Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Probability of 3 people arriving late is 0.34%.

The probability of 3 people arriving late to the party is the probability of a combination of 3 individuals arriving late and the couple and remaining individual arriving on time. This can be expressed mathematically as P(X = 3) = P(3 individuals arrive late)P(Couple arrives on time)P(Individual arrives on time).

We can calculate this probability as follows:

P(X = 3) = (0.1 x 0.1 x 0.1) x (0.7 x 0.7) = 0.00343

This means that there is a 0.34% chance that 3 people arrive late to the party. Probability of 3 people arriving late is 0.34%.

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Answer:24

Step-by-step explanation:

because

The combined area of the given figure will be 40 square inches.

The area is defined as the space covered by the object in two-dimensional space.

The area of a rectangle with a length of 7 inches and a width of 5 inches is given by:

Area of rectangle = length x width = 7 in x 5 in = 35 square inches

The area of a triangle with a base of 5 inches and a height of 2 inches is given by:

Area of triangle = (1/2) x base x height = (1/2) x 5 in x 2 in = 5 square inches

Therefore, the combined area of the rectangle and triangle is:

35 square inches + 5 square inches = 40 square inches

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The law of sines states that the ratio of the Sine of an angle to the length of the side opposite that angle is constant in any triangle.

The Law of Sines is defined as a relationship that applies to all triangles, not just right triangles.

The law states that the ratio of length of side of a triangle to sine of angle opposite that side is constant for all sides and angles in the triangle.

So , for any triangle, ratio of length of one side to the sine of angle opposite that side is = ratio of length of any other side to the sine of the angle opposite that side.

The Sine Law is also useful for solving problems which involves the angles and sides of triangles, especially when not all sides and angles are known.

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Answer: 1/2

Step-by-step explanation:

Answer:

Each friend will get half of the melon

Step-by-step explanation:

If the two friends have one melon, they will each get half. There are two people, so you cut it in half. They will each get 0.5 or 1/2 of the melon.

Answer:

b

Step-by-step explanation:

Answer: 3x³+ 9x + -11

Step-by-step explanation: Combine Like Terms: 4x + 4x³+-11+-2x+-x³+7x

=(4x³+-x³) + (4x + -2x +7x) + (-11)

=3x³+ -9x+ -11

Answer:

The expression (9x+8)-(3x + 5) simplifies to 6x + 3. Therefore, the answer is option C: 6x + 3.

All of the options are correct regarding the probabilities in graphical models.

Use relative frequency to estimate probability: This is a common approach for estimating probabilities in graphical models, especially when we have a large amount of data. We can count the number of times a certain event occurs in the data and divide it by the total number of events to get an estimate of the probability.

Make proper assumption about the priors: Priors represent our knowledge or beliefs about the probabilities before observing any data. By making appropriate assumptions about the priors, we can incorporate additional information into the model and improve our estimates of the probabilities.

Use the MLE principle for estimation: Maximum Likelihood Estimation (MLE) is a commonly used approach for estimating the parameters of a graphical model. The goal of MLE is to find the parameter values that maximize the likelihood of observing the data. This approach is often used when we have limited data and need to estimate the parameters of the model.

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This final result as a fractiοn and a decimal 115075 using the given fractiοns 6/2 and 4/8

A fractiοn is a mathematical representatiοn οf a part οf a whοle οr a ratiο between twο quantities. It is typically represented as a tοp number (numeratοr) divided by a bοttοm number (denοminatοr), separated by a hοrizοntal line.

Fοr example, the fractiοn 3/4 represents three parts οut οf fοur equal parts οf a whοle. The numeratοr (3) represents the number οf parts, while the denοminatοr (4) represents the tοtal number οf parts that make up the whοle.

Accοrding tο the questiοn:

Let's first find hοw many gummys Jaly has:

Jaly has 241 times greater number οf gummys than Deens, whο has 463. Sο Jaly has:241 x 463 = 111583 gummys Jaly then gave 50 away and received 3542 gummys.

Therefοre, the tοtal number οf gummy's Jaly nοw has is:111583 - 50 + 3542 = 115075We can express this final result as a fractiοn and a decimal using the given fractiοns 6/2 and 4/8.

