Solve the inequality
x²(x + 2)(x-7) ≥0

Subspaces: The set of all vectors in of the form where are real numbers, and the set of all vectors in whose endpoint lies on the line.

One of the properties that is not a property of being a subspace is:

- The set is in whenever and are vectors in .

Explanation: The statement "is in whenever and are vectors in " is not a property of being a subspace. In a subspace, closure under vector addition and scalar multiplication are required, which means that for any vectors and scalars in the subspace, the sum of those vectors and the scalar multiple of a vector should also be in the subspace. However, the given statement does not specify closure under vector addition or scalar multiplication, so it does not satisfy the requirements of a subspace.

To determine which subsets are subspaces, let's analyze each option:

  - This set is a subspace because it satisfies all the properties of a subspace: closure under vector addition, closure under scalar multiplication, and containing the zero vector.

  - This set is not a subspace because it fails the closure under scalar multiplication property. If a polynomial with a non-zero term is multiplied by zero, the result is the zero polynomial, which does not have a non-zero term.

  - This set is not a subspace because it fails the closure under scalar multiplication property. If we multiply a matrix in this set by a scalar, the resulting matrix may have entries outside the given range of values.

  - This set is a subspace because it satisfies all the properties of a subspace: closure under vector addition, closure under scalar multiplication, and containing the zero vector.

Therefore, the subsets that are subspaces are options 1 and 4.

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The best-selling online product in the 'North America' sales territory group is option C) Road-150 Red with a quantity of 62.

In order to determine the best-selling online product in the 'North America' sales territory group, we need to analyze the data from the FactInternetSales, dimProduct, and dimSalesTerritory tables. The quantity of each product sold in the 'North America' region needs to be examined. Among the given options, option C) Road-150 Red has the highest quantity sold, which is 62. Therefore, it is the best-selling online product in the 'North America' sales territory group

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If the largest number in the data set increases the standard deviation will increase.

Let us suppose that we are given a data set with 9 distinct observations.

It is given that the largest number in the data set increases.

We know that,

Standard deviation = \(\sqrt{ \frac{sum[(X-m)^{2}]}{N}}\)

Where,

X = Element of data set

m = mean of the data set

N = number of elements in the data set

Let us consider our data set to be:-

1,2,3,4,5,6,7,8,9

Here,

Mean, m = (1+2+3+4+5+6+7+8+9)/9 = 45/9 = 5

Hence,

\(sum(X-m)^{2}=(1-5)^{2}+(2-5)^{2}+(3-5)^{2}+(4-5)^{2}+(5-5)^{0}+(6-5)^{2}+(7-5)^{2}+(8-5)^{2}+(9-5)^{2} = 16+9+4+1+0+1+4+9+16=60\)

N = 9

Hence

Standard deviation = \(\sqrt{\frac{60}{9} }=\sqrt{\frac{20}{3} } =2.58 (approximately)\)

Now, let the largest element of the set that is 9 increases to 18.

Hence,

Mean , m = (1 +2+3+4+5+6+7+8+18)/9 = 54/9 = 6

N = 9

\(sum(X-m)^{2}=(1-6)^{2}+(2-6)^{2}+(3-6)^{2}+(4-6)^{2}+(5-6)^{0}+(6-6)^{2}+(7-6)^{2}+(8-6)^{2}+(18-6)^{2} = 25+16+9+4+1+0+1+4+144=206\)

Standard deviation = \(\sqrt{\frac{206}{9} }=4.78(approximately)\)

Hence, we can clearly see that the standard deviation increases.

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Answer:

If you don't try yes

Step-by-step explanation:

Answer:

im not sure but you should try your best

Explanation:

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

x=26/5

Step-by-step explanation:

2(x - 5) = 9 - 3x + 7.

2x-10=9-3x+7

+3x         +3x

5x+-10=16

     +10=+10

5x=26

divide by 5x

x=26/5

Answer: \(36\pi\) inches

or 113.04 inches

Step-by-step explanation:

The area of a circle is indicated as \(\pi r^2\)

r=radius

Since the radius is given, plug in 6 for r.

\(\pi (6)^2\)=\(36\pi\)

For a decimal answer, find the product of 36 and \(\pi\), which results in 113.04 inches

The height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

The volume of the cylinder can = 1000 cubic cm

Consider the height of the cylinder as h and the radius of the base is r

Volume of the cylinder = π\(r^2\)h = 1000

h = 1000 / π\(r^2\)

The surface area of the cylinder

A = 2π\(r^2\) + 2πrh

A = 2π\(r^2\) + 2πr(1000 / π\(r^2\) )

A = 2π ( \(r^2\) + 1000 / π\(r^2\))

Differentiate the terms

A' =  2π (2r + 1000 / π\(r^3\))

When the minimum surface area

2π (2r + 1000 / π\(r^3\)) = 0

r = \((1000/2\pi )^\frac{1}{3}\)

r = 5.41 cm

Then,

h =  1000 / π\(r^2\)

= 1000 / (π × 5.41 × 5.41)

= 1000 / 91.94

= 10.87 cm

Hence, the height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

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The average population being studied is people with warts. Specifically, this population includes individuals of all ages who have been diagnosed with any type of wart caused by a virus, such as common warts, plantar warts, and flat warts.

