese costs $4.40 per pound. Find the cost per kilogram. (1kg = 2.2lb)

Answers

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

What is the answer to (n+4) +7 =

Answers

(n+4) +7 remove the parenthesis

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

Find q, r in \mathbb{Z} so that 105 = 11q + r

with 0 \leq r < 11 as in the division algorithm

Answers

Answer:

[tex]q=9\,,\,r=6[/tex]

Step-by-step explanation:

Division Algorithm :

As per division algorithm , for numbers a and b , there exist numbers q and r such that [tex]a=bq+r\,\,,0\leq r< b[/tex]

Here ,

a = Dividend

b = Divisor

q = quotient

r = remainder

Given : 105 = 11q + r such that [tex]0 \leq r < 11[/tex]

Here, clearly a = 105 , b = 11

To find : q and r

Solution : On dividing 105 by 11 , we get [tex]105=11\times 9+6[/tex]

On comparing [tex]105=11\times 9+6[/tex] with [tex]a=bq+r\,\,,0\leq r< b[/tex] , we get [tex]q=9\,,\,r=6[/tex]

A recipe calls for 1 cup of ground almonds. How many ounces of ground almonds should you use for this recipe if 1 pint of ground almonds weighs 0.42 pounds?

Answers

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.

Solve each of the following systems by Gauss-Jordan elimination. (b) X1-2x2+ x3- 4x4=1 X1+3x2 + 7x3 + 2x4=2 -12x2-11x3- 16x4 5 (a) 5x1+2x2 +6x3= 0 -2x1 +x2+3x3 = 0

Answers

Answer:

a) The set of solutions is [tex]\{(0,-3x_3,x_3): x_3\; \text{es un real}\}[/tex] y b) the set of solutions is [tex]\{(-6,\frac{-41}{17}-\frac{30}{17}x_4 , \frac{37}{17}+\frac{8}{17} x_4 ,x_4): x_4\;\text{es un real}\}[/tex].

Step-by-step explanation:

a) Let's first find the echelon form of the matrix [tex]\left[\begin{array}{ccc}5&2&6\\-2&1&3\end{array}\right][/tex].

We add [tex]\frac{2}{5}[/tex] from row 1 to row 2 and we obtain the matrix [tex]\left[\begin{array}{ccc}5&2&6\\0&\frac{9}{5} &\frac{27}{5}\end{array}\right][/tex]From the previous matrix, we multiply row 1 by [tex]\frac{1}{5}[/tex] and the row 2 by [tex]\frac{5}{9}[/tex] and we obtain the matrix [tex]\left[\begin{array}{ccc}1&\frac{2}{5} &\frac{6}{5} \\0&1&3\end{array}\right][/tex]. This matrix is the echelon form of the initial matrix.

The system has a free variable (x3).

x2+3x3=0, then x2=-3x3 0=x1+[tex]\frac{2}{5}[/tex]x2+[tex]\frac{6}{5}[/tex]x3=

       x1+[tex]\frac{2}{5}[/tex](-3x3)+[tex]\frac{6}{5}[/tex]x3=

      x1-[tex]\frac{6}{5}[/tex]x3+[tex]\frac{6}{5}[/tex]x3

     then x1=0.

The system has infinite solutions of the form (x1,x2,x3)=(0,-3x3,x3), where x3 is a real number.

b) Let's first find the echelon form of the aumented matrix [tex]\left[\begin{array}{ccccc}1&-2&1&-4&1\\1&3&7&2&2\\0&-12&-11&-16&5\end{array}\right][/tex].

To row 2 we subtract row 1 and we obtain the matrix [tex]\left[\begin{array}{ccccc}1&-2&1&-4&1\\0&5&6&6&1\\0&-12&-11&-16&5\end{array}\right][/tex]From the previous matrix, we add to row 3, [tex]\frac{12}{5}[/tex] of row 2 and we obtain the matrix [tex]\left[\begin{array}{ccccc}1&-2&1&-4&1\\0&5&6&6&1\\0&0&\frac{17}{5}&\frac{-8}{5}&\frac{37}{5}   \end{array}\right][/tex].From the previous matrix, we multiply row 2 by [tex]\frac{1}{5}[/tex] and the row 3 by [tex]\frac{5}{17}[/tex] and we obtain the matrix [tex]\left[\begin{array}{ccccc}1&-2&1&-4&1\\0&1&\frac{6}{5} &\frac{6}{5}&\frac{1}{5}\\0&0&1&\frac{-8}{17}&\frac{37}{17} \end{array}\right][/tex]. This matrix is the echelon form of the initial matrix.

The system has a free variable (x4).

x3-[tex]\frac{8}{17}[/tex]x4=[tex]\frac{37}{17}[/tex], then x3=[tex]\frac{37}{17}[/tex]+ [tex]\frac{8}{17}x4.x2+[tex]\frac{6}{5}[/tex]x3+[tex]\frac{6}{5}[/tex]x4=[tex]\frac{1}{5}[/tex], x2+[tex]\frac{6}{5}[/tex]([tex]\frac{37}{17}[/tex]+[tex]\frac{8}{17}x4)+[tex]\frac{6}{5}[/tex]x4=[tex]\frac{1}{5}[/tex], then

      x2=[tex]\frac{-41}{17}-\frac{30}{17}[/tex]x4.

x1-2x2+x3-4x4=1, x1+[tex]\frac{82}{17}[/tex]+[tex]\frac{60}{17}[/tex]x4+[tex]\frac{37}{17}[/tex]+[tex]\frac{8}{17}[/tex]x4-4x4=1, then x1=[tex]1-\frac{119}{17}=-6[/tex]

The system has infinite solutions of the form (x1,x2,x3,x4)=(-6,[tex]\frac{-41}{17}-\frac{30}{17}[/tex]x4,[tex]\frac{37}{17}[/tex]+ [tex]\frac{8}{17}[/tex]x4,x4), where x4 is a real number.