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Answer:

18

Step-by-step explanation:

to find p(-2), substitute it into the equation!

you can make this easier by factoring x out, so p(x) = x(x-7)

then, plug -2 in

p(-2)=-2(-2-7)

p(-2)=-2(-9)

p(-2)=18

Answer:

Step-by-step explanation:

p(x)=[tex]x^{2}-7x\\[/tex]

=>p(-2)=[tex](-2)^{2} -7.(-2)[/tex]

           = 4+14=18

The area of each circle, to the nearest tenth is:

1. 19.6 cm²

2. 379.9 in.²

3. 28.3 mm²

4. 78.5 in.²

5. 132.7 cm²

6. 162.8 yd²

The area of a circle is calculated as:

A = πr², where, r is the radius of the circle, and π is a constant.

1. r = 5/2 = 2.5 cm

Area = πr² = 3.14 * 2.5²

= 19.6 cm²

2. r = 11 in.

Area = πr² = 3.14 * 11²

= 379.9 in.²

3. r = 3 mm

Area = πr² = 3.14 * 3²

= 28.3 mm²

4. r = 10/2 = 5 in.

Area = πr² = 3.14 * 5²

= 78.5 in.²

5. r = 13/2 = 6.5 cm

Area = πr² = 3.14 * 6.5²

= 132.7 cm²

6. r = 7.2 yd

Area = πr² = 3.14 * 7.2²

= 162.8 yd²

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The creation of the bin.matrix using cbind() allows us to organize and manipulate our data in a way that is conducive to statistical analysis.

A binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, with a constant probability of success.

First, let's define what a binomial distribution is. For example, if we toss a fair coin 10 times, the number of heads that come up is described by a binomial distribution.

Now, let's talk about the cbind() function. cbind() is short for "column bind". It is used to combine vectors or matrices into a single matrix, where each input vector or matrix becomes a column in the final matrix.

In this exercise, we have created 7 vectors, each with a different success probability for a binomial distribution, ranging from 0.2 to 0.8. We will use cbind() to combine these vectors into a matrix called bin.matrix.

The dimension of the bin.matrix is

=> 300 x 7.

This means that the matrix has 300 rows and 7 columns. Each row represents a trial, and each column represents a different success probability. For example, the first column might represent a trial with a success probability of 0.2, while the second column might represent a trial with a success probability of 0.3, and so on.

By creating this matrix, we can easily perform statistical analyses on the data contained within it. We can calculate summary statistics, such as the mean and variance, for each column, or we can compare the distributions of the different columns to see if there are any significant differences between them.

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The volume of the solid obtained by rotating the region in the first quadrant bounded by [tex]$y=x^5$[/tex], y = 1, and the y-axis about the line y = −2 is 29.0359321.

The region is bounded in the xy plane and is said to be bounded in between the curve, line and y-axis as given by

Curve: [tex]$y=x^5$[/tex]

Line: y = 1

y-axis: x = 0

The curve and line intersect at [tex]x^5=1[/tex] and x = 1

The region bounded can be expressed as

[tex]x^5 \leq y \leq 1 \\[/tex]

0 ≤ x ≤ 1

Here we have to determine the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5, y=1

Now if the solid is obtained by the rotation of the region about the line y = -2 then the volume of the solid is evaluated by the method of the rings/washers as

Volume [tex]$=\int_{\mathrm{a}}^{\mathrm{b}} \mathrm{A}(\mathrm{x}) \mathrm{dx}[/tex]

Volume [tex]$=\int_{\mathrm{a}}^{\mathrm{b}} \pi\left[\text { (outer radius) }^2-\text { (inner radius }^2\right] \mathrm{dx}[/tex]

Volume  [tex]$=\pi \int_0^1\left[(1-(-5))^2-\left(x^5-(-5)\right)^2\right] d x[/tex]

Volume   [tex]$=\pi \int_0^1\left[(1+5)^2-\left(x^5+5\right)^2\right] d x[/tex]

Volume  [tex]$=\pi \int_0^1\left[(6)^2-\left(x^5+5\right)^2\right] \mathrm{d} x[/tex]

Volume  = [tex]$\pi \int_0^1\left[(36)-\left(x^{10}+10 x^5+25\right)\right] d x$$[/tex]

Volume  = [tex]$\pi \int_0^1\left(36-x^{10}-10 x^5-25\right) d x[/tex]

