P=70q, p=-q^2+12000
Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given

Corresponding to the data, we can deduce that the stairs can be broken into a series of blockish prisms.

The stairs can be broken into a series of blockish prisms. The confines of each blockish prism would be the same range and height as the stairs, but the length of each blockish prism would be the depth of one step.

To determine the quantum of concrete demanded to form the stairs, you would need to calculate the total volume of all the blockish prisms that make up the stairs. This can be done by multiplying the length, range, and height of each blockish prism and also adding the volumes of all the blockish prisms together.

The formula for calculating the volume of a blockish prism is V = l x w x h, where V is the volume, l is the length, w is the range, and h is the height. So, for illustration, if each stair is 3 bases wide,1.5 bases high, and 1 bottom deep, and there are 10 stairs, also the total volume of concrete demanded would be

V = (3 x 1.5 x 1) x 10 = 45 cubic feet of concrete.

Note that this calculation assumes that there is no space between the stairs or the rectangular prisms making up the stairs. If there is any space between the stairs or the rectangular prisms, this would need to be accounted for in the calculation.

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the amount of paint required is dependent on the size of the area that needs to be painted.

In an equation or algebraic expression, an uncertain amount is denoted by a symbol in algebra, which is often a letter. A variable is, in the simplest terms, a quantity that can change and is not fixed. The two primary categories of variables are categorical and numerical. Then, for both categorical and numerical variables, discrete or continuous subcategories are created for each category. In this section, a summary of several categories is provided. a measure that can take many different forms. Something that can alter; the sign of a variable; a variable in a scientific experiment.

Because it is the variable which the homeowner may alter or control, the area of the house that needs to be painted in this scenario is the independent variable. Because it depends on the portion of the home that needs to be painted, the overall quantity of paints that need to be obtained is a variable that is dependent. To put it a different way, the amount of paint required depends on the size of the area that needs to be painted.

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slope= y2 - y1/ x2 - x1 ( take (-4, -6) as 1 and (8,9) as 2 where 9 and -6 are y2 and y1 respectively and 8 and -4 as x2 and x1 respectively)

- slope = 9 - (-6) / 8 - (-4)= 9 + 6/ 8 + 4

- slope = 15 / 12 (simplify)

- slope = 5/ 4

Answer:

[tex]m = \frac{14 - 7}{2 - 0} = \frac{7}{2} [/tex]

[tex]14 = \frac{7}{2} (2) + b[/tex]

[tex]14 = 7 + b[/tex]

[tex]b = 7[/tex]

[tex]y = \frac{7}{2} x + 7[/tex]

Answer:

351-7 cm³

Step-by-step explanation:

Volume a cylinder = π r² h

π = 3.14

r = radius = 4cm

h = height = 7cm

Then:

Volume = 3.14 * 4² * 7

volume = 3.14 * 16 * 7

volume = 351.7 cm³

The accountant should use a left-tailed hypothesis test to analyze whether the average amount of a tax refund is less than 250 dollars.

A left-tailed test is used when the null hypothesis states that the population mean is greater than or equal to a certain value, and the alternative hypothesis states that the population mean is less than that value. In this case, the null hypothesis would be that the average amount of a tax refund is greater than or equal to 250 dollars, and the alternative hypothesis would be that the average amount is less than 250 dollars.

what is average amount?

The average amount, also known as the mean, is a measure of central tendency that represents the sum of a set of values divided by the total number of values in the set. It gives an idea of the typical value or the central value of a dataset.

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only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

How to solve the question?

The mathematical term "indirectly proportional" refers to a relationship in which two variables are related in such a way that when one increases, the other decreases, and vice versa. In other words, the two variables vary in opposite directions.

Out of the four equations given, only one shows an indirect proportional relationship. This equation is:

y=1/x

In this equation, y and x are indirectly proportional. As x increases, the value of 1/x decreases, and therefore, the value of y decreases as well. Similarly, as x decreases, the value of 1/x increases, and the value of y increases as well. This relationship is commonly known as an inverse relationship, where the two variables vary in opposite directions.

On the other hand, the other three equations do not show an indirect proportional relationship. The equation y=5x shows a direct proportional relationship, where y increases as x increases and vice versa. The equation y=-2x+1 is a linear equation with a negative slope, where y decreases as x increases, and y increases as x decreases. Lastly, the equation y=3x+5 is also a linear equation with a positive slope, where y increases as x increases, and y decreases as x decreases.

In summary, only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

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For a hypothesis testing, [tex]H_0 : µ = µ_0[/tex] ; [tex]H_1 : µ > µ_0.[/tex] the calculated P-value for test statistic value are following a) 0.9906 ; b) 0.9370 ; c) 0.9773; d) 0.9678 ; e) 0.4404.

