Select all the equations that share a solution with this system of equations:

5x+4y=25
2x-7y=26


A. 7x+3y=50

B. 7x-3y=50

C. 5x+4y=2x-7y

D. 3x-11y=-2

E. 3x+11y=-2

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Explanation:

We have four values to pick from {1,3,5,9} and we want to form a three-digit number.

Kick one of those values out, let's say we kick out "9" at the end to get the subset {1,3,5}.

The sum of these remaining values is 1+3+5 = 9 which is a multiple of 3. Therefore three-digit numbers that have any order of 1,3,and 5 will be a multiple of 3.

Eg: 135/3 = 45 exactly.

There are 3*2*1 = 6 such numbers as shown at the very bottom of this solution post.

This is a permutation since the order matters.

Let A = 6 so we can use it later.

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

Go back to {1,3,5,9}

Now let's say we kicked "5" out this time.

We go from {1,3,5,9} to {1,3,9}

The digits sum to 1+3+9 = 13 which is not a multiple of 3

No matter how we arrange these digits, we won't get a multiple of 3.

Eg: 139/3 = 46.33 approximately

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

Let's go back to {1,3,5,9}. This time we'll kick out "3" from the group.

{1,3,5,9} shrinks to {1,5,9}

Add the values: 1+5+9 = 15 which is a multiple of 3.

Therefore, we get 6 more permutations (refer to the first section for similar steps). Let B = 6 so we can use it later.

Example: 159/3 = 53 exactly

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

Return back to {1,3,5,9} once more. We have one final value to kick out.

Let's remove the "1" to end up with {3,5,9}

Add the values: 3+5+9 = 17 which isn't a multiple of 3, so we ignore this sub-case. It's similar to the 2nd section shown above.

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

Each previous section had us remove exactly one value to have 3 digits leftover. This is a methodical way to guarantee we have looked through all possible cases.

The first case had us kick out 9 so that a permutation of {1,3,5} led to some multiple of 3. There were A = 6 cases for that section.

The third section had {1,5,9} which led to B = 6 more cases.

In total, there are A+B = 6+6 = 12 different three-digit numbers possible if we are only allowed to use {1,3,5,9} without repeats allowed. In other words, all three digits must be different.

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

Check:

Here are the first 6 cases involving 1,3,5

Here are the other 6 cases involving 1,5,9

To explain how many cubic inches are in a cubic foot, we first need to understand the concept of volume. Volume is the amount of space occupied by an object or substance.

It is measured in cubic units such as cubic inches, cubic feet, cubic meters, etc. Now, one cubic foot is a cube-shaped container with each side measuring one foot. So, the volume of a cubic foot is calculated by multiplying the length, width, and height of the cube. That is, 1 foot x 1 foot x 1 foot = 1 cubic foot.

On the other hand, one foot is equal to 12 inches. Therefore, one cubic foot would contain 12 inches x 12 inches x 12 inches (or 12^3) cubic inches. This simplifies to 1,728 cubic inches in one cubic foot. Therefore, the answer to the question is that there are 1,728 cubic inches in a cubic foot.

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Answer:

352 quintillion gallon milk jugs

Step-by-step explanation:

Hello!

\(\large\boxed{V = 471cu ft}\)

Find the volume of the cylinder using the formula:

\(V = h(\pi r^{2})\)

We are given the diameter, so solve for the radius:

\(d = 2r\\\\10 = 2r\\\\r = 5 ft\)

Use the given height and radius to solve for the volume:

\(V = 6(5^{2}\pi )\\V = 6 * 25\pi \\\\V = 471 cu ft\)

Answer:

mean   (1/6){92 + 97 + 53 + 90 + 95 + 98}

= 87.5

variance (1/6){(92-87.5)^2 + (97-87.5)^2 + (53-87.5)^2 + (90-87.5)^2 + (95-87.5)^2 + (98-87.5)^2}

= 245.6

standard deviation   √{1/6*[(92-87.5)^2 + (97-87.5)^2 + (53-87.5)^2 + (90-87.5)^2 + (95-87.5)^2 + (98-87.5)^2]}

= 15.7

Answer:

The 3 numbers are 0, 6, and 6.

Step-by-step explanation:

Let the 3 numbers be a, b, and c. We can write the following system of equations to represent the given information:

a + b + c = 12

a^2 + b^2 + c^2 = 66

Subtracting the first equation from the square of the second equation, we get:

a^2 + b^2 + c^2 - (a + b + c)^2 = 0

Expanding the square on the right side gives:

a^2 + b^2 + c^2 - a^2 - 2ab - 2ac - 2bc - b^2 - c^2 = 0

Combining like terms and simplifying the equation gives:

-4ab - 4ac - 4bc = 0

This equation tells us that the sum of the products of any two of the numbers is equal to 0. Since the sum of the products of any two of the numbers is 0, it follows that at least one of the numbers must be 0. Without loss of generality, let a=0.