The population being studied is people with warts. Warts are caused by a virus and can occur anywhere on the body. Common warts, plantar warts, and flat warts are the most common types. Common warts are usually found on the hands and fingers, and are usually round and raised. Plantar warts are found on the soles of the feet and can be painful. Flat warts are usually found on the face, arms, and legs, and are generally flat and smooth. People of all ages can be affected by warts, and they are highly contagious and can be spread through contact with an infected person or surface. Treatment options include over-the-counter medicines and prescription medications, as well as cryotherapy and laser treatments. This population is being studied to better understand the causes, risk factors, and treatments for warts.

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The complete question is

what is the population being studied warts and  the prevalence of warts in the population being studied?

The One Weakness of the maximum likelihood principle that should be kept in mind is the Sensitivity to Outliers .

The Sensitivity to Outliers is one of the weakness of the Maximum Likelihood principle in statistical modeling.

The Outliers are the observations which are significantly different from the majority of the data, and they can have a large impact on the Maximum Likelihood estimates.

The Maximum Likelihood principle involves finding the set of parameters that maximize the likelihood of observing the data .

When Outlier is present in the data, it can have a disproportionate effect on the likelihood, which leads to biased estimates of the parameters.

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The expression for the number of games Holly now has in standard form is 37 - 6x, where x represents the number of games she gave away.

The expression for the number of games Holly has after starting with 3x3 games, buying 7x4 games, giving away x games, selling 5x games, and donating 9 games can be written in standard form.

Let's break down the given information step by step:

Holly starts with 3x3 games, meaning she has a total of 3 * 3 = 9 games.

She buys another 7x4 games, which adds 7 * 4 = 28 games to her collection.

She gives away x games, resulting in a decrease in the total number of games by x.

She sells 5x games, further decreasing her collection by 5x.

Finally, she donates another 9 games, resulting in a decrease of 9 games.

To express the total number of games Holly has after all these actions in standard form, we can add or subtract the respective quantities:

Total number of games = (9 + 28) - x - 5x - 9

Simplifying the expression, we have:

Total number of games = 37 - 6x

Therefore, the expression for the number of games Holly now has in standard form is 37 - 6x, where x represents the number of games she gave away.

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We can express the polynomial \(ax^2+bx+c\) as a linear combination of the basis polynomials 1, x, and x^2:

\(ax^2 + bx + c = a(x^2)\)+ b(x) + c(1)

Therefore, we can apply the linear transformation T to each basis polynomial and use linearity to find T(ax^2+bx+c):

T(1) = \(T((1/2)(-2x^2) + (-5)(-0.5x) + (3x^2-1))\)

= \((1/2)T(-2x^2) - 5T(-0.5x-5) + T(3x^2-1)\)

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

=\(-18x^2 + 29x - 14\)

T(x) = \(T((1/2)(-2x^2) + (-5)(-0.5x) + (3x^2-1)) - T(1)\)

=\((-1/2)T(-2x^2) + 5T(-0.5x-5) - T(3x^2-1) - T(1)\)

= \((-1/2)T(-2x^2) + 5T(-0.5x-5) - T(3x^2-1) - T(1)\)

= \(16x^2 - 23x + 3\)

\(T(x^2) = T(-2x^2) + T(3x^2-1)\)

=\((-2x^2+2x) + (-2x-4)\)

= \(-2x^2 - 2x - 4\)

\(T(ax^2+bx+c) = aT(x^2) + bT(x) + cT(1)\)

= \(a(-2x^2-2x-4) + b(16x^2-23x+3) + c(-18x^2+29x-14)\)

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According to the statement, the new flavour received 3 votes for every vote received by the original flavour. Denoting:

• x = # of votes of the original flavour,

• n = # of votes of the new flavour.

We can write the following equation for the number of votes:

Now, according to the statement, the number of votes of the new flavour is n = 723, replacing this number in the equation above and solving for x, we get:

Answer

The original flavour received 241 votes.

To determine if the means of the weights of the hard body type and soft body type upright vacuum cleaners are different, a two-sample t-test can be conducted.

