A mixture is 25% red paint, 30% yellow paint, and 45%water. If 4 quarts of red paint are added to 20 quarts of the mixture, what is the percentage of red paint in the new mixture?

Answer:

10

Step-by-step explanation:

50%, or 1/2 of 20 is 10.

Answer:

10!

Step-by-step explanation:

50% is half, so half of 20 is 10!

The only automorphism of a well-ordered set is the identity.

To prove this statement, we need to show that any automorphism of a well-ordered set must be the identity function. An automorphism is a bijective function that preserves the order structure of the set.

Assume we have a well-ordered set (W, ≤), where W is the set and ≤ is the order relation.

Let f: W → W be an automorphism of the set.

We aim to prove that f is the identity function, i.e., f(x) = x for all x ∈ W.

Suppose, for contradiction, that there exists an element a ∈ W such that f(a) ≠ a.

Since f is a bijective function, there must exist some b ∈ W such that f(b) = a.

Since (W, ≤) is well-ordered, there is a least element c in the set {x ∈ W : f(x) ≠ x}.

Let d = f(c). Since f is an automorphism, f(c) ≠ c, and thus d ≠ c.

Since (W, ≤) is well-ordered, there is a least element e in the set {x ∈ W : f(x) = d}.

Consider the element f(e). Since f is a bijective function, there must exist some f^{-1}(f(e)) = e' ∈ W such that f(e') = f(e) = d.

By the definition of automorphism, f(f^{-1}(y)) = y for all y ∈ W. Applying this property to e', we have f(f^{-1}(f(e'))) = f(e') = d.

However, f^{-1}(f(e')) = e' ≠ c, and thus f(e') ≠ d. This contradicts the fact that e is the least element in the set {x ∈ W : f(x) = d}.

Therefore, our assumption that there exists an element a such that f(a) ≠ a is false.

Since we assumed f(a) ≠ a for arbitrary a ∈ W, it follows that f(x) = x for all x ∈ W.

Hence, the only automorphism of a well-ordered set is the identity function.

Therefore, we have proven that the only automorphism of a well-ordered set is the identity function.

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The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)

Answer:

D

Step-by-step explanation:

It helps to break the pyramid into shapes

triangles:  ((b x h) ÷ 2) x 5

((4 x 8) ÷ 2) x 5= 80in

base: 27.5in

total sa: 27.5 + 80 = 107.5in

The inequality tha calculates the possible values of x is x < 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

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Answer:

j plus sixteen is thirty-five

Step-by-step explanation:

Answer:

The sum of an unknown number and 16 gives a total of 35. find the unknown number

hope this helps

Option A is correct that is the results comparing each box size and comparing flashy vs simple graphics.

Given this, a marketing firm tested several package variations, including size, complexity, and simplicity, to determine which would encourage customers to buy more cereal.

Which of the following would be the key conclusions of the study?

We are aware of this since we are comparing various box and graphic sizes.

When contrasting the sizes of each box and the flashy vs. simple images, the influence of the research can be noticed.

The comparison of the sizes of each box and the effectiveness of flashy vs. straightforward images shows that Option A is the best choice.

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(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Let w = x^3

Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6

In short: w^2 = x^6

The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2

Set this equal to zero and use the quadratic formula. We'll plug in

So,

\(w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\\)

If w = -2/3, then that rearranges to the following

w = -2/3

3w = -2

3w+2 = 0

This makes (3w+2) a factor of -3w^2+w+2

If w = 1, then it rearranges to w-1 = 0.

This makes (w-1) a factor of -3w^2+w+2

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

To summarize the previous section, we found the factors of -3w^2+w+2 were:

It leads to (3w+2)(w-1)

We must stick a negative out front because the leading coefficient is negative.

Therefore, -3w^2+w+2 = -(3w+2)(w-1)

You can use the FOIL rule to confirm.

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

Recall we made w = x^3

Let's replace each w with x^3

-(3w+2)(w-1)

-(3x^3+2)(x^3-1)

This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)

The next task is to factor x^3-1 using the difference of cubes factoring rule.

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)

x^3 - 1 = (x-1)(x^2 + x + 1)

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

So,

2+x^3-3x^6

-3x^6 + x^3 + 2

-(3x^3+2)(x^3-1)

-(3x^3+2)(x-1)(x^2 + x + 1)

-(2 + 3x^3)(-(1-x))(1 + x + x^2)

(2 + 3x^3)(1 - x)(1 + x + x^2)

Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.

Answer:

0.33

Step-by-step explanation:

See comment for complete question

Given

\(H = 60\%\)

\(W=25\%\)

\(HW = 20\%\) --- at-home wins

Required

The proportion of at-home games that were wins

This proportion is represented as:

\(Pr = HW : H\)

Substitute values for HW and H

\(Pr = 20\% : 60\%\)

Divide by 20%

\(Pr = 1 : 3\)

Express as fraction

\(Pr = 1 /3\)

\(Pr = 0.33\)

SIMPLE INTREST = P X NX R/100

P= 500 ,N=?, R=9%

AMOUNT WILL ONLY GET DOUBLE WHEN INTREST EQUALS TO DEPOSIT.

