If f(x + 3) = x^2 + 4x − 7, find f(2).

It is possible to determine the theoretical probability of an occurrence without doing the event itself. A number cube has 6 alternative outcomes, giving each one a theoretical probability of 1 out of 6.

For example, the likelihood of drawing an ace at random is 4 out of 52 since there are 4 aces in a deck of cards. The probability of hitting a double bullseye on a regular dartboard is roughly 78 out of 100,000 because the area of the double bullseye in the center is 0.078% of the dartboard's overall area.

The likelihoods of potential possibilities are instead calculated using the frequencies of past outcomes in empirical probability. They are merely projections. The empirical chance of rolling a 4 or a 5 on the following roll is 58 out of 96 since you rolled 4s and 5s more often than any other number when you rolled the number cube.

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Answer: 1/6 is the probability

Answer:

heya !!

Answer:

n = 15

Step-by-step explanation:

10 x 15 = 150.

Hope this helps!

Answer:

Explanation: We need to find the answer to the inequality

Solution:

Graph:

The solution as found through solving inequality and demonstrated in the graph is

Answer:

180

Step-by-step explanation:

we are increasing by 20 for every increasing spot

Answer:

u = 11

Step-by-step explanation:

6(u+5)=96

Divide both sides by 6

u+5=16

Subtract 5 from both sides

u=11

The variable, u, is equivalent to 11

Answer:

u=11

Step-by-step explanation:

If you multiply  the parentheses by the outside number (6) it will bring you

6u+30=96 then take away 30 from each side to get

6u=66 last step is to divide by six

u=11

The height of the cube brick is 7 units and the volume is equal to 343 unit³

The volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.

The length of an edge for the cube brick is 7 units which implies the height represented by h is also 7 units and the volume is calculated as follows:

volume of cube brick = 7 units × 7 units × 7 units

volume of cube brick = 343 units ³

Therefore, the height of the cube brick is 7 units and the volume is equal to 343 unit³

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Answer:

\((x+3)^2=-4(y-3)\)

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry

\(\large\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}\)

\(\textsf{Vertex}=(h, k)\)

\(\textsf{Focus}=(h,k+p)\)

\(\textsf{Directrix}:y=(k-p)\)

\(\textsf{Axis of symmetry}:x=h\)

If p > 0, the parabola opens upwards.

If p < 0, the parabola opens downwards.

From inspection of the given graph:

Therefore:

Substitute the found values of h, k and p into the formula:

\(\implies (x-(-3))^2=4(-1)(y-3)\)

\(\implies (x+3)^2=-4(y-3)\)

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Answer:

What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?

Step-by-step explanation:

November 2021 EDGE

Given that the study was conducted using a sample of 513 bolts produced at a single facility when there is no bias resulting from data gathering procedures, broad inferences may then be drawn.

All bolts manufactured by that factory would be covered by the conclusion?

Due to the fact that bolts made in the same factory will follow the results of an analysis of a sample made up of bolts from the same factory. The finding or conclusion would therefore be applicable to all bolts produced in the same factory because the environment for experimentation and production is the same there while it may differ in other factories. Conclusions from the study may not apply to the bolts made by other companies as a result of this bias.

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Answer:

About $1.40 per each monthly magazine.

Step-by-step explanation:

16.80 / 12 = 1.4

a) P(X+Y = 12) = p6r6

b) True

Using the convolution formula, where X and Y are the outcomes of rolling the two dice, we can find the probability distribution of their sum for k=2, 7, and 12.

P(X+Y = k) = Σ P(X=i)P(Y=k-i)

For k = 2, we have:

P(X+Y = 2) = P(X=1)P(Y=1) = p1r1

For k = 7, we have:

P(X+Y = 7) = P(X=1)P(Y=6) + P(X=2)P(Y=5) + P(X=3)P(Y=4) + P(X=4)P(Y=3) + P(X=5)P(Y=2) + P(X=6)P(Y=1)

= p1r6 + p2r5 + p3r4 + p4r3 + p5r2 + p6r1

For k = 12, we have:

P(X+Y = 12) = P(X=6)P(Y=6) = p6r6

To show that P(S = 7) > P(S = 2)r6/r1 + P(S = 12)r1/r6, we can use the formulae we derived in part (a).

