What is the solution to the system of equations below

Answer:

1 : 5000

0.02%

Step-by-step explanation:

A solution = solute + solvent

A 2 Litre solution = (2 * 1000) = 2000 mg

Having, 400 mg of solute ;

Recall ;

1 mg = 0.001 ml

400 mg = (0.001 * 400) = 0.4 ml

The strength of the solution :

Amount of solute / Amount of solution

0.4 / 2000

As a ratio :

0.4 / 2000 = (0.4 * 10) / (2000*10) = 4 / 20000 = 1 / 5000 = 1 : 5000 (as a ratio)

0.4 / 2000

= 0.0002

(0.0002 * 100%) = 0.02% (As a percentage)

Answer:

No.

Step-by-step explanation:

y/x has to be the same number no matter what except at point (0 0) which it must also include for it to be a direct variation.

*y=2x+3 is not a direct variation because you can not write it as y/x=k where k is some constant number. If we were y=2x, then yes since y/x=2.

*You could also take two points and see if they are proportional. That is, you can see if y2/x2 gives the same value as y1/x1 where (x1,y1) and (x2,y2) are points on the line y=2x+3. This must work for every pair of points on the linear relation except at x=0 (where you would or should have y=0 if it is directly proportional).

Let's try it out. If x=1, then y=2(1)+3=5.

5/1=5

If x=2, then y=2(2)+3=7

7/2=3.5

As you can see 5 doesn't equal 3.5.

*For it to be a direct variation, it also must contain the point (0,0) and be a diagonal line when graphed. It can also be written in form y=kx where k is a constant number. This fails two of the the things I mentioned. It doesn't contain point (0,0) because y=2(0)+3=3 not 0. It cannot be written in form y=kx because of the plus 3.

If it were y=2x, then the answer would be yes.

Answer:

a) 0.0062 = 0.62% probability that the return will exceed 55%.

b) 0.3085 = 30.85% probability that the return will be less than 25%

c) 30%.

d) The 75th percentile of returns is 36.75%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 30% and standard deviation 10%.

This means that [tex]\mu = 30, \sigma = 10[/tex]

(a) Find the probability that the return will exceed 55%.

This is 1 subtracted by the p-value of Z when X = 55. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 30}{10}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a p-value of 0.9938

1 - 0.9938 = 0.0062

0.0062 = 0.62% probability that the return will exceed 55%.

(b) Find the probability that the return will be less than 25%

p-value of Z when X = 25. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{25 - 30}{10}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.3085

0.3085 = 30.85% probability that the return will be less than 25%.

(c) What is the expected value of the return?

The mean, that is, 30%.

(d) Find the 75th percentile of returns.

X when Z has a p-value of 0.75, so X when Z = 0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 30}{10}[/tex]

[tex]X - 30 = 0.675*10[/tex]

[tex]X = 36.75[/tex]

The 75th percentile of returns is 36.75%.

Answer:

d(A,B)=100

Step-by-step explanation:

The distance between two points A([tex]x_A,y_A[/tex]) and B=([tex]x_B,y_B[/tex]) is:

d(A,B)=[tex]\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]

In this case:

[tex]x_B = - 93\\x_A = 3\\y_B = -37\\y_A = -9[/tex]

In this case:

[tex]d(A,B)=\sqrt{( - 93 -3)^2+( - 37 - (-9))^2} =\\=\sqrt{( - 96)^2+(-28)^2} =\\=\sqrt{9.216+784} \\=\sqrt{10000}=\\=\sqrt{10^4} =\\=100[/tex]

Answer:

(4, 2 )

Step-by-step explanation:

Given the 2 equations

3x + y = 14 → (1)

7x - 4y = 20 → (2)

Rearrange (1) making y the subject by subtracting 3x from both sides

y = 14 - 3x → (3)

Substitute y = 14 - 3x into (2)

7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side

7x - 56 + 12x = 20

19x - 56 = 20 ( add 56 to both sides )

19x = 76 ( divide both sides by 19 )

x = 4

Substitute x = 4 into (3) for corresponding value of y

y = 14 - 3(4) = 14 - 12 = 2

solution is (4, 2 )

Answer:

[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]

Step-by-step explanation:

So, so, to attempt this, we need to use the formula :-

2 (l + b) × h ---> For Lateral surface area

2(30+30) h = 7200

2×60×h = 7200

120 × h = 7200

h = 7200/120

h = 60 cm

Now, volume = l×b×h

= 30×30×60

= 54000 cm³ is the required answer.

Hope it helps! :D

Answer:

a) A

b) C and E

c) C, D and F

d) two

e) Equal

here you go it's too easy

Step-by-step explanation:

Explanation is in the attachment .

