Solve the system : { x1+x2-2x3=-1 , 5x1+6x2-4x3=8.

Answer:

B.   The maximum occurs at the function's x-intercept.

Step-by-step explanation:

Given table:

\(\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & -5 & -4 & -3 & -2 & -1 & 0\\\cline{1-7} g(x) & -1 & 0 & -1 & -4 & -9 & -16\\\cline{1-7}\end{array}\)

From inspection of the table, we can see that:

This indicates symmetry.  

The line of symmetry is the mid-point between the two x-values.

Therefore, the line of symmetry is x = -4

The vertex (minima/maxima) is on the line of symmetry, therefore the vertex is at (-4, 0).  As the function decreases as x → 0, the vertex is a maximum.

As the y-value of the vertex is 0, the maximum occurs at the function's x-intercept.

Answer:

B

Step-by-step explanation:

Finding the line of symmetry :

⇒ Two x-values have the same y-coordinate → (-5) and (-3)

⇒ This means the symmetry is exhibited and it lies between these 2 x-values

⇒ Line of symmetry : x = -4

=============================================================

Now, on plotting these points on a graph we see that this graph has a negative coefficient.

⇒ This means this graph will have a maximum point as the vertex

⇒ The vertex lies on the line of symmetry, hence the vertex (according to the graph and table) is (-4, 0)

Hence, we can say that the maximum occurs at the function's x-intercept.

Answer:

1. 0.7

2. 0.75

3. 23

Step-by-step explanation:

You didn't provide a fourth number.

Answer:1.6

Step-by-step explanation:

25/5=5

8/5=1.6

Answer:

Step-by-step explanation:

if 5miles = 25 minutes

then, 8 miles = X

hence X minutes

\(x = \frac{25minutes}{5miles} \times 8miles\)

The number of scholarships that pay for both books and meals is 1.

To solve this problem, we need to use the concept of set intersection. Let B be the set of scholarships that pay for books, and M be the set of scholarships that include a meal ticket. We want to find the number of scholarships that pay for both books and meals, which is the size of the set intersection B ∩ M.

From the problem statement, we know that:

|B| = 7 (seven scholarships pay for books)

|M| = 4 (four scholarships include a meal ticket)

We can use the inclusion-exclusion principle to find |B ∩ M|:

|B ∩ M| = |B| + |M| - |B U M|

We need to find the size of the union of the sets B and M, which includes all scholarships that pay for books, all scholarships that include a meal ticket, and possibly some scholarships that pay for both. From the problem statement, we know that there are two scholarships that exclude both meals and books, so we can subtract that from the union:

|B U M| = |B| + |M| - |B ∩ M| + 2

Substituting the known values, we get:

|B ∩ M| = |B| + |M| - |B U M| + 2

|B ∩ M| = 7 + 4 - (7 + 4 - |B ∩ M| + 2) + 2

|B ∩ M| = 1 + |B ∩ M|

Solving for |B ∩ M|, we get

|B ∩ M| = 1

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The given question is incomplete, the complete question is:

A student applies for ten different scholarships to various universities. seven of the scholarships pay for books. four scholarships include a meal ticket. two of the scholarships exclude meals and books. how many scholarships pay for both books and meals?

a. the value of c is 2. b. the probability P(X < 1, Y < 1) is given by 1 - e^-1 - e^-2 + e^-3. c. P(X > Y ) is  (-e^(-x-2y) + e^(-2y)y) + e^(-2y) - e^(-2y)y.

a. Finding the value of c:

To find the value of c, we need to integrate the joint probability density function (PDF) over the entire range of x and y and set it equal to 1, since the PDF must satisfy the normalization condition.

The joint PDF is given by f(x, y) = ce^(-x-2y)

∫∫f(x, y) dx dy = 1

∫∫ce^(-x-2y) dx dy = 1

Integrating with respect to x first:

∫[0,∞] ce^(-x-2y) dx = [-ce^(-x-2y)] [0,∞] = ce^(-2y)

Integrating the result with respect to y:

∫[0,∞] ce^(-2y) dy = [-1/2 * ce^(-2y)] [0,∞] = 1/2

Setting this equal to 1:

1/2 = 1/c

Solving for c:

c = 2

Therefore, the value of c is 2.

b. Calculating P(X < 1, Y < 1):

To find the probability P(X < 1, Y < 1), we need to integrate the joint PDF over the given region.

P(X < 1, Y < 1) = ∫[0,1] ∫[0,1] 2e^(-x-2y) dx dy

Integrating this expression, we get:

P(X < 1, Y < 1) = ∫[0,1] [-2e^(-x-2y)] [0,1] dy

= ∫[0,1] -2e^(-1-2y) + 2e^(-2y) dy

= [-e^(-1-2y) + e^(-2y)] [0,1]

= (-e^(-1-2) + e^(-2)) - (-e^(-1) + e^0)

= (-e^-3 + e^-2) - (-e^-1 + 1)

= 1 - e^-1 - e^-2 + e^-3

Therefore, the probability P(X < 1, Y < 1) is given by 1 - e^-1 - e^-2 + e^-3.

c. Finding P(X > Y):

To find the probability P(X > Y), we need to integrate the joint PDF over the region where X > Y.

P(X > Y) = ∫[0,∞] ∫[y,∞] 2e^(-x-2y) dx dy

Integrating this expression, we get:

P(X > Y) = ∫[0,∞] [-e^(-x-2y)] [y,∞] dy

= ∫[0,∞] -e^(-x-2y) + e^(-2y)y dy

= [-e^(-x-2y) + e^(-2y)y] [y,∞]

= (-e^(-x-2y) + e^(-2y)y) - (-e^(-2y) + e^(-2y)y)

= (-e^(-x-2y) + e^(-2y)y) + e^(-2y) - e^(-2y)y

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Answer:

B, D

Step-by-step explanation:

Sorry if I'm wrong. I dont know if E is right or not

Answer:

B, D

Step-by-step explanation

Answer:

d. 4x² + 19x + 15.

Step-by-step explanation:

To simplify the given polynomial expression, we will apply the distributive property and combine like terms.

The expression is:

3x(4x + 5) - 4(-x - 3)(2x - 5)

Let's simplify each term step by step:

Expand the first term, 3x(4x + 5):

= 12x² + 15x

Expand the second term, -4(-x - 3)(2x - 5):

= -4(-x - 3)(2x) + (-4)(-x - 3)(-5)

= 8x² + 12x + 20x + 60

= 8x² + 32x + 60

Now, let's combine like terms:

12x² + 15x - 4x² - 32x - 60

Combining the x² terms and the x terms:

(12x² - 4x²) + (15x - 32x) - 60

= 8x² - 17x - 60

Therefore, the simplified form of the polynomial expression 3x(4x + 5) - 4(-x - 3)(2x - 5) is:

8x² - 17x - 60

Hence, the correct option is d. 4x² + 19x + 15.

Answer:

h = -9

Step-by-step explanation:

Distribute the 2 to the parentheses:

5h + 2(11 - h) = -5

5h + 22 - 2h = -5

Add like terms:

3h + 22 = -5

3h = -27

h = -9

Answer:

h = -4.5

Step-by-step explanation:

5h + 2(11-h) = -5

5h + 2(11-h)

+h          +h

6h + 2 x 11 = -5

6h + 22 = -5

    - 22     -22

6h = -27

/6     /6

h = -4.5

I hope this helps, I know the explanation is kinda confusing but I tried my best to explain :))

Answer:

1.25 lawns/per hour

Step-by-step explanation:

Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

A forest manager is using Landsat satellite images to determine whether 1,250 plots of land have been logged within the past ten years.

The proportion of logged plots is represented by 'p'.

The manager follows these steps daily:
1. Selects a simple random sample of four plots.
2. Examines the image pairs for each selected plot.
3. Categorizes the plots as logged or not logged.
4. Records the results in a spreadsheet.

The forest manager repeats this process daily to gather data on the proportion of logged plots (p) among the 1,250 plots of land.

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To use the quadratic formula, we need to identify the values of a, b, and c.

1. In this case, the equation is 4x² - 3x - 8 = 0, so a = 4, b = -3, and c = -8.

2. x = (-b ±√(b² - 4ac))/2a.

3.  x = (3 ±√137)/8.

The Quadratic Formula is a mathematical equation used to solve second-degree equations.

To use the quadratic formula, we need to identify the values of a, b, and c in the equation ax² + bx + c = 0.

In this case, the equation is

4x² - 3x - 8 = 0,

so a = 4, b = -3, and c = -8.

Once the values of a, b, and c are known, we can substitute them into the Quadratic Formula:

x = (-b ±√(b² - 4ac))/2a.

In this equation, a = 4, b = -3, and c = -8, so the equation becomes

x = (-(-3) ±√((-3)² - 4(4)(-8)))/2(4).

Simplifying, we get x = (3 ±√(9 + 128))/8.

Finally, solving for x yields x = (3 ±√137)/8.