Find the greatest common divisor of 252 and 60

Answers

Answer:

12

Step-by-step explanation:

The greatest common divisor(gcd) is also known by the name highest common factor(hcf), greatest common factor(gcf).

Greatest common factor of two number can be defined as the highest  integer that divides both the number.

We have to find greatest common divisor of 252 and 60.

The prime factorization of 252 is:

252 = 2×2×3×3×7

The prime factorization of 60 is:.

60 = 2×2×3×5

Common factors are: 2×2×3

Hence, greatest common divisor of 252 and 60 = 2×2×3 = 12

You are to give an injection of a drug. The dosage is 0.4 mg per kilogram of bod The concentration of the drug in vial is listed as 500 ug/ml. The patient's chart Hists weight as 168 pounds. How many milliliters (= cc) are you to inject? Patient's weight Concentration of drug Show calculations: mg/ml

Answers

Answer:

You inject 60.9628 milliliters of dosage

Step-by-step explanation:

1 pound = 0.453592kg,

Patient's weight in pounds = 168

Patient's weight in kg = [tex]76.2035  kg[/tex]

Now we are given that The dosage is 0.4 mg per kilogram of bod

So, dosage = [tex]0.4 \times 76.2035 mg = 30.4814 mg[/tex]

1 microgram = 0.001 mg

Concentration of drug = [tex]500 micrograms/ml = 500 * 0.001 mg/ml = 0.5 mg/ml[/tex]

Now we are supposed to find How many milliliters (= cc) are you to inject?

So,milliliters of dosage required to inject = [tex]\frac{30.4814}{0.5} = 60.9628[/tex]

Hence you inject 60.9628 milliliters of dosage

In European roulette, the wheel is divided into 37 compartments numbered 1 through 36 and 0. (In American roulette there are 38 compartments numbered 1 through 36, 0, and 00.) One-half of the numbers 1 through 36 are red, the other half are black, and the number 0 is green. Find the expected value of the winnings on a $7 bet placed on black in European roulette. (Round your answer to three decimal places.)

Answers

Answer:

The expectation is -$0.189.

Step-by-step explanation:

Consider the provided information.

In European roulette, the wheel is divided into 37 compartments numbered 1 through 36 and 0.

One-half of the numbers 1 through 36 are red, the other half are black, and the number 0 is green.

We need to find the expected value of the winnings on a $7 bet placed on black in European roulette.

Here the half of 36 is 18.

That means 18 compartments are red and 18 are black.

The probability of getting black in European roulette is 18/37

The probability of not getting black in European roulette is 19/37. Because 18 are red and 1 is green.

If the ball lands on a black number, the player wins the amount of his bet.

The bet is ball will land on a black number.

The favorable outcomes are 18/37 and unfavorable are 19/37.

Let S be possible numerical outcomes of an experiment and P(S) be the probability.

The expectation can be calculated as:

E(x) = sum of S × P(S)

For[tex] S_1 = 7[/tex]

[tex]P(S_1) = \frac{18}{37}[/tex]

For [tex]S_2 = -7[/tex](negative sign represents the loss)

[tex]P(S_2) = \frac{19}{37}[/tex]

Now, use the above formula.

[tex]E(x) = 7\times \frac{18}{37}-7\times \frac{19}{37}\\E(x) = -0.189[/tex]

Hence, the expectation is -$0.189.

Bob, the proprietor of Midland Lumber, believes that the odds in favor of a business deal going through are 9 to 5. What is the (subjective) probability that this deal will not materialize? (Round your answer to three decimal places.)

Answers

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.

Before the industrial revolution in 1800 the concentration of carbon in Earth’s atmo- sphere was 280 ppm. The concentration in 2015 was 399 ppm. What is the percent increase in the amount of carbon in the atmosphere?

Answers

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.

Round the following number to the indicated place. 66.1086 to hundredths

Answers

Answer:

66.11

Step-by-step explanation:

We are given that  a number

66.1086

We have to round the number to hundredths

Place of 6=One;s

Place of second 6=Tens

Place of 1=Tenths

Place of 0=Hundredths

Place of 8=Thousandths

Place of 6=Ten thousandths

Thousandths place is 8 which is greater than 5 therefore, one will be added to hundredth place and other number on the left side of  hundredth place remain same and the numbers on the right side of hundredth place will be replace by zero.

Therefore, the given number round to hundredths=66.11

A minor league baseball team plays 128 games a seanson. If the tam won 16 more than three times as many games as they lost how many wins and losses did the team have.

Answers

The baseball team won 100 games and lost 28 games. We found the number of losses by solving the equation formed by the relationship between wins and losses, and the total number of games played.

To solve the problem, let's denote the number of games the baseball team lost as L, and hence, the games they won would be 3L + 16 as per the condition given. Considering that the team played a total of 128 games, the equation representing the total number of games played is:

L + (3L + 16) = 128

Combining like terms, we get:

4L + 16 = 128

Subtracting 16 from both sides, we have:

4L = 112

Dividing both sides by 4 yields:

L = 28

Now that we have the number of losses, we can calculate the number of wins by substituting L back into 3L + 16:

Wins = 3(28) + 16 = 84 + 16 = 100

Therefore, the team won 100 games and lost 28 games in the season.

Show your work:

Express 160 pounds (lbs) in kilograms (kg). Round to the nearest hundredths.

Answers

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

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