evaluate the expression 5a-30
a=6

The probability of event a occurring is 0 and the conditional probability of event b occurring given that event a has occurred is 0.5.

The probability that both event A and event B occur is calculated using the formula P(A and B) = P(A) x P(B|A).

In this case, P(A) = 0 and P(B|A) = 0.5. When we plug these values into the equation, P(A and B) = 0 x 0.5 = 0. Therefore, the probability of both event A and event B occurring is 0. The probability that both events a and b occur is determined by multiplying the probability of event a occurring with the conditional probability of event b occurring given that event a has already occurred. This can be expressed mathematically as P(A∩B)=P(A)*P(B|A). In this case, the probability of both events a and b occurring is 0.5*0.5=0.25, since the probability of event a occurring is 0 and the conditional probability of event b occurring given that event a has occurred is 0.5.

This makes sense, since event A has a probability of 0 and cannot occur in the first place, so the probability of both events occurring together is 0.

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The direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.

Motion maps are used to illustrate the direction and position of an object. Using the motion map, the description of the object position and velocity is as follows:

The object starts its movement from the origin with a large velocity, before moving back to the origin with a smaller velocity. It stops for 1 second in the origin, then moves away with a larger velocity, Finally, it moves back towards the origin with a smaller velocity.

See attachment for the motion map, where the number on each arrow in the map, represents the position of the object.

Note that; the long arrow means large velocity while the short arrow means small velocity.

We analyze the direction and position using the arrows

Therefore, the direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.

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Answer:

Based on the motion map, the object starts at the reference point "x" on the left side of the position line. The three dots with short vector arrows moving toward "x" indicate that the object is moving in the direction of the reference point and gaining speed. This suggests that the object is accelerating. Then, there is a single dot, which might indicate a momentary pause or a constant velocity. Afterward, the two dots with longer vector arrows moving away from "x" suggest that the object is decelerating or slowing down. In summary, the motion map shows an object that starts from rest, accelerates towards the reference point, maintains a constant velocity for a brief moment, and then decelerates away from the reference point.

Step-by-step explanation:

Use chat gpt to give you unique answer.

The mean and approximate standard deviation of the difference in the total weight of lobster john traps in a day are 2 pounds and 8.32 pounds respectively. Hence, option d is the right answer.

Since the weight of lobsters produced by each trap is independent of the other, we can find the mean and standard deviation of the difference in the total weight of lobsters trapped in a day by subtracting the mean and standard deviation of the west bay trap from the mean and standard deviation of the east bay trap.

Mean = 12 pounds (east bay) - 10 pounds (west bay) = 2 pounds

Standard deviation = √(7^2 + 4.5^2) = √69.25 ≈ 8.32 pounds

So, the mean and approximate standard deviation of the difference in the total weight of lobsters trapped in a day is -

Mean = 2 pounds

Standard deviation = 8.32 pounds

Therefore, the answer is (d) Mean=2; Standard deviation= 8.32.

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The complete question is -

John maintains two separate lines of lobster traps in Penobscot bay. the east bay trap produces a mean of 12 pounds of lobsters per day with a standard deviation of 7 pounds. the west bay trap produces a mean of 10 pounds of lobsters a day with a standard deviation of 4.5 pounds. the weight of lobsters produced by each trap is independent of the other. which of the following are the mean and approximate standard deviation of the difference in the total weight of lobsters john traps in a day?

(a) Mean=11; Standard deviation=2.50

(b) Mean=2; Standard deviation=2.50

(c) Mean=2; Standard deviation= 5.36

(d) Mean=2; Standard deviation =8.32

(e) Mean=2; Standard deviation=11.50

The inequality equation is 8.498 > 8.478

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the first number be represented as = p

Let the second number be represented as = q

Now , the value of p = 8.498

The value of q = 8.478

And , the hundredths value in the number 8.498 is greater than the hundredths value in the number 8.478

So , the value of p is greater than q

Therefore , 8.498 > 8.478

Hence , the inequality is 8.498 > 8.478

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Answer:

  6√2

Step-by-step explanation:

You want one side of a square whose half-diagonal has length 6.

