Employees of a painting service paint the interior walls of homes and office buildings.

The following table shows the number of cans of paint the employees use, and the

number of square feet they cover,

1

2

3

4

Cans of paint

Area painted (square feet)

375

750

1125

1500

Which equation describes the relationship between the number of cans of paint

used, and the number of square feet that are covered?

The statement (x xor y)′ = xy (x y)′ is true which is proven using De Morgan's Law and Distributive Law.

To prove this use logical equivalences:

(x XOR y)' = (x AND y') OR (x' AND y) [De Morgan's Law and definition of XOR]

= xy' + x'y [Distributive Law]

(x AND y)' = x' OR y' [De Morgan's Law]

= (x' OR y') AND (x OR y') [Distributive Law]

Therefore, (x y)' = (x' OR y') AND (x OR y').

Using this expression in the first equation:

(x XOR y)' = xy' + x'y = (x y)'

Hence, (x XOR y)' = (x y)'.

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Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

Therefore, the global maximum value of the function on the region B is 12, and the global minimum value is 4.

To find the global maximum and minimum values of the function f(x, y) = x² + y² + x²y + 4y² + x²y + 4 on the region B = {(x, y) ∈ R² | −1 ≤ x ≤ 1, -1 ≤ y ≤ 1}, we need to evaluate the function at its critical points within the given region and compare the function values.

1. Critical Points:

To find the critical points, we need to find the points where the gradient of the function is zero or undefined.

The gradient of f(x, y) is given by:

∇f(x, y) = (df/dx, df/dy) = (2x + 2xy + 2x, 2y + x² + 8y + x²).

Setting the partial derivatives equal to zero, we get:

2x + 2xy + 2x = 0          (Equation 1)

2y + x² + 8y + x² = 0      (Equation 2)

Simplifying Equation 1, we have:

2x(1 + y + 1) = 0

x(1 + y + 1) = 0

x(2 + y) = 0

So, either x = 0 or y = -2.

If x = 0, substituting this into Equation 2, we get:

2y + 0 + 8y + 0 = 0

10y = 0

y = 0

Thus, we have one critical point: (0, 0).

2. Evaluate Function at Critical Points and Boundary:

Next, we evaluate the function f(x, y) at the critical point and the boundary points of the region B.

(i) Critical point:

f(0, 0) = (0)² + (0)² + (0)²(0) + 4(0)² + (0)²(0) + 4

       = 0 + 0 + 0 + 0 + 0 + 4

       = 4

(ii) Boundary points:

- At (1, 1):

f(1, 1) = (1)² + (1)² + (1)²(1) + 4(1)² + (1)²(1) + 4

       = 1 + 1 + 1 + 4 + 1 + 4

       = 12

- At (1, -1):

f(1, -1) = (1)² + (-1)² + (1)²(-1) + 4(-1)² + (1)²(-1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, 1):

f(-1, 1) = (-1)² + (1)² + (-1)²(1) + 4(1)² + (-1)²(1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, -1):

f(-1, -1) = (-1)² + (-1)² + (-1)²(-1) + 4(-1)² + (-1)²(-1) + 4

          = 1 + 1 + 1 + 4 + 1 + 4

          = 12

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Answer:

its not loading??

Step-by-step explanation:

The probability that a randomly chosen person has diabetes is approximately 10.45%.

The probability that a randomly chosen person has diabetes can be calculated by dividing the number of people with diabetes by the total population. Using the given data, we have:

Total population = 100%Probability of having diabetes = 10.5%Number of people with diabetes = 34.2 million

To find the probability of a randomly chosen person having diabetes, we divide the number of people with diabetes by the total population as follows:

Probability of having diabetes = (Number of people with diabetes / Total population) x 100%

= (34.2 million / 327 million) x 100%

= 0.1045 or 10.45%

Therefore, the probability that a randomly chosen person has diabetes is approximately 10.45%.

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Answer:

sin(x-60)-3

Step-by-step explanation:

The rule for translating a trigonometric function towards the right is y=f(x-a) so you substitute 60 for a which gives you y=sin(x-60).

Finally you subtract 3 from the whole function so the final answer should be y=sin(x-60)-3

Hope this helps.  

Answer:

the answer for the first part is 260

the equation is n+8

Step-by-step explanation:

all you need to do is take the starting number witch is 13 then you add 8 and then take that number and add 8 so thats why the equation is n+8 n equaling the starting number and 8 equaling to the reoccurring number.

As a student, you can calculate the probability of this event occurring by using the multiplication rule of probability.  The probability of the die landing on the face numbered 1 and the coin landing showing tails is 1/12.

