3x - 5y = 4
-2x + 6y = 18
Type the answer in the boxes below. What does x and y =

Answer:

18) y = (24-4x)/7

19) y = 5/7x

20) y = a/b

Check the picture below.

Answer:

do you have the graph to solve it?

The density of the liquid substance Y can be determined by using the conversion factor 1 atm = 41.5 ft⁻Y and the density of the liquid substance Y is approximately 19.68 ft⁻Y.

Conversion factor: 1 atm = 41.5 ft⁻Y

The "feet of liquid substance - Y" unit is defined as the pressure equivalent to the pressure that exists one foot below the surface of substance Y. In other words, if we go one foot below the surface of substance Y, the pressure will be equivalent to 1 ft⁻Y.

Since pressure is directly related to the density of a liquid, we can equate the pressure in units of atm to the pressure in units of ft⁻Y.

Therefore, we can say:

1 atm = 41.5 ft⁻Y

From this equation, we can conclude that the conversion factor for pressure between atm and ft⁻Y is 41.5.

we can calculate the conversion factor from "feet of liquid substance - Y" (ft⁻Y) to atm.

To convert from ft⁻Y to atm, we can use the inverse of the given conversion factor:

Conversion factor: 1 atm = 41.5 ft⁻Y

Taking the reciprocal of both sides:

1 / 1 atm = 1 / 41.5 ft⁻Y

Simplifying the equation:

1 atm⁻¹ = 0.024096 ft⁻Y⁻¹

Now, to find the density of the liquid substance Y in units of ft⁻Y, we can multiply the given density in g/cm³ by the conversion factor:

Density in ft⁻Y = 816.55 g/cm³ * 0.024096 ft⁻Y⁻¹

Calculating the density in ft⁻Y:

Density in ft⁻Y ≈ 19.68 ft⁻Y

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Answer:

Step-by-step explanation:

First order from smallest to largest.

70.8, 71.9, 72.1, 82.4, 85.3, 98.1.

Median is the middle number/s.

72.1+82.4/2 so The median is 77.25

Range is the largest number minus the smallest number.

85.3-70.8=14.5

Mode is the most repeated number.

Since there are no repeated numbers there is no mode.

Second question:

Again rearrage: 6, 9, 11, 14, 17

In order to make the median 10 you would have to add another 9 becasue

11+9/2 = 10

Third: remove 6 to make 12 the middle number

Fourth: add all numbers 90+x/6=20 so x has to be 30

Answer:

.

Step-by-step explanation:

Answer: a) \(\dfrac{13}{7}\)

Step-by-step explanation:

Median: Line segment from one vertex of a  triangle to the midpoint of the opposite side. i.e. it bisects the opposite side.

Centriod: Point of intersection of a triangle of its medians

.Also, it is \(\dfrac23\) of the distance from vertex to the midpoint of opposite side.

Given:  CD is a median in triangle ABC and M is centriod.

\(\Rightarrow CM=\dfrac23 CD\)

Since CM = x +5 and CD = 5x + 1

\(\Rightarrow\ x+5=\dfrac{2}{3}(5x+1)\\\\\Rightarrow\ 3(x+5)=2(5x+1)\\\\\Rightarrow\ 3x+15=10x+2\\\\\Rightarrow\ 10x-3x=15-2\\\\\Rightarrow\ 7x=13\\\\\Rightarrow\ x=\dfrac{13}{7}\)

Correct option is a)

The feasible region is not empty and the objective function is bounded because it achieves its minimum value at the corner point (0, 0). Hence, the solution to the given LP problem is (x, y) = (0, 0).

Given an LP problem Minimize \(c = x + 2y\) subject to the constraints \(x + 3y ≤ 223 8x + y ≤ 23 x ≥ 0, y ≥ 0\)

Now we can start solving this LP problem by drawing the graph for the given constraints :

Plotting the constraints on a graph.

We can see that the feasible region is the shaded region bounded by the lines x = \(0, y = 0, 8x + y = 23, and x + 3y = 223\)

Now we can check the corner points of this region for finding the optimal solution of the given problem.

Corner points of the feasible region are:

(0, 0), (0, 7.67), (2.88, 71.07), (23, 66.33), and (27.33, 65).

Now we can substitute these values of x and y into the objective function \(c = x + 2y\) and see which corner point gives us the minimum value of c.

The table below summarizes this calculation.

Corner point

\((x, y)c = x + 2y\) (0,0)0(0,7.67)15.34(2.88,71.07)145.03(23,66.33)112.67(27.33, 65)157.67.

Thus, we can see that the minimum value of the objective function \(c = x + 2y\) is achieved at (0, 0),

which is one of the corner points of the feasible region.

Therefore, the optimal solution of the given LP problem is \(x = 0\) and \(y = 0\)

Also, we can see that the feasible region is not empty and the objective function is bounded because it achieves its minimum value at the corner point (0, 0).

Hence, the solution to the given LP problem is \((x, y) = (0, 0)\)

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Answer:

2.5n is larger than or equal to (> with the line under) 5.25

Step-by-step explanation:

let's say the number is "n"

2 1/2 of n is at least 5 1/4

at least is a synonym to larger than or equal to, which is the fourth symbol, >_ with the line underneath.

The inequality 2.5x ≥ 5.25 represents the statement "Two and a half times a number is at least five and one-fourth"

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality symbol "≥" represents "at least," indicating that the result should be greater than or equal to 5.25.

The inequality that represents this statement is:

2.5x ≥ 5.25

Where x is the number,

This means that if we multiply a number by 2.5, the result should be greater than or equal to 5.25. In other words, 2.5x should be greater than or equal to 5.25.

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Answer:

\(V=7238.22\ \text{inches}^3\)

Step-by-step explanation:

The diameter of a sphere, d = 24 inches

Radius, r = 12 inches

We need to find the volume of sculpture which is in the shape of sphere. The formula for the volume of a sphere is given by :

\(V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\pi \times (12)^3\\\\V=7238.22\ \text{inches}^3\)

So, the volume of the sculpture is \(7238.22\ \text{inches}^3\).

The closest answer choice to this value is option 1, 33. Therefore, the best estimate for the unicity distance for an affine cipher is 33.

To find the best estimate for the unicity distance for an affine cipher, we can use the following formula:

Unicity Distance  (U) = (keyspace / entropy) × log2(1 / redundancy).

Given the answer choices:
1. 33
2. 35
3. 33
4. 26
5. 17.5

For an affine cipher, the keyspace is 26^2 (since there are 26 possibilities for both 'a' and 'b' in the equation

y = (ax + b) mod 26).

The entropy of English text is roughly 1.5 bits/character, and the redundancy is approximately 0.7.

Using the formula, we have:

U = (26^2 / 1.5) × log2(1 / 0.7)

U ≈ 33.49

Therefore, the best estimate for the unicity distance for an affine cipher is 33.

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Answer:

slope is 5

Step-by-step explanation:

y = 5x

This is in the form

y = mx+b where m is the slope and b is the y intercept

The slope is 5 and the y intercept is 0

Answer:

the highest amount is heart disease its such high risk to die from it the number would be high.

Step-by-step explanation:

Answer:

397/378=0.971

Step-by-step explanation:

plato/edmentum

Answer:

88×2.54 = 223.52cm ×3.14 =701.8528 =702cm

Answer:

The crafts worker would need 702 cm of trim.

Hope this helps!

Step-by-step explanation:

The trim is the circumference of the circle.

Circumference is 2πr.

The radius of the circle is 44 inches.

2 × π × 44 = 276.46 inches

276.56 inches × 2.54 = 702.4624 cm

If two positive numbers are multiplied or divide then the result is always positive but if we take one positive and one negative number and then after multiply or divide we get always negative number.

What is Number system?

A system of writing to express the number with positive or negative sign is called number system.

Now, There are many applications for the use of positive and negative numbers to represent mathematical ideas.

⇒ Negative and positive numbers are used to describe the distance from a reference point.

⇒ If two positive numbers are multiplied or divide then the result is always positive but if we take one positive and one negative number and then after multiply or divide we get always negative number.

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Answer:

The number is 24

Step-by-step explanation:

The quotient is the answer of a division problem. If a number is divided by 3 and the answer is 8, then the number would be 24. You could set it up into an  equation.

x/3=8

then you multiply both sides by 3 and you will get

x=24

The quotient is indeed the number generated by dividing one integer by the other. Whenever a fraction is simplified, the division is the whole amount that results.

Calculation of the equation:

\(\to \bold{\frac{x}{3}=8}\\\\\to \bold{x=8\times 3} \\\\\to \bold{x=24}\)

Therefore, the final answer is "24".

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Answer:

see the attachment!

i hope this can help you!

Answer:

5/1 (below for more possible answers)

Step-by-step explanation:

Proportional is a corresponding in size,

15/3 is equal to 5 (5/1)        15 divided by 3

also possible answers...

10/2

20/4

25/5

30/6

35/7

40/8

45/9

50/5

55/11

60/12

65/13

70/14

75/15

which all these equal 5

During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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Answer:b 0.07

Step-by-step explanation:

Because I said so

Answer:

0.07

Step-by-step explanation:

I just took the quiz and got it right.

Hope this helps! ^^

The probability of advertise footwear is fewer than nine from the given number of pages on catalog is equal to 0.9978( rounded to four decimal places).

Total number of pages = 192

Number of pages of footwear advertised = 28

Number of pages selected randomly = 20

Interested in the number of pages that advertise footwear out of a sample of 20 pages,

The probability of a page advertising footwear is

p = 28/192

    = 0.1458.

Number of pages have advertising footwear is less than 9,

Probability of having 0, 1, 2, 3, 4, 5, 6, 7, or 8 pages advertising footwear out of the 20-page sample.

Use the binomial probability formula,

P(X < 9)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

We know,

P(X = x) = (ⁿCₓ) × p^x × (1 - p)^(n-x)

sample size n =20

x is the number of pages advertising footwear

(ⁿCₓ) = n! / (x! × (n - x)!)

Using statistical software,

Probabilities and sum them to find the probability of having fewer than 9 pages advertising footwear,

P(X < 9) = 0.9978

Therefore, the probability that fewer than nine pages will advertise footwear on them is 0.9978( rounded to four decimal places).

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The above question is incomplete , the complete question is:

In one of Catalog , footwear advertised on 28 of its 192 catalog pages. Suppose we randomly surveyed 20 pages. We are interested in the number of pages advertised footwear. Each page may be picked up more than once. what is the probability that fewer than nine will advertise footwear on them? (round your answer to four decimal places.)

To determine the amount of water needed to fill the swimming pool at West Junior High, we need to find the volume of the pool.

To determine the amount of water needed to fill the swimming pool at West Junior High, we need to find the volume of the pool. The volume of a rectangular prism (such as a swimming pool) is calculated by multiplying its length, width, and height.

Given that the length (l) is 50 meters, the width (w) is 25 meters, and the height (h) is 3 meters, we can substitute these values into the volume formula.

The volume of the pool can be calculated as follows:

V = l * w * h

Substituting the given values:

V = 50 * 25 * 3

Now, let's simplify this expression:

Multiplying 50 by 25 gives us 1250:

V = 1250 * 3

Multiplying 1250 by 3 gives us 3750:

V = 3750

Therefore, the volume of the pool is 3750 cubic meters. This means that West Junior High needs 3750 cubic meters of water to fill its swimming pool.

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For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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All of the following terms are interchangeable except e. none of the above

The terms "quantitative analysis," "operations research," and "management science" are interchangeable because they all refer to research activities. All of these terms will have roughly the same meaning. As a result, they are interchangeable.

Operations research, abbreviated as OR, is a discipline concerned with the development and application of analytical methods to improve decision-making. It is regarded as a subfield of mathematical sciences. Management science is sometimes used as a synonym.

In this case, it should be noted that the terms are all synonyms. In conclusion, the correct option is E.

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Answer:

24cm

Step-by-step explanation:

a radius is half the diameter

12x2=24

Answer:

Step-by-step explanation:

Diameter of a circle = 2 x radius

= 2 x 12 = 24cm

Answer:

thanks

Step-by-step explanation:

go to another app

Answer:

5 is the base

4 is the exponent

The value of x and y that will prove triangle ABC is congruent to DEF is 5 and 20 Respectively.

Congruent triangles have both the same shape and the same size. This means that if two angles have equal angles and equal length they are congruent.

Therefore;

48 = 9x+3

9x = 48 -3

9x = 45

divide both sides by 9

x = 45/9

x = 5

Angle D = angle C

angle D = 180-( 54+ 88)

= 180- 142

= 38

therefore ,

1.9y = 38

y = 38/1.9

y = 20

Therefore,the value of x and y that will prove triangle ABC is congruent to DEF is 5 and 20 Respectively.

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Let x = p+qi be the complex root and x = r be the the real root. The p and q are real numbers.

Multiply the two factors like so:

(x-p-qi)(x-r)

y(x-r) ..... let y = x-p-qi

xy - ry ..... distribute

x( y ) - r( y )

x( x-p-qi ) - r( x-p-qi ) ........ plug in y = x-p-qi

x^2 - px - (qi)x - rx + pr + qr*i ........ distribute

x^2 + (-px-qi*x-rx) + (pr+qr*i)

x^2 + (-p-qi*-r)x + (pr+qr*i)

x^2 + ((-p-r)-qi*)x + (pr+qr*i)

We end up with an expression in the form ax^2 + bx + c where the coefficients are:

The coefficients b and c are complex numbers. So it is possible to have one real root and exactly one complex root; however, as shown above, it leads to some of the coefficients being complex numbers. I'm assuming your teacher wants all coefficients to be real numbers. If that's the case, then a quadratic equation cannot have one real root and one complex root. You would need to have the complex roots come in conjugate pairs. Meaning that if a quadratic equation with real coefficients has a complex root, then there's another complex root as its nearly "twin" pair so to speak.

Recall that quadratic equations have at most 2 roots according to the fundamental theorem of algebra. Having 2 complex conjugate pairs for the roots will then mean there isn't enough room for that third real root. In other words, here are all the possible scenarios:

Again this only applies if all coefficients a,b,c are real numbers. For scenario B, the root repeats itself and we consider it a double root. For instance, x^2+10x+25 = 0 has the root x = -5 repeat itself. In scenarios A and B, we don't have any complex roots happen.

Because always that we have a discriminant different than zero, we have two solutions.

A quadratic equation has complex roots when its discriminant is negative, where for the general quadratic:

y = a*x^2 + b*x + c

The discriminant is:

D = b^2 - 4ac

And the solutions of the roots are:

\(x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}\)

Because we have two possible signs for the square root of the discriminant, we always will have two solutions when the discriminant is different than zero.

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The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g which is false.

A statement, opinion, or rule that forms a linking of two variables is characterized as a function. Mathematics has functions, which are necessary for the design of meaningful relationships.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

The denominator of the rational function shouldn't be 0. The function is not defined if the denominator is 0.

Thus, the given statement is false.

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