Make x the subject
gk=(x+a)^2/10

Answer:

The correct answers was C not A.

Step-by-step explanation:

The true statement about the conditional probability is P(B/A) = \(\frac{P(AandB)}{B}\), when two events are not independent.

Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

Given that, A and B are two events. The notation for conditional probability is P (B/A).

We know that, formula give for conditional probability is  P(B/A) = \(\frac{P(AandB)}{B}\),

Where A and B are non-dependent events.

Since, the events are non-dependent, So it is P(B|A) = P(B) that represents that the occurrence of B does not depend on the occurrence of A.

Hence, The true statement about the conditional probability is P(B/A) = \(\frac{P(AandB)}{B}\), when two events are not independent.

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Answer:

m = 3

Step-by-step explanation:

Pick two points from the table.

(-1, 1) and (1, 7)

Apply the slope formula.

\(m=\frac{7-1}{1+1}=\frac{6}{2}=\boxed{3}\)

Hope this helps.

Answer:

696

Step-by-step explanation:

\(\frac{m}{8} = 87\)

First I would multiply each side by 8 to find what M is (because if you multiple m/8 by 8 the 8s will cancel out).

\(m=87*8\\m = 696\)

Because any number divided by 1 would just be itself, 696/1 is just 696.

Answer: m/1= 7.125 or 7.1 (rounded)

Step-by-step explanation:

if m/8=57 then m/1 multiplied by 8 would be 57 . so you do the opposite and divide 57 by 8.

Measure of all angles must equal 180 degrees.

Therefore,
(4x+20) + (2x+34) + x = 180

6x + 54 + x = 180

7x + 54 = 180

7x = 126

x = 18

4(18)+20 = 92

Angle A = 92

2(18)+34 = 60
Angle C = 60 degrees

Unknown angle is 18 degrees because the "x" represents the third angle.

When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.

Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.

So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.

So, option D is the correct answer.

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Answer: To solve this system of equations, we need to find two points that satisfy both equations. We can then use these two points to graph the equations and find their point of intersection, which will be the solution to the system.

Let's start by finding some points that satisfy the second equation, y = |2x^2 - 5|:

When 2x^2 - 5 is positive, y = 2x^2 - 5

If we set x = 0, then y = |-5| = 5, so one point is (0, 5).

If we set x = 1, then y = |2 - 5| = 3, so another point is (1, 3).

When 2x^2 - 5 is negative, y = -(2x^2 - 5) = 5 - 2x^2

If we set x = 0, then y = 5, so another point is (0, 5).

If we set x = -1, then y = 5 - 2 = 3, so another point is (-1, 3).

Now we have four points that satisfy the second equation: (0, 5), (1, 3), (-1, 3), and (0, 5). We can use these points to graph the equation y = |2x^2 - 5|, as shown below:

   |    

5 -+    +------------*------+------------*------+--

  |                         |                       |

4 -+                                                +--

  |                                                   |

3 -+    +------------*------+------------*------+     |

  |                         |                       |

2 -+                                                +--

  |                                                   |

1 -+                                                   +--

  |                                                      |

  +------------------------------------------------------+

    -1    -0.5    0    0.5     1     1.5    2      2.5    3

Next, we need to find the points that satisfy the first equation, 3x + y = 0. One way to do this is to plug in values of x and solve for y:

If x = 0, then y = 0, so one point is (0, 0).

If x = 1, then y = -3, so another point is (1, -3).

Now we have two points that satisfy both equations: (0, 5) and (1, -3). We can use these points to graph the equations and find their point of intersection:

   |    

5 -+    +------------*------+------------*------+--

  |                         |                       |

4 -+                                                +--

  |                                                   |

3 -+    +------------*------+------------*------+     |

  |                         |                       |

2 -+                                                +--

  |                                                   |

1 -+                                                   +--

  |                                                      |

  +------------------------------------------------------+

    -1    -0.5    0    0.5     1     1.5    2      2.5    3

                (0, 5)

                /

             __/_____

            /   /    \

          /   /        \

(-1.5, 0) /   / (0,0)   \ (1.5, 0)

         \  /            \ /

          \/--------------*---------------> x

                       (-3/4, -9/4)

From the graph, we can see that the two equations intersect at approximately (-0.75, -2.25). Therefore, the solution to the

Step-by-step explanation:

Therefore, the probability of pumping gas into more than 5 cars during the 30-minute period is 0.

To find the probability of an event, we sum the probabilities of the individual outcomes that make up the event. In this case, we want to find the probability that the service station will pump gas into more than 5 cars during the 30-minute period.

The given probabilities for pumping gas into 0, 1, 2, 3, 4, and 5 or more cars are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17, respectively.

To find the probability of pumping gas into more than 5 cars, we need to sum the probabilities of pumping gas into 0, 1, 2, 3, 4, and 5 cars and subtract it from 1:

P(more than 5 cars) = 1 - [P(0 cars) + P(1 car) + P(2 cars) + P(3 cars) + P(4 cars) + P(5 cars)]

P(more than 5 cars) = 1 - (0.03 + 0.18 + 0.24 + 0.28 + 0.10 + 0.17)

P(more than 5 cars) = 1 - 1.00

P(more than 5 cars) = 0

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A function for the area A of the enclosure in terms of w is A(w) = w * ((800 - w) / 2). 200 feet width would maximize the area. The maximum area is 60,000 square feet.

a) To write a function for the area A of the enclosure in terms of w, we first need to express the length l in terms of w. Since one side of the pen is against the barn and only 3 sides require fencing, we can write the equation for the total length of fencing (800 feet) as:

800 = w + 2l

Now, solve for l:

2l = 800 - w
l = (800 - w) / 2

Next, write the area function A(w) using the formula for the area of a rectangle, A = w * l:

A(w) = w * ((800 - w) / 2)

b) To find the width w that maximizes the area, we need to find the maximum value of A(w). To do this, take the first derivative of A(w) with respect to w and set it to zero:

dA(w)/dw = (800 - 2w) / 2 - w

Now, set dA(w)/dw to zero and solve for w:

0 = (800 - 2w) / 2 - w
0 = 400 - w - w
2w = 400
w = 200 feet

The width w that maximizes the area is 200 feet.

c) To find the maximum area, plug the optimal width w (200 feet) back into the area function A(w):

A(200) = 200 * ((800 - 200) / 2)
A(200) = 200 * (600 / 2)
A(200) = 200 * 300
A = 60,000 square feet

The maximum area of the enclosure is 60,000 square feet.

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The component of F₁ acting in the direction of F₂ is 250 N in its Cartesian form.

To find the component of F₁ acting in the direction of F₂, we can use the dot product of the two vectors. The dot product gives us the magnitude of one vector in the direction of another vector.

Given:

F₂ = 400 N

F₁ = 250 N

The dot product of two vectors A and B is given by:

A · B = |A| |B| cosθ

Where |A| and |B| are the magnitudes of vectors A and B, respectively, and θ is the angle between the two vectors.

In this case, we want to find the component of F₁ in the direction of F₂, so we can write:

F₁ component in the direction of F₂ = |F₁| cosθ

To find the angle θ, we can use the fact that the dot product of two vectors A and B is also equal to the product of their magnitudes and the cosine of the angle between them:

F₁ · F₂ = |F₁| |F₂| cosθ

Since we know the magnitudes of F₁ and F₂, we can rearrange the equation to solve for cosθ:

cosθ = (F₁ · F₂) / (|F₁| |F₂|)

Substituting the given values:

cosθ = (250 N * 400 N) / (|250 N| * |400 N|)

Taking the magnitudes:

cosθ = (250 N * 400 N) / (250 N * 400 N)

cosθ = 1

Since cosθ = 1, we know that the angle between the two vectors is 0 degrees or θ = 0.

Now, we can calculate the component of F₁ in the direction of F₂:

F₁ component in the direction of F₂ = |F₁| cosθ

F₁ component in the direction of F₂ = 250 N * cos(0)

F₁ component in the direction of F₂ = 250 N * 1

F₁ component in the direction of F₂ = 250 N

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The graph that represents the geometric sequence f(x) = (1) ∙ (2)^(x-1) is graph C.

A geometric sequence is a sequence of numbers where each term is equal to the previous term multiplied by a constant value, called the common ratio. In this case, the common ratio is 2. This means that the first term of the sequence is 1, the second term is 1 * 2 = 2, the third term is 2 * 2 = 4, and so on.

The graph of a geometric sequence is a curve that gets closer and closer to the y-axis as x gets larger. This is because the terms of the sequence get smaller and smaller as x gets larger. In the case of the sequence f(x) = (1) ∙ (2)^(x-1), the terms of the sequence get smaller and smaller as x gets larger because the common ratio is 2, which is greater than 1.