However, before conducting the test, it must be checked if the assumptions are met. The variables are assumed to be normally distributed and the variances are assumed to be unequal.
Assuming that the sample sizes are large enough (at least 30), a two-sample t-test with unequal variances can be used. The null hypothesis is that the means of the weights of the two types of vacuum cleaners are equal, while the alternative hypothesis is that they are different.
The t-test calculates a t-statistic, which measures the difference between the sample means in terms of the standard error. The higher the t-value, the more likely it is that the means are different. If the calculated t-value exceeds the critical value at the chosen level of significance (usually 0.05), the null hypothesis is rejected.
In conclusion, to determine if the means of the weights of the hard body type and soft body type upright vacuum cleaners are different, a two-sample t-test can be conducted. The assumptions of normality and unequal variances should be checked before conducting the test.

To determine if the means of the weights of hard body and soft body upright vacuum cleaners are different, we need to conduct a hypothesis test. Since the variances are unequal, we'll use the Welch's t-test. Here are the steps:
1. State the null hypothesis (H0) and the alternative hypothesis (H1):
  H0: The means of the weights of hard body and soft body upright vacuum cleaners are equal.
  H1: The means of the weights of hard body and soft body upright vacuum cleaners are different.
2. Calculate the t-value and degrees of freedom using the provided sample data of weights in pounds for both hard body and soft body vacuum cleaners. Make sure to use the formula for Welch's t-test, which accounts for unequal variances.
3. Determine the critical t-value for the desired significance level (e.g., 0.05) and the calculated degrees of freedom from Step 2.
4. Compare the calculated t-value with the critical t-value. If the calculated t-value is greater than the critical t-value, reject the null hypothesis in favor of the alternative hypothesis.
In conclusion, by following these steps and using the sample data of weights in pounds for hard body and soft body upright vacuum cleaners, you can determine if there's enough evidence to conclude that the means of the weights are different.

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Therefore, the interquartile range of the company scores for the reference population is approximately 26.96.

To find the interquartile range (IQR) of the intelligence scores for the reference population, we need to calculate the difference between the third quartile (Q3) and the first quartile (Q1).

Since the scores are normally distributed with a mean of 120 and a standard deviation of 20, we can use the properties of the normal distribution to determine the quartiles.

The first quartile, Q1, corresponds to the 25th percentile, which is located at z = -0.674. We can calculate the value of Q1 as:

Q1 = mean + z * standard deviation = 120 + (-0.674) * 20 = 120 - 13.48 = 106.52

Similarly, the third quartile, Q3, corresponds to the 75th percentile, which is located at z = 0.674. We can calculate the value of Q3 as:

Q3 = mean + z * standard deviation = 120 + (0.674) * 20 = 120 + 13.48 = 133.48

Finally, we can calculate the interquartile range (IQR) as the difference between Q3 and Q1:

IQR = Q3 - Q1 = 133.48 - 106.52 = 26.96

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Answer:

x = 255/2

Step-by-step explanation:

225 X = 2

(Decimal: x = 112.5) x.2-225 = 0

Steps x.2-225 = 0

Add 225 to both sides x.2-225 + 225 = 0+ 225

Simplify x.2 = 225

Divide both sides by 2 x. 2 2 225-learn 2

Simplify 225 X = 2

20.11 cm3/min is the rate at which the snowball's volume is decreasing.

Given,

The decreasing diameter when the spherical ball is melting = 0.2 cm/min

We have to find the rate in decrease in volume of snowball when diameter is 8 cm.

Here,

Volume of sphere, V = 4/3 π r³ = 4/3 π (D/2)³ = 1/6 π D³

Considering differences according to time,

dV/dt = d/dt (1/6 π D³) = 1/6 π × 3D² dD/dt

dV/dt = 1/2 π D² dD/dt

Substituting

D is 8 cm, and the diameter is changing at a rate of 0.2 cm/min.

dV/dt = 1/2 π D² dD/dt

dV/dt = 1/2 × π × 8² × 0.2 = 20.11 cm³/min

Therefore,

Decreasing snowball volume at a rate of 20.11 cm3/min

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When sampling without replacement, the standard deviation (SD) of a binomial distribution can be calculated using the following formula:

SD = sqrt((N - n) * p * (1 - p) / (N - 1))

where N is the population size, n is the sample size, and p is the probability of success (in this case, the proportion of echidnas with diets consisting mostly of termites).

Given that the population proportion of echidnas with termite diets is 40% (or 0.4) and the sample size is 20, we can calculate the standard deviation.

SD = sqrt((N - n) * p * (1 - p) / (N - 1))

= sqrt((N - 20) * 0.4 * (1 - 0.4) / (N - 1))

Since we don't have information about the total population size (N), we cannot calculate the exact standard deviation.

However, we can provide an estimation by assuming a large population, which means that the difference between N and N-1 is negligible.

