Complete the function table
f(x)
f(-4)
f(0)
f(6)
3x²-14
x²
2x²-7x+5

There is 48% probability that the two socks will match .

The branch of mathematics concerned with the occurrence of random events. Values ​​are represented from 0 to 1. Probability was introduced into mathematics to predict the probability of an event occurring. Probability basically means how likely it is that something will happen. This is the basic theory of probability and is also used in probability distributions to learn possible outcomes of random experiments. To determine the probability of a single event occurring, we first need to know the total number of possible outcomes.

Since there are a total of 35 socks, the probability of both socks being blue is

P(blue) = 15/35 * 14/35 = 3/35 * 14/7 = 3/35 * 2 = 6/35

The probability of both being grey is

P(grey) = 20/35 * 19/35 = 19/35 * 4/7  = 76 / 245

The probability that they match is

P(blue) + P(grey) = 6/35 + 76/245  =  42+76/245 = 118/245 = 0.48 = 48%

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No, the function (U, V) = U1V1 does not define an inner product on R2 because it fails to satisfy the linearity, symmetry, and positive definiteness properties required for an inner product.

An inner product on a vector space should satisfy certain properties, including linearity in the first argument, symmetry, and positive definiteness. Let's evaluate these properties for the given function (U, V) = U1V1:

In conclusion, the given function (U, V) = U1V1 does not define an inner product on R2 as it fails to satisfy the linearity, symmetry, and positive definiteness properties.

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Answer:

a

Step-by-step explanation:

bc look

Answer:

Step-by-step explanation:

Here, 4 teams given. Each teams has played every other teams 4 times.

so here we will name each team

team a = bulls

team b = lakers

team c = knickers

team c = warriors

So to find total number of games, we know that Bulls played with the other 3 teams by 4 times that is (4×3) = 12, Lakers played with the other two teams by 4 times that is (4×2) = 8, Knicks played with Warriors 4 times.

Therefore, total number of games = .

Total points given, for Bulls = 22, for Lakers = 19, for Knickers = 14, for Warriors = 12.

So sum of total points =

For a win a team earned 3 points and for a tie two teams win 1 point.

That means for tie total point = 1+1 = 2.

Let's take total number of game which ended as win played be x and total number of game which ended as a tie be y.

We have got total number of games is 24.

So we can write the equations as,

.......Equation 1

And also we have got total number of points is 67. So the equation is,

.......Equation 2

From equation 1, if we move x to the right side we will get,

Now let's substitute this value in equation 2, to get the value of x. By substituting the value we will get,

We will expand 2 now.

We will move 48 to the other side by subtracting it from both sides. We will get,

So the number of games which ended as a win = 19

The number of games which ended as a tie = 24 -19 =5  

So we have got the required answers.

u can just check the answer and this answer is copy righted from its rightful owner

Answer:

B 1296

Step-by-step explanation:

Area of a rectangle = Length × Width

Area of a triangle = \(\frac{1}2\) × Base × Height

3 sides are rectangles with the measurements of (9mm by 21mm)

So 3(9 × 21) = 567mm^2

6 sides are rectangles with the measurements of (9mm by 9mm)

So 6(9 × 9) = 486mm^2

1 side is a rectangle with the measurements of (9mm by 15mm)

So (9 × 15) = 135mm^2

2 sides are triangles with unknown, but equal bases.

To calculate the base, you subtract 9 from 21:   21 - 9 = 12mm

Therefore the base = 12mm

The other measurement can be found by looking to the left of the triangle (9mm from the side)

So   2(\(\frac{1}2\) × 12 × 9) = 108mm^2

Add the sides up:

567 + 486 + 135 + 108 = 1296 mm^2

By using Pythagorean identities the expression can be written as

         -8 (sin ( x ) + 1 -sin 2x)

The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:

sin2θ + cos2θ = 1 (gives the relationship between sin and cos)

There are two other Pythagorean identities as follows :

sec2θ - tan2θ = 1 (gives the relationship between sec and tan)

csc2θ - cot2θ = 1 (gives the relationship between csc and cot)

Given expression is:

-8tanx/ 1 +tan2x

we know that:

By the Pythagorean Theorem:

1 + tan²x = sec²x

and tan x = sin x/cos x

and, sec x = 1/cos x

Now, we can write as:

   -8tanx / 1 +tan²x

= -8 tan x / sec²x

= -8 sin x /cos x ÷ 1/cos²x

= -8 sin x/cos x × cos²x/1

= -8 (sin ( x ) + 1 -sin 2x)

Complete Question:

Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:

−8tan 1 + tan2x.

