Which point is a solution to y< 6x + 2? (-1,0) (1,8) (0,1) (2,15)

The probability of having two black balls after the first draw is 1/6.

The probability of having two black balls after the second draw is 91/216.

Scenario 1: draw two black on the first draw

P(B,B) = (4/9)(3/8) = 12/72 = 1/6

The probability of ending up with two black by scenario 1 is 1/6.

Scenario 2: draw one black and one white; put back the white, and draw a black

P(B,W) = (4/9)(5/8) = 20/72 = 5/18

P(W,B) = (5/9)(4/8) = 20/72 = 5/18

P(one black and one white on first draw) = 5/18+5/18 = 5/9

When you put the white back, there are now 5 white and 3 black; the probability of drawing a black on the second draw is 3/8.

The probability of ending up with two black by scenario 2 is (5/9)(3/8) = 15/72. = 5/24

Scenario 3: draw two white; put both back and draw again, getting two black

P(W,W) = (5/9)(4/8) = 20/72 = 5/18

Since you put back both whites, the bag now contains the same balls it did at the beginning. The probability of drawing two black on the second draw is then 12/72 = 1/6, as before.

The probability of ending up with two black by scenario 3 is (5/18)(1/6) = 5/108.

Thus, The probability of having two black balls after the first draw is 1/6.

The probability of having two black balls after the second draw is the sum of the probabilities for the three scenarios: 1/6+5/24+5/108 = 36/216+45/216+10/216 = 91/216.

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The kinetic energy of the toy motorized airplane is 8 Joule.

Kinetic energy is the work or energy an object has due to it's motion. The standard unit of kinetic energy is Joule which is kg m²/s².

The formula for calculating Kinetic energy is,

KE = [tex]\frac{1}{2}[/tex] mv²

where m is the mass of the object and v is the velocity of the object.

Here, mass = 4 kg and velocity = 2 meter/second

KE = [tex]\frac{1}{2}[/tex] × 4 × 2²

     = 8 Joule

Hence the kinetic energy of the airplane is 8 Joule.

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The probability for green sedan and purple truck can be obtained as  1/3 and 1/6 respectively.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The probability can be found by looking at the diagram as,

P(Sedan) = 2/3

And,  P(Truck) = 1/3

P(green) = 1/2

P(purple) = 1/2

(a) The probability of green sedan is given as,

P(green sedan) = P(Green) × P(Sedan)

⇒ 1/2 × 2/3 = 1/3

(b) The probability of purple truck is given as,

P(purple truck) = P(purple) × P(truck)

⇒ 1/2 × 1/3 = 1/6

Hence, the required probabilities by spinning are given as 1/3 and 1/6 respectively.

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The rational expressions matched to their rewritten forms. Simplification is given below.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given expression:

We have the rewritten form,

(1).

(x-2) + 6/(x-2)

Simplifying,

= {(x-2)² + 6}/(x-2)

= (x²-4x+4+6)/(x-2)

= (x²-4x+10)/(x-2)

This is the required expression of the rewritten form of (1).

(2).

(x+3) + 10/(x-2)

Simplifying,

= {(x-2)(x+3)+ 10}/(x-2)

= (x²+x+4)/(x-2)

This is the required expression of the rewritten form of (2).

(3).

(x+1) + 6/(x-2)

Simplifying,

= {(x-2)(x+1)+ 6}/(x-2)

= (x²-x+4)/(x-2)

This is the required expression of the rewritten form of (3).

(4).

(x-3) + 10/(x-2)

Simplifying,

= {(x-2)(x-3)+ 10}/(x-2)

= (x²-5x+16)/(x-2)

This is the required expression of the rewritten form of (4).

Therefore, the rational expressions matched to their rewritten forms.

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Answer:

see photo #6

Step-by-step explanation:

Answer:

a₄₀ = 35

Step-by-step explanation:

substitute n = 40 into the nth term rule, that is

a₄₀ = - 5 + 40 = 35

The type parameters act as placeholders for the types of the arguments passed to a method. The type parameter names throughout the method declaration must match those declared in the type parameter list.

Pass an array as a pointer to pass it as a parameter to a function (since it is a pointer). For instance, the following method sets array A's first n cells to 0.

In C++, an entire array cannot be provided as an argument. However, by mentioning the array's name, you can supply a pointer to an array without an index.

Only the array name is supplied as a parameter to pass a full array to a function. calculateSum(num), result But take note of how [] is used in the function specification. This tells the compiler that you are handing the function a one-dimensional array.

When we provide an array to a function as an argument, we are actually passing the address of the array in memory, which is the reference. To pass an array to a function, simply pass the array as the function's parameter (like normal variables).

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The percentage error, given the length of the pencil, can be found to be

The percentage error is simply the error of the length of the pencil, expressed as a percentage. The error in this case is the length of the pencil of 1 cm that is to be added or subtracted from the length of 20 cm.

The percentage error is:

= Length to be added to or subtracted from the pencil / Total length x 100 %

= 1 / 20 x 100 %

= 0. 05 x 100 %
= 5 %

In conclusion, the percentage error is 5 %.

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The approximate probability that the driver will be fined is 0.25.

If the driver of a truck loaded with 900 boxes of books will be fined if the total weight of the boxes exceeds 37,350 pounds, then the weight of each box of book must not exceed 41.5 pounds.

37,350 pounds / 900 boxes = 41.5 pounds

Suppose that distribution of the weight is a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 41.5

μ = mean = 41.1

σ = standard deviation = 6

z-score = (41.5 - 41.1) / 6

z-score = (0.4) / 6

z-score = 0.06667

Find the probability that corresponds to the z-score in the z-table. (see attached images)

at z = 0.06667,     p = 0.7472

Since the fine will be given if the load exceeds 41.5, we have to consider the values greater than 41.5. Subtract the answer from 1.

probability = 1 - 0.7472 = 0.25

Hence, the approximate probability that the driver will be fined is 0.25.

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The difference between the polynomial -3x + x³ - 2x² and 4x³ - 2x² - 4x is -3x³ + x

A polynomial is an expression composed of variables, constants and exponents using operations of addition, subtraction, multiplication and division

Polynomial are classified based on degree as linear, quadratic, cubic, etc.

The difference between the polynomial -3x + x³ - 2x² and 4x³ - 2x² - 4x is:

(-3x + x³ - 2x²) - (4x³ - 2x² - 4x)

= (-3x + x³ - 2x² - 4x³ + 2x² + 4x)

Collecting like terms:

= x³ - 4x³ - 2x² + 2x² - 3x + 4x

Simplifying gives:

-3x³ + x

The solution to the polynomial is -3x³ + x

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The scatter plot shows any linear association. Option (B)

A scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.

A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure.

Advantages of scatter plot

From the above advantages, we can conclude on the answer which is Option (B)

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Answer:

Step-by-step explanation:

slope of red line =

+2

Answer:

The answer is 3w - g - 4

Step-by-step explanation:

(8w - 4g + 1) - (5w + 3g - 5)

8w - 4g + 1 - 5w + 3g - 5

Rearrange terms

8w - 5w - 4g + 3g + 1 - 5

Combine like terms

(8w - 5w) = 3w   ( -4g + 3g) = -g  (1 - 5) = - 4

Answer:

3w - g - 4

The number 0.9  tells us about the patient's flossing behavior. The patient floss their teeth completely once time a day.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given equation is

y = 7(0.9) +7

Which estimates the actual times the patient flossed weeks after the procedure.

They floss their teeth properly one time a day.

But they don't floss their teeth properly one time a day.

They do 0.9 = 90% floss their teeth.

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Answer:

Should be 20

Step-by-step explanation:

1in=3ft

So that means you would divide 60/3 which is 20

The value of x=4.

Revenue is equal to the number of units sold times the price per unit. To obtain the revenue function, multiply the output level by the price function.

Given that,

R(x) = 200 х² + 8

differentiating we get,

R'(x)= 400x

Now,

400x=1600

i.e. x=4

Hence, The value of x=4.

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The percentage represented by the shaded area will be 51.5%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Each big square below represents one whole.

In each big square, there are 100 small squares.

Then the number of blue small squares is 103. Then the percent represented by the shaded area is calculated as,

P = (103 / 200) x 100

P = 0.515 x 100

P = 51.5%

The percentage represented by the shaded area will be 51.5%.

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2.54 centimeters = 1 inch.1 feet = 12 inches then 6*12 =72 inch and hence 72*2.54= 183cm

What is a Metric system?

A metric system may be defined as a type of system that significantly weighs and measures the mass and distance respectively in which the meter is the unit of length and the kilogram is the unit of weight.

A metric system is a standard system of measurement which utilizes the meter, liter, and gram as base units of length for distance, capacity for volume, weight for mass, etc.

According to the question, the height of a student in cm = 175 cm.

Then, from the general conversion rule,

1 meter = 100 cm.

1 cm = 1/100 meter.

175 cm. = 175/100 = 1.75 meters.

Therefore, if a student is 175 cm tall, then according to the metric system the same student is 1.75 m tall.

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The solution of the system of equations is x = 0.6 and y = 1.6.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given system of equations are,

2x + 3y = 6

7x - 2y = 1

Multiplying throughout the first equation with 7 and the second equation with 2, we get the system of equations as,

14x + 21y = 42

14x - 4y = 2

Subtracting the first equation with second,

21y + 4y = 40

25y = 40

y = 1.6

Substituting the value y = 1.6 in 2x + 3y = 6, we get,

2x + (3 × 1.6) = 6

x = 0.6

Hence the solution of the equations is the intersecting point (0.6, 1.6).

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It appears that you have some values for angles and sides in a triangle and you are trying to find the value of the side PO=OM.

