Palpa's Company manufactures bookbags, when the bookbags price is $75 the demand is 25; when the price is $20 the demand is 100 bookbags. But when the price is $50 the supply is 100 and for $25 the supply is 20.a. What is the demand function? b. What is the supply function c. What are the equilibrium price and quantity?

The numeric value of the exponential expression in this problem is given by the following option:

A. 2^12.

The exponential expression for this problem is defined as follows:

8^x/2^y.

8 is the third power of 2, hence:

8 = 2^3.

When a term is elevated to two of it's powers, the powers are multiplied, hence:

(2^3)^x = 2^(3x).

Meaning that the exponential expression is then written as follows:

8^x/2^y = 2^(3x)/2^y.

When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:

2^(3x)/2^y = 2^(3x - y).

As stated in the problem, the numeric value of the expression 3x - y is given as follows:

3x - y = 12.

Hence the entire expression is simplified as follows:

2^(3x - y) = 2^12.

Meaning that the correct option is given by option A.

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Answer:A. 2^12.

Step-by-step explanation:i did it and got it right

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

Step-by-step explanation:

The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:

Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ​

where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35​=−0.75

This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35​=0.5

This means that 36 psi is 0.5 standard deviations above the mean.

Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.

Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649

This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.

Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%

a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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Answer:

Step-by-step explanation:

45

The probability that the song will be played on exactly 2 days out of 5 days is approximately 0.164.

To find the probability that a particular song is played exactly 2 days out of 5 days at radio station WMZH, we can use the binomial probability formula.

The binomial probability formula is given by P(x) = C(n, x) * p^x * (1-p)^(n-x), where P(x) is the probability of x successful outcomes, n is the number of trials, p is the probability of a successful outcome on a single trial, and C(n, x) represents the binomial coefficient, which is the number of ways to choose x items from a set of n items.

In this case, we want to find the probability of the song being played exactly 2 days out of 5 days, so x = 2, n = 5, and p = 3/8.

Using the formula, we have:

P(2) = \(C(5, 2) * (3/8)^2 * (1 - 3/8)^(^5^-^2^)\)

C(5, 2) = 5! / (2! * (5-2)!) = 10

P(2) = 10 * (3/8)^2 * (5/8)^3

P(2) ≈ 0.164 (rounded to three decimal places)

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The value of m ∠ABD will be;

⇒ ∠ ABD = 50°

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

In the diagram, the parallel lines are cut by transversal BC.

And,  BD bisects ∠ABC and m∠3 = 80.

Now,

Since, The parallel lines are cut by transversal BC.

Hence, We get;

⇒ ∠ 3 + ∠ 2 = 180°

⇒ 80° + ∠ 2 = 180°

⇒ ∠ 2 = 180 - 80

⇒ ∠ 2 = 100

And, We have;

⇒ ∠ 2 = ∠ ABC

⇒ ∠ ABC = 100°

Since, BD bisects ∠ABC.

Hence, We get;

⇒ ∠ ABD = 100 / 2

⇒ ∠ ABD = 50°

Thus, The value of m ∠ABD = 50°

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Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

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The Length of the rectangle is: B. 6 2/3.

The area of a rectangle is calculated as: Area = (length)(width). Therefore, if we known the area of a rectangle and its width, we can find the length of the rectangle using:

Length of rectangle = area of rectangle / width of rectangle.

Given the following:

Area of a rectangle = 21 and 2 over 3 square inches

Width = 3 and 1 over 4 inches

Length of the rectangle = 21 2/3 ÷ 3 1/4

Length of the rectangle = 65/3 ÷ 13/4

Length of the rectangle = 65/3 × 4/13

Length of the rectangle = 260/39 = 6 2/3.