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A certain plane is described by 2x+3y+4z=16. Find the unit vector normal to the surface in the direction away from the origin.Firstly, we will obtain the coefficients of the x, y and z variables from the equation of the plane:2x + 3y + 4z = 16The coefficients are 2, 3, and 4 respectively.

Now, we will calculate the magnitude of the normal vector, ||N||, using the formula:||N|| = √(a² + b² + c²)where a, b, and c are the coefficients of the x, y, and z variables respectively.||N|| = √(2² + 3² + 4²)= √(4 + 9 + 16)= √29Therefore, the unit normal vector in the direction away from the origin is given by:N = (2/√29) i + (3/√29) j + (4/√29) k. Given the equation of a plane as 2x + 3y + 4z = 16, we have to find the unit vector normal to the surface in the direction away from the origin. Here's how we can do it:To find the unit vector normal to the surface, we first need to find the coefficients of the x, y, and z variables from the equation of the plane. In this case, the coefficients are 2, 3, and 4 respectively.Next, we can use the formula ||N|| = √(a² + b² + c²) to calculate the magnitude of the normal vector, where a, b, and c are the coefficients of the x, y, and z variables respectively. In this case, ||N|| = √(2² + 3² + 4²) = √29.Finally, we can find the unit normal vector in the direction away from the origin by dividing each coefficient by the magnitude of the normal vector, ||N||. Thus, the unit normal vector is:N = (2/√29) i + (3/√29) j + (4/√29) k

Therefore, the unit vector normal to the surface in the direction away from the origin is (2/√29) i + (3/√29) j + (4/√29) k.

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Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;

60° + 70° + y = 180°

130° + y = 180°

y = 180° - 130°

y = 50°

Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.

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Answer:

t = 1.4

Step-by-step explanation:

If you multiply 5 and 1.4 together, you get 7. Then, you do 7 - 1, and you get 6.

The inverse operation symbol things don't matter if the answer you get inside the two vertical bars is positive.

Answer: t=1

Step-by-step explanation:

|5t-1 |=6

5t+1=6

5t=5

t=1

Step-by-step explanation:

3[12.2+4]

3[24+4]

3.28

84 answer

To determine the total amount raised, we need to calculate the number of seats in each row and then multiply it by the number of rows. Then we can multiply that by the ticket price.

The first row has 20 seats, the second row has 24 seats, and from the third row onwards, each row has 30 seats.

To find the number of seats in the first 10 rows, we can observe that the number of seats increases by 4 for each subsequent row. Therefore, we can use an arithmetic progression formula to calculate the number of seats in the first 10 rows:

Sum = (n/2) * (2a + (n-1)d)

Where:

n = number of terms (rows)

a = first term (20)

d = common difference (4)

For the first 10 rows:

Sum = (10/2) * (2(20) + (10-1)(4))

= 5 * (40 + 9(4))

= 5 * (40 + 36)

= 5 * 76

= 380

For the remaining rows (from the 11th row onwards), all the rows have 30 seats. So, there are 20 - 10 = 10 additional rows with 30 seats each.

Total number of seats = Seats in the first 10 rows + Seats in the remaining rows

= 380 + (10 * 30)

= 380 + 300

= 680

Now, we can calculate the total amount raised by multiplying the total number of seats by the ticket price:

Total amount raised = Total number of seats * Ticket price

= 680 * 20

= 13600

Therefore, the correct option is A) 18000 (assuming there is no mistake in the problem statement).

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Answer:

The property that is shown here is communitive property.

Step-by-step explanation:

It is that because the number are switched but you can still get the same answers.

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

The equation of the graphed parabola is y=a\((x+3)^{2}\)-4.

Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).

We are required to find the equation of the graphed parabola.

The equation of a quadratic function of vertex (h,k) is given by:

y=a\((x-h)^{2}\)+k

In the above equation a is the leading coefficient.

We have been given point (-3,-4).

We have to just put the value of h=-3 and k=-4 and the required equation will be as under:

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

Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a\((x+3)^{2}\)-4.

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Answer:

yes

Step-by-step explanation:

Answer:

yesssssssssssss

Step-by-step explanation:

Answer:

Factored equation: (x-4)² = 55

Solution set
x = 11.416 and x = -3.416

Step-by-step explanation:

Given equation is
x² - 8x = 39

We have to somehow get this equation in the form (x + a)² = b

(x + a)² = x² +2ax + a²

Comparing we get
2ax = -8x

==> a = -4

Add a² = (-4)² = 16 to both sides of x² - 8x = 39

==>  x²  - 8x +16 = 39 + 16

==> x²  - 8x +16 = 55

x²  - 8x + 16 = (x - 4)²

==> (x-4)² = 55

I think this is what they were asking, not exactly the solution to the original equation.

Nevertheless,

(x-4)² = 55

==> x - 4 = ±√55

==> x = 4 ± √55

==> x = 4 + √55 and x = 4 - √55 are the two roots

This works out to

x = 11.416 and x = -3.416

Answer:

A-Kite

B-Parallelogram

C-Rectangle

D-Trapezoid

Step-by-step explanation: Just took the quiz

Answer:

AE = 43.2 units

Step-by-step explanation:

As per the given question image, it can be seen that in the \(\triangle ADC \text { and }\triangle AEB :\)

1. \(\angle B = \angle C = 90^\circ\)

2. \(\angle A\) is common to both the triangles.

3. Two angles are common, so the third angle \(\angle E\) is also equal to \(\angle D\).

All the three angles in the \(\triangle ADC \text { and }\triangle AEB\) are equal to each other, hence the triangles are similar.

As per the property of similar triangles, the ratio of their sides will be equal.

AB : AC = AE : AD

AC = 88 units

BC = 55 units

AB = AC - AB = 33 units

Let side AE = \(x\) units

Side AD = AE + ED

So, AD = \(x + 72\)

Using the ratio:

\(\dfrac{AB}{AC} = \dfrac{AE}{AD}\\\Rightarrow \dfrac{33}{55} = \dfrac{x}{x+72}\\\Rightarrow 55x = 33 \times 72\\\Rightarrow x = \dfrac{3\times 72}{5}\\\Rightarrow x = 43.2\ units\)

So, AE = 43.2 units

Answer:

  B = 43°

  a = 11.0

  b = 10.2

Step-by-step explanation:

The relationship between side lengths and trig functions in a right triangle is summarized in the mnemonic SOH CAH TOA. It tells you, for example, ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

__

Applied to this triangle, the unknown sides can be found from ...

  sin(47°) = a/15

  a = 15·sin(47°) ≈ 11.0

and

  cos(47°) = b/15

  b = 15·cos(47°) ≈ 10.2

__

The second acute angle in a right triangle is the complement of the first:

  B = 90° -47° = 43°

If  Raj spent a total of $83. 30 on 5 pens and 19 erasers for his friends, pen costs 6 times as much as an eraser, the cost of a pen is $10.20.

Let's assume that the cost of an eraser is x dollars. Then, according to the problem, the cost of a pen is 6 times the cost of an eraser, or 6x dollars.

We know that Raj bought 5 pens and 19 erasers, so we can set up an equation to represent the total cost of his purchases:

5(6x) + 19x = 83.30

Simplifying this equation, we get:

30x + 19x = 83.30

49x = 83.30

x = 1.70

Therefore, the cost of an eraser is $1.70. To find the cost of a pen, we can substitute this value back into our expression for the cost of a pen:

6x = 6(1.70) = 10.20

In summary, we first set up an equation using the total cost of Raj's purchases, and then solved for the cost of an eraser. Finally, we used the relationship between the cost of a pen and the cost of an eraser to find the cost of a pen.

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At the 0.01 significance level, there is sufficient evidence to warrant rejection of the claim that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.

To test the claim, we perform a one-sample t-test using the given data. The null hypothesis (H0) is that the mean waiting time for bus number 14 is 10 minutes or more, and the alternative hypothesis (Ha) is that the mean waiting time is less than 10 minutes.
Given that Karen's mean waiting time was 7.5 minutes with a standard deviation of 1.6 minutes, we calculate the t-value using the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / √n), where n is the sample size.
With 18 observations, we can calculate the t-value and compare it to the critical t-value at the 0.01 significance level, with degrees of freedom equal to n - 1.
If the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis. However, if the calculated t-value is greater than the critical t-value, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.
In this case, if the calculated t-value is greater than the critical t-value at the 0.01 significance level, we can conclude that there is sufficient evidence to warrant rejection of the claim that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.

