how many ounces of ceylon tea worth $1.50/oz and how many ounces of formosa tea worth $2.00/oz must be mixed to produce a mizture 8 oz worth $1.62/oz?

Answer:

[tex]x_1 + x_2 = \boxed{-5}[/tex]

Step-by-step explanation:

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]

[tex]x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\implies x_{1,\:2}=\dfrac{-b}{2a}\pm\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]

Let's have

[tex]x_{1}=\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]\

[tex]x_{2}=\dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x_1 + x_2 =\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a} + \dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}\\[/tex]

[tex]\dfrac{\sqrt{b^{2}-4ac}}{2a} - \dfrac{\sqrt{b^{2}-4ac}}{2a} = 0\\\\[/tex]

Leaving us with
[tex]\dfrac{-b}{2a} + \dfrac{-b}{2a}\\\\\implies 2 \cdot \left(\dfrac{-b}{2a}\right)\\\\\implies -\dfrac{b}{a}\\\\[/tex]

The given equation is
[tex]3x^2+15x+9=0[/tex]

Here a = 3, b = 15

So
[tex]-\dfrac{b}{a} = --\dfrac{15}{3} = -5\\[/tex]

Answer:
[tex]x_1 + x_2 = \boxed{-5}[/tex]

The amount that Riley paid for the hair dryer is $225.37.

Given the information in the question, the dryer is depreciating in value. Depreciation is when the value of an asset declines with the passage of time.

The formula that can be used to determine the amount paid for the hair dryer is:

p = FV / (1 - r)^n

Where:

p = $100 / (1 - 0.15)^5

p = $100 / 0.85^5

p = $225.37

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100 kernels are randomly selected from a population that is in Hardy-Weinberg equilibrium. 9 yellow kernels and 91 purple kernels are discovered. In this population, the yellow allele is 0.09 times more common.

Both citizens who are physically present in a country or who are temporarily away from it, as well as all foreigners who have permanently emigrated to that country, are included in the phrase "people." This indicator represents the population of a particular area. Growth rates are used to describe the differences in population that occur each year as a result of births, deaths, and net migration. In 2022, Russia had the highest population density in Europe—144.7 people per square mile. In terms of population size, Turkey came in second with 85 million people, followed by Germany with 83.4 million, the United Kingdom with 67.4 million, and France with 65.6 million. Vatican City has a population of just over 800, making it the world's least populous country. Vatican City is the smallest totally sovereign nation-state in the world.

The  frequency is 9/10 or 0.09

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Answer:

70x+44y

Step-by-step explanation:

step 1: distribute

84x+82y−(14x+38y)

84x+82y−14x−38y

step 2: combine like terms

84x+82y−14x−38y

84+82−14−38

70x+44y

The solution to the system of equations is (-2, -2)

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

The graph

On the graph, we have two lines that intersect at the point (-2, -2)

The point of intersection represent the solution

This means that the solution to the system of equations is (-2, -2)

Hence, the required solution is (-2, -2)

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Answer:

The third angle is 60

Step-by-step explanation:

The interior angle of a triangle is equal to the 180 minus the exterior angle.

[tex]180-80=100[/tex]

So one of the interior angles is equal to 100

All of the interior angles of a triangle add up to 180

[tex]180=100+20+x[/tex]

[tex]x=60[/tex]

Answer:

Below

Explanation:

y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y  ( equate the equations)

1/2 x + 1  = 3/2 x + 4    solve for 'x'

-3 = x      then use this value in one of the equations to calculate 'y'

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

An extraneous solution is not part of the solution set because it is not valid in the original problem context and may not satisfy the problem's constraints.

The scenario in problem 14 generates an extraneous solution because it is a solution obtained by squaring both sides of an equation, which can lead to extraneous solutions. These extraneous solutions may not satisfy the original equation, and hence, cannot be considered as a valid solution. To determine if a solution is extraneous, we must check if it satisfies the original equation. If it does not, then it is considered extraneous and should not be used.

In other words, an extraneous solution is an extraneous or unintended answer that is obtained as a result of an error in the solution method, but it may not satisfy the original equation or problem. This can occur when using algebraic methods that involve squaring, square roots, or other operations that can cause the equation to change in such a way that some solutions are no longer valid. To ensure that a solution is valid, it is always important to check that the solution satisfies the original equation, and not just the simplified or transformed equation.

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The image of △ABC is the triangle with vertices (-1, -6), (1, -2) and (3, -2)

The image of point (x,y) after reflecting across the x-axis is (x, -y) and after the translation it is (x + 4, -y).