SI=500

n=100/9

n=11.11

so it will take about 11.11 years

The answer is 11.11 years

Answer:

\( \frac{x - 9}{2} = 5 \\ x - 9 = 5 \times 2 \\ x = 10 + 9 \\ x = 19\)

Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

Answer:

The number of possible license plates will be;

8,714,977,920

Step-by-step explanation:

The number of digits is 1-9 making 9

The number of alphabets is A-Z making a total 26

Number of characters is 26 + 9 = 35

Now for the 1st character

we have 9 choices

Second character, we have 34 choices since no character appear more than once

Third character, we have 33 choices

fourth 32 choices

fifth 31 choices

sixth 30 choices

seventh 29 choices

Number of possible license plates will be;

9 * 34 * 33 * 32 * 31 * 30 * 29 = 8,714,977,920

The values nearest to these middle elements are 60 and 63 inches.

The dataset is given as:

62 33 50 90 80 50 40 70 50 63 74 53 55 64 60 60 78 70 43 82

Then, we sort the information elements in ascending request

33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78 80 82 90

The length of the dataset is 20.

Thus, the elements at the middle are the tenth and the 11 elements.

From the arranged dataset, these elements are: 60 and 62

Thus, the values nearest to this median are 60 and 63

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We want to find the velocities of two cyclists in the given situation.

The velocity of one cyclist is 17.5 mi/h, and the velocity of the other cyclist is -14.5 mi/h.

The information that we have is that:

Let's say that cyclist 1 starts in the position 0 and has a velocity v₁.

Then the position equation of cyclist 1 is:

p₁(t) = v₁*t

Now cyclist 2 starts at the position 98 miles, and has a velocity v₂, then we can write the position equation of cyclist 2 as:

p₂(t) = v₂*t + 98mi

Assuming that cyclist 2 is the slower one, we can write:

v₂ = -(v₁ - 3mi/h)

Where the negative sign comes because they move in opposite directions.

Then the position equation becomes:

p₂(t) = -(v₁ - 3mi/h)*t + 98mi

Then we know that after 3 hours they are 2 miles apart, then we can write:

p₂(3h) - p₁(3h) = 2mi

Then we need to solve:

-(v₁ - 3mi/h)*3h + 98mi - (v₁*3h) = 2mi

(-6h)*v₁ + 9mi + 98mi = 2mi

(-6h)*v₁ + 107mi = 2mi

(-6h)*v₁  = 2mi - 107mi = -105mi

v₁ =  -105mi/(-6h) = 17.5 mi/h

So the velocity of cyclist 1 is 17.5 mi/h

And the velocity of cyclist 2 is:

v₂ = -(17.5 mi/h - 3mi/h) = -14mi/h.

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The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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Answer:

4,300

Step-by-step explanation:

I don’t have an explanation just trust me it’s right

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

The required solution is 5+39e.

What is arithmetic?

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications

Given :

Write down the question as an algebra problem, with the unknown as X

The unknown is a number plus 5, so we write it as (X+5). The product is four times (X+5), so we write it as 39(X+5). Set it equal to e, as per the question, 5+39e

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Answer:

-2x^2+5y^3+

Step-by-step explanation:

Answer:

there are 3 ways to answer this and I don't know which way you teacher wants it so I have included sqare root, simplified square root, and rounded four decimal places

I also counted to the points since they were not included (also I forgot to put the - in front of the 2 of (-6,-2) but I did put it in the equation)

Answer: 7

and maybe 5.83

Step-by-step explanation:

If she worked 5 days a week, and worked the same hours of those days, then the answer is 7. You simply divide 35/5 which gives you that answer. And they’ve already given you the answer for Saturday, so yeah.

But you did say she only worked 5 days a week—in 35 hours. And you also said “how many hours did she work on the other days”. If Saturday’s hours was already stated, then are you implying she worked for 6 days instead of 5? Because there’s 7 days a week and if Saturday is unaccounted for, then she worked 6 days. In that case, your answer would be 5.83.

Answer:

c.60

Step-by-step explanation:

The correct statement regarding the mean of the data-set when the score of 47 is removed is given as follows:

The mean increased by about 6.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The observations for this problem are given as follows:

100, 95, 47, 83, 87, 89, 89.

There are 7 observations, and their sum is given as follows:

100 + 95 + 47 + 83 + 87 + 89 + 89 = 590.

Hence the mean is of:

590/7 = 84.29.

Removing the observation of 47, there will be 6 observations, with a sum of 590 - 47 = 543, hence the mean is of:

543/6 = 90.5.

Meaning that the mean increases by about 6.

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Answer:

The 95% confidence interval for the proportion of all US adults who would say they subscribe to a video-streaming service is (0.5362, 0.6048).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Of the 801 participants in the survey, 457 indicated they subscribed to at least one video-streaming service.

This means that \(n = 801, \pi = \frac{457}{801} = 0.5705\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5705 - 1.96\sqrt{\frac{0.5705*0.4295}{801}} = 0.5362\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5705 + 1.96\sqrt{\frac{0.5705*0.4295}{801}} = 0.6048\)

The 95% confidence interval for the proportion of all US adults who would say they subscribe to a video-streaming service is (0.5362, 0.6048).