Substituting a=0 into the first equation gives:

b + c = 12

Therefore, the two non-zero numbers are b and c, and their sum is 12. The only possible solution for b and c is 6 and 6, respectively. Therefore, the 3 numbers are 0, 6, and 6.

The margin of error if we want a 90% confidence interval for the true population mean age is calculated to be 1.62 years, therefore option (a) is correct.

We can use the formula for the margin of error:

Margin of error = z × (σ / √(n))

where z is the z-score for the desired level of confidence, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the z-score is 1.645. Substituting the given values, we get:

Margin of error = 1.645 × (9.84 / √(100)) = 1.62

Therefore, the margin of error is 1.62 years, which is option (a).

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The standard error of the mean for a simple random sample of 100 observations, with a sample mean of 80 and a standard deviation of 12, is 1.20 (option a).

The standard error of the mean measures the precision or variability of the sample mean estimate. It is calculated by dividing the standard deviation of the population by the square root of the sample size.

Given that the sample mean is 80 and the standard deviation is 12, we can calculate the standard error of the mean as follows:

Standard Error of the Mean = Standard Deviation / Square Root of Sample Size

Standard Error of the Mean = 12 / √100 = 12 / 10 = 1.20

Therefore, the standard error of the mean for this sample is 1.20. This value indicates the average amount of variability or uncertainty we can expect in the sample mean compared to the population mean. It represents the precision of the sample mean estimate and is an important measure in inferential statistics for making inferences about the population based on the sample.

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Answer:

false

Step-by-step explanation:

Answer:

$318.70

Step-by-step explanation:

To find the cost of one boxed lunch, we can divide the total cost of the 8 boxed lunches by the number of boxed lunches: 99.60 / 8 = $12.45.

To find the cost of 26 boxed lunches, we can multiply the cost of one boxed lunch by the number of boxed lunches: 26 * $12.45 = $<<26*12.45=318.70>>318.70. Answer: \boxed{318.70}.

The solution to the elimination of the parameters is \(\mathbf{y = 27 \Bigg(\dfrac{\sqrt{x}}{3}, -\dfrac{\sqrt{x}}{3} \Bigg)^3}\)

In the scenario of two parametric equations, the parameter can be removed by first resolving it in equation 1 and then replacing it in equation 2.

Given that:

x = 9t² and y = 27t³

Set up the parametric equation for x(t) to solve the equation for t.

9t² = x

Divide both sides by 9

9t²/9 = x/9

t² = x/9

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

\(t = \pm \sqrt{\dfrac{x}{9}}\)

\(t = \pm {\dfrac{\sqrt{x}}{3}}\)

The complete solution is the result of both the positive and the negative portions of the solution.

\(t = {\dfrac{\sqrt{x}}{3}}\)

\(t = - {\dfrac{\sqrt{x}}{3}}\)

Replace t in the equation for y to get the equation in terms of x.

\(\mathbf{y = 27 \Bigg(\dfrac{\sqrt{x}}{3}, -\dfrac{\sqrt{x}}{3} \Bigg)^3}\)

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The marginal average cost function for the given production cost function C(X) = 0.35x^2 + 29x + 2000 is MAC(X) = 0.7x + 29, where X represents the number of jerseys produced.

The marginal average cost (MAC) represents the rate at which the average cost changes with respect to the quantity produced. To find the MAC function, we need to differentiate the cost function C(X) with respect to X and then divide it by X.
Differentiating C(X) = 0.35x^2 + 29x + 2000 with respect to X using the power rule, we get C'(X) = 0.7x + 29.
To obtain the MAC function, we divide C'(X) by X, resulting in MAC(X) = (0.7x + 29) / X.
Therefore, the marginal average cost function for the given production cost function C(X) = 0.35x^2 + 29x + 2000 is MAC(X) = 0.7x + 29. The MAC(X) equation shows that the marginal average cost increases linearly with X, indicating that the cost per unit increases as more jerseys are produced.

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Answer:

Step-by-step explanation:

The sides of a triangle measure 6, 8 and 10 cm. What is the area of the triangle?

from the data it is a right triangle, 10 cm is the hypotenuse

so

1/2 (6 * 8) =

1/2 * 48 =

24 units²

Answer:

\(x > 5.3333.... \\x > 5 \frac{1}{3}\)

Step-by-step explanation:

Given:

\(16(\frac{1}{4} x-\frac{1}{2} ) > 24-2x\)

and (assuming) we are solving for x, first distribute the 16 among numbers in parenthesis:

\(4x-8 > 24-2x\)

add 2x to both sides

\(6x - 8 > 24\)

add 8 to both sides

\(6x > 32\)

divide both sides by 6

\(x > 5.3333.... \\x > 5 \frac{1}{3}\)

Hope this helps! :)

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

Below.

Step-by-step explanation:

What we know: 4 Shaded. 12 in total.

That means,

12 divided by 4=3.

1/3 of the shape is shaded.