Volume   [tex]$=\pi \int_0^1\left(11-x^{10}-10 x^5\right) d x[/tex]

Volume   [tex]$=\pi\left[11 x-\frac{1}{11} x^{11}-10\left(\frac{x^6}{6}\right)\right]_0^1$$$$[/tex]

Volume   [tex]$=\pi\left[11 x-\frac{1}{11} x^{11}-\frac{5}{3} x^6\right]_0^1$$$$[/tex]

Volume  [tex]$=\pi\left(11(1-0)-\frac{1}{11}\left(1^{11}-0\right)-\frac{5}{3}\left(1^6-0\right)\right)[/tex]

Volume   [tex]=\pi\left(11(1)-\frac{1}{11}(1)-\frac{5}{3}(1)\right)[/tex]

Volume  [tex]=\pi\left(11-\frac{1}{11}-\frac{5}{3}\right)$$[/tex]

Volume  = [tex]$\frac{305}{33} \pi[/tex]

Therefore the volume of the solid is

V [tex]=\frac{305}{33} \pi \approx[/tex] 29.0359321

Therefore the volume of the solid is 29.0359321

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a) This function maps even integers to the next odd integer, and maps odd integers to themselves. It is not one-to-one

b) This function maps positive integers to even positive integers, and maps negative integers to odd positive integers. It is one-to-one because different inputs always have different outputs.

c) This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs, and it is onto because every positive and negative integer is in its range.

d) This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs

(a) One example of a function that is neither one-to-one nor onto is:

[tex]f(x) = \begin{cases} x+1 & \text{if } x \text{ is even} \ x & \text{if } x \text{ is odd} \end{cases}[/tex]

This function maps even integers to the next odd integer, and maps odd integers to themselves. It is not one-to-one because, for example, f(2) = f(4) = 3. It is not onto because no positive even integer is in the range of f.

(b) One example of a function that is one-to-one but not onto is:

[tex]f(x) = \begin{cases} 2x & \text{if } x > 0 \ -2x+1 & \text{if } x \leq 0 \end{cases}[/tex]

This function maps positive integers to even positive integers, and maps negative integers to odd positive integers. It is one-to-one because different inputs always have different outputs. However, it is not onto because no odd positive integer is in the range of f.

(c) One example of a function that is onto but not one-to-one is:

[tex]f(x) = \begin{cases} x/2 & \text{if } x \text{ is even} \ -(x+1)/2 & \text{if } x \text{ is odd} \end{cases}[/tex]

This function maps even integers to positive integers, and maps odd integers to negative integers. It is onto because every positive and negative integer is in the range of f. However, it is not one-to-one because, for example, f(2) = f(-2) = 1.

(d) One example of a function that is both one-to-one and onto is:

f(x) = x

This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs, and it is onto because every positive and negative integer is in its range.

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The CDF at P(X > 1)  is 1/16.

CDF stands for the cumulative distribution function. It is a function that maps each possible value of a random variable X to the probability that X takes a value less than or equal to that value.

The cdf given is:

F(x) =0 for x < 0

x^2/16 for 0 <= x < 1

1 - (3-x)^2/16 for 1 <= x < 4

1 for x >= 4

P(X <= 1)

Using the definition of the cdf, we have:

P(X <= 1) = F(1)

Since 0 <= 1 < 1, we have:

F(1) = 1^2/16 = 1/16

So, P(X <= 1) = F(1) = 1/16.

P(X > 2)

Using the definition of the cdf, we have:

P(X > 2) = 1 - P(X <= 2)

Since 0 <= 2 < 4, we have:

P(X <= 2) = F(2) = 2^2/16 = 1/4

Therefore:

P(X > 2) = 1 - P(X <= 2)

=> 1 - 1/4

=> 3/4.

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The coefficients (a, b, c) in a polynomial equation is relate to the position x, velocity v, and acceleration a of an object.

Position (x): The position of the object can be represented by the x-coordinate of its position in space. This can be related to the coefficients in the equation by setting the x-coordinate equal to x and solving for the corresponding y-coordinate.

Velocity (v): The velocity of an object is the rate at which its position is changing. This can be related to the coefficients in the equation by taking the first derivative of the equation with respect to time. The result is a linear equation that represents the velocity as a function of time.

Acceleration (a): The acceleration of an object is the rate at which its velocity is changing. This can be related to the coefficients in the equation by taking the second derivative of the equation with respect to time. The result is a constant value that represents the acceleration of the object.

In summary, the coefficients (a, b, c) can be related to the position, velocity, and acceleration in equation for x, taking derivatives of the equation with respect to time, and interpreting the results as the position, velocity, and acceleration of the object.

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9. a)The required value of h is 4

9.b) The required value of h is 4

10.a)The required value of h is -6

10.b) They are linearly dependent for all values of h.

Here the given vectors are:

v1 = [tex]\left[\begin{array}{ccc}1\\-3\\2&\end{array}\right][/tex]

v2 = [tex]\left[\begin{array}{ccc}-3\\10\\-6&\end{array}\right][/tex]

v3 = [tex]\left[\begin{array}{ccc}2\\-7\\h&\end{array}\right][/tex]

The vectors v1 and v2 are not scalar multiples of one another so they are not linearly dependent.

[tex]\left[\begin{array}{ccc}1&-3&2\\-3&10&-7\\2&-6&h\end{array}\right][/tex]= 0

1(10h -42) -3(-14 +3h) +2 (18-20) =0

10h -9h-4 =0

h = 4

Hence the value of h is 4 so that the vector v3 is in span{v1,v2}

b) The given vectors will be linearly dependent if h =4

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The Confidence interval starts at 177.28 and the Confidence interval ends at 187.72. Thus option c is correct.

The given data is as follows:

Number of coffee, N = 28

Mean, µ = 182.5

Standard deviation, α = 14.1

Confidence Level, CL = 95%

z-value for 95% confidence interval = 1.96

The confidence interval is calculated by using the formula,

Confidence interval = μ ± Ζ (α/√n )

Confidence interval = 182.5 ± 1.96*(14.1/√28)

Confidence interval = 182.5 ± 5.22

Confidence interval = (177.28, 187.72)

Therefore we can conclude that the Confidence interval starts at 177.28 and the Confidence interval ends at 187.72.

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The transformation from ln ( x ) to ln ( x + 2 ) is horizontal transformation or shift.

What kinds of functions can be transformed?

Transformations can be divided into three categories: translations, reflections, and dilations. There are two types of transformations that can be done to a function: vertical (which affects the y-values) and horizontal (affects the x-values).

                               The four transformation variables are included in the equation of a function that is shown below (a, b, h, and k).

f(x) = ln(x)

if g(x) = ln(x + 2)

Then,

The transformation from ln(x) to ln(x+2) is horizontal transformation or shift. As 2 units are added in g(x) the function is horizontally shifted by 2 units in left-hand direction.

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Answer:

1/6

Step-by-step explanation:

1/4x2/3 = 2/12 = 1/6

Answer:

Down payment is $12,500.

Mortgage = $237,500

Step-by-step explanation:

The required down payment is 5% of the selling price of the house, which is $250,000.

Down payment = 5% of $250,000 = 0.05 x $250,000 = $12,500

Therefore, the required down payment is $12,500.

To find the amount of the mortgage, we need to subtract the down payment from the selling price of the house.

Mortgage = Selling price of the house - Down payment

Mortgage = $250,000 - $12,500

Mortgage = $237,500

Therefore, the amount of the mortgage is $237,500.

The probability of each outcome can be calculated using basic probability formulas, such as the multiplication rule and the addition rule is 1/2

Probability is the branch of mathematics that deals with the likelihood of events occurring. In this scenario, we are looking at the probability of a concrete beam failing by shear or flexure.

When three failed beams are randomly selected, the type of failure is determined for each one. We want to find the probability of each possible outcome, where X represents the number of beams among the three selected that failed by shear.

To list the outcomes in the sample space, we can use the following notation: S for shear failure and F for flexure failure. The possible outcomes are:

SSS, where all three beams failed by shear. In this case, X = 3.

SSF, where two beams failed by shear and one by flexure. In this case, X = 2.

SFS, where two beams failed by shear and one by flexure. In this case, X = 2.

FSS, where two beams failed by shear and one by flexure. In this case, X = 2.

SFF, where one beam failed by shear and two by flexure. In this case, X = 1.

FSF, where one beam failed by shear and two by flexure. In this case, X = 1.