The probability of the die landing on the face numbered 1 is 1/6, as there are six possible outcomes and only one of them is a 1. The probability of the coin landing showing tails is 1/2, as there are two possible outcomes and only one of them is tails.

To find the probability of both events occurring together, you multiply the probability of the die landing on 1 by the probability of the coin landing on tails:

P(die landing on 1 AND coin landing on tails) = P(die landing on 1) x P(coin landing on tails)

= 1/6 x 1/2

= 1/12

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To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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Answer:

x=12.9444444

Step-by-step explanation:

Answer:

x=12.94

Step-by-step explanation:

Answer:

b option is the weight answer I think.

The probability that there will be at least two applicants is 0.60, the probability of at most three applicants is 0.80, and the probability of three or four applicants is 0.20.

To calculate the cumulative probability distribution, we need to sum up the probabilities for each outcome up to a certain point. Starting with the first outcome, we can calculate the cumulative probabilities as follows:

Cumulative Probability Distribution:
Outcome: 1 2 3 0 4
Probability: 0.40 0.25 0.15 0.15 0.05
Cumulative Probability: 0.40 0.65 0.80 0.95 1.00

Using the cumulative probabilities, we can answer the given questions:

The probability that there will be at least two applicants is 1 - cumulative probability of 1 applicant = 1 - 0.40 = 0.60.

The probability that there will be at most three applicants is the cumulative probability of 3 applicants = 0.80.

The probability that there will be three or four applicants is the difference between the cumulative probabilities of 3 and 4 applicants = cumulative probability of 4 applicants - cumulative probability of 3 applicants = 1.00 - 0.80 = 0.20.

These probabilities are obtained by analyzing the cumulative probabilities of the given outcomes in the probability distribution.

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Answer:

It C man.

Step-by-step explanation:

You don't need this

The possible values of x, so that the relation does not form a function, is given as follows:

x = -2 or x = -5.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The points for the function in this problem are given as follows:

(-2,5),(-5,9),(x,-3)

The meaning of each point is that:

The relation is not a function, meaning that the value of x is either of x = -2 or x = -5, which are already mapped to another value of x.

The problem asks for the values of x so that the relation is not a function, considering the three points that were given on the problem.

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Answer:

-8

Step-by-step explanation:

bc a negative time a negative give u a positive

-3x-8=24

Answer:

x=2

Step-by-step explanation:

2*6, 3*6

Answer:

5^(1/2)

Step-by-step explanation:

Square root means to the power of (1/2)

cube root means to the power of (1/3)

and so on

The correlation coefficient of 0.88 reveals that there is an intense linear connection between the two variables.

It should be noted that to ascertain the correlation coefficient, we can utilize the formula:

r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

Retaining the same numeric values from before, we can compute:

r = (9(976) - (36)(605)) / sqrt[(9(182) - (36)^2)(9(11681) - (605)^2)] ≈ 0.88

Therefore, the correlation coefficient is fairly close to 0.88.

The correlation coefficient implies a strong positive relationship between hours expended studying and test outcomes. As the quantity of hours committed to studying increases, the test scores will tend to keep up accordingly. A correlation coefficient of 0.88 reveals that there is an intense linear connection between the two variables, and the line of best fit serves as a desirable standard representation of the data.

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Answer:

Step-by-step explanation:

It appears there is an error in the table. The correct table is:

\(\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-11}\vphantom{\dfrac12}\textsf{Hours spent studying $(x)$}&0&1&2&4&4&4&6&6&7&8\\\cline{1-11}\vphantom{\dfrac12}\textsf{Test score $(y)$}&35&40&46&65&67&70&82&88&82&95\\\cline{1-11}\end{array}\)

The simplest method to find the linear regression equation and the correlation coefficient for this data set is to use a statistical calculator.

After entering the data into a statistical calculator we get:

The regression line of y on x is y = a + bx.

Therefore, substitute the found values of a and b into the formula to write the linear regression equation for the given data set:

\(\boxed{y=34.27+7.79x}\)

The correlation coefficient is the value of r, so r = 0.98 to the nearest hundredth.

The correlation coefficient, r, measures the strength of the linear correlation between two variables. |t is always between +1 and -1.

As r = 0.98, there is a very strong positive correlation.

In context, this suggests that the more hours of studying for a test a student does, the higher their test score.

The graph of P(x) is below the x-axis in the intervals (-∞, -3) and (-2, ∞) and above the x-axis in the interval (-3, -2).

