These graphs represent functions f and g. Which ordered pair represents (f + g)(6) on the graph of the combined function? A. (12,14) B. (6,7) C. (6,14) D. (12,10)

Step-by-step explanation:

When you divide both sides of an inequality by a positive number, the inequality sign remains the same. When you divide both sides of an inequality by a negative number, you must reverse the inequality sign.

For example:

8 > 2 is a true inequality.

Let's divide both sides by 2:

4 > 1 is also a true inequality. The inequality sign remained > since we divided by a positive number.

Now let's start again with

8 > 2, and divide both sides by -2.

-4 > -1 is false. When the inequality sign remains the same after dividing both sides by a negative number, the inequality is no longer true. To keep the inequality true, we must change the inequality sign when dividing both sides by a negative number.

8 > 2

Divide both sides by -1.

-4 < -1 is true.

Answer:

8x^2

7y^2+ 4y^3

3d^3+ 4d^2

Answer:

x = 250

y = 125

u(x,y) = 3125500

Step-by-step explanation:

As given,

The utility function u(x, y) = 100xy + x + 2y

\(P_{x}\) = 2 , \(P_{y}\) = 4

Now,

Budget constraint -

\(P_{x}\) x + \(P_{y}\) y = 1000

⇒2x + 4y = 1000

So,

Let v(x, y) = 2x + 4y - 1000

Now,

By Lagrange Multiplier

Δu = Δv

⇒< 100y + 1, 100x + 2 > = < 2, 4 >

By comparing, e get

100y + 1 = 2         ........(1)

100x + 2 = 4        .........(2)

Divide equation (2) to equation (1) , we get

\(\frac{100y + 1}{100x + 2} = \frac{1}{2}\)

⇒2(100y+1) = 1(100x+2)

⇒200y + 2 = 100x + 2

⇒200y = 100x

⇒2y = x

Now,

As 2x + 4y = 1000

⇒2x + 2(2y) = 1000

⇒2x + 2x = 1000

⇒4x = 1000

⇒x = 250

Now,

As 2y = x

⇒2y = 250

⇒y = \(\frac{250}{2}\) = 125

∴ we get

x = 250

y = 125

Now,

u(250, 125) = 100(250)(125) + 250 + 2(125)

                   = 3125000 + 250 + 250

                  = 3125000 + 500

                 = 3125500

⇒u(250, 125) = 3125500

The maximized value of the utility function is $3125500

The utility function is given as:

\(U(x,y) = 100xy + x + 2y\)

The prices per unit are also given as:

\(P_x = 2\)

\(P_y = 4\)

When a person receives $1000, then the budget function is:

\(2x + 4y = 1000\)

Divide through by 2

\(x + 2y = 500\)

Differentiate the utility function with respect to x and y

\(U'(x) = 100y + 1\)

\(U'(y) = 100x + 2\)

So, we have:

\(U'(x) = P_x\) and \(U'(y) = P_y\)

The above equations become

\(100y + 1 = 2\) and \(100x + 2 = 4\)

Divide both equations

\(\frac{100y + 1}{100x + 2} = \frac 24\)

Reduce the fractions

\(\frac{100y + 1}{100x + 2} = \frac 12\)

Cross multiply

\(100x + 2 = 200y + 2\)

Subtract 2 from both sides

\(100x = 200y\)

Divide both sides by 100

\(x = 2y\)

Recall that:

\(x + 2y = 500\)

So, we have:

\(2y + 2y = 500\)

\(4y=500\)

Divide through by 4

\(y=125\)

Recall that:

\(x = 2y\)

So, we have:

\(x = 2 \times 125\)

\(x = 250\)

Also, we have:

\(U(x,y) = 100xy + x + 2y\)

Substitute the values of x and y, in the above function

\(U(250,125) = 100 \times 250 \times 125 + 250 + 2 \times 125\)

\(U(250,125) = 3125500\)

Hence, the maximized value of the utility function is 3125500

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Answer:

42 students

Step-by-step explanation:

1.) If 42% of students or 42 out of 100 students said they could text blindfolded it means 42 out of the 100 students surveyed can text blindfolded.

A percentage is out of 100

Answer:

Option A. The student incorrectly used < instead of > for the second inequality. The correct inequality is >.

Step-by-step explanation:

Boundary lines that are often used in systems of linear inequalities determine the location of the solutions region in a coordinate plane.

Given the systems of linear inequalities: y ≤ 0.5x + 1 and y = -2x + 1:

In order to determine what is the appropriate inequality symbols for both equations, we must first set the second equation with an equal sign. Then, choose a test point (not in either lines) to determine which half-plane region must be shaded.

Test point: (0, 0)

Substitute the test point into both equations to determine whether it satisfies the given equation:

0 ≤ 0.5(0) + 1

0 ≤ 0 + 1

0 ≤  1  (True statement).

0 = -2(0) + 2

0 = 0 + 2

0 = 2 (False statement). Therefore, the half-plane region that doesn't contain the test point must be shaded.  Hence, we must use the ">" symbol for this equation, as we're shading "above" where the values for y is greater than the y-intercept, (0, 2).

Therefore, the correct answer is Option A:  The student incorrectly used < instead of  > for the second inequality. The correct inequality is  > (greater than symbol).

The rectangular prism will have a maximum height of prism is 12m and inequality is \(x^{2} -12x+0\leq 0\)

a) To find maximum height of prism

As per question,

x = height of prism

Area of rectangular base = Length x Width

Thus, A = \(\leq 27\)

Now,

L x W \(\leq 27\)  (inequality Z)

Given, W = x - 9 (equation  1)

L = W + 6 (equation 2)

Substituting equation 1 in equation 2

We get, L = (x-9)+6

= x-3  (equation 3)

Substituting, equation 1 and equation 3 in the inequality Z

we get, \((x-3)(x-9) = x^{2} -12x+27\)

subtracting 27 we get \(x^{2} -12x+0\leq 0\)

Thus, the coordinates will be (0,12)

As given in question, width of base must be 9 meters less than height of prism. Therefore,

The solution of x interval comes out as (9,12)

Hence, the height of prism is 12m

b) selecting inequality that represents problem

Length = x-3

Width = x-9

Multiplying, we get \((x-3)(x-9) = x^{2} -12x+27\)

Area will come out as \(\leq 27\)

The final expression will be, \(x^{2}-12x+27\leq 27\)

Now subtracting 27 from the expression we get,

\(x^{2} -12x+0\leq 0\)

Note that the full question is:

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less than the height of the prism. The length of the base must be 6 meters more than the width of the base. Find the maximum height of the prism.

Let x = the height of the prism

x – 9 = the width of the base

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less than the height of the prism. The length of the base must be 6 meters more than the width of the base. Find the maximum height of the prism.

Let x = the height of the prism

x – 9 = the width of the base

x -3 = the length of the prism

Select the inequality that represents the problem.

x2 – 3 x – 81 ≤ 0

x2 – 3 x – 27 ≤ 0

x2 – 12 x – 27 ≤ 0

x2 – 12 x ≤ 0

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Answer:

a = -0.5

Step-by-step explanation:

\( \rm Solve \: for \: a: \\ \rm \longrightarrow - \dfrac{1}{4}a - 4 = \dfrac{7}{4}a - 3 \\ \\ \rm Put \: each \: term \: in \: - \dfrac{1}{4}a - 4 \: over \: the \\ \rm common \: denominator \: 4: \\ \rm - \dfrac{a}{4} - 4 = - \dfrac{a}{4} - \dfrac{16}{4} : \\ \rm \longrightarrow - \dfrac{a}{4} - \dfrac{16}{4} = \dfrac{7}{4}a - 3 \\ \\ \rm - \dfrac{a}{4} - \dfrac{16}{4} = \dfrac{ - a - 16}{4} : \\ \rm \longrightarrow \dfrac{ - a - 16}{4} = \dfrac{7}{4}a - 3 \\ \\ \rm Put \: each \: term \: in \: \dfrac{7}{4}a - 3 \: over \: the \\ \rm common \: denominator \: 4: \\ \rm \dfrac{7a}{4} - 3 = \dfrac{7a}{4} - \dfrac{12}{4} : \\ \rm \longrightarrow \dfrac{ - a - 16}{4} = \dfrac{7a}{4} - \dfrac{12}{4} \\ \\ \rm \dfrac{7a}{4} - \dfrac{12}{4} = \frac{7a - 12}{4} : \\ \rm \longrightarrow \dfrac{ - a - 16}{4} = \dfrac{7a - 12}{4} \\ \\ \rm Multiply \: both \: sides \: by \: 4: \\ \rm \longrightarrow \dfrac{ - a - 16}{ \cancel{4}} \times \cancel{4}= \dfrac{7a - 12}{ \cancel{4}} \times \cancel{4} \\ \\ \rm \longrightarrow -a - 16 = 7 a - 12 \\ \\ \rm Subtract \: 7 a \: from \: both \: sides: \\ \rm \longrightarrow (-a - 7 a) - 16 = (7 a - 7 a) - 12 \\ \\ \rm -a - 7 a = -8 a: \\ \rm \longrightarrow -8 a - 16 = (7 a - 7 a) - 12 \\ \\ \rm 7 a - 7 a = 0: \\ \rm \longrightarrow -8 a - 16 = -12 \\ \\ \rm Add \: 16 \: to \: both \: sides: \\ \rm \longrightarrow (16 - 16) - 8 a = 16 - 12 \\ \\ \rm 16 - 16 = 0: \\ \rm \longrightarrow -8 a = 16 - 12 \\ \\ \rm 16 - 12 = 4: \\ \rm \longrightarrow -8 a = 4 \\ \\ \rm Divide \: both \: sides \: of \: -8 a = 4 \: by \: -8: \\ \rm \longrightarrow

\dfrac{ - 8a}{ - 8} = \dfrac{4}{ - 8} \\ \\ \rm \dfrac{ - 8}{ - 8} = 1: \\ \rm \longrightarrow a = - \dfrac{4}{ 8} \\ \\ \rm - \dfrac{4}{ 8} = - \dfrac{1}{2} : \\ \rm \longrightarrow a = - \dfrac{1}{2} \\ \\ \rm \longrightarrow a = - 0.5\)

If the representative fraction scale is 1:48000, then the verbal scale from inches to feet is  1 inch represents 0.00025 feet.

We have to find the verbal (written) scale from inches to feet that represents a map with a representative-fraction (RF) scale of 1:48,000,

We use the formula:

⇒ Verbal scale = RF × Inches per foot,

We know that the RF scale is 1:48,000, which means that one unit on the map represents 48,000 units in the real world.

There are 12 inches in a foot,

So, we can convert the verbal scale to inches-per-foot by dividing by 12:

⇒ Inches per foot = (Verbal scale)/(12),

⇒ Inches per foot = (1/48000) × (12/1) = 0.00025

Therefore, the verbal scale from inches to feet is : 1 inch represents 0.00025 feet.

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Answer:

the cross is the blue color

1) the probability that both girls G1, G2 are both assigned to the same group 0.0043, or 0.43 percent. 2) the probability that G2 is also in this group 0.0364, or 3.64 percent . 3)  the probability is:P (G1 is in a group with M1, and G2 is in a group 0.8897, or 88.97 percent.

(1) The probability that both girls G1, G2 are both assigned to the same groupLet's assume that we are going to make a random selection. There are 40 individuals in the class, and we will select 4 at a time. As a result, there are C(40,4) ways to select 4 individuals, which equals 91,390 ways.

To place the two girls G1, G2 in a single group, there are C(38,2) ways to select two people from the remaining 38 individuals. As a result, the total number of ways to assign G1 and G2 to a single group is C(38,2) × C(36,2) × C(34,2) × C(32,2) × C(30,2) × C(28,2) × C(26,2) × C(24,2) × C(22,2) × C(20,2). That's 214,277,650,957,810,000.

So the probability is as follows:P (both girls in the same group) = C(38,2) × C(36,2) × C(34,2) × C(32,2) × C(30,2) × C(28,2) × C(26,2) × C(24,2) × C(22,2) × C(20,2) / C(40,4) × C(36,4) × C(32,4) × C(28,4) × C(24,4) × C(20,4) × C(16,4) × C(12,4) × C(8,4) × C(4,4)= 194,779,921 / 45,379,776,000= 0.0043, or 0.43 percent

(2)We already know that G1 has been assigned to a group with 2 women. As a result, there are C(20,2) ways to select 2 women to be in G1's group. Among the remaining 36 students, there are C(34,1) ways to select 1 additional woman and C(16,1) ways to select 1 man.

The number of ways to create this group is C(20,2) × C(34,1) × C(16,1). To calculate the probability, we need to divide by the number of ways to put G1 in a group with 2 women, which is C(40,4) / C(18,2).

So the probability is:P (G2 is in a group with G1, which has 2 women) = C(20,2) × C(34,1) × C(16,1) / (C(40,4) / C(18,2))= 4,080 / 111,930= 0.0364, or 3.64 percent

(3) Let's assume that we are going to make a random selection. There are 40 individuals in the class, and we will select 4 at a time. As a result, there are C(40,4) ways to select 4 individuals, which equals 91,390 ways. We need to determine the number of ways to put G1 in a group with M1 and G2 in a group with M2. As a result, we must choose 2 more people to join G1 and M1 and 2 more people to join G2 and M2.

There are C(38,2) ways to choose these two people, and C(36,2) ways to choose two more people from the remaining 36. The number of ways to create these groups is C(38,2) × C(36,2).

So the probability is:P (G1 is in a group with M1, and G2 is in a group with M2) = C(38,2) × C(36,2) / C(40,4)= 81,324 / 91,390= 0.8897, or 88.97 percent.

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B, because you would just assume the line continues forever on both sides.

Answer:

E

Step-by-step explanation:

=√9pr / (pr)^-3/2

=3√(pr) × (pr)^3/2

= 3p²r²

Answer:

E. 3p²r²

Step-by-step explanation:

√9pr / (pr)^-3/2=

3(pr)^1/2*(pr)^3/2=

3(pr)^(1/2+3/2)=

3(pr)^2=3p^2r^2

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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The equation of the tangent plane to f(x, y) = x^2 - 2xy + 3y^2, with slopes 2 in the positive x direction and 2 in the positive y direction, is 2x + 4y - 8 = 0.