If X is the center point of the square where the diagonals cross at right angles, triangle EXG is an isosceles right triangle with leg length 6. The hypotenuse of an isosceles right triangle is √2 times the leg length, so ...

  EG = 6√2

__

Additional comment

If you like, you can use the Pythagorean theorem to prove that.

  EG² + EX² +GX² = 6² +6² = 72

  EG = √72 = √(36·2) = 6√2

A square is a rhombus, so the diagonals cross at right angles. A square is a rectangle, so the diagonals are the same length. A square is a parallelogram, so the diagonals bisect each other.

Answer:

  G(u+t, s)

Step-by-step explanation:

Given coordinates E(-1, 0), F(0, s), and H(u, 0) of parallelogram EFGH, you want the coordinates of point G.

Segment FG is a horizontal line. Its length will be the same length as horizontal line EH. Since the lines are horizontal, the length is the difference of x-coordinates.

Point H is (u -(-t)) = u+t units to the right of point E. The x-coordinate of point G will be the same number of units to the right of point F.

The x-coordinate of G is 0 +(u+t) = u+t, the length of EH added to the x-coordinate of F.

The y-coordinates of any point on a horizontal line are the same. The y-coordinate of point F is 's'. Point G lies on that same horizontal line, so has the same y-coordinate.

The coordinates of point G are (u+t, s).

__

Additional comment

The midpoints of the diagonals are the same. This means ...

  (E+G)/2 = (F+H)/2

  E+G = F+H . . . . . . multiply by 2

  G = F +H -E . . . . . subtract E

Using the given coordinates:

  G = (0, s) +(u, 0) -(-t, 0) = (0+u+t, s+0+0) = (u+t, s) . . . . as above

All of your "parallelogram" problems are worked the same way. The fourth point has coordinates that are the sum of the coordinates of the end points of the known diagonal, less the known point on the unknown diagonal.

If you work the problem any of several other ways, you get the same answer.

Point E is (u -(-t)) = (u +(-t)) units away from point H. Point G will be located the same amount of units to the right of point F in terms of its x-coordinate.  G(u+t, s)

You need to know the coordinates of point G in the parallelogram EFGH given the coordinates E(-1, 0), F(0, s), and H(u, 0).

FG is a horizontal segment. It will have a length equal to that of a horizontal line, EH. The length is determined by the difference in x-coordinates because the lines are horizontal.

The length of EH multiplied by the x-coordinate of F yields the x-coordinate of G, which is 0 +(u+t) = u+t.

Horizontal line

In a horizontal line, all points have the same y-coordinates. Point F has the y-coordinate of's'. Point G's y-coordinate is the same because it is located on the same horizontal line.

The coordinates of point G are (u+t, s).

__

Additional comment

The midpoints of the diagonals are the same. This means ...

 (E+G)/2 = (F+H)/2

 E+G = F+H . . . . . . Multiply by 2

 G = F +H -E. . . . . Subtract E

Using the given coordinates:

G = (0, s) +(u, 0) (u, 0) (-t, 0) = (u+t, s) + (u+t, s) + (u+t, s) . . . . As mentioned earlier

Your “parallelogram” issues are all solved in the same manner. The fourth point's coordinates are equal to the sum of the coordinates of the known diagonal's end points, minus the known diagonal's known point.

The solution is the same regardless of how you approach the issue.

Vertical line

Any point on a horizontal line has the same y-coordinates. Point F's y-coordinate is's'. Point G has the same y-coordinate since it is located on the same horizontal line.

Point G's coordinates are (u+t, s).

Further commentary

The diagonals' midpoints are identical. This implies...

(E+G)/2 = (F+H)/2

E+G = F+H, multiply by 2, and so on.

G = F + H -E.... Remove E.

Using the coordinates provided:

G = (0, s) +(u, 0) (u, 0) (-t, 0) = (u+t, s) + (u+t, s) + (u+t, s) . . . . as mentioned earlier

Therefore, Your “parallelogram” issues are all solved in the same manner. The fourth point's coordinates are equal to the sum of the coordinates of the known diagonal's end points, minus the known diagonal's known point.

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The presented system of linear equations has no solution.

