From 1999 to 2000, the number of days of unhealthy air quality in Charlotte, North Carolina, dropped from 5 to 2. Find the percent of decrease in the number of days of unhealthy air.


A.
15%


B.
6%


C.
1.5%


D.
60%

Answer:

Step-by-step explanation:

-2.5,-0.15,0.50,5/8

The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

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Ren will have to wait for approximately 31 years for the money compounded annually and a rate of 2.3% to double it's original investment.

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.

The formula of compound interest is given as

A = P(1 + r/n)^nt

Substituting the values into the equation;

It will take approximately 31 years to double the investment.

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The probability of a carryout order being ready within 20 minutes is approximately 0.5507

We know that the time required for a carryout order to be ready for customer pickup follows an exponential distribution with a mean of 25 minutes. The probability density function for an exponential distribution is given by

f(x) = λe^(-λx)

where λ is the rate parameter

We can find the rate parameter λ using the mean

mean = 1/λ

λ = 1/mean = 1/25 = 0.04

So the probability of a carryout order being ready within 20 minutes is

P(X ≤ 20) = ∫₀²⁰ λe^(-λx) dx

P(X ≤ 20) = [-e^(-λx)]₀²⁰

P(X ≤ 20) = [-e^(-0.04x)]₀²⁰

P(X ≤ 20) = [-e^(-0.8)] - [-1]

P(X ≤ 20) = 0.5507

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The given question is incomplete, the complete question is:

Collina’s Italian Café in Houston, Texas, advertises that carryout orders take about 25 minutes (Collina’s website, February 27, 2008). Assume that the time required for a carryout order to be ready for customer pickup has an exponential distribution with a mean of 25 minutes. What is the probability than a carryout order will be ready within 20 minutes?

The selling price of the 501 carat diamond rings is approximately $168,750.00, rounded to the nearest cent.

To find the selling price of the 501-carat diamond rings, we need to use the information given about the cost of the purchase and the markup percentage.

Let's assume the markup percentage is m. Then, the selling price S can be calculated as:

S = C * (1 + m/100)

where C is the cost of the purchase ($125,000 in this case).

If the markup percentage is not given, we can use another piece of information to calculate it. For example, if we know that the company wants to earn a profit of P dollars on the sale, we can set the equation:

S - C = P

and solve for the markup percentage:

m = (P/C) * 100

Assuming a markup percentage of 35%, we can calculate the selling price as:

S = 125,000 * (1 + 35/100)

S ≈ $168,750.00

Therefore, the selling price of the 501 carat diamond rings is approximately $168,750.00, rounded to the nearest cent.

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Answer:

33%

Step-by-step explanation:

If you add all them together you get 24 right? Then do 8/24 then you get 0.3333333

Answer:

18:30 or 9:15 depending on if you need to simplify

Step-by-step explanation:

Answer:

\(3 \div 2 \times 7 \div 2 \times 4 \div 1\)

\(21 \div 4 \times 4 \div 1\)

So the correct ans. Is 21

i know its 21

i took quiz

Answer:

Question 1)

One possible equation is:

\(\displaystyle 11x^2 - 15x + 10 = 0\)

Question 2)

Choice C

The equation is:

\(2x^2 + 6x + 3=0\)

Step-by-step explanation:

Question 1)

Recall that the quadratic formula is given by:

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

We want to find a quadratic with the solutions:

\(\displaystyle x = \frac{15\pm\sqrt{-215}}{22}\)

Each value must be equal to its corresponding expression. That is:

\(\displaystyle -b = 15,\, 2a = 22, \text{ and } b^2 -4ac = -215\)

We can solve for b and a:

\(\displaystyle b = -15 \text{ and } a = 11\)

Now, we can solve for c:

\(\displaystyle \begin{aligned} b^2 - 4ac &= -215 \\ \\ (-15)^2 - 4(11)c &= -215 \\ \\ (225) - 44c &= -215 \\ \\ -44c &= -440 \\ \\ c &= 10 \end{aligned}\)

Hence, a = 11, b = -15, c = 10.

The quadratic formula is applied to quadratics in the form:

\(\displaystyle ax^2 + bx + c =0\)

Substitute. Hence, one possible equation is:

\(\displaystyle 11x^2 - 15x + 10 = 0\)

Note: There are infinitely many equations that will have the given solutions. The new equations will simply be the above equation multiplied by a constant.

Question 2)

We are given the equation:

\(ax^2 + 6x + c= 0\)

And we want to find two integer values for a and c such that the equation has two real solutions.

Recall that the number of solutions of a quadratic is given by its discriminant:

\(\displaystyle \Delta = b^2 - 4ac\)

The quadratic will have two real solutions for positive discriminants. In other words:

\(b^2 - 4ac > 0\)

We know that b = 6. Substitute and simplify:  

\(\displaystyle \begin{aligned}b^2 - 4ac & >0 \\ \\ (6)^2 - 4ac & > 0 \\ \\ 36 - 4ac &> 0 \\ \\ -4ac &> -36 \\ \\ ac &< 9 \end{aligned}\)

So, the product of a and c must be less than 9.

From the given answer choices, only Choice C is correct.

Therefore, a = 2 and b = 3.

Then our equation is:

\(2x^2 + 6x + 3=0\)

The area of the surface is  found to be π using the integrating over the region R.

The given surface equation is z=√1−y².

To find the area of the surface z=√1−y² over the disk x²+y²≤1,

we can use the surface area formula for a surface given by a function of two variables:

Surface area = ∫∫√(f_x)²+(f_y)²+1 dA,

where f(x,y) = z = √1-y

²In this case, the surface area can be found by integrating over the region R, the disk x²+y²≤1.

∴ Surface area = ∫∫√(f_x)²+(f_y)²+1 dA

= ∫∫√(0)²+(-2y/2√1-y²)²+1 dA

= ∫∫√(4/4-4y²) dA = ∫∫1/√(1-y²) dA,

where the region of integration R is the disk x²+y²≤1

On integrating with polar coordinates, we get

∴ Surface area = ∫∫√(f_x)²+(f_y)²+1 dA

= ∫∫√(0)²+(-2y/2√1-y²)²+1 dA

= ∫∫√(4/4-4y²) dA

= ∫∫1/√(1-y²) dA

∫∫√(f_x)²+(f_y)²+1 dA = ∫0^{2π}∫_0^1 r/√(1-r²sin²θ) drdθ

= 2π∫_0^1 1/√(1-r²) dr = π

Therefore, the area of the surface is π.

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Answer:

(2, 20) makes both equations true

Step-by-step explanation:

If a point is a solution for 2 equations, that means that it makes both equations true.

So, since (2, 20) is a solution to both y = 10x and x + y = 22, that means it makes both of the equations true.

Answer:

the answer is b (Barbara's equation did not consider the number of bottles of iced tea.)

Step-by-step explanation:

its math i did years ago its like simple math for me. trust me i know its right

Answer:

c = 4t + 8

Step-by-step explanation:

Answer:

Solve the equation 119 = n - 66 and the options are: a. 53, b.186, c. -185, d. 185

solution :

From these we can get is;

119 = n – 66

=> n = 119 + 66

=> n = 185

So option d ) 185 is the correct answer

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Disclaimer: the question was given incomplete on the portal. Here is the Complete Question.

Question: Solve the equation 119 = n - 66 and the options are: a. 53, b.186, c. -185, d. 185

We get that the value of n is option (d) 185 for the equation n - 66 = 119.

We are given an equation:

n - 66 = 119.

An equation is an expression that has an equality sign in between.

For example: 3 x + 3 y = 6 or 7 x + 5 y = 9

We have to solve the equation to find the value of n.

First, we will add 66 to both the sides of the equation.

n - 66 + 66 = 119 + 66 .

Now simplifying the expression, we get that:

n = 119 + 66

Solving the expression to get the value of n:

n = 185

So, option (d) 185 is correct.

Therefore, we get that the value of n is option (d) 185

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The p-value is a statistical term that represents the probability of observing an outcome as extreme as or more extreme than the observed outcome, given that the null hypothesis is true. It is used to determine whether the null hypothesis should be rejected or accepted. If the p-value is less than the level of significance (alpha), the null hypothesis can be rejected, and the alternative hypothesis can be accepted.

Large p-values indicate that there is not enough evidence to reject the null hypothesis. A large p-value implies that the observed result is not significant, and the null hypothesis is supported.

The alpha level is a significance level that is set in advance of conducting a hypothesis test. It determines the level of evidence required to reject the null hypothesis. The alpha level is usually set at 0.05, meaning that the null hypothesis can be rejected if the p-value is less than 0.05.

A result is statistically significant if it is unlikely to have occurred by chance. In other words, if the p-value is less than or equal to the alpha level, the result is considered statistically significant, and the null hypothesis can be rejected.

A 95% confidence interval corresponds to a two-sided hypothesis test at an alpha level of 0.05. This means that the null hypothesis can be rejected if the observed outcome falls outside the confidence interval with a probability of 0.05 or less.

A 90% confidence interval corresponds to a one-sided hypothesis test at an alpha level of 0.1. This means that the null hypothesis can be rejected if the observed outcome falls outside the confidence interval with a probability of 0.1 or less.

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From the given information, we get the value of ABC = 120°.

Given: In the figure, O exists the center of the circle and OABC exists as a parallelogram.

Now, the radius of the circle exists

OA = OB = OC

Opposite sides of a parallelogram are equal

AB = OC and OA = BC

In ∆OAB,

OA = OB = AB and,

In ∆OCB,

OC = OB = BC

Therefore, ∆OAB and ∆OCB exist in equilateral triangles.

All angles of an equilateral triangle are equivalent to 60°.

Hence, ∠ABC = ∠OBA + ∠OBC

∠ABC = 60° + 60°

∠ABC = 120°

Therefore, the value of ∠ABC = 120°.

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By the use of the trigonometric ratios, the height of the paraglide is 244 ft.

The trigonometric ratios are used to obtain the sides of a right angled triangle. In this case, the geometry of the problem can be reduced to a right angled triangle.

Thus we have;

sin 35 = x/400

x = 400 sin35 = 229 ft

Hence, height of the paraglider = 229ft + 15 ft = 244 ft

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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The statement "the first step in the sampling design process is to determine the sample size" is false because according to the text, the first step in the sampling design process is to clearly define the target population.

The first step in the sampling design process is typically to define the target population and the research objectives.

This involves specifying the characteristics of the population under study and identifying the specific research questions or objectives that the sampling will address.

Once the target population and research objectives are established, the next steps in the sampling design process typically involve determining the appropriate sampling method (such as random sampling, stratified sampling, or cluster sampling) and selecting the sampling frame (the list or source from which the sample will be drawn).

After these initial steps, researchers can then consider factors such as the desired level of precision, confidence level, and variability in the population to determine the appropriate sample size.

The determination of the sample size usually comes after clarifying the research objectives and selecting the appropriate sampling method.

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Answer:

Explanation:

The first step is to find the equation of each line. The equation of a line in the slope intercept form is expressed sd

y = mx + c

Answer: she needs to go 12 times

Step-by-step explanation:

Answer:

*12=3x+4m-3x2.......THE ANSWER IS 10

Step-by-step explanation:

divide 12 by 3

add that answer by 4

subract that by 3

then multiply it by 2

and it gives you... (10)

Your Welcome

Answer:

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

Find each area and then find their difference.

The difference is:

The length of the segment in the complex plane is 5.

The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:

Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.

Plugging these values into the formula, we have:

Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
         = sqrt(3^2 + (-4)^2)
         = sqrt(9 + 16)
         = sqrt(25)
         = 5

Therefore, the length of the segment in the complex plane is 5.

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Answer:

?

Step-by-step explanation:

Heyo!

So, the best prediction for the height of the rocket after 5.5 seconds, based on the given data above, I believe would be C. 220 ft.

Hope this helps! Pls, LMK if it does! Good Luck!

The best prediction for the height of the rocket after 5.5 sec will be 220 feet.

A quadratic equation is an equation where the highest power of the variable is 2.

Given data for the height of the rocket at different time is modeled by the function  h(t) = -16t² + 128t

The height of the rocket after 5.5 sec will be

= h(5.5) = [- 16(5.5)² + 128 × 5.5] feet = (- 484 + 704) feet = 220 feet.

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The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).

In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.

Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).

Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).

Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).

To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:

Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)

Simplifying this expression, we get:

Total number of strings = (n-1) x (n-2)

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