We are testing the null hypothesis versus alternative hypothesis. Both are defined as [tex]H_0 : µ = µ_0[/tex]

[tex]H_1 : µ > µ_0.[/tex].

We have to calculate the P-value for the following observed values test statistic one by one.

a)z = 2.35

The P -value is calculated for as follows P ( z > Zo) = 1 - P( z≤ z0)

= 1 - P( z≤ 2.35)

Now, using the normal distribution table, the value of P( z≤ 2.35) is equals to 0.009387. So, P( z> 2.35) = 1 - 0.009387

= 0.990613

b) z₀ = 1.53

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.53)

Now, using the normal distribution table , the value of P( z≤ 1.53) is equals to 0.063008. So, P( z> 1.53) = 1 - 0.063008

=0.936992

c) z₀ = 2.00

The P-value is calculated for as follows, P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 2.00)

Now, using the normal distribution table , the value of P( z≤ 2.00) is equals to 0.02275. So, P( z> 2.00) = 1 - 0.02275

=0.97725

d) z₀ = 1.85

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.85)

Now, using the normal distribution table , the value of P( z≤ 1.85 ) is equals to 0.032157. So, P( z> 1.85) = 1 - 0.032157

=0.967843

e) z₀ = -0. 15

The P-value is calculated for as follows P ( z > -z₀) = P( z ≤ z₀)

= P( z≤ 0.15 )

Now, using the normal distribution table , the value of P( z≤ 0.15) is equals to 0.440382. So, P( z > - 0.15) = 0.44038. Hence the required P-value is 0.44038.

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Answer:

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

The current volume of the cylinder is:

V = π(12cm)^2(15cm)

V = π(144cm^2)(15cm)

V = 2160π cm^3

If the dimensions of the cylinder are tripled, then the new cylinder will have a radius of 3(12cm) = 36cm and a height of 3(15cm) = 45cm.

The new volume of the cylinder is:

V = π(36cm)^2(45cm)

V = π(1296cm^2)(45cm)

V = 58320π cm^3

Simplifying the expression, we get:

V ≈ 183,124.8 cm^3

Therefore, the volume of the new cylinder, when the dimensions are tripled, is approximately 183,124.8 cm^3.

The answer is C) 183,124.8 cm^3.

Hi,

-The correct answer should be "option 4," 45,781.2 cm ^3.

Let me know if my answer is wrong or not what you were looking for because I would like to help all I can.

If you have any questions let me know and I may be able to help.

I hope that my answer helped you out. :)

Here is the correct figure if anybody needs it. ⇅

The area of the floor of the igloo is 842.9 m²

We know that the formula for the volume of hemisphere is given by,

V = (2/3) × π × r³

where r is the radius of the hemisphere

Here, a hemisphere igloo has a volume of about 9,202.8 m³

Using above formula of the volume of hemisphere,

V = (2/3) × π × r³

9202.8 = (2/3) × π × r³

r³ = 9202.8 × (3/2π)

r³ = 4394.01

r = 16.38 m

We know that the area of the floor of the igloo is equivalent to the area of circle, as the base of hemisphere is a circle.

So, the area of the floor of the igloo would be,

A = π × r²

A = π × 16.38²

A = 842.9 m²

Therefore, the required area is 842.9 m²

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The expansion of the polynomial (-p²+4p-3)(p²+2) would be is -p⁴ + 4p³ - 5p² + 8p - 6  

Here we need to expand the polynomial (-p²+4p-3)(p²+2)

To do so we need to multiply each of the term with the first bracketby the each term of second bracket.

So, the expansion of the polynomial (-p²+4p-3)(p²+2) would be,

(-p² + 4p - 3)(p² + 2)

= [p² × (-p² + 4p - 3)] + [2 × (-p² + 4p - 3)]

= [p² × (-p²) + p² × 4p - p² × 3] + (-2p² + 8p - 6)

= (-p⁴ + 4p³ - 3p²) + (-2p² + 8p - 6)

= -p⁴ + 4p³ - (3 + 2)p² + 8p - 6       .......(add like terms)

=  -p⁴ + 4p³ - 5p² + 8p - 6  

Therefore, the required polynomial is -p⁴ + 4p³ - 5p² + 8p - 6  

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Answer: 350

Step-by-step explanation:

First, 32% divided by 100 becomes a decimal.

     32% / 100 = 0.32

Next, let x be equal to a number.

Then, "of" indicates multiplication and "is" indicates equals.

     0.32x = 112

Lastly, we will divide both sides of the equation by 0.32.

     x = 350

This problem can be represented by turning 32% into a decimal and rewriting it like this: .32x = 112, where x is the unknown number. Dividing both sides of the equation by .32 gives you x = 350, so 32% of 350 is 112

The probability of drawing a matching pair of socks is 1/5 or 0.2.

The basic principle of probability, states that the probability of an event happening is the number of ways the event can occur divided by the total number of possible outcomes.

In this problem, we first calculated the number of ways to draw a matching pair of socks for each of the three possible colors.

We then added these probabilities together to get the total probability of drawing a matching pair of socks.

Here we have

A box contains two white socks, two blue socks, and two red socks.

To find the probability of drawing a matching pair of socks, consider the different cases of matching pairs of socks that can be drawn.

Case 1: Matching white socks

The probability of drawing one white sock = 2/6

After drawing one white sock,

Remains 5 socks and of which 1 is white

The probability of drawing 2nd white sock =  1/5  

Hence, probability of selecting 2 white socks = (2/6) × (1/5) = 1/15

Similarly, we can calculate probabilities for Red and Blue socks

Case 2: Matching blue socks

The probability of drawing two blue socks is (2/6) × (1/5) = 1/15  

Case 3: Matching red socks

The probability of drawing two red socks is (2/6) × (1/5) = 1/15.

Therefore, the total probability of drawing a matching pair of socks is the sum of the probabilities of each of these cases:

P(matching pair) = P(white) + P(blue) + P(red)

= 1/15 + 1/15 + 1/15 = 3/15 = 1/5

Therefore,

The probability of drawing a matching pair of socks is 1/5 or 0.2.

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Answer:

Step-by-step explanation:

4x - 3 ≤ -7

Add 3 to both sides of the inequality to isolate the term with x on one side:

4x - 3 + 3 ≤ -7 + 3

4x ≤ -4

Divide both sides of the inequality by 4 to solve for x:

4x/4 ≤ -4/4

x ≤ -1

So, the solution to the inequality is x ≤ -1. The largest integer value of x that satisfies this inequality is -1.

Answer:

Less

Step-by-step explanation:

Look at the hundreds number in set L the numbers are greater in Set L than Set K.

The two questions should you ask are:

The given answers to the above questions, one can be able to know the ranges of values that the four numbers have, as well as their relative positions.

In the event that we know the smallest and biggest numbers, we can be ready to mark those points on the number line and after that put the other two numbers in between them agreeing to their relative positions.

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Answer: No, it is not likely that 60% of Skyline College students say math is their favorite subject based on the given confidence interval of (0.6358, 0.7532).

The confidence interval tells us that we are 95% confident that the true proportion of Skyline College students who say math is their favorite subject lies between 0.6358 and 0.7532. This means that if we were to take many random samples from the population of Skyline College students and construct 95% confidence intervals for the proportion of students who say math is their favorite subject, 95% of those intervals would contain the true population proportion.

Since 0.60 is not within the interval (0.6358, 0.7532), it is unlikely that the true proportion of Skyline College students who say math is their favorite subject is 60%. However, we cannot make any definitive statements about the population proportion based on this one confidence interval alone.

Step-by-step explanation:

Answer:

x=162

Step-by-step explanation:

55+x-87+50=180

x+18=180

x=162

Starting from the same point when bike riding, two individuals are riding. Tom and Juanita goes on biking in opposite directions to each other. Tom rides at speed of 30 mph and Juanita rides at speed of 30 mph in one hour. This will both be added together. And later will be add both speed in third hour that gives us the final value. The answer of this will be seventy two miles.

[tex]30+30[/tex] in one hour

[tex]30+30[/tex] in second hour

[tex]30+30[/tex] in the third hour

[tex]\boxed{\bold{= 270 \ miles}}[/tex]

Since the 95% confidence interval includes zero, we cannot conclude that the population means are different without conducting the test in part a.

a. Significance test:

Null hypothesis (H0): The population means are equal for females and males (μ1 = μ2).

Alternative hypothesis (H1): The population means are not equal for females and males (μ1 ≠ μ2).

Significance level (α): 0.05

We will use a two-sample t-test for independent samples to compare the means:

Calculate the pooled variance (Sp^2):

Sp^2 ≈ 5.27

Calculate the standard error (SE):

SE ≈ 0.11

Calculate the t-statistic:

t ≈ 1.18

Calculate the degrees of freedom (df):

df = N1 + N2 - 2

df = 1117 + 870 - 2

df = 1985

Comparing the t-statistic and the critical t-value for a two-tailed test with α = 0.05:

t_critical ≈ ±1.96 (from t-distribution table)

Since -1.96 < 1.18 < 1.96, we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to conclude that the population means differ for females and males at a 0.05 significance level.

b. 95% confidence interval:

Calculate the margin of error (ME):

ME = t_critical * SE

ME = 1.96 * 0.11

ME ≈ 0.22

Calculate the difference in means (M_diff):

M_diff = M1 - M2

M_diff = 2.99 - 2.86

M_diff = 0.13

Determine the 95% CI for the difference in means:

CI = (0.13 - 0.22, 0.13 + 0.22)

CI ≈ (-0.09, 0.35)

Since the 95% confidence interval includes zero, we cannot conclude that the population means are different without conducting the test in part a.

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The number of kilometres that are equivalent to 28.5 cm² is 2.85 × 10⁹ km². Hence, after careful consideration concerning every option, the required answer for the given question is Option A.

Here, we have to depend on the principles of conversation of units and using this principles derive a formula.

To convert 28.5 cm² to km², we have to implement the formula

Total number of square centimeters x 1.0 x [tex]E^{-10}[/tex] = Total number of square kilometers .

The number of kilometres that are equivalent to 28.5 cm² is 2.85 × 10⁹ km². Hence, after careful consideration concerning every option, the required answer for the given question is Option A.

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The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.

The total number of combinations of selecting 5 cards from a deck of 52 cards is 52C5 = 5251504948/120 = 2598960.

The probability of exactly 4 of the 5 cards being Aces is 48*100/2598960 = 0.0018%.

The probability of all 5 of the cards being Spades is 1287*100/2598960 = 0.0495%.

The probability of exactly 4 of the 5 cards being face cards is 49540100/2598960 = 0.7618%.

The probability of exactly 2 Aces and exactly 2 Kings being selected is 1584*100/2598960 = 0.0609%.

The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.

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The measure of the angle m∠HLK subtended by the arc HK is derived to be equal to 45°.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference.

Given that the arc HK = 90°

arc measure and the angle it subtends at the center of the circle are directly proportional.

so arc HK = m∠HJK = 90°

m∠HJK = 2(m∠HLK)

2(m∠HLK) = 90°

m∠HLK = 90°/2 {divide through by 2}

m∠HLK = 45°

Therefore, the measure of the angle m∠HLK subtended by the arc HK is derived to be equal to 45°.

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A measure of relative fit for a simple regression line is called the r² or coefficient of determination.

A regression line, or line of best fit, is a straight line used to model the relationship between two variables in a data set. It is drawn through the data points to minimize the distance between the line and the points, representing the best fit. The line's equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the value of y when x is equal to 0. The line is often used to predict the dependent variable based on the independent variable, and the accuracy of the predictions depends on how well the line fits the data.

The coefficient of determination, also known as r², is a statistical measure used to determine the relative fit of a simple regression line. This measure represents the proportion of variance in the dependent variable that can be predicted by the independent variable. The calculation involves squaring the correlation coefficient (r) between the two variables. The resulting value of r² ranges from 0 to 1, where 0 indicates that the independent variable has no explanatory power over the dependent variable, while 1 implies that the independent variable explains all the variability in the dependent variable.

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The roof area is 468.75 square feet.

To find the roof area, we need to follow these steps:
Determine the rise (vertical distance) using the slope of 9 inches per foot:

Since the run is 10 feet, the rise is 9 inches/foot × 10 feet = 90 inches.
Convert the rise to feet: 90 inches ÷ 12 inches/foot = 7.5 feet.
Calculate the length of the rafter using the Pythagorean theorem:

Rafter length = √(run² + rise²) = √(10² + 7.5²) = √(100 + 56.25) = √156.25 = 12.5 feet.
Determine the total length of the gable roof:

Since the rake slope is 1.25, we have Total length = Rafter length × Rake slope = 12.5 feet × 1.25 = 15.625 feet.
Calculate the roof area:

Roof area = Eaves length × Total length = 30 feet × 15.625 feet = 468.75 square feet.
None of the given options matches the calculated roof area.

It is possible there is a mistake in the question or the provided options.

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Answer: 6(x - (23/2))² = 14x + 1044

Step-by-step explanation:

First, we need to move all the terms to one side of the equation:

6x² - 46x - 312 - 14x = 0

Next, we need to factor out the coefficient of the x² term:

6(x² - (46/6)x) - 312 - 14x = 0

Simplifying:

6(x² - 23x) - 312 - 14x = 0

To complete the square, we need to add and subtract the square of half the coefficient of the x-term inside the parentheses:

6[(x - (23/2))² - (23/2)²] - 312 - 14x = 0

Simplifying:

6(x - (23/2))² - 6(23/2)² - 312 - 14x = 0

Expanding the square term:

6(x - (23/2))² - 1044 - 14x = 0

Finally, adding 1044 to both sides and simplifying:

6(x - (23/2))² = 14x + 1044

The intermediate step after completing the square is:

6(x - (23/2))² = 14x + 1044

Answer:

35.00 - (0.85x) = remaining amount

Step-by-step explanation:

To find out how much money she has left, we need to subtract this amount from her starting amount of $35.00:

35.00 - 0.85x

Therefore, the expression that shows how much money Pam has left after buying (x) peaches is:

35.00 - 0.85x

Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

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