PO/sin90 = (OM/sin(90-PX-16)) = (5(X+12))/sin90

PO = OM (since they are equal)

PO = 5(X+12)

This is the value of the side PO=OM in the triangle.

Regenerate response

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The magnetometers revealed that the basalt rocks along the mid-ocean ridges are aligned in alternating, symmetrical patterns. This is due to the Earth's geomagnetic field which constantly fluctuates in intensity and direction.

When molten basalt cools and sets, it orients itself in the direction of the Earth's field. As this field changes, the orientation of the rocks changes as well.

This creates the alternating, symmetrical pattern seen in the magnetometer readings. In addition, the seafloor spreading which occurs along the mid-ocean ridges can also contribute to the pattern of the rocks. As the seafloor spreads, new basalt rocks are formed and orient themselves by the Earth's field.

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Answer: 1.25

2 1/2 (1/2)

2 1/2 (servings) x 1/2 (cups of milk)

a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.

b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.

a) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.

b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.

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The values of x for which the expression makes sense are given as follows:

x > 3.

The values of x for which the expression makes sense are the domain of the relation, which is the set of possible values assumed by the input x of the relation.

There are two restrictions in this problem, given as follows:

Hence the numeric restrictions are given as follows:

Hence the interval of values of x that respect all three conditions is given as follows:

x > 3.

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Part (a)

Dividing by 5 yields,[tex]\frac{d}{5}[/tex].

Part (b)

Oliver is 7 years older than Amira.

Answer:

Part (a)

Dividing by 5 yields,.

Part (b)

Oliver is 7 years older than Amira.

Step-by-step explanation:

Answer:

[tex]\frac{x^{18}}{64}[/tex]

Step-by-step explanation:

[tex]\left(\frac{x^3}{2} \right)=\frac{(x^3)^6}{2^6}=\frac{x^{18}}{64}[/tex]

Answer: 3. 5.4

Step-by-step explanation:

we can convert all of these numbers to decimal form. 3 = 3.00,1.05=1.05, 5.4 = 5.40, and 4.2= 4.20. As we can see here, 1.05 is clearly the smallest, 3.00 is the second smallest, and 5 is larger than 4 s o its 5.4

Answer:

13 divided by 16 is 0.8125, which is greater than 0 and less than 1. Therefore, 13/16 is located between 0 inches and 1 inch on the ruler.

Step-by-step explanation:

A function f(x) = -(x+4)^2 + 2 has vertex (-4,2) which is a maximum point and a function g(x) = (x-2)^2 - 2 has vertex (2,-2) which is a minimum point.

In this question we have been given two functions  f(x) = −(x + 4)2 + 2 and g(x) = (x − 2)2 − 2which  have been rewritten using the completing-the-square method.

We need to determine if the vertex for each function is a minimum or a maximum.

We know that, the vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants.

The graph of parabola is at (h, k).

So, the vertex of the quadratic function f(x)=-(x+4)^2+2 is (-4,2)

The vertex of quadratic function g(x) =(x-2)^2-2 is vertex (2,-2)

The graph of both the functions is shown below.

A vertex (-4,2) is a maximum point of function f(x) = −(x + 4)2 + 2  and a vertex (2,-2) is a minimum point of function g(x) = (x − 2)2 − 2

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The vertex of the equation is (x, y) = (2, 0). This also makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

The function f(x) = −(x + 4)2 + 2 is in vertex form and can be written as:

f(x) = −(x + 4)2 + 2 = −(x + 4)2 + 4 − 2

Using the completing-the-square method, the equation can be rewritten as:

f(x) = −(x + 4)2 + 4 − 2 = −(x + 4)2 + 4 − 4 + 2 = −(x + 4)2 + 4 = −(x + 4 + 2)(x + 4 − 2)

Now, we can determine the vertex of the equation. To do this, we can set the equation equal to 0.

0 = −(x + 4 + 2)(x + 4 − 2)

From this equation, we can solve for x to get the x-coordinate of the vertex.

x = −2

Now, we can plug this x-coordinate into the equation to get the y-coordinate of the vertex.

f(−2) = −(−2 + 4)2 + 4 = 0

Therefore, the vertex of the equation is (x, y) = (−2, 0). Since the y-coordinate of the vertex is 0, this means that the vertex is a minimum. This makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

We can use the same method for the function g(x) = (x − 2)2 − 2. First, we can rewrite the equation using the completing-the-square method.

g(x) = (x − 2)2 − 2 = (x − 2)2 − 4 + 2 = (x − 2)2 − 4 = (x − 2 + 2)(x − 2 − 2)

Set the equation equal to 0 and solve for x to get the x-coordinate of the vertex.

0 = (x − 2 + 2)(x − 2 − 2)

x = 2

Plug this x-coordinate into the equation to get the y-coordinate of the vertex.

g(2) = (2 − 2)2 − 4 = 0

Therefore, the vertex of the equation is (x, y) = (2, 0). Since the y-coordinate of the vertex is 0, this means that the vertex is a minimum. This also makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

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