The final form of the augmented matrix suggests that the system of linear equations has no solution, as the last row represents an equation with 0 = 0, which is always true but doesn't provide any information about the variables.

To see this more clearly, let's use the augmented matrix to write out the system of linear equations:

1x - 1y + 2z = 4

2y + 1z = -1

z = 1

The first two equations are consistent and have a unique solution, but the last equation is trivial and provides no information about x and y. In other words, infinitely many pairs of x and y satisfy the first two equations, but none satisfy the third equation. Therefore, the given system of linear equations has no solution.

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The remaining portions from the three pizzas together make up 13/27 of a large pizza.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Shauntee ate 2/3 of her pizza, so she has 1/3 left.

Carlos ate 8/9 of his pizza, so he has 1/9 left.

Rocco ate 26/27 of his pizza, so he has 1/27 left.

To determine the combined fraction of the remaining portions of the three pizzas, we add the fractions that are left:

1/3 + 1/9 + 1/27 = (1/3) + (1/9) + (1/27)

Simplifying this fraction by finding the least common denominator, which is 27:

(1/3) + (1/9) + (1/27) = (9/27) + (3/27) + (1/27) = 13/27

So they together make up 13/27 of a large pizza.

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The expected waiting time in hours until the first call arrived is 0.00045.

The formula for poisson distribution is expressed as

P(x = r) = (e^- µ × µ^r)/r!

Where ,

µ=  represents the mean of the theoretical distribution.

r = represents the number of successes of the event.

According to the question,

µ = 5            

For the probability that there are one in one hour, it is expressed as

P(x = 1) ,

Therefore,

P(x = 1)

= (e^- 10 × 10^1)/1! = 0.00045

Therefore,

P(x = 1)

= 0.00045

Poisson distribution

A Poisson distribution is a discrete probability distribution. It gives the probability of an event happening a certain number of times (k) within a given interval of time or space.

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Answer:

3,2 °C

Step-by-step explanation:

40,2 °C - 37 °C = 3,2 °C

Answer:

The Z-score (also known as a standard score) represents the number of standard deviations a value is away from the mean of a distribution. The formula for the Z-score is:

Z = (X - μ) / σ

Where X is the value of interest, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Given the information in the problem, we know that the mean of the fruit fly's lifespan is 32 days and the standard deviation is 5 days.

To find the Z-score of a fruit fly whose lifespan is 37 days:

Z = (37 - 32) / 5 = 1

To find the Z-score of a fruit fly whose lifespan is 30 days:

Z = (30 - 32) / 5 = -0.4

To find the Z-score of a fruit fly whose lifespan is 47 days:

Z = (47 - 32) / 5 = 2.4

Therefore, a fruit fly whose lifespan is 37 days has a Z-score of 1, a fruit fly whose lifespan is 30 days has a Z-score of -0.4, and a fruit fly whose lifespan is 47 days has a Z-score of 2.4.

The complete table is given as follows -

Brain (part)    0.6    1.3    1.8     3

Body (part)    6.6   14.3  19.8   33

Total (whole) 7.2   15.6  21.6   36

Given is that an interior designer recently spent £1359.55 buying 25 kettles and 20 toasters for a smaller group of new houses. For her current assignment she needs 80 kettles and 56 toasters.

The given table is -

Brain (part)   0.6   B   1.8      E

Body (part)   A    14.3   19.8  33

Total (whole) 7.2  C      D     36

We can write the expressions as -

0.6 + A = 7.2                                           .... Eq( 1 )

A = 6.6

1.8 + 19.8 = D                                            .... Eq( 2 )

21.6 = D

E + 33 = 36

E = 3                                                              .... Eq( 3 )

Therefore, the complete table is given as follows -

Brain (part)    0.6    1.3    1.8     3

Body (part)    6.6   14.3  19.8   33

Total (whole) 7.2   15.6  21.6   36

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The circumference of a circle whose radius is 21 feet, is 132 feet, thus the first option is the correct one.

We know that for a circle of radius R, the circumference is given by:

C = 2*π*R

Where π = 22/7

And here we know that the radius is 21 feet, then we can replace that in the formula above and we will get:

C = 2*(22/7)*21 feet = 132 feet

The circumference of that triangle is 132 feet, thus, the correct option is the first one.

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Answer:

raised 53%

Step-by-step explanation:

goal = $8,000

raised = $4,200

$4,200/$8,000 = 0.525 = about 53%

The answer would be x^-10, since the question asks you to rewrite it with a single variable.

I hope this helps!  o(〃＾▽＾〃)o

The numeric value of the function is given as follows:

2x + h + 9.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function in this problem is given as follows:

f(x) = x² + 9x.

At x = x + h, the function is defined as follows:

f(x + h) = (x + h)² + 9(x + h)

f(x + h) = x² + 2xh + h² + 9x + 9h

f(x + h) = x² + 2xh + h² + 9x + 9h.

Subtracting by f(x), we have that:

f(x + h) - f(x) = h² + 2xh + 9h.

f(x + h) - f(x) = h(h + 2x + 9).

Dividing by h, the numeric value is given as follows:

2x + h + 9.

Meaning that the first option is the correct option.

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Answer: 43 because 7 is greater than 5 so you round up. Have a nice day ;)

The correct answer is 43.  0.735 is greater than 0.5, so you round it up to 43

we can conclude that option (A) , (B) and (C) are true.

We know that in a triangle,

• Sum of any to sides is greater than the third side.

• Difference between any two sides is smaller than the third side.

So, in ∆EFG, we have,

• EF + FG > EG

• FG + EG> EF

• EF + EG > FG

and,

• EF - FG <EG or FG - EF <EG

• FG - EG < EF or EG - FG < EF

• EF - EG <FG or EG - EF < FG

From options now we get,

A) EF + FG > EG is true

B)EG + FG > EF is true

C) EG - FG < EF is true

D) EF - FG > EG is false

E) EG + EF < FG is false

Therefore, we can conclude that option () , () and () are true.

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We can conclude that option (A) , (B) and (C) are true.

We know that in a triangle,

• Sum of any to sides is greater than the third side.

• Difference between any two sides is smaller than the third side.

So, in ∆EFG, we have,

• EF + FG > EG

• FG + EG> EF

• EF + EG > FG

and,

• EF - FG <EG or FG - EF <EG

• FG - EG < EF or EG - FG < EF

• EF - EG <FG or EG - EF < FG

From options now we get,

A) EF + FG > EG is true

B)EG + FG > EF is true

C) EG - FG < EF is true

D) EF - FG > EG is false

E) EG + EF < FG is false

Therefore, we can conclude option (A) , (B) and (C) are true.

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In the horizontal direction and by 4 units to the left, f(x) should be shifted to match g(x).

The correct option is A.

The function provided by the basic function f(x) and the constant

g(x) = f(x - k),

may be drawn by horizontally moving the f(x) k unit coordinates.

The shift's direction depends on the value of k. Specifically,

The base graph moves k units to the right if k > 0, and

The base graph moves k units to the left if k < 0.

Given:

The quadratic functions f(x) and g(x) are described in the table.

From the table, the functions,

f(x) = x².

And g(x) = (x + 4)².

In the attached image,

the blue curve is the function of f(x).

And red line is the function of g(x).

From the graph,

Left by 4 units, f(x) should be shifted  to match g(x).

Therefore, left by 4 units, f(x) should be shifted to match g(x).

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Answer: A

Step-by-step explanation: took the test

In a case whereby you mix 1 half cup of salt with 3 cups of sugar the ratio of salt to sugar.

The concept that will be used is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

we were told that there were 1 half cup of salt with 3 cups of sugar

Then the ratio can be written as

salt/sugar

= (1 1/2)/3

Since the amount of the salt is in mixed fraction, we can reduce to improper fraction for easy calculation.

=( 3/2)/ 3

= 3/6

=1/2

Hence, the ratio is 1:2

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missing options:

A. 2:3

B.1:2

C.2:1

D. 5:6

Answer:

Step-by-step explanation:

Answer:

1.91 lb

Step-by-step explanation:

1 3/4 cups of pecans per pie = 1.75 cups.

For 5 pies, 5 × 1.75 cups = 8.75 cups are needed.

1 cup = 99 g

8.75 cup × (99 g) / (1 cup) = 866.25 g

Exact conversion: 453.59237 g = 1 lb

866.25 g × (1 lb)/(453.59237 g) = 1.91 lb

Answer: 1.91 lb

A graph that represents the solution set of the compound inequality is: graph D.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given compound inequality by making x the subject of formula as follows;

x + 3 < 1/2(4x - 12) < 20

Multiplying all through by 2, we have the following:

2x + 6 < 4x - 12 < 40

Next, we would solve the compound inequality in parts:

2x + 6 < 4x - 12

4x - 2x < 12 + 6

2x < 18

x < 18/2

x < 9.

4x - 12 < 40

4x < 40 + 12

4x < 52

x < 52/4

x < 13.

In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).

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The algebraic expression which represents the total cost of buying watermelons and tomatoes as described is; C = 0.68w + 3.25t.

The cost of buying a watermelon that weighs 18.5 pounds and 5 pounds of tomatoes is; $28.83.

It follows from the task content that the cost of buying Tomatoes are $3.25 / lb and Watermelon is $0.68 / lb.

Hence, the algebraic expression which represents the cost of buying a watermelon that weighs, w pounds and tomatoes that weigh t pounds is;

C = 0.68w + 3.25t.

Hence, if the watermelon bought weighs 18.5 pounds and tomatoes weigh 5 pounds,

C = 0.68 (18.5) + 3.25 (5)

C = 12.58 + 16.25

C = $28.83.

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When we are aligning two shafts, the reason behind rotating the coupling hubs before taking each measurement is so that each of the measurements is taken from the same place on the hub every time.

Shafts are basically a component of circular cross section which rotates and transmits the power from a driving device like an engine or a motor through a particular machine. Coupling hubs are basically the attachment of the coupling to shaft in a device.

During the alignment of two shafts, the angular as well as parallel misalignment is thoroughly checked. The coupling hubs are rotated before taking each measurement is so that each of the measurements is taken from the same place on the hub every time.

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Both f(x) and g(x) have one x-intercept at x = -1/3.

Theorem A states that for a cubic function of the form f(x) = x^3 + x + b, with b > 1, the function f has exactly one x-intercept. Using Theorem B, we can conclude that for any nonzero real number k, the function g(x) = kf(x) = kx^3 + kx + bk also has exactly one x-intercept.

For example, if f(x) = x^3 + x + 5 and k = 2, then g(x) = 2x^3 + 2x + 10. Both f(x) and g(x) have exactly one x-intercept. This can be shown by solving the quadratic equation formed by setting f(x) = 0 or g(x) = 0. Doing this yields x = -1/3. Therefore, both f(x) and g(x) have one x-intercept at x = -1/3.4

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There are 56 students as freshmen. The correct answer would be an option (A).

The percentage is defined as a ratio expressed as a fraction of 100.

A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent.

This can be determined by multiplying the percentage of freshmen who selected Jaguars (40%) by the total number of students surveyed (140).

⇒ 40% × 140 = 56

So there are 56 students as freshmen.

Hence, the correct answer would be option (A).

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Answer: We know that:

x + y = 12 (because he can work at most 12 hours in total)

7x + 10y ≥ 90 (because he must earn no less than $90)

We can graph these inequalities on the coordinate plane.

The equation x + y = 12 represents a line with a slope of -1 and y-intercept of 12. This is the line that separates the region where he works more hours babysitting and the region where he works more hours clearing tables.

The inequality 7x + 10y ≥ 90 represents the region where he earns more than $90.

You can find the solution by finding the intersection of the line and the shaded region. The solution will be a point that lies on both the line and the shaded region.

One possible solution would be for Mason to work 8 hours babysitting and 4 hours clearing tables, earning him $56 from babysitting and $40 from clearing tables, for a total of $96.

Step-by-step explanation:

Answer:

This is nonsense, if GP = 16 and GH = 12 then HP = 4 (16 - 12 = 4). FP is looking basically the same size as HP, so FP = 4, not 2.

Step-by-step explanation:

These are all lies, your teacher is a liar and EF must be around 12 too.

Answer:

30

Step-by-step explanation: