Willie runs 2 miles in 18 minutes. If Willie runs at the same rate, how many miles can he run in 90 minutes?

The term that fits in the blank is "cardinality". Cardinality refers to the number of instances of one entity that can be linked to a certain number of instances of another entity. In other words, it defines the relationship between entities and how they can be associated with each other.

For instance, if we consider two entities, "employee" and "department", the cardinality between them would determine the number of employees that can be associated with each department. It can be "one-to-one", "one-to-many", "many-to-one", or "many-to-many".

The cardinality of an entity relationship is an important factor to consider while designing a database as it helps in creating efficient and effective database structures. It helps to ensure data integrity and avoid data redundancy. By specifying the cardinality, we can also define the minimum and maximum number of instances that are allowed for each entity. Overall, cardinality plays a crucial role in determining the relationship between entities and how they interact with each other within a database system.

learn more about cardinality here: brainly.com/question/29623755

#SPJ11

The term that fits in the blank is "cardinality". Cardinality refers to the number of instances of one entity that can be linked to a certain number of instances of another entity. In other words, it defines the relationship between entities and how they can be associated with each other.

For instance, if we consider two entities, "employee" and "department", the cardinality between them would determine the number of employees that can be associated with each department. It can be "one-to-one", "one-to-many", "many-to-one", or "many-to-many".

The cardinality of an entity relationship is an important factor to consider while designing a database as it helps in creating efficient and effective database structures. It helps to ensure data integrity and avoid data redundancy. By specifying the cardinality, we can also define the minimum and maximum number of instances that are allowed for each entity. Overall, cardinality plays a crucial role in determining the relationship between entities and how they interact with each other within a database system.

learn more about cardinality here: brainly.com/question/29623755

#SPJ11

Answer: To find Jordan's balance after he makes the minimum payment for May, we need to calculate his balance at the end of each month, taking into account his purchases, the interest charged, and the minimum payment made.

In March, Jordan's balance was $628.16 and he made a minimum payment of:

$628.16 x 3.96% = $24.92

His purchases in March totaled $50.81, so his balance after March was:

$628.16 + $50.81 = $678.97

The interest charged in March would be:

$678.97 x (10.59%/12) = $5.72

So his balance after interest was added in March would be:

$678.97 + $5.72 = $684.69

In April, Jordan's balance was $684.69 and he made a minimum payment of:

$684.69 x 3.96% = $27.13

His purchases in April totaled $77.36 + $32.40 + $49.20 = $159.96, so his balance after April was:

$684.69 + $159.96 = $844.65

The interest charged in April would be:

$844.65 x (10.59%/12) = $7.10

So his balance after interest was added in April would be:

$844.65 + $7.10 = $851.75

In May, Jordan's balance was $851.75 and he made a minimum payment of:

$851.75 x 3.96% = $33.77

His purchases in May totaled $25.79 + $79.39 + $79.08 = $184.26, so his balance after May would be:

$851.75 + $184.26 = $1,036.01

The interest charged in May would be:

$1,036.01 x (10.59%/12) = $8.71

So his balance after interest was added in May would be:

$1,036.01 + $8.71 = $1,044.72

Therefore, Jordan's balance after he makes the minimum payment for May would be $1,044.72, which is closest to answer (a) $1,094.10.

The function f is continuous on the closed interval (1,7). If 7 to 1 f(x) dx= 42 and 3 to 7 f(x) dx= -32, then 3 to 1 2f(x) dx=-148 is not correct. The correct answer is option a.

We can use the linearity property of definite integrals to evaluate 3 to 1 2f(x) dx as follows:

3 to 1 2f(x) dx = 2 times the definite integral of f(x) from 1 to 3

+ 2 times the definite integral of f(x) from 3 to 7

- 2 times the definite integral of f(x) from 7 to 1

(Note that we have reversed the limits of integration for the last term.)

Using the given values, we have:

3 to 1 2f(x) dx = 2 times the definite integral of f(x) from 1 to 3

+ 2 times the definite integral of f(x) from 3 to 7

- 2 times (7 to 1 f(x) dx)

= 2 times (-32) + 2 times 42 - 2 times 42

= -64

Therefore, the answer is A. -148 is not correct.

To know more about function refer to-

https://brainly.com/question/12431044

#SPJ11

Answer:

There could have been 30 windows and only two of the have been repaired

Step-by-step explanation:

That is what I think

The probability P(-2.14 ≤ z ≤ -0.33) is approximately 0.3545, rounded to four decimal places.

To find the probability P(-2.14 ≤ z ≤ -0.33) for a random variable z with a standard normal distribution, follow these steps:
1. Identify the given values: Lower bound = -2.14 and Upper bound = -0.33.
2. Use a standard normal distribution table or calculator to find the area to the left of each bound (also known as the cumulative probability or z-score).
3. For the lower bound, find the area to the left of -2.14. Let's call this value A1.
4. For the upper bound, find the area to the left of -0.33. Let's call this value A2.

5. Subtract the area of the lower bound from the area of the upper bound to find the probability between the two bounds: P(-2.14 ≤ z ≤ -0.33) = A2 - A1.
Using a standard normal distribution table or calculator:
A1 (area to the left of -2.14) = 0.0162
A2 (area to the left of -0.33) = 0.3707
Now, subtract A1 from A2 to find the probability between the two bounds:
P(-2.14 ≤ z ≤ -0.33) = A2 - A1 = 0.3707 - 0.0162 = 0.3545
Therefore, the probability P(-2.14 ≤ z ≤ -0.33) is approximately 0.3545.

To know more about probability click here

brainly.com/question/30034780

#SPJ11

Answers in bold:

S9 = 2

i = 20

R = -2

=====================================================

Explanation:

[tex]S_0 = 20[/tex] is the initial term because your teacher mentioned [tex]A_0 = I[/tex] as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

[tex]\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}[/tex]

Then here is S5 though S8

[tex]\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}[/tex]

And finally we arrive at S9.

[tex]S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\[/tex]

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

Because we have an arithmetic sequence, there is a shortcut.

[tex]a_n[/tex] represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

[tex]a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\[/tex]

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why [tex]S_9 = 2[/tex]

The angle between the net displacement vectors for the two birds is 23 degrees

Given that;

A bird flies 3.0 km due west and then 2.0 due north. Another bird flies 2.0 km due west and 3.0 KM due north.

Now, First we need to find the angle between west direction and vectors given.

The angle between west direction and vector 1 is,

arctan(2/3) = 33.69

And, The angle between west direction and vector 2 is,

⇒ arctan(3/2) = 56.31

Hence, Angle between vector 2 and vector 1 is,

56.31-33.69 = 22.62 degrees

                    = 23 degree

Thus, The angle between the net displacement vectors for the two birds is 23 degrees.

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ4

The probability of randomly drawing seven cards from a deck of cards and getting three Jacks and two Kings is approximately 0.00000027 or 2.7 in 10 million.

To compute the probability of randomly drawing seven cards from a deck of cards and getting three Jacks and two Kings, we can use the formula for hypergeometric probability.

The number of ways to draw three Jacks and two Kings from a deck of cards is given by:

(4 choose 3) * (4 choose 2) = 6 * 6 = 36

where (n choose k) represents the number of ways to choose k items from a set of n items.

The total number of ways to draw seven cards from a deck of cards is given by:

(52 choose 7) = 133,784,560.

So the probability of getting three Jacks and two Kings when drawing seven cards from a deck of cards is:

36 / 133,784,560 ≈ 0.00000027.

For similar question on probability.

https://brainly.com/question/27371271

#SPJ11

The length of the square garden is s = ( 3x - 4 ) feet

Given data ,

Let the length of the square garden be s

Now , The area of a square is given by the formula A = s², where s is the length of one side of the square.

We are given that the area of the garden is:

A = 9x² - 24x + 16

To find the length of the garden, we need to take the square root of the area:

s = √(A)

Substituting the given expression for A, we get:

s = √(9x² - 24x + 16)

We can simplify this expression by factoring the quadratic under the square root sign:

s = √[(3x - 4)(3x - 4)]

Using the property that the square root of a product is equal to the product of the square roots, we can simplify further:

s = (3x - 4)

Hence , the length of the garden is 3x - 4 feet

To learn more about area of square click :

https://brainly.com/question/17707380

#SPJ1

The two theoretical quantities of ANOVA (Analysis of Variance) are:
1. Between-group variance.

2. Within-group variance:

1. Between-group variance.

This is the variance that can be attributed to differences between the group means.

It is calculated by comparing the mean of each group to the overall mean of all the data points.

The larger the between-group variance, the more likely there are significant differences between the groups.
2. Within-group variance:

This is the variance that can be attributed to differences within each group, i.e., the individual differences among the data points in each group.

It is calculated by comparing the individual data points in each group to their respective group mean.

The smaller the within-group variance, the more likely the groups are homogeneous.
In ANOVA, these two quantities are compared using an F-ratio.

If the between-group variance is significantly larger than the within-group variance, it indicates that there are significant differences between the group means, and the null hypothesis can be rejected.

For similar question on theoretical quantities.

https://brainly.com/question/30667471

#SPJ11

An illustration showing a pentagon lying on ray AB, which when extended forms an exterior angle and is marked as 2x plus 14 degrees, the correct statements are (2x + 14)° + (7x + 13)° = 180°, (7x + 13)° = 132°, x = 7°.

In the given illustration, we have a pentagon with base AB lying on a line or ray AB. Let's call the first interior angle to the right of the exterior angle marked as 2x + 14 degrees as angle C.

We can see that the sum of the measures of all interior angles of a pentagon is 180 degrees. Hence, the sum of all interior angles of this pentagon is:

C + angle D + angle E + angle F + angle G = (5 - 2) x 180 degrees (since a pentagon has five sides and angles)

(2x + 14)° + (7x + 13)° = 180° (sum of interior angles of a pentagon)

(7x + 13)° = 132° (simplifying the above equation)

x = 7° (solve for x by subtracting 14 from both sides of the first equation)

Therefore, options 2, 3, and 4 are correct.

For more details regarding pentagon, visit:

https://brainly.com/question/17054992

#SPJ1

Comparing statistics from different stores can provide valuable insights into price variations and help make informed purchasing decisions.

When comparing statistics from different stores, it's important to look at a variety of factors, such as the average price, the range of prices, and any discounts or promotions being offered. It can also be helpful to look at historical trends and compare prices over time to identify any patterns or changes in pricing. Additionally, it's important to consider other factors that may influence purchasing decisions, such as the quality of the product, the reputation of the store, and the availability of customer support or warranties. By carefully comparing these factors and weighing the pros and cons of each store, consumers can make informed decisions and maximize the value of their purchases.

Learn more about statistics here

https://brainly.com/question/15525560

#SPJ11

What statistical measures can Braden use to compare the prices of DVD players from two different stores?

A hypothesis is a tentative explanation for a phenomenon that is based on limited evidence and requires further investigation to be confirmed or rejected. When a researcher conducts a study, they formulate a hypothesis that they seek to test through their research.

In scientific research, a researcher aims to disprove or reject their hypothesis rather than prove it. This is because it is impossible to prove a hypothesis with complete certainty, but it is possible to gather evidence that contradicts it. By trying to disprove or reject their hypothesis, a researcher can either find evidence to support their hypothesis or identify flaws in their reasoning that they can address in future research.

For example, a researcher might hypothesize that a new drug will improve memory in Alzheimer's patients. To test this hypothesis, the researcher would administer the drug to a group of Alzheimer's patients and compare their memory performance to a control group that received a placebo. If the results show that the drug did not improve memory performance, the researcher would reject their hypothesis and revise their understanding of the drug's effects.

In conclusion, a hypothesis is a tentative explanation that a researcher tries to disprove or reject through their research. By doing so, they can either find evidence to support their hypothesis or identify flaws in their reasoning that they can address in future research.

learn more about the hypothesis here: brainly.com/question/21092528

#SPJ11

The isoelectric point (pI) for histidine is 3.92. The correct answer is option (b).

To determine the isoelectric point (pI) for histidine, we need to consider the pKC, pKN, and pKR values, which are 1.80, 9.33, and 6.04, respectively. The isoelectric point is the pH at which the amino acid has a neutral charge.
Step 1: Identify the two relevant pK values. Since histidine has three ionizable groups, we need to find the two pK values that involve the amino and carboxyl groups. These are pKC (1.80) and pKR (6.04).

Step 2: Calculate the average of these two pK values: (1.80 + 6.04) / 2 = 3.92.
The isoelectric point (pI) for histidine is 3.92, which corresponds to option b. This means that at a pH of 3.92, histidine will have a neutral charge.

To know more about isoelectric point click here

brainly.com/question/31609011

#SPJ11

The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)

Given data ,

To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.

The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:

Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>

Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)

= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))

= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)

= 40 / √(33)

To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:

Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)

= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)

= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))

= (-160/9√(33), -40/9√(33), 340/9√(33))

Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)

To learn more about distance between a point and plane click :

https://brainly.com/question/14442366

#SPJ1

4/5 + 2/9 is rational and can be expressed as the ratio of two integers: 46/45.