Therefore, the solution to the equation is

x = (3 ±√137)/8.

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Answer:

27 words per minute

Step-by-step explanation:

1080/40= 27

Answer:

You can type 27 words/min  

Step-by-step explanation

The probability that none of the 8 bulbs are defected is 0.12035, or approximately 12.04%. And the probability that exactly one of the 8 is defective will be 0.36256, or approximately 36.26%.

a) In the first case, we are required to calculate the probability that none of the 8 bulbs are defected. So, we need to obtain the probability of selecting 8 non-defected bulbs out of the 15 non-defected bulbs.

The probability of selecting one good bulb out of the 15 good bulbs is 3/4. Since we are selecting 8 bulbs without replacing it, the possibility of selecting 8 good bulbs out of the 15 good bulbs can be calculate here,

(15/20) x (14/19) x (13/18) x (12/17) x (11/16) x (10/15) x (9/14) x (8/13) = 0.12035

Hence , the probability that none of the 8 bulbs will be defective is calculated to be 0.12035, or approximately 12.04%.  

b) Now to calculate the probability that exactly one of the 8 bulbs will be defected, there can be two possible cases which are needed to be considered. First case is  selecting 1 defective bulb out of the 5 defective bulbs and 7 good bulbs out of the 15 good bulbs, and second, selecting 7 good bulbs out of the 15 good bulbs and 1 defective bulb out of the 5 defective bulbs.

The probability of selecting 1 defected bulb out of the 5 defected bulbs and 7 good bulbs out of the 15 good bulbs can be found by the calculation below :

(5/20) x (15/19) x (14/18) x (13/17) x (12/16) x (11/15) x (10/14) x (9/13) = 0.18128

The probability of selecting 7 working bulbs out of the 15 working bulbs and 1 defective bulb out of the 5 defective bulbs is the same as the probability of selecting 1 defected bulb out of the 5 defected bulbs and 7 good bulbs out of the 15 good bulbs, so the total probability of selecting exactly one defective bulb is calculated by the addition of the both probabilities

0.18128 + 0.18128 = 0.36256

Therefore, the probability of selecting exactly one of the 8 bulbs is defective is found to be 0.36256, or approximately 36.26%.

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Answer:

I'll edit the answer and try to answer it, but where is the graph?

Answer:

C: g(x)= x- 3

Step-by-step explanation:

translated 3 units down means you go 3 down on the y-axis. Therefore it is g(x)= x-3

Answer:

Since the calculated value of z= -1.496 does not fall in the critical region z < -1.645 we conclude that the new program is effective. We fail to reject the null hypothesis .

Step-by-step explanation:

The sample proportion is p2= 7/27= 0.259

and q2= 0.74

The sample size = n= 27

The population proportion = p1= 0.4

q1= 0.6

We formulate the null and alternate hypotheses that the new program is effective

H0: p2> p1   vs  Ha: p2 ≤ p1

The test statistic is

z= p2- p1/√ p1q1/n

z= 0.259-0.4/ √0.4*0.6/27

z=  -0.141/0.09428

z= -1.496

The significance level ∝ is 0.05

The critical region for one tailed test is z ≤ ± 1.645

Since the calculated value of z= -1.496 does not fall in the critical region z < -1.645 we conclude that the new program is effective. We fail to reject the null hypothesis .

According to the given equation, the solution is f = 19

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=).

We can start by simplifying the expression inside the parentheses:

f - (13 - 2) = f - 11

Then, we can rewrite the original equation using this simplified expression:

8 = f - 11

To solve for f, we want to isolate it on one side of the equation. We can do this by adding 11 to both sides:

8 + 11 = f - 11 + 11

19 = f

Therefore, the solution is:

f = 19

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Answer:

3

Step-by-step explanation:

If you notice the y is the change in distance, so #3 has the best explanation.

The area under a curve between two points can be found out by doing the integral between the two points. In other words, the integral

Let's make a picture of the problem

Then, the integral will be equal to

The area of the black region is given by the area of the triangular part plus the rectangular part, that is

The area of the red zone is the area of the rectangle

The green area is equal to the area of the green triangle,

and the blue area is the area of the blue triangle,

By substituting these values, the integral is given by

Therefore, the answer is:

The answer is 3.4

Because the 3 is in the tenths place. Since 6 is greater than 5 it gives 1 to the 3 which makes it a 4.

The total amount of pentagons and hexagons that Shari does need altogether is given as follows:

32.

The total amount is obtained applying the proportions and ratios in the context of the problem.

Sheri needs 3 pentagons for every 5 hexagons, hence the equation is:

H = 5P/3.

Sheri needs between 10 and 15 pentagons, hence the possible amounts are given as follows:

Hence the amount is of 12 pentagons and 20 hexagons, thus the amount is:

12 + 20 = 32 pentagons and hexagons altogether.

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Answer is option-A and option-C

Translate and scale factor of Circle:

The translation rule can be expressed as ,

\((x,y) = > (x+a,y+b)\)

And the radius of dillated circle = scale factor * radius of original circle.

(Here),

First, Translate circle A using the rule (x + 4, y + 3)

i.e., to translate circle A we translate the Center of circle.

=> Center of Circle-A = (2 + 4 , 4 + 3)

=> Center of Circle-A = (6, 7)

scale factor = 4

Now, radius of dillate Circle-A i.e., the radius of circle-A is multiplied by 4.

i.e., radius of Circle A = 4 * 4 = 16.

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Therefore, the estimated average length of the line is 3 customers.

We can approach this problem by using the M/M/1 queueing model, which assumes a Poisson arrival process, an exponential service time distribution, and a single server.

In this case, the arrival rate (lambda) is 10 customers per hour, the service rate (mu) is 5 customers per hour (since the average servicem time is 14 minutes or 0.2333 hours), and there is one server.

The utilization factor (rho) is given by rho = lambda / mu = 10 / 5 = 2, which is greater than 1. This means that the system is not stable, and the queue will grow indefinitely.

To find the average length of the line, we can use Little's Law, which states that the long-term average number of customers in a stable system is equal to the long-term average arrival rate multiplied by the long-term average time spent in the system:

L = lambda * W

where L is the average number of customers in the system, lambda is the arrival rate, and W is the average time spent in the system.

In this case, since the system is not stable, we cannot use Little's Law directly. However, we can still estimate the average length of the line as follows:

Let's assume that the queue is at its steady-state when there are N customers in the system (i.e., being served plus waiting in the line). Then, the average length of the line (Lq) is:

Lq = N - 1

since one customer is being served and the remaining N-1 customers are waiting in the line.

The steady-state condition requires that the arrival rate equals the departure rate, which is the service rate in this case. Therefore, we can use the following formula to estimate N:

N = lambda / (mu - lambda)

Plugging in the values, we get:

N = 10 / (5 - 10) = -2

This negative value indicates that the system is not stable, and there are more customers arriving than the system can handle. However, we can still estimate the average length of the line as:

Lq = |N - 1| = |-2 - 1| = 3

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Answer:

\(yes \\ 1 : 3 = 3 : 9\)

Step-by-step explanation:

yes.

\(1 : 3 = 3 : 9\)

Let see how is it possible,

\(3 \times 1 : 3 \times 3 = 3 :9 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3 : 9 = 3 : 9\)

Also,

\(1 : 3= 3 \div 3 : 9 \div 3 \\ 1 : 3 = 1 : 3\)

hope this helps

brainliest appreciated

good luck! have a nice day!

V = (1/3)(225)(20) = 1500 cubic inches. The volume of a pyramid with a square base can be calculated using the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.

To find the area of the base, we need to first find the length of one side of the square base by dividing the perimeter (60 inches) by 4, which gives us 15 inches. Then, we can find the area of the base by squaring this length, which gives us 225 square inches. Plugging in the values of B = 225 and h = 20 into the formula, we get V = (1/3)(225)(20) = 1500 cubic inches.

we used the formula for the volume of a pyramid with a square base, which is V = (1/3)Bh. We then found the area of the base by finding the length of one side of the square base (perimeter divided by 4) and squaring it. Finally, we plugged in the values of the base area and height into the formula to get the volume in cubic inches.

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Answer:

the most you can buy is 15 red paints and 10 blue. discounted the red paint is 18 and the blue is 20.

Step-by-step explanation:

18x15 is 270

20x10 is 200

so in total you would have spent 470

The trigonometric equation is:

y = 2*cos(2x) - 2

The general form of the equation is:

y = A*cos(k*x) + M

Where A is the amplitude, k is the angular frequency and M is the midline.

First, A is half of the difference between a maximum and a minimum, soi:

A = (0 - (-4))/2 = 2

M is the maximum minus the amplitude:

M = 0 - 2 = -2

So we have:

y = 2*cos(kx) - 2

And we can see that we have a maximum at 0 and the next one is at π/2.

So the value of K must be 2, because the number of maximums is doubled in that interval.

y = 2*cos(2x) - 2

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Answer:

The answer is 7/15