Substituting k=7, we have:

P(S = 7) = p1r6 + p2r5 + p3r4 + p4r3 + p5r2 + p6r1

Substituting k=2 and k=12, we have:

P(S = 2) = p1r1

P(S = 12) = p6r6

Substituting these into the inequality, we get:

p1r6 + p2r5 + p3r4 + p4r3 + p5r2 + p6r1 > p1r1(r6/r1) + p6r6(r1/r6)

p1r6 + p6r6 > p1r6 + p6r6

which is true. Therefore, P(S = 7) > P(S = 2)r6/r1 + P(S = 12)r1/r6.

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Answer:

Slope is 2/3.

Step-by-step explanation:

I can't help you plot the points, but the slope formula is y2-y1/x2-x1.

2-4/3-6. -2/-3. This simplifies to 2/3.

The formula to calculate the slope is

Replacing the values we have

Then, the answer is C. 1/7

Jared had about 75 minutes left for miscellaneous tasks.

During his 360-min.

shift at the local grocery store, Jared spent 122 min.

stocking shelves, 74 min.

bagging groceries, and 62 min.

sweeping the floors.

He also took a 35-min.

lunch break.

Use front-end estimation to find about how many minutes Jared had left for miscellaneous tasks.

To find how many minutes Jared had left for miscellaneous tasks, we have to subtract the time he spent stocking shelves, bagging groceries, sweeping the floors, and his lunch break from his total shift time of 360 minutes.

First, let's find an estimate of the total time Jared spent on his tasks :

Total time on tasks ≈ 120 min + 70 min + 60 min = 250 min.

Let's find the total time including his lunch break :

Total time including lunch ≈ 250 min + 35 min = 285 min.

Now we can estimate the time Jared had left for miscellaneous tasks :

Time left for miscellaneous tasks ≈ 360 min - 285 min ≈ 75 min.

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Answer: D) 100 min

Step-by-step explanation:

i pressed it and i got it right

45 + 2.25 + 4 + 0.6 =

45 + 6.85 =

51.85

OLS regression, which stands for Ordinary Least Squares regression, is not rotationally invariant.

Geometrically, this can be understood by considering the slope of the regression line. In OLS regression, the slope is determined by the ratio of the covariance between the independent and dependent variables to the variance of the independent variable.

When the variables are rotated, the covariance and variance terms change, leading to different slope estimates.

To achieve rotational invariance in regression, a method called Total Least Squares (TLS) can be used. TLS minimizes the perpendicular distances between the data points and the regression line, rather than the vertical distances as in OLS.

This ensures that the estimated regression line remains invariant under rotation. TLS is particularly useful when there is uncertainty or measurement error in both the independent and dependent variables.

In summary, OLS regression is not rotationally invariant, but TLS can be used as an alternative method to achieve rotational invariance in regression analysis.

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Answer: here's the answers to the problems

6) 17

8) 2.5

Answer:

6.  17

8.  2.5

Step-by-step Explanation:

4 x 3 + 6+9/3          12/3 + 2+7/5-3 - 6

12 + 15/3                  4 + 9/2 - 6

12 + 5                       4 + 4.5 - 6

= 17                          8.5 - 6

                                = 2.5

Given that the triangle are similar  the values of x and y ​are;

x = 3.75

y = 9.8

To solve, we need to use ratio

Since Triangles ABC and DEF are similar, their corresponding sides will be of the same ratio.

x/5 = 9/12 = y/b

x = (5 x 9) /12 = 15/4 = 3.75

From Pythagoras' theorem,

y² = x² + 9²

= (15/4)² + 9²

= 95.0625

y = √95.0625

y ≈ 9.8

thus, it is correct to state that x = 3.75 while, y = 9.8

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Full question:

Given the similar right triangles in the figure. Find the exact values of x and y?

See attached image

Answer: The number of sets contain any 4 numbers = 210

Step-by-step explanation:

Given: Universal set = {0,1,2,3,4,5,6,7,8,9}.

i.e. Total choices = Numbers in set = 10

By combinations, the number of sets contain any 4 numbers =\(^{10}C_4\)

\(=\dfrac{10!}{4!6!}\ \ \ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{10\times9\times8\times7\times6!}{4\times3\times2\times1 \times6!}\\\\=210\)

Hence, the number of sets contain any 4 numbers = 210

1. The most likely color for the taxi = green

2. The probability that the taxi is blue = 0.25

Let us assume that tg represents the taxi was green and tb represents the taxi was blue;

Also yg represents the taxi appeared green and yb  represents the taxi appeared blue.

9 out of 10 athenian taxis are green

So, P(tg) = 0.90

And, P(tb) = 1 - P(tg)

                = 1 - 0.90

                = 0.10

As under the dim lighting conditions, discrimination between blue and

green is 75% reliable,

P(yb | tb) = 0.75.

So, P(yg | tb) = 1 - P(yb | tb)

                     = 0.25

Similarly P(yg | tg) = 0.75

Thus, P(yb | tg) = 1 - P(yg | tg)

                         = 0.25

P(tb | yb) = P(tb, yb) / P(yb)

               = [P(yb | tb) P(tb)] / [P(yb, tg)P(tg) + P(yb | tb) P(xb)]

               = 0.25

Thus the probability that the taxi is blue = 0.25

P(tg | yb) = 1 - P(tb | yb)

              = 0.75

We can observe that P(tb | yb) > P(tb) but the posterior P(tb | yb) is smaller than 0.5, since the prior P(tb) is very small. Thus, the taxi was most likely green.

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The complete question is:

Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens.All taxi cars in Athens are blue or green. You swear under oath that the taxi was blue.Extensive testing shows that, under the dim lighting conditions, discrimination between blue and green is 75% reliable.

1. is it possible to calculate the most likely color for the taxi? (*hint:* distinguish carefully between the proposition that the taxi *is* blue and the proposition that it *appears* blue.)

2. what is the probability of the taxi being blue, if you know that 9 out of 10 athenian taxis are green?

Answer:

B

Step-by-step explanation:

44/77

=0.55

The outcomes in Ec= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1), (3,2), (4,1), (5,1)}.

The event E is the sum of two rolled dice being greater than or equal to 9. To list the outcomes in Ec (the complement of E), we need to find all possible outcomes where the sum of two rolled dice is less than 9.

There are 36 possible outcomes when two dice are rolled, and the sum ranges from 2 to 12. To find the outcomes in Ec, we need to list all possible outcomes where the sum is less than 9.

The possible outcomes in Ec are (1,1), (1,2), (1,3), (2,1), (2,2), (3,1), (3,2), (4,1), and (5,1). These nine outcomes satisfy the condition that the sum of two rolled dice is less than 9.

Therefore, the answer is Ec = {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1), (3,2), (4,1), (5,1)}.

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The compression technique that encodes the digital value of an analog sample based on the change from the previous sample is known as Differential Pulse Code Modulation (DPCM).

In this technique, the digital value of the current sample is predicted by using the value of the previous sample. The difference between the predicted value and the actual value of the sample is then encoded and transmitted or stored. By only transmitting the difference between the predicted and actual values, DPCM can achieve a higher compression ratio than other compression techniques that rely on transmitting the absolute value of each sample. DPCM is commonly used in applications such as speech and audio compression, where small differences between consecutive samples can be accurately predicted and transmitted with minimal loss of quality. Overall, DPCM is a powerful compression technique that is widely used in various industries to efficiently encode and store analog signals in a digital format.

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Answer:

x= 24

Step-by-step explanation:

open the bracket

4×3x =12x + 4 × 2 =8

12×+ 8-6×6

12×+ 12

x= 24

Answer:

12x - 28

Step-by-step explanation:

Because of PEMDAS you start with the parentheses and distribute the 4.

So,

(12x + 8) -6 x 6

Then, solve for the 6's

(12x + 8) -36

Remove the parentheses

12x + 8 - 36

Lastly, you get

12x - 28.

This is as far as you can go because there is no equals sign so you cannot actually solve for x.

Answer:

x-int=(2,0)

y-int=(0,4)

Step-by-step explanation: