Ten is less than or equal to the difference of a number and negative 4:


Four times the sum of a number and 5 is at least 48:

In a hash table of size 6 with chaining, the keys 31, 32, and 19 will be placed in the table as follows:

Key 31: The hash value of 31 will be calculated using a hash function, which will generate a value between 0 and 5. Let's assume that the hash function generates a value of 1 for key 31. The value 31 will be placed in the linked list at index 1 of the hash table.

Key 32: The hash value of 32 will be calculated using the same hash function, which may generate a value different from 1. Let's assume that the hash function generates a value of 3 for key 32. The value 32 will be placed in the linked list at index 3 of the hash table.

Key 19: The hash value of 19 will be calculated using the same hash function, which may generate a value different from 1 and 3. Let's assume that the hash function generates a value of 0 for key 19. The value 19 will be placed in the linked list at index 0 of the hash table.

The evolution of the hash table for each key placement can be illustrated as follows:

Initially, the hash table is empty:
| | | | | | |

After placing key 31 in index 1:
| |31| | | | |

After placing key 32 in index 3:
| |31| |32| | |

After placing key 19 in index 0:
|19|31| |32| | |

As you can see, the values are placed in the linked lists at the respective indices of the hash table. This allows for efficient retrieval of values based on their keys, as the hash table can quickly locate the linked list where the value is stored.

To learn more about hash function : brainly.com/question/31579763

#SPJ11

Preferred stockholders will receive $31,200 and common stockholders will receive $11,500 from the $42,700 cash dividend declared at the end of Year 2.

Crossett Corporation issued 5,200 shares of $50 par, 6 percent cumulative preferred stock, and 9,500 shares of $14 par common stock when it was organized in January Year 1. In Year 1, the company experienced a net loss of $13,500 and did not pay a dividend. At the end of Year 2, after a net income of $64,700, the board of directors declared a cash dividend of $42,700.

Preferred stockholders are entitled to receive their dividends first, including any unpaid dividends from previous years. In Year 1, the preferred stockholders were entitled to a dividend of $15,600 (5,200 shares x $50 x 6%), which remained unpaid. In Year 2, they are again entitled to $15,600.

The total amount due to preferred stockholders is $31,200 ($15,600 for Year 1 arrearage + $15,600 for Year 2 preferred dividends). Since the total dividend declared is $42,700, the remaining $11,500 ($42,700 - $31,200) will be distributed to the common stockholders.

You can learn more about stockholders at: brainly.com/question/16225453

#SPJ11

Answer:hope this helps

Step-by-step explanation:

(x^2 - 2) (5 x^3 - 3)

(x (5 x^2 - 10) - 3) x^2 + 6

Polynomial discriminant:

Δ = -1772976600

Derivative:

d/dx(5 x^5 - 3 x^2 - 10 x^3 + 6) = x (25 x^3 - 30 x - 6)

Indefinite integral:

integral(6 - 3 x^2 - 10 x^3 + 5 x^5) dx = (5 x^6)/6 - (5 x^4)/2 - x^3 + 6 x + constant

Answer:

g(1) = 2

Step-by-step explanation:

g(x)=−x+3

g(1)=

Let x = 1

g(1) = -1+3 = 2

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

Read more about Linear equation graph at: https://brainly.com/question/28732353

#SPJ1

Answer:

The answer is B

Step-by-step explanation:

Got it right

(a) Let S be a subset of an n-dimensional vector space V. Suppose S contains less than n vectors. Then, the maximum number of linearly independent vectors in S is also less than n. Therefore, the dimension of the span of S is less than n, and hence, S cannot span V.

(b) The nullity of a matrix is the dimension of its null space, which is the set of all solutions to the homogeneous equation Ax = 0, where A is the matrix. The smallest possible nullity for a 4 x 7 matrix is 3, since the nullity cannot be greater than the minimum of the number of rows and columns. The largest possible rank is 4, since the rank cannot be greater than the number of rows.

(c) The smallest possible nullity for a 7 x 4 matrix is also 3, since the nullity cannot be greater than the minimum of the number of rows and columns. The largest possible rank is 4, since the rank cannot be greater than the number of columns. This follows from the rank-nullity theorem, which states that the rank plus the nullity of a matrix equals its number of columns.

To know more about   matrix here

https://brainly.com/question/1279486

#SPJ4

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
To know more about explicit formula visit:

https://brainly.com/question/18069156

#SPJ11

Answer:

2

Step-by-step explanation:

Answer:

2 is the smallest number

So the probability that the waiting time until the next call is more than three minutes is approximately 0.223.

The Poisson distribution is a probability distribution that describes the number of events occurring in a fixed interval of time or space, given that these events occur independently and at a constant rate.

In this case, we are dealing with the number of calls received at a call center, and we are told that the average time between calls is 2 minutes.

If the number of calls follows a Poisson distribution, we can use the Poisson probability formula to calculate the probability of getting a certain number of calls in a given time period.

However, in this case, we are interested in the waiting time until the next call, which is not directly related to the number of calls. To solve this problem, we can use the fact that the time between two consecutive calls follows an exponential distribution,

which is a continuous probability distribution that describes the time between two events occurring independently and at a constant rate.

The probability density function of the exponential distribution is given by f(x) = λe^(-λx), where λ is the rate parameter (i.e., the reciprocal of the average time between events) and x is the waiting time.

In this case, λ = 1/2 (since the average time between calls is 2 minutes), and we are interested in the probability that the waiting time until the next call is more than three minutes. This can be expressed mathematically as P(X > 3), where X is the waiting time.

To calculate this probability, we can use the cumulative distribution function (CDF) of the exponential distribution, which gives the probability that X is less than or equal to a certain value.

The CDF of the exponential distribution is given by F(x) = 1 - e^(-λx). Therefore, P(X > 3) = 1 - P(X ≤ 3) = 1 - F(3) = 1 - (1 - e^(-1.5)) = e^(-1.5) ≈ 0.223, So the probability that the waiting time until the next call is more than three minutes is approximately 0.223.

This means that there is about a 22.3% chance that the call center will not receive a call for more than three minutes, given that the calls arrive independently and at a constant rate.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

Answer:

$5.75

Step-by-step explanation:

Find the difference between the weeks as this will give you the difference hence the amount deposited each week

0->1

is 12.00->17.75

diffrence is $5.75

1->2

is 17.75->23.50

diffrence is  $5.75

the amount saved each week is $5.75

Answer:

your answer is below

-20x +15

Let the rocket is launched at an angle of \theta with respect to the positive direction of the x-axis with an initial velocity u=15m/s.

Let the initial position of the rocked is at the origin of the cartesian coordinate system where the illustrative path of the rochet has been shown in the figure.

As per assumed sine convention, the physical quantities like displacement, velocity, acceleration, have been taken positively in the positive direction of the x and y-axis.

Let the point P(x,y) be the position of the rocket at any time instant t as shown.

Gravitational force is acting downward, so it will not change the horizontal component of the initial velocity, i.e. \(U_x=U cos\theta\) is constant.

So, after time, t, the horizontal component of the position of the rocket is

\(x= U \cos\theta t \;\cdots(i)\)

The vertical component of the velocity will vary as per the equation of laws of motion,

\(s=ut+\frac12at^2\;\cdots(ii)\), where,s, u and a are the displacement, initial velocity, and acceleration of the object in the same direction.

(a) At instant position P(x,y):

The vertical component of the initial velocity is, \(U_y=U sin\theta\).

Vertical displacement =y

So, s=y

Acceleration due to gravity is \(g=9.81 m/s^2\) in the downward direction.

So, \(a=-g=-9.81 m/s^2\) (as per sigh convention)

Now, from equation (ii),

\(y=U sin\theta t +\frac 12 (-9.81)t^2\)

\(\Rightarrow y=U \sin\theta \times \frac {x}{U \cos\theta} +\frac 12 (-g)\times \left(\frac {x}{U \cos\theta} \right)^2\)

\(\Rightarrow y=U^2 \tan\theta-\frac 1 2g U^2 \sec^2 \theta\;\cdots(iii)\)

This is the required, quadratic equation, where \(U=15 m/s\) and \(g=9.81 m/s^2\).

(b) At the highest point the vertical velocity,v, of the rocket becomes zero.

From the law of motion, \(v=u+at\)

\(\Rightarroe 0=U\sin\theta-gt\)

\(\Rightarroe t=\frac{U\sin\theta}{g}\cdots(iv)\)

The rocket will reach the maximum height at \(t= 1.53 \sin\theta s\)

So, from equations (ii) and (iv), the maximum height, \(y_m\) is

\(y_m=U\sin\theta\times \frac{U\sin\theta}{g}-\frac 12 g \left(\frac{U\sin\theta}{g}\right)^2\)

\(\Rightarrow y_m=23 \sin\theta -11.5 \sin^2\theta\)

In the case of vertical launch, \(\theta=90^{\circ}\), and

\(\Rightarrow y_m=11.5 m\) and \(t=1.53 s\).

Height from the ground= 11.5+3=14.5 m.

(c) Height of rocket after t=4 s:

\(y=15 \sin\theta \times 4- \frac 12 (9.81)\times 4^2\)

\(\Rightarrow y=15 \sin\theta-78.48\)

\(\Rightarrow -63.48 m >y> 78.48\)

This is the mathematical position of the graph shown which is below ground but there is the ground at \(y=-3m\), so the rocket will be at the ground at t=4 s.

(d) The position of the ground is, y=-3m.

\(-3=U\sin\theta t-\frac 1 2 g t^2\)

\(\Rightarrow 4.9 t^2-15 \sin\theta t-3=0\)

Solving this for a vertical launch.

\(t=3.25 s\) and \(t=-0.19 s\) (neglecting the negative time)

So, the time to reach the ground is 3.25 s.

(e) Height from the ground is 13m, so, y=13-3=10 m

\(10=U\sin\theta t-\frac 1 2 g t^2\)

Assume vertical launch,

\(4.9 t^2-15 \sin\theta t+10=0\) [using equation (ii)]

\(\Rightarrow t=2.08 s\) and \(t=0.98 s\)

There are two times, one is when the rocket going upward and the other is when coming downward.

Answer:

The quadratic equation is f(x)=20x^{2} -400x +3000.

1. This number represents the amount of money it was sold for.

2. Vertex =(10,1000)

Step-by-step explanation:

This point represents the amount of money the computer was worth at its lowest point.

[just answering so you can give the other guy brainiest]

The total hours joe spent watching TV each day for two weeks is 12 1/2 hours

Total hours spent watching TV for two weeks = Number of hours × days

= (0 × 1) + (1/4 × 1) + (1/2 × 1) + (3/4 × 3) + (1 × 3) + (1 1/4 × 4) + (1 1/2 × 1)

= 0 + 1/4 + 1/2 + 9/4 + 3 + 5 + 3/2

= 8 + (1+2+9+6) / 4

= 8 + 18/4

= 8 + 4 2/4

= 8 + 4 1/2

= 12 1/2 hours

Learn more about number line:

https://brainly.com/question/24644930

#SPJ1

Answer:

( 6 , 5 )

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer: S<\-2

Hope i was some help.

Step-by-step explanation: sorry I can’t put the right sign my keybored won’t let me but you know what it stands for.

3s+6s</-5(s+2)

start off with -5(s+2) you multiply -5 with s and it is -5s then you do the same for +2 take -5 and multiply by +2 pos times a neg is always a neg so it’s -10.

3s+6<\-5s-10

So you have to get rid of the -5s so your going to do the inverse which is add 5 to -5 and it will get rid of -5s but then you have to add 5 to 3s and that will be 8s.

8s+6</-10

Now your going to get rid of the +6 and to do that you do the inverse you subtract 6 and it will get rid of it now you have to do the same for -10 so you will subtract 6 to -10 and that will equal -16.

Now you have to divide!

8s/8 </ -16/8

And it should equal s <\-2

Answer:

It is a trinomal because there is 3 terms

It is a quadratic because the highest degree is x^2

All in all, It is a Quadratic Trinomal

Step-by-step explanation:

The conclusion of the hypothesis is that we fail to reject the null hypothesis and conclude that the means are different.

Let us first define the hypothesis;

Null Hypothesis; H₀: μ_a = μ_b

Alternative Hypothesis; Hₐ: μ_a ≠ μ_b

From the given significance value, we can say that we will reject H₀ if the calculated test statistic is greater than 2.797 or t is less than 2.797.

The pooled variance from the attached table with the aid of a statistics calculator gives;

Pooled variance = 0.5938

The test statistic from online calculator is; t = -3.299 or 3.299

This test statistic falls falls within the rejection region and so we reject the null hypothesis and conclude that there is a difference in the average errors of the two processes.

Read more about Hypothesis Conclusion at; https://brainly.com/question/15980493

#SPJ1

According to the given example, the correct order of letters to the finish line is А, B, C, G, H.

Based on the given example "ABCGH," we can determine the correct order of letters to the finish line. Comparing the given example with the options, we find that the first letter is "A." Moving on, the next letter in the given example is "B," followed by "C."

Therefore, the correct order of the first three letters is "А, B, C." As for the remaining letters, "G" appears after "C" in the given example, and finally "H" is the last letter. Combining all the identified letters, the correct order of letters to the finish line is "А, B, C, G, H."

Learn more about Letters here: brainly.com/question/13943501

#SPJ11

A has a value of 6.875.

We have a right-angled triangle at vertex B. Therefore, its hypotenuse will be the longest side, and it will be opposite the right angle. The hypotenuse will connect the points A and C. As a result, we may use the Pythagorean Theorem to solve for A. The distance between any two points on the coordinate plane may be calculated using the distance formula.

So, we'll use the distance formula to calculate AC and BC, then use the Pythagorean Theorem to solve for a.

AC² = (a + 9)² + (2 - 4)² = (a + 9)² + 4

BC² = (-7 - (a + 9))² + (-2 - 4)² = (-a - 16)² + 36

By the Pythagorean Theorem, a² + 16² + 36 = (a + 16)².

Then:a² + 256 + 36 = a² + 32a + 256

Solve for a on both sides: 220 = 32a

a = 6.875

Therefore, a has a value of 6.875.

Know more about  Pythagorean Theorem here,

https://brainly.com/question/14930619

#SPJ11

The polygon shape that possesses the bigger area from the two given is: Hexagon

Polygons are defined as closed shapes that are two-dimensional. They possess straight sides and have the same number of sides as they have angles. Polygons have names that relate to how many sides they have.

A hexagon has more sides than a pentagon.

A hexagon is a polygon that has six sides and a pentagon is a polygon that has five sides.

Now, the more sides the polygon has, the more area it covers inside the circle as it will obviously be wider.

Thus, we can infer that the hexagon will have a bigger area.

Read more about Polygon area at: https://brainly.com/question/8409681

#SPJ1

Answer:

---------------------------

Given similar triangles:

We know that corresponding sides of similar triangles have same ratio.

The ratios are:

Substitute values and solve for x:

Answer:

Its the 2nd Dot

Step-by-step explanation:

Answer:

38.9°

Step-by-step explanation:

The three angles in a triangle add up to 180°. Also, a right triangle has a right angle in it. A right angle is 90°.

90° + 51.1° + x = 180°

141.1 + x = 180°

subtract 141.1°

x = 38.9°

The 99% confidence interval for the population mean length of the pin is (3 - 0.3355, 3 + 0.3355) approximately equal to  2.864 to 3.136.

The equation for the certainty interim for the populace mean is:

CI = test mean ± t(alpha/2, n-1) * \((test standard deviation/sqrt (n))\)

Where alpha is the level of importance (1 - certainty level), n is the test estimate, and t(alpha/2, n-1) is the t-value for the given alpha level and degrees of opportunity (n-1).

In this case, the test cruel is 3 inches, the test standard deviation is the square root of the fluctuation, which is 0.3 inches, and the test estimate is 9.

We need a 99% certainty interim, so alpha = 0.01 and the degrees of flexibility are 9-1=8. Looking up the t-value for a two-tailed test with alpha/2=0.005 and 8 degrees of opportunity in a t-table gives an esteem of 3.355.

Substituting these values into the equation gives:

CI = 3 ± 3.355 * (0.3 / sqrt(9))

CI = 3 ± 0.3355

So the 99% confidence interval for the population mean length of the pin is (3 - 0.3355, 3 + 0.3355), which simplifies to (2.6645, 3.3355).

The closest choice is 2.864 to 3.136.

learn more about standard deviation

brainly.com/question/23907081

#SPJ4

Answer:

4=3

x=1

4=3x

4/3=x

1.3=x

The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

What is the intermediate value theorem?

Intermediate value theorem is theorem about all possible y-value in between two known y-value.

x-intercepts

-x^2 + x + 2 = 0

x^2 - x - 2 = 0

(x + 1)(x - 2) = 0

x = -1, x = 2

y intercepts

f(0) = -x^2 + x + 2

f(0) = -0^2 + 0 + 2

f(0) = 2

(Graph attached)

From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3

For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.

Your question is not complete, but most probably your full questions was

Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?

Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

Learn more about intermediate value theorem here:

brainly.com/question/28048895

#SPJ4