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the intersection points is where both equations' graph meet, or namely where one equation equals the other, or for this case when y = y, so

\(\begin{cases} y = 4x - 5\\ y = 2x^2-5x-10 \end{cases}\qquad \stackrel{y}{4x-5}~~ = ~~\stackrel{y}{2x^2-5x-10} \\\\\\ -5=2x^2-9x-10\implies 0=2x^2-9x-5 \\\\\\ 0=(x-5)(2x+1)\implies \begin{cases} 0 = x-5\\ 5 = x\\[-0.5em] \hrulefill\\ 0 = 2x+1\\ -1=2x\\ -\frac{1}{2}=x \end{cases}\)

well, we know what "x" is at those point, to get the "y" value, we can use either of the equations and substitute our "x" in it, hmmmm let's use the 1st equation for that

\(y = 4(\stackrel{x}{5})-5\implies y = 20-5\implies y = 15 \\\\\\ y = 4\stackrel{x}{\left( -\frac{1}{2} \right)}-5\implies y = -2-5\implies y = -7 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{intersection points}}{(5~~,~~15)\qquad \left(-\frac{1}{2}~~,~-7 \right)}~\hfill\)

The intersection points of the given system would be at the point:

\((5, 15) (-1/2, -7)\)

The two equations,

\(y=4x-5\)        \(...(i)\)

\(y=2x^2-5x-10\)     \(...(ii)\)

so,

\(-5 = 2x^2 - 9x - 10\) ⇒ \(0 = 2x^2 - 9x - 5\)

we get,

\((x - 5) (2x + 1) = 0\)

∵ \(x = 5 and x = -1/2\)

Now solving for \(y\) by putting the value of \(x\) in equation (i),

\(y = 4(5) - 5\)

∵ \(y = 15\)

\(y = 4(-1/2)^2 - 5\)

∵ \(y = -7\)

Thus, the values are \((5, 15) (-1/2, -7)\)

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Answer:

2.5

Step-by-step explanation:

We Know

You buy 4 5/8 blue fabric and 2 1/8 green fabric .

4 5/8 = 37/8 = 4.625 blue fabric

2 1/8 = 17/8 = 2.125 green fabric

How much blue than green did you buy?

We Take

4.625 - 2.125 = 2.5

So, you buy 2.5 blue more than green.

Answer:

x-a

Step-by-step explanation:

Mean=sum of data /no of data

=x-3a+x-2a+x-a+x+x+a/5

=5x-5a/5

=5(x-a)/5

=x-a

Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

Mr. X reduces his weight in a ratio of 4:17. This means that for every 4 units of weight he loses, his initial weight was divided into 17 equal parts.

To determine the ratio by which Mr. X reduces his weight, we need to compare his initial weight of 85 kg with his target weight of 65 kg.

The reduction in weight is calculated as the difference between the initial weight and the target weight, which in this case is 85 kg - 65 kg = 20 kg.

The ratio can be expressed as a fraction, where the numerator represents the reduction in weight and the denominator represents the initial weight:

Reduction in weight / Initial weight

Substituting the values, we have:

20 kg / 85 kg

Simplifying the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 5 in this case:

(20 kg / 5) / (85 kg / 5) = 4/17

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Answer:

The answer to the inequality is c >= 19.5. This means that the unknown number, represented by the variable c, must be greater than or equal to 19.5 in order for the inequality to hold true.

Step-by-step explanation:

Twice the difference of a number and 6 is at least 27

2 * (c - 6) >= 27

2c - 12 >= 27

2c >= 39

c >= 19.5

Please let me know if you have any questions.

Answer:

v = 10

Step-by-step explanation:

Solve for v:

3v + 2 = 32

3v = 30

v = 10

Verify with substitution:

3v + 2 = 32

Plug in 10 as v:

3v + 2 = 32

3(10) + 2 = 32

30 + 2 = 32

32 = 32

So, since these are equal, the solution is correct.

Step-by-step explanation:

v=10

3(10)+2 = 32

proved

The solution for the given expression is 14∛x. The correct option is (C).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

5∛x + 9∛x

The given expression can be simplified as follows,

5∛x + 9∛x

Here, both the terms have equivalent variables. So, both are like terms.

As per the rules like terms can be added or subtracted keeping the variable as the same.