\(\huge\text{Hey there!}\)

\(\textsf{Assuming:}\)

\(\mathsf{w + (w - \dfrac{12}{2^2} \times 3)(7)}\)

\(\textsf{If so:}\)

\(\mathsf{w + (w - \dfrac{12}{2^2} \times 3)(7)}\)

\(\mathsf{= 10 + (10 - \dfrac{12}{2^2} \times 3)(7)}\)

\(\mathsf{= 10 + (10 - \dfrac{12}{2\times2} \times 3)(7)}\)

\(\mathsf{= 10 + (10 - \dfrac{12}{4} \times 3)(7)}\)

\(\mathsf{= 10 + (10 -3 \times 3)(7)}\)

\(\mathsf{= 10 + (10 - 9)(7)}\)

\(\mathsf{= 10 + (1)(7)}\)

\(\mathsf{= 10 + 7}\)

\(\mathsf{= 17}\)

\(\huge\textsf{Therefore, your answer should be:}\)

\(\huge\boxed{\textbf{Option D. }\frak{017}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

B is the answer your looking for

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

Answer:

3 months

Step-by-step explanation:

Jessie starts with $120 and get $40 a month

peter has $180 and get $20 a month

1 month passed Jessie now has $160 and Peter has $200

2 months passed Jessie now has $200 and Peter has $220

3 months passed Jessie now has $240 and Peter has $240

Answer:

Step-by-step explanation:

Polynomials are factored after they are set equal to 0. This i because the factors of the polynomial are also known as the x-intercepts, and x-intercepts exist where y = 0. Therefore, if the factors of the polynomial are

(x + 8)(x + 4) = 0, then by the Zero Product Property,

x + 8 = 0 so x = -8 or

x + 4 = 0 so x = -4. Choice A.

Answer:

16% drop

Step-by-step explanation:

4/25 drop

Multiply by 4/4

16/100

16% drop

Answer:

16%

Step-by-step explanation:

SInce 4 students left the class, and there are 25 students, let's make it a fraction.

4/25.

As it is asking for a percentage though we could simply convert our fraction to a percentage.

Simply divide the numerator (4) by the denominator (25).

This gives us 0.16.

Which is 16%.

The hardener needed for 600 g of carbon fiber is 85.04 g.

We are given that the ratio of the composite is 40 % matrix to 60 % fiber.

This can be written as:

Matrix : fiber = 40 % : 60 %

Matrix : fiber = 40 : 60

Matrix : fiber = 2 : 3

Now, we know that the carbon fiber = 600 g

Matrix : 600 g = 2 : 3

Matrix / 600 = 2 / 3

Matrix = 1200 / 3 g

Matrix = 400 g

Also, we are given that the ratio of the matrix is 100 parts resin to 27 parts of hardener.

This means that:

Hardener = 27 / 127 of matrix.

Hardener = 27 / 127 × ( 400 g )

Hardener = 85.04 g

Therefore, the hardener needed for 600 g of carbon fiber is 85.04 g.

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Using Algebraic equations, the dimensions of the frame are 6in: 9 in.

The word "area" refers to a free space. A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc. But a shape's area is a two-dimensional measurement. Hence, it is expressed in square units such as square inches (in2), square feet (ft 2), square yards (yd2), etc.

Given, the area of the rectangular picture frame is 54 in².

length of the frame is 3 feet longer than the width,

Let us assume width = x

length of the frame will be = x + 3,

Area of rectangle = length × breadth

⇒ 54 = (x) (x + 3)

⇒ 54 = x² + 3x

Now, factorizing the given equation,

x² + 3x - 54

x² + 9x - 6x - 54

x(x + 9) -6 (x + 9)

(x + 9) (x - 6)

The value of x will be x = -9 and x = 6

As the negative length of the rectangle is not possible, we will consider, x = 6 and width = 9,

∴ The length of the rectangle = 6 inch,

Width of the rectangle will be = 6 + 3 = 9 inch.

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According to the question The most appropriate distribution to model the number of hits on a personal website in a week would be the Poisson distribution.

The Poisson distribution is commonly used to model rare events that occur randomly and independently over a fixed interval of time or space. It is characterized by a single parameter, λ (lambda), which represents the average rate of occurrence of the event.

In this case, since hits on a personal website occur quite infrequently with an average of five per week, the Poisson distribution is suitable. The parameter λ would be set to 5, indicating the average rate of hits per week.

By using the Poisson distribution, you can calculate the probabilities of different numbers of hits occurring in a week and make predictions about the website's traffic patterns.

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The amount of KES that one would have to get for R150 is given as 1053.54 KES

​The KES tells us of the Kenyan currency. That is the Kenyan shillings. The R is the name that is used to refer to the Rands

Hence we would have to convert rands to KES

1 south African Rand is given as 7.0236

then 150 rand would be = ?

Hence the amount you would get of KES is: 7.0236 * 150

= 1053.54 KES

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Answer: (1, -10)

Step-by-step explanation:

Substituting the coordinates of each of the points into the given inequalities, we see that (1, -10) is the only point that results in two true statements.