Hope it is helpful to you ❣️☪️❇️

Answer:

16[tex]\sqrt{5}[/tex]

Step-by-step explanation:

[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]

16[tex]\sqrt{5}[/tex]

The perimeter of the square is 16√5 units.

We have,

The concept used here is straightforward: to find the perimeter of a square, you sum the lengths of all four sides because all sides of a square are equal in length.

In this case, the side length is given as 4√5, so you multiply it by 4 to calculate the total perimeter.

To find the perimeter (P) of a square with a side length of 4√5 units, you simply add up all four sides of the square, as all sides of a square are equal in length.

So,

P = 4 * side length

P = 4 * 4√5

P = 16√5 units

Thus,

The perimeter of the square is 16√5 units.

Learn more about squares here:

https://brainly.com/question/22964077

#SPJ3

Answer:

see down

Step-by-step explanation:

d is correct answer

Answer:

Random sample, [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], so yes, both conditions were satisfied.

Step-by-step explanation:

60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.

This means that [tex]p = 0.6[/tex]

A recent survey was conducted from 1000 of these individuals.

This means that [tex]n = 1000[/tex]

Also, a random sample, so the first condition was satisfied.

The sample size must be large (so that at least 10 or more successes and failures).

[tex]np = 1000*0.6 = 600 \geq 10[/tex]

[tex]n(1-p) = 1000*0.4 = 400 \geq 10[/tex]

So yes, both conditions were met.

Answer: [tex]\dfrac{3}{16},\ \dfrac{1}{2}, \dfrac{7}{2}\ \text{inch}[/tex]

Step-by-step explanation:

Given

Javier created a table for the amount of water evaporated in each week

After two weeks, the amount of water evaporated is

[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}\\\\\Rightarrow \dfrac{2+1}{16}=\dfrac{3}{16}\ \text{inch}[/tex]

Total amount of water evaporated in four weeks is

[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}+\dfrac{3}{16}+\dfrac{2}{16}\\\\\Rightarrow \dfrac{2+1+3+2}{16}=\dfrac{8}{16}\\\Rightarrow \dfrac{1}{2}\ \text{inch}[/tex]

If Javier originally puts 4 inches of water, amount of water left in the bucket

[tex]\Rightarrow 4-\dfrac{1}{2}\\\\\Rightarrow \dfrac{4\times 2}{2}-\dfrac{1}{2}\\\\\Rightarrow \dfrac{8-1}{2}=\dfrac{7}{2}\ \text{inch}[/tex]

Answer:

[tex]x =10[/tex]

Step-by-step explanation:

Given

[tex]AB = 12[/tex]

[tex]BC = 18[/tex]

[tex]AC = 3x[/tex]

Required

Solve for x

Since B is in between both points, then:

[tex]AC = AB + BC[/tex]

This gives

[tex]3x = 12 + 18[/tex]

[tex]3x = 30[/tex]

Divide by 3

[tex]x =10[/tex]

Given:

The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24.

To find:

The 2-digit numbers.

Solution:

Let the two digit number be [tex]ab[/tex]. Then the 4 digit number will be [tex]55ab[/tex].

We know that the number [tex]55ab[/tex] lies in the range 5500 to 5599.

Now,

[tex]5500=229\times 24+4[/tex]

It means, [tex]5500-4=5496[/tex] is divisible by 24. So, the numbers lie in the range 5500 to 5599 and divisible by 24 are:

[tex]5496+24=5520[/tex]

[tex]5520+24=5544[/tex]

[tex]5544+24=5568[/tex]

[tex]5568+24=5592[/tex]

Therefore, the possible 2-digit numbers are 20, 44, 68, 92.

Answer: the answer is 12/13

First, find 40% of 3,000:

0.40 * 3000 = 1200

So they raised 1200 so far.

Now subtract 1200 from the total they want to raise:

3000 - 1200 = 1800

So they need $1,800 more to meet their goal.

Answer:

8iriiruruj

Step-by-step explanation:

u4u the UK. We have a good idea to advertise the UK. I have been a

Answer/Step-by-step explanation:

Recall: an angle can be named in three different ways:

i. Using one letter which is the vertex of the angle. i.e. if the vertex of the angle is A we can name the angle as <A.

ii. Using the number of the labelled angle. i.e. is the angle is labelled 2, we can name it <2

iii. Using the three letters of the angles with the vertex angle in the middle. i.e. if the three points that form an angle are A, B, C and the vertex is B, we can name the angle as <ABC.

✔️Let's name the each angle given according:

1. <G, <3, and <FGH

2. <D, <4, and <CDE

3. <S and <TSR (the number seems blur and difficult to read. Whatever number is used to label the angle is what you'd use in naming the angle)

Answer:

0.001

Step-by-step explanation:

(0.0001)^-3/4=((0.1)⁴)^-3/4

(0.1)^4×-3/4

0.1^‐3

0.001

Answer:

0.9802 = 98.02% probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A bottle maker believes that 23% of his bottles are defective.