A. P(x) = x³ + 3x² − 4x − 12

To factor the polynomial P(x) = x³ + 3x² − 4x − 12:

Rearrange the polynomial into pairs of terms:

x³ + 3x² − 4x − 12 = x²(x + 3) − 4(x + 3)

Factor out the common binomial:

x³ + 3x² − 4x − 12 = (x² − 4)(x + 3)

Factor the quadratic:

x² − 4 = (x + 2)(x − 2)

So the complete factorization of P(x) is:

P(x) = (x + 2)(x - 2)(x + 3)

2. Find the zeros:

Zeros are the values of x that make P(x) = 0.P(x) = (x + 2)(x - 2)(x + 3)

So the zeros are:

x + 2 = 0

x = -2

x - 2 = 0

x = 2

x + 3 = 0

x = -3

The zeros are -2, 2, and -3.3.

Use testing points to algebraically identify if the graph of the polynomial is above or below the x-axis within the intervals determined by the zeros:

We need to look at the sign of P(x) in each of the three intervals determined by the zeros:

x < -3, -3 < x < -2, and x > 2. We can use a table of signs or sign chart to determine this:

From the sign chart, we can see that P(x) is negative in the interval (-∞, -3), positive in (-3, -2), and negative in (-2, ∞).

Therefore, the graph of P(x) is below the x-axis in the intervals (-∞, -3) and (-2, ∞) and above the x-axis in the interval (-3, -2).

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Answer:

40%

Step-by-step explanation:

\( \frac{48}{120} \times 100 = 40\)

Answer:

40%

Step-by-step explanation:

To find out what percentage of 2 hours is 48 minutes, we need to first convert both values to the same unit of time, such as minutes.

2 hours is equal to 120 minutes (2 x 60).

So, the fraction of 2 hours that is represented by 48 minutes is:

48/120

Simplifying this fraction by dividing both the numerator and denominator by 12, we get:

4/10

Multiplying the numerator and denominator by 10 to convert this fraction into a percentage, we get:

40%

Therefore, 48 minutes is 40% of 2 hours.

Answer:

Yes, 40 is correct. The valuable r is basically just a blank line and you have to fill it in this problem.

Step-by-step explanation:

Answer:

C) a = 432

Step-by-step explanation:

\(\frac{a}{27}=16\\\rule{150}{0.5}\\(\frac{a}{27})27 = 16 (27)\\\\\boxed{a = 432}\)

ANSWER: dA/dt=0.17A A(0)=950

The correct differential equation and initial condition for the continuous compounding of a sum of 950$ at 17% interest are given by dA/dt = 0.17A and A(0) = 950. This represents the rate of change of the amount A(t) with respect to time and the initial investment value, respectively.

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The angles formed by the angle bisector BF are ∠FBA and ∠FBC.

The step in which the mistake was made is step 3; Then, she placed the compass on point C and drew an arc on the interior of ∠ABC which intersects the previous arc.

Reasons:

The steps to draw an angle bisector are;

Place the compass at the vertex of the angle and draw an arc intersecting the the two rays forming the angle at points D and E

Place the compass at point D and draw an interior arc to the given angle

Place the compass at point E and draw a second interior arc intersecting the previous arc

The point of intersection of the two arcs can be labelled F and joined to the vertex of the given angle to complete the angle bisection

Therefore, the step in which the mistake was made is; Step 3 where the compass is placed at point C rather than point E to draw the second arc of the angle bisector

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Answer:

Step three

Step-by-step explanation:

she placed the point on C when it was supposed to be on E

Answer:

Step-by-step explanation:

You need to use the distributive property to take out the common factor. But that doesn't tell you what the common factor is.

Look inside the brackets. You need to find something that is exactly the same on either side of the minus sign. In this case you have a huge cle about what it is.

2x^5 is it not? I'm assuming that's the correct way to read it.

So that's the answer to your question 2x^5.

The distributive property will tell you that 2x^5 can be taken out, and what is left is

2x^5 ( x^3 - 4)

The proof that "u" is a subspace of "v" is given below.

Suppose that t:v->w is a linear transformation where "v" and "w" are vector spaces.

Let "z" be the subspace of "w".

Since "t" is a linear transformation, the zero vector of "w" is in "z".

Let x, y ∈ U.

Then t(x), t(y) ∈ z.

Since, "z" is a subspace of "w".

So, "z" is closed under vector addition.

Thus, t(x) + t(y) ∈ z.

Now, t(x) + t(y) = t(x + y), since, t is a linear transformation.

Therefore, t(x + y) ∈ z.

Thus, x + y ∈ u.

Therefore, "u" is closed under vector addition.

Hence proved.

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