q(x)=-7x^3+9x^2-8x+2 (a) Possible number(s) of positive real zeros: & (b) Possible number(s) of negative real zeros:

Answer:

C. (x+2)2=3

Step-by-step explanation:

Take the root of both sides and solve.

Both x2+4x-5=0 and (x+2)2=3 have the solution of x=1,-5

have a great day and thx for your inquiry :)

Obsa will need 2 smaller prisms to fill the larger prism, with each smaller prism having a volume of 4/3 cubic feet.

To find out how many smaller prisms it would take to fill the larger one, we need to first determine the volume of the larger prism. We know that the larger prism has a volume of 2 1/3 cubic feet, which can also be expressed as 7/3 cubic feet.
Next, we need to find out how many of the smaller prisms will fit into the larger one.

To do this, we can divide the volume of the larger prism by the volume of the smaller prism.

The smaller prism has a volume of 4/3 cubic feet, so:
(7/3 cubic feet) / (4/3 cubic feet) = 7/4
This means that it will take 7/4 smaller prisms to fill the larger prism.

However, since we can't have a fraction of a prism, we need to round up to the nearest whole number.
Therefore, it will take 2 smaller prisms to fill the larger prism. One prism will fill up 4/3 cubic feet, and the other will fill up 4/3 cubic feet, totaling to 8/3 cubic feet, which is just a bit more than the 2 1/3 cubic feet of the larger prism.
This means that it takes 1 and 3/4 smaller prisms to fill the larger container.

However, since we cannot have a fraction of a prism, we need to round up to the nearest whole number, which is 2.

Therefore, it would take 2 smaller prisms to fill the larger prism-shaped container.

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The graph of the inequality is a downward-opening parabola that passes through (0, 7) and (8, -9). The shaded region is below the curve.

y≤-1/2x² + 4x + 7

The inequality is a quadratic function in standard form.

To graph it, we can find the vertex and the x-intercepts.

The vertex is at the point (h, k) where h = -b/2a and k = f(h), and f(x) = -1/2x² + 4x + 7.

a = -1/2, b = 4, and c = 7,

so h = -b/2a = -4/(-1) = 4, and

k = f(h) = -1/2(4)² + 4(4) + 7 = 15.

So the vertex is at (4, 15).

Now let us find the x-intercepts by setting y value as 0 and solve for x:

0 ≤ -1/2x² + 4x + 7

1/2x² - 4x - 7 ≤ 0

x² - 8x - 14 ≤ 0

We find roots by using the quadratic formula

x = (8 ± √8² - 4(1)(-14))) / 2

x = 4 ± √18

So the x-intercepts are  0.34 and 7.66.

Hence, the graph of the inequality is a downward-opening parabola that passes through (0, 7) and (8, -9). The shaded region is below the curve.

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Explain the graph of the inequality y≤-1/2x² + 4x + 7?

Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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Answer:

p=$16.5

Step-by-step explanation:

By using the distributive Property, you can say:

5p-15=63

Then add 15 on both sides to make the equation balanced:

5p=78

Then divide by 5:

p=78/5=$16.5

Answer: b

Step-by-step explanation: b

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =\frac{\pi }{6} \end{cases}\implies A=\cfrac{(\frac{\pi }{6})(6)^2}{2} \\\\\\ A=3\pi \implies A\approx 9.42~m^2[/tex]

The level of accounts receivable will be $479,452.05.

If Harley-Davidson Inc. reduces its DSO to 35 days by pressuring more of its customers to pay their bills on time, the company’s average sales will fall by 15%. To calculate the level of accounts receivable following this change, we need to use the formula for DSO:

DSO = (Accounts Receivable / Average Daily Sales) x Number of Days in Period

We know that the current DSO is 55 days, and the company wants to reduce it to 35 days. Therefore, we can assume that the current average daily sales are:

Average Daily Sales = Annual Sales / 365
DSO = (Accounts Receivable / Average Daily Sales) x Number of Days in Period
55 = ($750,000 / (Annual Sales / 365)) x 365

Solving for Annual Sales, we get:

Annual Sales = $1,095,890.41

If the company’s average sales will fall by 15%, then the new Annual Sales will be:

New Annual Sales = $931,507.85 ($1,095,890.41 - 15%)

Using this new Annual Sales figure, we can now calculate the new level of accounts receivable following the change:

35 = (New Accounts Receivable / (New Annual Sales / 365)) x 365
New Accounts Receivable = $479,452.05

Therefore, if Harley-Davidson Inc. reduces its DSO to 35 days by pressuring more of its customers to pay their bills on time and its average sales fall by 15%, the level of accounts receivable will be $479,452.05.