Thus, 5∛x + 9∛x = 14∛x

Hence, the given expression can be evaluated as 5∛x + 9∛x = 14∛x.

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Step-by-step explanation:

yan po ang sagot ko dahil yan po ang pagkakaintindi ko

Answer:

~

Step-by-step explanation:

To make it easier to graph using a translation, we can rewrite the given equation as:

y - 5 = √√4x + 16

This is obtained by subtracting 5 from both sides of the equation.

The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.

Answer:

The correct option is D

The  standard deviation is mathematically represented as

    \(\sigma_p = 0.0244\)

Step-by-step explanation:

From the question we are told that

       The  population size is  \(N = 30,000\)

       The  sample  size is  \(n = 400\)

       The  population proportion is  \(p = 0.6\)

Generally for the sampling distribution of  \(\r p\) to be  normal  

         \(n = 0.05 N\)

and  \(np (1 - p ) \ge 10\)

Now  testing we have that

        \(0.05 N = 0.05 * 30 000 = 1500\)

So

     \(n < 1500\)

Now  let test the next condition

        \(np(1- p) = 400 * 0.6 (1-0.6) = 96\)

So

       \(np(1- p) > 10\)

Given that the  sampling distribution of \(\r p\) meets the above requirement it mean that the shape is normal

  Generally the standard deviation of the sampling distribution of \(\r p\) is mathematically represented as

      \(\sigma_p = \sqrt{\frac{p (1 - p)}{n} }\)

=>     \(\sigma_p = \sqrt{\frac{0.6 (1 - 0.6)}{400} }\)

=>     \(\sigma_p = 0.0244\)

The sampling distribution of the \(\hat{p}\) meets the requirement as shown above therefore the shape is normal. The correct option is D) Approximately normal because n≤0.05N and np(1−p)≥10.

Given :

In sampling distribution \(\hat{p}\) to be normal when:

n = 0.05N  

\(np(1-p)\geq 10\)

Now, check the above condition.

\(\rm 0.05N = 0.05\times 30000 = 1500\)

but n < 1500

Now, check \(np(1-p)\geq 10\).

\(30000\times 0.6\times (1-0.6) = 7200 > 10\)

The sampling distribution of the \(\hat{p}\) meets the requirement as shown above therefore the shape is normal.

Now, the standard deviation is given by:

\(\rm \sigma = \sqrt{\dfrac{p(1-p)}{n}}\)

\(\sigma_p = \sqrt{\dfrac{0.6(1-0.6)}{400}}\)

\(\sigma_p = 0.0244\)

Therefore, the correct option is D).

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The correct answer is: χ2 = 2.48, P-value is between 0.10 and 0.15.

First, let's calculate the expected frequencies for each political party affiliation in the sample:

Expected frequency for Democrats: 0.42 x 500 = 210

Expected frequency for Republicans: 0.34 x 500 = 170

Expected frequency for Independents: 0.24 x 500 = 120

Next, we can set up the chi-square test:

χ² = Σ((O - E)² / E)

Where:

O = observed frequency

E = expected frequency

Let's calculate the chi-square test statistic:

χ² = ((200-210)² / 210) + ((187-170)² / 170) + ((113-120)² / 120)

Calculating the above expression gives us:

χ² = (10² / 210) + (17² / 170) + (7² / 120)

χ^2 = 100/210 + 289/170 + 49/120

χ^2 ≈ 0.476 + 1.700 + 0.408

χ^2 ≈ 2.584

The calculated chi-square test statistic is 2.584.

Since we have 3 political party affiliations, the degrees of freedom would be 3 - 1 = 2.

Looking at the chi-square distribution table with 2 degrees of freedom, we find that the P-value for a chi-square test statistic of 2.584 is between 0.10 and 0.15.

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The x-values are the inputs.

The y-values are the outputs.

The missing value in the table for x = –1 is y = 6.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.

Conversely, a range is the set of all possible output numerical values (y-values) to a function and the range of a graph comprises all the output numerical values (real numbers) which are located on the y-coordinate.

Note: The coefficient of this equation y = 2 – 4x is 4.