Graph C is the only graph that meets all of these criteria. The curve in graph C gets closer and closer to the y-axis as x gets larger. This is because the terms of the sequence f(x) = (1) ∙ (2)^(x-1) get smaller and smaller as x gets larger. Therefore, graph C is the graph that represents the geometric sequence f(x) = (1) ∙ (2)^(x-1).

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We can fit 25 notebooks on the space.

Now, According to the question:

The width of the notebook is 2/5

The length of the space is 10 inches.

To find the number of the notebooks can put there divide 30 by 2/3

Number of the books : \(\frac{10}{\frac{2}{5} }\) = 10 × \(\frac{5}{2}\)

=> 50/2 = 25

The number of the notebook is 25

We can fit 25 notebooks on the space.

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The expression that best represents the volume is (b) \(V = \pi (13.5)^2 (4)\)

The given parameters are:

Diameter, d = 27

Height, h = 4

Start by calculating the radius using:

r = d/2

This gives

r = 27/2

r = 13.5

The volume is then calculated as:

\(V = \pi r^2 h\)

This gives

\(V = \pi (13.5)^2 (4)\)

Hence, the expression that best represents the volume is (b) \(V = \pi (13.5)^2 (4)\)

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Answer:

684 mm squared

Step-by-step explanation:

Very simple. It's 18mm multiplied by 38 mm.

18 mm * 38 mm = 684 mm2

Answer:

\((fof^{-1})(x)=x\)

Step-by-step explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤ \(-\frac{8}{6}\)]

Another function is the inverse of f(x),

\(f^{-1}(x)=-\frac{\sqrt{x}+8}{6}\)

Now composite function of these functions will be,

\((fof^{-1})(x)=f[f^{-1}(x)]\)

                  = \([-6(\frac{\sqrt{x}+8}{6})-8]^{2}\)

                  = \([-\sqrt{x}+8-8]^2\)

                  = \((-\sqrt{x})^2\)

                  = x

Therefore, \((fof^{-1})(x)=x\)

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Logarithm (a) log2(64) = 6

The definition of a logarithm states that for any base "b" and a positive number "x", if bx = y, then logb(y) = x. In other words, the logarithm tells us the exponent to which the base must be raised to obtain a given number.

In this case, we are asked to find log2(64), which means we need to determine the exponent to which 2 must be raised to obtain 64.

To find this exponent, we can think of 2^6 = 64. This means that log2(64) = 6, since the exponent 6 is required to get 64 as the result when 2 is raised to that power.

Therefore, log2(64) = 6.

Using the definition of logarithm, we can find the exponent needed to obtain a given number when raised to a certain base. In this case, applying the definition of logarithm allows us to determine that log2(64) is equal to 6, indicating that 2 must be raised to the power of 6 to yield 64.

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The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.

Given parallelogram A B C D below, DE = 31 If EB = x - 7.

By the definition, then the equation is given as,

EB = DE

x - 7 = 31

Simplify the equation, then we have

x - 7 = 31

x = 31 + 7

x = 38

The value of the variable 'x' is 38.

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After finding the square root of 64/100, the value obtained in terms of a fraction will be 4/5.

In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.

As per the given information in the question,

The given fraction is,

The square root of 64/100

So,

√64 = 8 and,

√100 = 10

Then, the fraction will be,

= 8/10 = 4/5

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Answer:

∠ ABC = 38°

Step-by-step explanation:

given AB = DB then Δ ABD is isosceles with base angles congruent, that is

∠ BDA = ∠ BAD = 71°

the sum of the 3 angles in Δ ABD = 180° , so

∠ ABC + 71° + 71° = 180°

∠ ABC + 142° = 180° ( subtract 142° from both sides )

∠ ABC = 38°

The y-intercept of a line is the point where the line crosses the y-axis. In other words, it is the point at which the line has an x-coordinate of 0.

To find the y-intercept of the line y = –10x + 1/9, we can set x = 0 in the equation and solve for y:

y = –10x + 1/9

= –10*0 + 1/9

= 1/9

Therefore, the y-intercept of the line is 1/9.

Therefore, approximately 70.2% of the variation in the data about the regression line is unexplained.

The coefficient of determination, denoted as R², is the proportion of the variation in the dependent variable that is explained by the independent variable(s). Therefore, the percentage of the variation in the data about the regression line that is unexplained can be found by subtracting the coefficient of determination from 1 and then multiplying the result by 100.