This means that [tex]p = 0.23[/tex]

Sample of 602 bottles

This means that [tex]n = 602[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.23[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{602}} = 0.0172[/tex]

What is the probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%?

p-value of Z when X = 0.23 + 0.04 = 0.27 subtracted by the p-value of Z when X = 0.23 - 0.04 = 0.19.

X = 0.27

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.27 - 0.23}{0.0172}[/tex]

[tex]Z = 2.33[/tex]

[tex]Z = 2.33[/tex] has a p-value of 0.9901

X = 0.19

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.19 - 0.23}{0.0172}[/tex]

[tex]Z = -2.33[/tex]

[tex]Z = -2.33[/tex] has a p-value of 0.0099

0.9901 - 0.0099 = 0.9802

0.9802 = 98.02% probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%

Answer:

Step-by-step explanation:

Answer:

hope it will help u

Answer:

68% is a special

value for these problems

empirical rule suggests ± 1 standard deviation

z = (x - μ)/σ

1 = (x - 38000)/1000

Between $37,000 and $39,000

Step-by-step explanation:

Hello!

[tex]\large\boxed{P = 300m}[/tex]

Use the following formula for the perimeter:

P = 2l + 2w, where:

l = length

w = width

Therefore:

P = 2(90) + 2(60)

Simplify:

P = 180 + 120 = 300 m

Answer:

well how about you use common sense 100 yards long on each side 200 yards then add 5o yards since the the that is how wide it is then add another 50 and you get 300 yards then convert that to meters

Answer:

-6x+15 < 10-5x

x>5

third equation, first graph

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

To find the height at 8 seconds, evaluate the formula for t=8.

  S(t) = -5t^2 +80t

  S(8) = -5(8^2) +80(8) = -320 +640 = 320

The height of the rocket is 320 meters 8 seconds after takeoff.

__

To find the time to 290 meters height, solve ...

  S(t) = 290

  290 = -5t^2 +80t

  -58 = t^2 -16t . . . . . . . divide by -5

  6 = t^2 -16t +64 . . . . . complete the square by adding 64

  ±√6 = t -8 . . . . . . . . . take the square root

  t = 8 ±√6 ≈ {5.551, 10.449}

The rocket is at 290 meters height after 5.6 seconds and again after 10.4 seconds.

Answer:

  a. $16.90

  b. 23.5%

Step-by-step explanation:

a. After the two discounts, the original price is multiplied by ...

  (1 -10%)(1 -15%) = 0.90×0.85 = 0.765

Then the original price is found from ...

  $12.93 = 0.765 × original price

  original price = $12.93 / 0.765 ≈ $16.90

__

b. The effective discount from the original price is ...

  1 -0.765 = 0.235 = 23.5%

Answer:

Domain: (-∞, 1]

Range: (-∞, 3]

Step-by-step explanation:

The function starts at point (1, 3) and goes to the left and down forever.

Domain: (-∞, 1]

Range: (-∞, 3]

Answer:

Domain: [tex](-\infty, 1][/tex]

Range: [tex](-\infty, 3][/tex]

Step-by-step explanation:

The domain of a function represents the range of x-values that are part of the function, read left to right. We can see that the function goes forever to the left and stops at [tex]x=1[/tex] when we read left to right. Therefore, the domain of this function is [tex]\boxed{(-\infty, 1]}[/tex].

The point at [tex]x=1[/tex] is a filled-in solid dot so it is included as part of the function. Use square brackets to denote inclusive.

The range of a function represents all y-values that are part of the function, read bottom to top. The function continues down forever and stops at [tex]y=3[/tex] when read bottom to top. Therefore, the range of this function is [tex]\boxed{(-\infty, 3]}[/tex]. Similar to the domain, we use a square bracket on the right to indicate that [tex]y=3[/tex] is included in the function. If the dot was not filled-in, then we would use a parenthesis to indicate that [tex]y=3[/tex] would not be part of the function.

9514 1404 393

Answer:

  (d)  2 : xy

Step-by-step explanation:

A common factor of 6x can be removed from the elements of the ratio. The ratio of radii is the same as the ratio of diameters.

  12x : 6x²y = (6x)(2) : (6x)(xy) = 2 : xy

Answer:D

Step-by-step explanation:

Answer:

The length of the rectangle is 10 inches, and the width is 4 inches.

Step-by-step explanation:

Given that the length of a rectangle is 6 inches more than the width, and the perimeter is 28 inches, the following calculation must be performed to find the length and the width:

(X + X + 6) x 2 = 28

2X + 2X + 12 = 28

4X = 28 - 12

X = 16/4

X = 4

Therefore, the length of the rectangle is 10 inches, and the width is 4 inches.