To show that 4/5 + 2/9 is rational, we need to find a common denominator and add the fractions. The least common multiple of 5 and 9 is 45, so we can rewrite the fractions with 45 as the denominator:

4/5 = 36/45

2/9 = 10/45

Now we can add the fractions:

4/5 + 2/9 = 36/45 + 10/45 = 46/45

Therefore, 4/5 + 2/9 is rational and can be expressed as the ratio of two integers: 46/45.

To know more about rational number refer to-

https://brainly.com/question/24540810

#SPJ11

In ANOVA, the factor refers to the different levels of the variable being studied.

So, the correct answer is C.

Specifically, it refers to the independent variable that is being manipulated and its effect on the dependent variable.

The experimenter is the person conducting the study and manipulating the independent variable, but the factor specifically refers to the levels of the variable being studied.

The content loaded in 120 words would explain the concept of factors in ANOVA and how they relate to the independent and dependent variables in the study. It would also clarify that the experimenter is not the same as the factor being studied.

Learn more about ANOVA at

https://brainly.com/question/31830194

#SPJ11

In the model ln(Yi) = β0 + β1 * Xi + ui, the elasticity of Y with respect to X is equal to β1.

The model is given in a logarithmic form: ln(Yi) = β0 + β1 * Xi + ui.
Elasticity measures the percentage change in one variable (Y) in response to a 1% change in another variable (X).
In a semi-logarithmic model like this, the coefficient of the independent variable (β1) directly represents the elasticity of Y with respect to X.

Therefore, the elasticity of Y with respect to X is β1.
Keep in mind that this result holds true for a semi-logarithmic model, where the dependent variable (Y) is in its natural logarithmic form, and the independent variable (X) is in its original form.

For similar question on elasticity.

https://brainly.com/question/30825283

#SPJ11

Domain is all real numbers except -2.

Range is all real numbers except 0.

Interval of increase is all real numbers except -2.

Horizontal asymptote: y = 0.

Vertical asymptote: x = -2.

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this rational expression (function)  [tex]y=-\frac{1}{x+2}[/tex] shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = (-∞, -2) U (-2, ∞); {x|x ≠ -2}.

Range = (-∞, -1/7) U (0, ∞); {y|y ≠ 0}.

Read more on domain here: brainly.com/question/17003159

#SPJ1

This pooled estimate provides a common probability of success for both populations under the null hypothesis H0: p1 = p2, and is used in the calculation of the test statistic for the hypothesis test.

To calculate the best pooled estimate p for the population probability of success using H0: p1 = p2, we first need to calculate the individual sample proportions for each population.

The sample proportion for the first population is r1/n1, and the sample proportion for the second population is r2/n2.

Then, we can calculate the pooled estimate p as:

p = (r1 + r2) / (n1 + n2)

This is the weighted average of the sample proportions, where the weight is proportional to the sample size.

Using this pooled estimate p, we can then calculate the test statistic for the hypothesis test of difference of proportions.

More on population probability: https://brainly.com/question/14125181

#SPJ11

For all integers a and d, d ⫮ n if, and only if, d is a common divisor of n and a, for any integer a.

The notation d ⫮ n means that d is a common divisor of n, or in other words, both n and a are multiples of d. The statement "d ⫮ n if, and only if, d is a common divisor of n and a, for any integer a" is equivalent to saying that d is a divisor of n, and that any other common divisor of n and a must also be divisible by d.

This property is important in number theory and is often used in proofs involving greatest common divisors (GCD) and least common multiples (LCM). By understanding the relationship between d, n, and a and the idea of common divisors, we can gain insight into the properties of numbers and their factors.

To know more about integers refer to-

https://brainly.com/question/15276410

#SPJ11

The remaining players have scored an average of 14 runs each.

The total runs scored by the 11 players are:

11 players * 23 runs/player = 253 runs

If the first player scored 113 runs, then the remaining 10 players must have scored:

253 total runs - 113 runs scored by the first player = 140 runs

To find the average runs scored by the remaining players, we divide the total runs scored by the remaining 10 players by the number of players:

Average runs scored by remaining 10 players = 140 runs / 10 players = 14 runs/player

Therefore, the average runs scored by the remaining players is 14 runs per player.

Learn more about Mean here:

https://brainly.com/question/521501

#SPJ1

The new dimensions of the pictures are 2.5 inches by 3.5 inches.

Chris did image resizing of Career Week, which originally measured 5 inches by 7 inches, by a factor of 1/2. This means that he reduced each dimension of the pictures by half of its original size.

To calculate the new dimensions, he multiplied each original dimension by the scaling factor of 1/2.  

If the pictures were resized by a factor of 1/2, it means that each dimension was reduced to half of its original size.

The original dimensions of the pictures were 5 inches by 7 inches.

Resizing each dimension by a factor of 1/2 gives:

5 inches x 1/2 = 2.5 inches

7 inches x 1/2 = 3.5 inches

Therefore, the new dimensions of the pictures are 2.5 inches by 3.5 inches.

This means that the new pictures are significantly smaller than the original ones, which may affect their resolution and quality.

However, depending on the intended use of the pictures, a smaller size may be suitable or even desirable.

Learn more about image resizing.

brainly.com/question/14204825

#SPJ11

The new balance after one month, given the finance charge and the down payment would be C. $2,114. 56

First, find the monthly interest :

= 16 % / 12

= 0. 013333

Then, get the interest in the first month on the loan :

= 2, 200 x 0. 013333

= $ 29.33

The amount that goes to the principal as repayment is:

= Monthly payment - interest

= 114. 66 - 29. 33

= $ 85. 33

The remaining loan balance is then :

= 2, 200 - 85. 33

= $ 2, 114. 56

Find out more on loan balance at https://brainly.com/question/16387657

#SPJ1

Answer: An upward shift of 4 units.

Step-by-step explanation:

The transformation of the function F(x) = 3x to F(x) = 3x + 4  indicates a vertical translation or shift of the graph of f(x) upward by 4 units.

More specifically, the original function f(x) = 3x has a y-intercept at (0,0) and a slope of 3, meaning that for every 1 unit of increase in x, there is a corresponding increase of 3 units in y. Adding 4 to the function shifts all the y-values up by 4 units, so the new function f(x) = 3x + 4 has a y-intercept at (0,4) and a slope of 3, which means that for every 1 unit of increase in x, there is a corresponding increase of 3 units in y, starting from the new y-intercept at (0,4).

Answer: For the extra large box, the scale factor is 4. The volume of the single serving box is:

V1 = l x w x h = 1.2 cubic inches

The volume of the extra large box, which is a dilation of the single serving box with a scale factor of 4, is:

V2 = (4l) x (4w) x (4h) = 64(l x w x h) = 64V1

So the extra large box will contain:

1.2 x 64 = 76.8 ounces of cereal.

For the family size box, the volume is 18.75 ounces, which is 15.6 times larger than the single serving box. The scale factor is the cube root of this ratio:

scale factor = (18.75/1.2)^(1/3) = 2.5

So the family size box will be a dilation of the single serving box with a scale factor of 2.5.

For the soup boxes, the largest box is a dilation of the smallest box with a scale factor of 2. The volume of the smallest box is 15 cubic inches, so the volume of the largest box is:

V2 = (2l) x (2w) x (2h) = 8(l x w x h) = 8 x 15 = 120 cubic inches.

We can choose any dimensions that satisfy this volume requirement. For example, we could use:

The volume of this box would be:

V = 10 x 3 x 4 = 120 cubic inches

Therefore, a set of dimensions for the largest soup box is 10 inches by 3 inches by 4 inches, or any other dimensions that satisfy the volume requirement of 120 cubic inches.

Answer:

270 minutes or 4.5 hours

Step-by-step explanation:

You need to find the unit rate in order to solve this problem with the given information. In order to find the unit rate (in minutes) let's find each minute. Do 3600/180=20. You use 180 because that's the amount of minutes in 3 hours. Then, you take 5400 and divide it by 20 to get 270. Convert back to hours and rounded you get 4.5 hours.

P(a) = |-2a-2|, P(a) can be evaluated by substituting the value of a into the expression and simplifying. The range of P(a) is [0, ∞) with a minimum value of 0 at a = -1.

The function P(a) is defined as P(a) = |-2a-2|.

To evaluate P(a) for a given value of a, we substitute the value of a into the expression |-2a-2| and simplify.

For example, if a = 3, then P(3) = |-2(3)-2| = |-8| = 8.

To find P, we need to find the range of possible values that P(a) can take as a varies over all real numbers. Since |-2a-2| is always non-negative, the minimum value of P(a) is 0, which occurs when -2a-2 = 0, or a = -1.

For any other value of a, |-2a-2| is positive, so P(a) is always positive. Therefore, the range of P(a) is [0, ∞).

To know more about function:

https://brainly.com/question/12431044

#SPJ1

The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Visit here to learn more about displacement vector  :  https://brainly.com/question/30466999
#SPJ11