To locate the equation of the tangent airplane to the floor described with the aid of the feature f(x, y) = \(x^2 - 2xy + 3y^2\), we need to decide the gradient vector and consider it at a given point.

The gradient vector will grant the ordinary vector to the tangent plane, and by way of the use of the slope information, we can discover the equation of the plane.

Calculate the partial derivatives of the feature with recognize to x and y:

f_x = 2x - 2y

f_y = -2x + 6y

Set up a device of equations the use of the given slope information:

f_x = 2

f_y = 2

Solve the machine of equations to discover the factor where the slopes are satisfied:

2x - 2y = 2 --> x - y = 1 --> x = y + 1

-2x + 6y = 2 --> -x + 3y = 1 --> -x = 1 - 3y --> x = 3y - 1

Setting the two expressions for x equal to every other:

y + 1 = 3y - 1

2 = 2y

y = 1

Substitute y = 1 into both expression for x:

x = 1 + 1

x = 2

Therefore, the factor the place the slopes are comfy is (2, 1).

Evaluate the gradient vector at the factor (2, 1):

grad(f) = (f_x, f_y) = (2x - 2y, -2x + 6y)

= (2(2) - 2(1), -2(2) + 6(1))

= (2, 4)

The ordinary vector to the tangent airplane is the gradient vector (2, 4).

Using the point-normal structure of the equation for a plane, the equation of the tangent airplane is:

2(x - 2) + 4(y - 1) + d = 0

To decide the price of d, alternative the coordinates of the factor (2, 1):

2(2 - 2) + 4(1 - 1) + d = 0

0 + 0 + d = 0

d = 0

The equation of the tangent airplane is:

2(x - 2) + 4(y - 1) = 0

Simplifying the equation, we have:

2x - 4 + 4y - 4 = 0

2x + 4y - 8 = 8

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Answer:

2,400

Step-by-step explanation:

Answer:

It will take 9 years for the population to double

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

\(P=P_o(1+r)^t\)

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The population of a city grows at a rate of r=8% = 0.08 per year. We are required to find when (t) the population will double, or P=2Po.

Substituting in the equation:

\(2P_o=P_o(1+0.08)^t\)

Simplifying:

\(2=(1.08)^t\)

Taking logarithms:

\(\log 2=\log (1.08)^t\)

Applying the exponent property of logs:

\(\log 2=t\log (1.08)\)

Solving for t:

\(\displaystyle t=\frac{\log 2}{\log (1.08)}\)

Calculating:

\(t\approx 9\)

It will take 9 years for the population to double

Answer:

15

Step-by-step explanation:

Total quantity of clay = 5 pound

Now, Reynolds  divides the clay into 1 third pound pieces.

this means each piece of clay weighs = 1/3 pounds

Therefore, number of pieces of clay = Total weight of clay/ weight of each piece

= 5/(1/3) = 15

Answer:

it looks great! i'd give you an a+

honestly I couldn't make that

Answer:

c. Yes because ∠2 and ∠6 are congruent.

Step-by-step explanation:

From the picture attached,

m(∠2) = m(∠3) = m(∠6) = 40°

m(∠1) = 140°

Since (∠2 ≅ ∠6) (corresponding angles)

Therefore, by the converse theorem of corresponding angles lines c and d are parallel.

Option c is the answer.

Answer:

The slope is 3

Step-by-step explanation:

(3x)-->slope=3

LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

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Answer:

Step-by-step explanation:

j represents the amount of juice

2 : 3 :: j : 18        proportion

3j = (2)(18)

Answer:

i dunno

Step-by-step explanation:

somebody help

Answer:

Step-by-step explanation:

\(a+c=23\\a+d=20\\e+c=21\\b+e=24\\d+b=22\\\)

...

After the growth of one tree,the new average height of the 10 trees is 2.65 meters.

To calculate the new average height of the 10 trees after the growth of one tree, we need to find the total height of all the trees, including the growth of the specific tree, and then divide it by the total number of trees.

Given:

Average height of 10 trees = 2.6 meters

We can calculate the total height of the 10 trees before the growth:

Total height before = Average height * Total number of trees = 2.6 meters * 10 = 26 meters

Now, we need to consider the growth of the specific tree. The growth is from 1.7 meters to 2.2 meters, which means the tree has grown by 2.2 - 1.7 = 0.5 meters.

To calculate the new total height, we add the growth to the previous total height:

New total height = Total height before + Growth = 26 meters + 0.5 meters = 26.5 meters

Since the total number of trees remains the same (10 trees), we can calculate the new average height:

New average height = New total height / Total number of trees = 26.5 meters / 10 = 2.65 meters

Therefore, the new average height of the 10 trees, after the growth of one tree, is 2.65 meters.

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