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In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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Let's calculate the total cost of all the items purchased by the computer club:

Cost of 14 portfolios = 14 * $24.59

Cost of 14 binders = 14 * $12.92

Cost of 14 school sweatshirts = 14 * $14.00

Cost of 14 music cases = 14 * $1.25

Cost of 14 phone cases = 14 * $1.99

Cost of 14 mouse pads = 14 * $2.14

Total cost of all items = Cost of 14 portfolios + Cost of 14 binders + Cost of 14 school sweatshirts + Cost of 14 music cases + Cost of 14 phone cases + Cost of 14 mouse pads

Plugging in the given values:

Total cost of all items = (14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14)

Now, the computer club will pay for 40% of the total cost. To calculate this, we can multiply the total cost by 40% (or 0.40):

Club's payment = 0.40 * Total cost of all items

The remaining cost will be divided equally among the 14 members:

Remaining cost per member = (Total cost of all items - Club's payment) / 14

Plugging in the values and calculating:

Club's payment = 0.40 * ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14))

Remaining cost per member = ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14) - Club's payment) / 14

So, each member of the computer club will owe the calculated value for "Remaining cost per member".

Hope this is good

First, we need to count the number of boxes that we have in a layer

We can count the number of boxes fast

we count the number of boxes of the length (boxes with a red point) the length is equal to 6

then we count the number of boxes of the width (boxes with a blue point) the width is equal to 6

then we do the next operation

number of boxes = (l)x(w)=6x6=36

In total 36 boxes in one layer

We know that the volume of each box is 1 cubic foot therefore the volume of one layer, is 36 cubic foot

In order to know the volume of 8 layers (volume of the container), we need to multiply 36 cubic ft (volume of one layer) by 8

The volume of the container is

The answer is B

Answer:

b

5

​

b

2

​

​

=

4

1

​

⇒

ar

4

ar

​

=

4

1

​

Where a is the first term & r is the common ratio.

⇒

r

3

1

​

=

4

1

​

⇒r

3

=4

⇒r=

3

4

​

=4

3

1

​

And,b

2

​

+b

5

​

=216

⇒ar+ar

4

=216

⇒ar(1+r

3

)=216

Replacing, r=4

3

1

​

⇒ar[1+(4

3

1

​

)

3

]=216

⇒ar[1+4]=216

⇒ar=

5

216

​

⇒a=

5r

216

​

=

5

3

4

​

216

​

∴ The first term is  5 34

​

216

​

Cost to put a 0. 5 ft layer of topsoil on the entire garden is $1000.

The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. Measurements are made in square units, with square meters serving as the reference unit 

Area of a Square = Side × Side.

Therefore, the area of square = Side square units.

Side of a square garden= 10 ft.

Area of a square garden= Side × Side= 10 × 10 =100 square ft.

Cost of the whole garden = 100×$5 =$500

Cost to put a 0. 5 ft layer of topsoil on the entire garden =$500/0.5

=$1000

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The cost need to put a 0. 5 ft layer of topsoil on the entire garden is $1000

According to the given statement

we have given that the

side length of the square garden is 10ft.

topsoil cost per foot is $5

And we have to find the cost which required to put a 0. 5 ft layer of topsoil on the entire garden.

So,

The  side length of the square garden is 10ft.

Now, the volume of the cube is (a)^2

And

Total volume of cube = 10*10

Total volume of cube = 100 per square foot.

Now, we find the cost required for a topsoil.

Cost required to put a topsoil of 1 foot in the total volume of cube = volume*cost

So,

Cost required to put a topsoil of 1 foot in the total volume of cube = 1000*5

Cost required to put a topsoil of 1 foot in the total volume of cube = $5000

if we put a topsoil of 0.5 feet then

The cost required = $5000/0.5

The cost required = $1000.

So, The cost need to put a 0. 5 ft layer of topsoil on the entire garden is $1000

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Answer:

1

Step-by-step explanation:

|x| means the absolute value, which is 4 and -4

Answer:

A

Step-by-step explanation:

So we have the equation:

\(|x|=4\)

Solve for x. Use the definition of absolute value:

\(|x|=4\)

This means that:

\(x=4\text{ or } x=-4\)

And... we're done :)

The answer is A.

In adding whole numbers with decimal points, here are the steps.

1. Arrange the numbers in such a way that the decimal points are aligned with each other.

2. Add the numbers normally like adding whole numbers. Do not mind the decimal point for now.

3. In the final answer, put a decimal point and align it with the others.

Hence, the sum of $5.89 and $1.15 is $7.04.

To summarize, the strategy is to align the decimal points of the two numbers and assume the numbers to be whole numbers and add them normally. In the final answer, put a decimal point and align it with the addends.