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Answer:

S=2t

or

T=1/2 S

Answer:

20

Step-by-step explanation:

16 / 20 = 0.80

0.80 = 80%

The final result of the expression is -12,173/10,083. First, let's find the sum of 2/9 and -3/7. To add fractions, we need a common denominator. The least common multiple of 9 and 7 is 63.

To simplify the given expression, let's break it down step by step:

The sum of 2/9 and -3/7 is:

(2/9) + (-3/7)

To add these fractions, we need a common denominator, which is the least common multiple (LCM) of 9 and 7, which is 63.

(2/9) + (-3/7) = (2 * 7)/(9 * 7) + (-3 * 9)/(7 * 9)

= 14/63 - 27/63

= (14 - 27)/63

= -13/63

The difference of 3/7 and -13/23 is:

(3/7) - (-13/23)

Again, we need a common denominator, which is the LCM of 7 and 23, which is 161.

(3/7) - (-13/23) = (3 * 23)/(7 * 23) - (-13 * 7)/(23 * 7)

= 69/161 + 91/161

= (69 + 91)/161

= 160/161

Now, we subtract the second result from the first result:

(-13/63) - (160/161)

To subtract fractions, we need a common denominator, which is the LCM of 63 and 161, which is 10,083.

(-13/63) - (160/161) = (-13 * 161)/(63 * 161) - (160 * 63)/(161 * 63)

= -2,093/10,083 - 10,080/10,083

= (-2,093 - 10,080)/10,083

= -12,173/10,083.

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The angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12) is approximately 112.62 degrees.

To find the angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12), follow these steps:
Step 1: Determine the coordinates of the given point. In this case, it is (-5, 12).
Step 2: Calculate the horizontal (x) and vertical (y) distances from the origin (0, 0) to the point. The horizontal distance is -5 and the vertical distance is 12.
Step 3: Calculate the angle using the arctangent function (tan^(-1)). The arctangent function takes the ratio of the vertical distance to the horizontal distance as its argument. So, angle = tan^(-1)(12 / -5).
Step 4: Compute the arctangent value using a calculator or an online tool. Angle ≈ tan^(-1)(-2.4) ≈ -67.38 degrees.
Step 5: Convert the angle to a positive value measured counterclockwise from the positive x-axis. Since the angle is measured in the second quadrant, subtract the angle from 180 degrees: 180 - 67.38 ≈ 112.62 degrees.
The angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12) is approximately 112.62 degrees.

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The piecewise function graphed in this problem is defined as follows:

A piece-wise function is a function that has different definitions, depending on the input of the function.

The definitions for this problem are given as follows:

For the function up to x = 1, the function is a linear function with slope of 1 and intercept of 6, hence:

y = x + 6, x ≤ 1.

For the function greater than x = 1, the quadratic function y = x² + 3 is defined, hence:

y = x² + 3, x > 1.

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The 75th percentile of the wait time in a restaurant, assuming it follows an exponential distribution with a mean of 10 minutes, can be found using the inverse of the exponential cumulative distribution function.

In an exponential distribution, the probability density function (PDF) is given by f(x) = λe^(-λx), where λ is the rate parameter. The mean of the exponential distribution is equal to 1/λ. In this case, we are given that the mean is 10 minutes, so λ = 1/10.

To find the 75th percentile, we need to find the value x for which P(X ≤ x) = 0.75. In other words, we want to find the value of x such that 75% of the wait times are less than or equal to x.

Using the exponential cumulative distribution function (CDF), we can solve for x by setting P(X ≤ x) = 0.75 and solving for x. The formula for the exponential CDF is F(x) = 1 - e^(-λx).

Setting 1 - e^(-λx) = 0.75, we can solve for x to find the 75th percentile of the wait time.

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The maximum number of gift packages that Rodarius can make is 30. Each gift package will contain 4 mini footballs and 1 signed autograph from the Titans.

To determine the maximum number of gift packages Rodarius can make so that each recipient gets an equal number of footballs and autographs, we need to find the greatest common factor (GCF) of the two numbers, 120 and 30.

The prime factorization of 120 is:

120 = 2³ x 3 x 5

The prime factorization of 30 is:

30 = 2 x 3 x 5

To calculate the GCF, multiply the product of the common factors by the lowest exponent:

GCF = 2 x 3 x 5 = 30

So the maximum number of gift packages that Rodarius can make is 30. Each gift package will contain 4 mini footballs and 1 signed autograph from the Titans.

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The value of x for the same angle based on the information is 13.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle

Since angles 5 and 10 are the same, we can set them equal to each other:

91 - 2x = 5x

Simplifying this equation, we can add 2x to both sides:

91 = 7x

Then, we can divide both sides by 7 to solve for x:

x = 13

Therefore, the value of x for the same angle is 13.

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Answer:

Step-by-step explanation:

it is 83/49 because I searched it up.

a) The radius of convergence is also 1, since it is the same as the radius of convergence of ln(1+x).

a) We can find a power series representation for f(x) = ln(1+x) by using the formula:

ln(1 + x) = ∑(-1)^(n-1) * x^n / n for |x| < 1

So, the power series representation for ln(1+x) is:

ln(1 + x) = x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - ...

The radius of convergence is 1, since the series converges for |x| < 1 and diverges for |x| > 1.

b) To find a power series for f(x) = xln(1+x), we can use the product rule of power series:

xln(1 + x) = x * [x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - ...]

= x^2 - x^3/2 + x^4/3 - x^5/4 + x^6/5 - ...

So, the power series representation for f(x) = xln(1+x) is:

f(x) = xln(1+x) = ∑(-1)^(n-1) * x^(n+1) / n for |x| < 1

c) To find a power series for f(x)ln(x^2 + 1), we can use the product rule of power series again:

f(x)ln(x^2 + 1) = [x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - ...] * ln(x^2 + 1)

= [xln(x^2 + 1)] - [x^2 ln(x^2 + 1)]/2 + [x^3 ln(x^2 + 1)]/3 - [x^4 ln(x^2 + 1)]/4 + [x^5 ln(x^2 + 1)]/5 - ...

We already have a power series for xln(1+x), which is the same as xln(x^2+1) for |x| < 1. So, we can substitute it in the above series:

f(x)ln(x^2 + 1) = ∑(-1)^(n-1) * x^(2n+1) / (2n+1) * [1 - 1/2 + 1/3 - 1/4 + 1/5 - ...]

= ∑(-1)^(n-1) * x^(2n+1) / (2n+1) * ln(x^2 + 1)

The radius of convergence of this power series is also 1, since it is the same as the radius of convergence of ln(1+x) and xln(1+x).

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Step-by-step explanation:

(3j - 5k^3) ( 3j + 5k^3)  =  9j^2 - 25k^6

Mike has under 1/4 of a tank of gas, and he decides to fill up his gas tank. his gas tank holds 16 gallons. the gas cost $3.59 per gallon. It will cost Mike $43.08 to fill up his car.

To help you with your question, we first need to determine the amount of gas Mike needs to fill up his car. Since he has less than 1/4 of a tank, let's assume he has exactly 1/4 of a tank for simplicity.
Mike's car has a 16-gallon gas tank, so:
1/4 * 16 gallons = 4 gallons already in the tank.
To fill up the tank, Mike needs to add:
16 gallons - 4 gallons = 12 gallons.
The gas costs $3.59 per gallon, so to find the total cost:
12 gallons * $3.59 = $43.08.
Approximately, it will cost Mike $43.08 to fill up his car.

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The approximate number of customers (waiting and being served) at the carwash is 3.

To determine the number of customers (waiting and being served) at the carwash, we can use Little's Law, which states that the average number of customers in a system is equal to the average arrival rate multiplied by the average time spent in the system.

In this case, the average arrival rate is 9 customers per hour, and the average waiting time is given as 23 minutes (which is equivalent to 23/60 = 0.3833 hours).

Using Little's Law, we can calculate the average number of customers in the system:

Average number of customers = Average arrival rate * Average time spent in the system

Average number of customers = 9 customers/hour * 0.3833 hours

Average number of customers = 3.4497 customers

Since we can't have fractional customers, we round the value to the nearest whole number.

Therefore, the approximate number of customers (waiting and being served) at the carwash is 3.

It's important to note that this calculation assumes steady-state conditions and that the arrival and service distributions are not known.

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the series ex2 converges for all real values of x.

The general term of the series ex2 = 1 + x^2 + x^4/2! + x^6/3! + x^8/4! + ... is given by:

an = xn/(n!) for n ≥ 0, where n is an even integer.

Here, xn represents the term with exponent n in the series.

Therefore, the range of values for the index n is all even non-negative integers starting from 0.

Note that n! (n factorial) in the denominator of the general term ensures that each term after the first term (which is 1) is smaller than the preceding term, as n increases.

what is integer?

An integer is a whole number that can be positive, negative, or zero. It does not include fractions or decimals. Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on. The set of integers is denoted by the symbol Z.

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The solution of the expression is,

⇒ 0 + (7/11)√5

We have to given that;

Expression is,

⇒ (7 + √5) / (7 - √5) - (7 - √5) / (7 + √5)

Take LCM we get;

⇒ (7 + √5)² - (7 - √5)² / (7 - √5) (7 + √5)

⇒ (49 + 5 + 14√5) - (49 + 5 - 14√5) / (7² - √5²)

⇒ (28√5) / (49 - 5)

⇒ 28√5 / 44

⇒ 7√5 / 11

⇒ 0 + (7/11)√5

Thus, The solution of the expression is,

⇒ 0 + (7/11)√5

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Answer:

Step-by-step explanation:

let the present age of mother and daughter be x and y

[tex]\frac{1}{2} * (x + y) = x - y\\x + y = 2x - 2y\\x = 3y --- (1)\\[/tex]

[tex]x+4 = 2(y+4)\\3y+4 = 2y + 8\\y = 4\\x = 3y = 12[/tex]

Age of mother = 12 yrs

Age of daughter = 4 yrs

The number of zeroes or x-intercepts of a polynomial function is related to its highest power, which is determined by the degree of the polynomial. Let's consider a polynomial of degree "n" where "n" is a positive integer.

The minimum number of zeroes or x-intercepts a polynomial can have is zero. This occurs when all the terms of the polynomial have non-zero coefficients and there are no factors that would cause the polynomial to equal zero. For example, a polynomial of degree 2, such as f(x) = x^2 + 1, has no zeroes.

The maximum number of zeroes or x-intercepts a polynomial of degree "n" can have is "n". This is known as the Fundamental Theorem of Algebra, which states that a polynomial of degree "n" can have at most "n" distinct zeroes.

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To determine the order in which Harry Potter should visit the 4 places and return to Gryffindor in the least amount of time, we need to look at the graph provided by Hermione.

We can start by looking for the shortest distances between each location. Once we have identified the shortest distances, we can then use this information to determine the most efficient order for Harry to visit each place.
It's important to note that there may be multiple routes that Harry can take to visit all 4 places, but we want to find the one that will take the least amount of time. To do this, we can start by identifying the shortest distance between two locations and continue to do this until we have identified the shortest path to all 4 locations.
Once we have determined the order in which Harry should visit each location, we can then calculate the amount of time it will take for him to travel between each place and return to Gryffindor. This will give us a total time for the entire journey.
We can say that determining the most efficient route for Harry to visit the 4 places and return to Gryffindor in the least amount of time requires careful analysis of the graph provided by Hermione. By identifying the shortest distance between each location and using this information to create the most efficient route, we can minimize the amount of time Harry spends traveling between each place. Once we have identified the order in which Harry should visit each location, we can then calculate the amount of time it will take him to travel between each place and return to Gryffindor. By doing this, we can determine the total amount of time it will take for Harry to complete his journey.

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The values of r where the area of the shaded region be greater are values at least 8

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

The area of the larger rectangle is

Area = 12 * 8

Area = 96

The area of the shaded region is

Area = r * 6

Area = 6r

When the shaded region is greater than or equal to half of the area of the larger rectangle, we have

6r ≥ 1/2 * 96

This gives

r ≥ 1/12 * 96

Evaluate

r ≥ 8

Hence, the values of r are r ≥ 8

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The small submarine must travel 1,140 feet and maintain a speed of 19 feet per minute in order to reach a depth of 180 feet below sea level within 60 minutes.

To determine the distance that the small submarine must travel to reach 180 feet below sea level, we need to use some basic math.
First, we need to determine the distance between the current position of the submarine (-1,320 feet) and its target depth (-180 feet below sea level). To do this, we subtract the target depth from the current depth:
-1,320 ft - (-180 ft) = -1,140 ft
This means that the submarine needs to travel 1,140 feet down in order to reach its target depth.
Next, we need to figure out how long it will take the submarine to travel that distance. We know that it has 60 minutes to do so, so we can use the formula:
distance = rate x time
We know the distance (1,140 feet), so we need to solve for rate. Rearranging the formula, we get:
rate = distance / time
Plugging in the values we know, we get:
rate = 1,140 ft / 60 min = 19 ft/min
So the small submarine needs to travel at a rate of 19 feet per minute in order to reach its target depth of 180 feet below sea level in 60 minutes.
In summary, the small submarine must travel 1,140 feet and maintain a speed of 19 feet per minute in order to reach a depth of 180 feet below sea level within 60 minutes.

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The statement "the sum of the percent frequencies for all classes in a frequency distribution will always equal" is True.

The sum of the percent frequencies for all classes in a frequency distribution will always equal 100%. This is because the percent frequency for each class is calculated by dividing the frequency of that class by the total number of observations and then multiplying by 100. Therefore, when we add up all the percent frequencies for all the classes, we get the total percentage of observations, which must be 100%.

In a frequency distribution, percent frequencies are calculated by dividing the frequency of each class by the total number of observations and then multiplying by 100. Since all observations are accounted for in the distribution, the sum of the percent frequencies for all classes will always equal 100%.

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