Percentage of variation unexplained = (1 - R^2) x 100%

Substituting R² = 0.298, we get:

Percentage of variation unexplained = (1 - 0.298) x 100%

Percentage of variation unexplained = 0.702 x 100%

Percentage of variation unexplained = 70.2%

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To create identical donation bags, you will need 55 hats and 40 scarves. You produce the most donation bags without any extra apparel. Each donation package contains 11 hats and 8 scarves.

To make the greatest amount of donation bags with no clothing left over, we need to find the greatest common factor (GCF) of 40 and 55. We can do this by finding the prime factors of both numbers:

\(40 = 2 * 2 * 2 * 5\)

55 = 5 x 11

The GCF is the product of the common prime factors, which is 5. This means we can make 5 identical donation bags.

To find out how many scarves and hats are in each donation bag, we can divide the total number of scarves and hats by the number of donation bags:

Number of scarves per bag = 40 / 5 = 8 scarves

Number of hats per bag = 55 / 5 = 11 hats

Therefore, each donation bag will contain 8 scarves and 11 hats.

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Answer:

15

Step-by-step explanation:

15 itself is a whole number

hence 15 rounded to the nearest whole number is still 15.

The next larger whole number is 16.

The next smaller whole number is 14.

Nether of those is any closer to 15 than 15 already is.

So the whole number nearest to 15 is 15 itself.

Answer:

22.5

Step-by-step explanation:

The required Distribution, selection and probability is X to U(4,11), x to N (7.5, 0.3415) and 0.87932 respectively.  

(a) Distribution of X is uniform distribution  X to U(4,11).

(b) Sample size (n) = 35, distribution of mean would be moderate with value = (4+11)/2 = 7.5

Standard deviation = √ [(11-4)^2/(12*35] = 0.3415
Now
x to N (7.5, 0.3415)

(c) We have to find probability that the average of 35 numbers will be less than 7.9.

P(x < 7.9) = P(x < 7.9; 7.5; 0.3415)
Z = (7.9 -7.5)/0.3415
Z = 1.1713
P(x< 7.9)= P(Z < 1.1713)= 0.87932.

Thus, The required Distribution, selection and probability is X to U(4,11), x to N (7.5, 0.3415) and 0.87932 respectively.  

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Answer:

3

Step-by-step explanation:

7 7/8÷51/4

3/2÷1/2

3

A=bh1/2

A=5 1/4×3×1/2

A=15 3/4×1/2

A= 7 7/8

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Answer:

-4/3

Step-by-step explanation:

let (13,-4) be (x1,y1) respectively

(1,12) be (x2,y2) respectively

From,

slope=(y2 -y1)/(x2-x1)

=(12+4) /(1-3)

=16/-12

=-4/3

Answer:

It is important to analyze the relationships between a sample and full population for several reasons:

To help make more informed statements about a population: Analyzing the relationships between a sample and full population helps us to make more accurate and informed statements about the population. By examining a sample, we can draw conclusions about the characteristics of the larger population.

To bring diverging data into analysis: Sometimes, a sample may not accurately reflect the larger population, particularly if the sample is small or biased. Analyzing the relationship between the sample and population can help to identify any diverging data and adjust the analysis accordingly.

To limit variance: Variance is a measure of how much the data varies from the mean. By analyzing the relationship between the sample and population, we can better understand the variance and take steps to limit it.

To find out how many data points are necessary to be statistically valid: Analyzing the relationship between the sample and population can help us to determine the sample size needed to be statistically valid. This can help us to avoid drawing inaccurate conclusions based on a sample that is too small.

Overall, analyzing the relationship between a sample and full population is important for ensuring that our analysis is accurate, representative, and informative.

It is important to analyze the relationships between a sample and the full population to limit variance and to help make more informed statements about a population.

Analyzing the relationships between a sample and the full population is important because it helps limit variance in the data and brings diverging data into the analysis. It also helps to determine how many data points are necessary to be statistically valid and make more informed statements about the population.

By examining a sample and comparing it to the full population, we can identify any biases or errors in our data and ensure that our conclusions are accurate and representative of the entire population. Additionally, understanding the relationship between the sample and the population can help us make predictions and draw conclusions with greater confidence and precision.
By understanding the relationship, you can ensure that the sample accurately represents the population, leading to better inferences and decision-making.

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