Applying these transformations to each vertex of △ABC:

So, the image of △ABC is the triangle with vertices:

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the answer is in the picture.. if you have any questions feel free to ask

(B) 8n  (C) -6y (A) 23x  (D) -17w

Evaluation:

B. 10 + (-2) is the same as 10 - 2, the answer is 8.

C. 8 - 14 could be rewritten as -14 + 8, depending on which is easier to comprehend. The answer is -6

A. 9 + 14 = 23.

D. -6 - 11 is the same as -11 + (-6), which is -17.

Cheers,

qxxi

Answer:

No, the following ratios are not proportional, because they are not equal, nor can be reduced.

Step-by-step explanation:

Hope it helps! =D

$18021 is value of the principal investment

percentage, a relative value indicating hundredth parts of any quantity.

Given that after 16 years in an account with a 4.8% annual interest rate compounded continuously an investment is worth a total of $38,744.77

We have to find the value of the principal investment

[tex]A=Pe^{rt}[/tex]

Where P is the principal amount, r is rate of interest and A is total amount.

[tex]38744.77=Pe^{0.048(16)}[/tex]

[tex]38744.77=Pe^{0.768}[/tex]

38744.77=2.15P

Divide both sides by 2.15

18021=P

Hence, $18021 is value of the principal investment

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Answer:

its the 1st option

Step-by-step explanation:

i jus took the test

For the markov chain will end up in state 2, the probability that when the process moves into state 2, it does so from state 1 will be calculated as:

Let,

[tex]\tau = \min\{n: X_{n+1}= 2\}[/tex]

Now,

[tex]p_{i,j} = P(X_{\tau}=i|X_{0}=j)[/tex]

We can observe that,

[tex]p_{0,0} = P(X_{\tau}=0|X_{0}=0) = \sum_{k=0}^{2}{P(X_{\tau}=0,X_{1}=k|X_{0}=0)} [/tex]

[tex]=\sum_{k=0}^{2}{P(X_{1}=k|X_{0}=0)P(X_{\tau}=0|X_{1}=k,X_{0}=0)}[/tex]

A Markov chain or Markov process is a stochastic model that depicts a series of potential events where each event's likelihood is solely determined by the state it reached in the previous event. This can be thought of colloquially as, "What happens next depends only on the situation right now. Discrete-time Markov chains (DTMC) are produced by a countably infinite sequence where the chain changes state at distinct time steps. A continuous-time Markov chain (CTMC) is a continuous-time process. It bears the name Andrey Markov after the Russian mathematician. As statistical representations of processes in the real world, Markov chains have numerous uses.

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Answer:

15 weeks

Step-by-step explanation:

1 write an equation fore each

you                    sister

y=25+3x            y=40+2x    

y is total money and x is weeks

we want to find when they have the same amount of  total money we set them equal to echother

25+3x=40+2x

-2x             -2x

25+x=40

-25      -25

x=15

you will have the same amount as yore sister in 15 weeks

Answer:

see below

Step-by-step explanation:

you: 25 +$3 /week * x weeks

sis: 40 + 2/week * x weeks

they have to equal to each other

so 25 + 3x = 40 +2x

move x around & simplify

so x = 15

total 25+3*15 = 25+45 = 70

Answer:

Yurrrr Tha answer to your question is 2.8

Step-by-step explanation:

now tha full Answer is 2.88571429

but hope this help and hope you pass type xhii

A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.

Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.

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The required image of (−4,−4) after dilation by a scale factor of 5 centered at the origin is (-20, -20).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

A dilation with a scale factor of k, centered at the origin, will take a point (x,y) in the pre-image to the point (kx,ky) in the image.

Given the required image of (−4,−4) after dilation by a scale factor of 5 centered at the origin.

For x-coordinate:

- 4 × 5 = -20

For y-coordinate:

- 4 × 5 = -20

Thus, the required coordinates are (-20, -20).

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The area of the triangular prism is calculated as; 170 cm²

The given triangular prism when broken down is made up of;

2 triangles (top and bottom)

2 side rectangles

1 back rectangle

Formula for area of triangle = ¹/₂ * base * height

Formula for area of rectangle = length * width

Thus;

Area of trapezoid = 2(¹/₂ * 5 * 4) + 3(10 * 5)

Area = 20 + 150

Area = 170 cm²

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The constant variation rate is given as follows:

62.5 miles per hour.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Hence we can solve for the constant as follows:

k = y/x.

In the context of this problem, the constant variation rate is the constant of the proportional relationship, obtained dividing one output by it's respective input, hence:

k = 375/6

k = 62.5 miles per hour.

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For the obtuse triangle with 16 and 21 as two sides of the triangle there are 18 possible lengths for the third side

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

With the obtuse triangle we have the following rule:

a^2 + b^2 < c^2

a + b > c

So, lets called the third side (c)

c + 16 > 21 =  c > 5

c+21 > 16 = c > - 5

21 + 16 > c =  37 > c

The third side must be:  5 < c < 37

To be an obtuse triangle we have:

c^2 > 21^2 +16^2

c^2 > 697

c > 26 (positive integer)

Calculating if the other angles are obtuse:

21^2 > c^2 + 16^2

c^2 < 185

c < 14

16^2 > c^2 + 21^2

c^2 < a negative integer, not possible

This means that for the angle opposite the third side to be obtuse should be:

26 < c < 37

27,28,29,30,31,32,33,34,35,36 = 10 possible lengths

And for the angle opposite the side 21 to be obtuse, should be:

5 < c < 14

6,7,8,9,10,11,12,13 = 8 possible lengths

Total possible lengths = 10 + 8 = 18 possible lengths

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The graph that represents the compound inequality –3 < n < 1 is option C.

The two sides of a mathematical equation having an inequality must be equal. We compare two values via inequality rather than equations. The equal sign is replaced by the signs less than (or less than or equal to), greater than (or greater than or equal to), or not equal to.

The straight line from -3 to 1 with a hollow circle at the -3 point and the 1 point serves as the graph for the compound inequality -3 n 1. This is because n can only have values larger than -3, excluding -3, and less than -1, excluding -1, according to the symbol.

Therefore, the graph that represents the compound inequality –3 < n < 1 is option C.

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If the mean arrival rate is 6 customers per hour, then the mean inter-arrival time is calculated to be 10 minutes.

The mean arrival rate of customers = 6 customers/ hour.

Therefore, the mean inter-arrival rate is given as:

Mean inter-arrival rate = 1/ mean arrival rate = 1/6 hour = 1/6 * 60 minutes = 10 minutes.

The inter-arrival time is the time between two consecutive arrivals and is often modeled as an exponential random variable. The exponential distribution has a mean equal to the reciprocal of the rate parameter, which in this case is 6 customers per hour. So, the mean inter-arrival time is 1/6 hour or 10 minutes.

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If you divide $320 by 40 your answer is 8, so Mary probably earns 8 dollars an hour.

The mean duration of the game will be 70%.

The likelihood of not receiving any color will be equal to the likelihood of receiving one fewer ball of each hue:

P(green) = 2/5 P(red after green) = 3/6

P(green after yellow after red) = 1/4 0.5 x 0.4 x 0.25 = 0.05

Suppose we follow a different order:

Yellow has the following probabilities: P(yellow) = 1/6, P(red after yellow) = 3/5, and P(green after red after yellow) = 2/4.

As you can see, we also get denominators of 4,5,6, and numerators of 1, 3, and 2!

Therefore, the result probably will be 0.05 for any feasible combination (believe me on this one)!

How many possible combinations exist?

RGY\sRYG\sYGR\sYRG\sGRY\sGYR

6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.

6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.

The likelihood of all outcomes minus the ones we discovered, or 1 - 0.3 = 0.7, is the probability of not receiving distinct colors.

So 70% is the answer.

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The original polynomial is x^3 - x^2 + 8x + 26.

The division of a polynomial by a linear factor (x + 4) can be reversed by multiplication:

f(x) = (x^2 - x + 8) * (x + 4) + (-6)

Expanding the product on the right-hand side, we get:

f(x) = x^3 - x^2 + 8x + 32 - 6

f(x) = x^3 - x^2 + 8x + 26

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The ratio of the areas of the rectangles will be 4:9.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

We know that the sides cannot be the same because it is a rectangle, therefore there is a width and length.

For the width, which is the shortest side, we will keep the radius as it is, that is, for rectangle 1 it will be 2 and for rectangle 2 it will be 3.

For the length, which is the longest side, we multiply the radius by two, which means that rectangle 1 will be 4 (2 x 2) and for rectangle 2 it would be 6 (2 x 3)

If we calculate the area it would be:

Rectangle 1:

2 x 4 = 8

Rectangle 2:

3 x 6 = 18

This means that the radius is 8/18 = 4/9

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Answer: Yes

Step-by-step explanation: The value of x is 3 therefore the equation is balanced.

The average speed of aircraft to dry dock on the trip is given by the equation S₁ = 8 km/h

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the average speed to dry dock be represented as S₁

The time for aircraft for dry docking = 10 hours

Now , the equation will be

The average speed on the return trip S₂ = 20 km/h

The time for aircraft for the return trip = 11 hours

So , Speed = Distance / Time

Substituting the values in the equation , we get

The distance = average speed on the return trip S₂ x time

On simplifying the equation , we get

The distance D = 20 x 11 = 220 km

And , the average speed to dry dock S₁ = 220 km / 10 hour

On simplifying the equation , we get

The average speed to dry dock S₁ = 22 km/hr

Hence , the average speed is 22 km/hr

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