When x = -1, the range (y-value) can be calculated as follows;

y = 2 – 4x

y = 2 – 4(-1)

y = 2 + 4

y = 6.

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Answer:

Rectangle

Step-by-step explanation:

Welcome to Brainly! :]

A rectangle uses A=lw to calculate area

Where l is length and w is width

Hope this helps,

:]

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(6,7) and B(-5,-9)

The midpoint is

\(M = ( \frac{6 - 5}{2} \: , \: \frac{7 - 9}{2} ) \\ = ( \frac{1}{2} \: , \: - \frac{2}{2} )\)

We have the final answer as

\(( \frac{1}{2} \: , \: - 1)\)

Hope this helps you

Answer:

Step-by-step explanation:

The first thing we need to focus on is the fact the large bag (30 cups) is 2.5 larger than the small bag. So, the first we need to do is divided 30 by 2.5, which is 12. (300/25 = 30/2.5 = 12, in case you're confused.) So the small bag has 12 cups of sugar.

What that down, we need to focus how many cakes the small bag can make, which was 9. 3/4 of a cup is left over. We can create an equation from that info, that being 9x + 0.75 = 12. Now let's solve for x.

9x + 0.75 = 12

First, subtract 0.75 from both sides. With that, we can solve for x directly.

9x = 12 - 0.75

9x = 11.25

Now, divide both sides by 9.

x = 11.25/9

x = 1.25

With that, we now know that each cake needs 1.25 cups of sugar.

With that, the last thing we need to is divide 30 by 1.25. Again, I can use powers of ten, to quickly divide 3000 by 125 (10²) to get 24 cakes.

With that done, we have our answer. 24 cakes can be made with a large bag of sugar.

I hope this helps!  (⌒ω⌒)

Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.

This shows, with dots, the number of times that each of the measures appears in a data set.

For finding the dot plot, we have that:

The shortest conifer measures 6 and 1/4

= 6.25 inches.

The tallest conifer measures 9.5 inches.

The difference is:

9.5 - 6.25 = 3.25 inches.

Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.

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Answer:

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Answer:

An angle are to rays that connect at one point.

Step-by-step explanation:

A ray is a straight line that cant not turn or change potions

when you take two rays and make them meet at one point you get an angle.Angles can be measured in degrees for example two rays meet both and there connected parts could make a square between the two sides this is a right angle and measures at 90 degrees. A protractor can be used to measure the exact angle. But I don't know if angle definition is different for collage students i'm in high school.

The measure of arc BC is 40⁰.

The measure of angle BPE is 50⁰.

The measure of angle BAD is 55⁰.

The measure of angle AOP is 110⁰.

The measure of angle AFB is 70⁰.

The value of arc DE is 110⁰.

The measure of each angle is calculated as follows;

if arc BA = arc CD, then value of arc BC is calculated as follows;

BA + CD + BC = 180 (sum of angles of a semi circle)

arc CD = 70 (intersecting chord theorem)

70 + 70 + BC = 180

140 + BC = 180

BC = 180 - 140

BC = 40

Arc AE = 70⁰, since angle EOF = 70 (vertical opposite angles)

Arc AB = 180 - (AE + BC)

arc AB = 180 - (70 + 40)

arc AB = 70⁰

The value of angle P is calculated as follows;

arc EB = 70 + 70 = 140⁰

m∠BPE = ¹/₂ (140 - 40)

m∠BPE = 50⁰

m∠BAD = ¹/₂ (BC + CD) (intersecting chord theorem)

m∠BAD = ¹/₂ (40 + 70)

m∠BAD = 55⁰

m∠AOP =  (AB + BC) (intersecting chord theorem)

m∠AOP = (70 + 40)

m∠AOP = 110⁰

m∠AFB = (AB) (intersecting chord theorem)

m∠AFB = 70⁰

The value of arc DE is calculated as follows;

DE = 360 - (180 + CD) (sum of angles of a circle)

DE = 360 - (180 + 70)

DE = 360 - 250

DE = 110⁰

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