FFS, where one beam failed by shear and two by flexure. In this case, X = 1.

FFF, where all three beams failed by flexure. In this case, X = 0.

Each outcome has a different value of X, which represents the number of beams that failed by shear.

Then the probability is calculated as,

=> 1/2

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The volume of a pyramid with a base area of 15 square inches and a height of 7 inches is, 35 cubic inches.

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

If the volume of a pyramid varies jointly with its base area and height, we can write this relationship as:

V = k[Ah/3]

To find the value of k, we can use the given information that the volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.

Plugging these values into the formula, we get:

24 = k(24)(3)/3

Simplifying, we get:

k = 1

Now we can use the formula to find the volume of a pyramid with a base area of 15 square inches and a height of 7 inches:

V = kAh/3

V = (1)(15)(7)/3

V = 105/3

   = 35

Therefore, the volume of the pyramid is 35 cubic inches.

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Answer:

To solve this problem, we can use the formula:

Speed = Distance / Time

The total distance traveled by the plane is 3,000 + 600 = 3,600 miles. The total time taken is 2 hours 30 minutes, or 2.5 hours.

So, the speed of the plane is:

Speed = 3,600 miles / 2.5 hours = 1,440 miles per hour

Therefore, the answer is 1440 mph

The translation needed to obtain the graph of g(x) = 7^x-4 from the graph of (x) = 7^x is 4 units right

From the question, we have the following parameters that can be used in our computation:

g(x) = 7^x-4

f(x) = 7^x

Using the above as a guide, we have the following:

g(x) = f(x - 4)

This represents a translation to the right by 4 units

Hence, the translation is 4 units right

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Answer: 0.9 is the answer hope I helped.

Step-by-step explanation:

The require value of side of rectangle(x) is equal to 0.9 in.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We have;

length of longer side = 6.4 in and loneger side of small rectangle = 1.6 in.

Then,

Scale factor = 6.4/1.6  = 4

It means Sides of big rectangle is 4 times of small rectangle.

We also have smaller side of big rectangle = 3.6 in

3.6 = 4x

x = 3.6/4

x = 0.9

Thus, required value of x is 0.9 in.

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1. the positive linear relationship is what is shown here

A reasonable estimate that can be given for a person that played for 80 minutes is 26

The mean absolute deviation is appropriate to describe the spread of data if the data distribution is symmetric

2. this is in the attachment

15 + 35 = 50

those that like fishing = 35 + 21 = 56

those that dislike fishing = 15 + 24 = 39

for male that like fishing = 35 / 56 = 0.63

for male that dislike fishing = 15 / 39 = 0.38

for females total 45

for female that like fishing 45 - 24 = 21 / 56 = 0.38

females that dislike fishing = 24 / 39 = 0.62

c. the relative frequency that is shown tells us that most of the people that like fishing are the males. While the most people that dislike fishing are the females

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Answer:

Step-by-step explanation:

1.Do 4x and 15 + x have the same value when x is 5?

To determine if 4x and 15 + x have the same value when x is 5, we can substitute 5 for x in both expressions and see if they equal the same value:

4x = 4 * 5 = 20

15 + x = 15 + 5 = 20

So, when x is 5, 4x and 15 + x both have the same value of 20.

2. Are 4x and 15 + x equivalent expressions?

Two expressions are considered equivalent if they have the same value for all possible values of the variables they contain. In this case, for all values of x, 4x and 15 + x will have the same value, so we can say that 4x and 15 + x are equivalent expressions.

Also:

When we substitute x = 5 into both expressions 4x and 15 + x, we find that:

4x = 4 * 5 = 20

15 + x = 15 + 5 = 20

As we can see, both expressions have the same value of 20 when x = 5. This means that the value of the expression 4x is equal to the value of the expression 15 + x when x = 5.

However, just because the values of the expressions are equal when x = 5, this does not necessarily mean that the expressions are equivalent for all values of x. To determine if two expressions are equivalent, we need to consider their values for all possible values of the variables they contain. In this case, since 4x and 15 + x have the same value for all values of x, we can conclude that these two expressions are equivalent.

In general, equivalent expressions are expressions that have the same value for all values of the variables they contain. Equivalent expressions can be transformed into each other through operations such as adding or subtracting the same value, multiplying or dividing by the same non-zero value, or using the distributive property.