Let's assume N is large, so N - 1 ≈ N:

SD ≈ sqrt((N - 20) * 0.4 * (1 - 0.4) / N)

≈ sqrt(0.24 * (N - 20) / N)

Given the answer choices provided, we can estimate the closest value to the standard deviation.

Let's substitute different values for N and find the closest answer choice.

For N = 100, we have:

SD ≈ sqrt(0.24 * (100 - 20) / 100)

≈ sqrt(0.24 * 80 / 100)

≈ sqrt(0.192)

≈ 0.438

For N = 200, we have:

SD ≈ sqrt(0.24 * (200 - 20) / 200)

≈ sqrt(0.24 * 180 / 200)

≈ sqrt(0.216)

≈ 0.465

Out of the provided answer choices, the closest value to the estimated standard deviation of 0.465 is 0.4.

Therefore, 0.4 is the closest choice to the standard deviation of x.

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We need to compute the limit of the expression\(\frac{ (cos(2x) + cot^2(x))}{(t^2 - sin^2(x))}\) as x approaches 0. If the limit exists, we'll evaluate it, and if it doesn't, we'll explain why.

To find the limit, we substitute the value 0 into the expression and simplify:

lim(x→0)\(\frac{ (cos(2x) + cot^2(x))}{(t^2 - sin^2(x))}\)

When we substitute x = 0, we get:

\(\frac{(cos(0) + cot^2(0))}{(t^2 - sin^2(0))}\)

Simplifying further, we have:

\(\frac{(1 + cot^2(0))}{(t^2 - sin^2(0))}\)

Since cot(0) = 1 and sin(0) = 0, the expression becomes:

\(\frac{(1 + 1)}{(t^2 - 0)}\)

Simplifying, we get:

\(\frac{2}{t^2}\)

As x approaches 0, the limit becomes:

lim(x→0) \(\frac{2}{t^2}\)

This limit exists and evaluates to \(\frac{2}{t^2}\) as x approaches 0.

Therefore, the limit of the given expression as x approaches 0 is \(\frac{2}{t^2}\).

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well, for the piece-wise function, we know that hmmm x = -1, -1 is less 1, so the subfunction that'd apply to that will be -2x + 1, because on that section "x is less than or equals to 1".

so f(-1) => -2(-1) + 1 => 3.

Answer:3

Step-by-step explanation:

In this case x=-1 so you will use the top equation because x<1

so f(-1) = -2(-1) + 1

          = 2+1

           =3

Answer:  $19.50

Step-by-step explanation:

An algebraic expression is a set of constants and variables connected by the signs for the basic mathematical operations of addition, subtraction, multiplication, and division.

Expressions are a special type of mathematical statement that must have at least two terms connected by an operator and including either integers, variables, or both.

A mathematical operation, such as subtraction, addition, multiplication, or division, is used to combine terms to produce an expression. A mathematical expression includes the following words:

An unchanging integer is referred to as a constant.

A symbol without a fixed value is said to be a variable.

Term: A term might be a single constant, a single variable, a mix of variables and constants, or both multiplied or divided.

A sum that is multiplied by a variable is referred to as a coefficient in an equation.

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Answer:

289

Step-by-step explanation:

6 sides to a cube, so the surface area would be the sum of all the sides. 1734/6 = 289

Answer:

17

Step-by-step explanation:

After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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Answer:

38/60 or 19/30

Step-by-step explanation:

The question isn't fully attached as stated by the person who submitted it.

The fraction of the cakes he has left is ( 5 / 6 ). The remaining number of cakes is 50.

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

The fraction is calculated as:-

The remaining fraction = 1 - ( 1 / 6 )

                                      = ( 6 - 1 ) / 6

                                      = 5 / 6

The remaining number of cakes,

Remaining number = 60 x ( 5 / 6 )

Remaining number = 50

Hence, the remaining number of cakes is 50.                                                          

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Answer:

0>-7

I'm not really sure last time I did this was last year

45 probably or maybe 2

Yolanda is buying school supplies. She buys n packages of pencils at 1.40 per package and m pads of paper at 1.20 each. The expression 1.4 represents the cost of one package of pencils while the expression 1.2 represents the cost of one pad of paper.

The given expressions represent the cost of one package of pencils and one pad of paper. Hence,1.4 represents the cost of one package of pencils.1.2 represents the cost of one pad of paper.Yolanda buys n packages of pencils.

Therefore, the total cost of pencils will be n × 1.4

Similarly, Yolanda buys m pads of paper.

Therefore, the total cost of pads will be m × 1.2

Therefore, the total cost of buying n packages of pencils at 1.40 per package and m pads of paper at 1.20 each will be,1.4n + 1.2m

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