Find (u x v) • w for the given vectors

If we want to select r items from n items, and the order of the arrangement is important, then permutations are used. Permutations are a way of counting the number of ways to arrange a set of objects where order matters.

The number of permutations is denoted by nPr, where n is the number of items and r is the number of items selected. The formula for permutations is n! / (n-r)!, where n! is the factorial of n, which is the product of all positive integers from 1 to n. Permutations are used in a variety of fields, such as mathematics, statistics, computer science, and cryptography.

For example, in cryptography, permutations are used to create secure encryption keys. In statistics, permutations are used to calculate probabilities and make predictions. In computer science, permutations are used in algorithms for sorting, searching, and data analysis. Overall, permutations are a powerful tool for analyzing and manipulating data sets where the order of the arrangement is important.

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According to Dr. Greg Tuggle's model, after 14 days, there are predicted to be approximately 29.35 (or about 29) infected people.

The formula f(x) = (2.025)x + 1 represents the predicted number of infected people as a function of the number of days since a particular strain of COVID was found.

To find how many people are infected after 14 days, we need to evaluate the function f(x) at x = 14:

f(14) = (2.025)14 + 1

f(14) = 28.35 + 1

f(14) = 29.35

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let firstly convert the mixed fraction to improper fraction, then get their product.

[tex]\stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{2}\cdot \cfrac{2}{3}\implies 1\qquad \textit{one whole pizza}[/tex]

Answer:

x = 5 or -6

Step-by-step explanation:

We can find the zeros of the function:

[tex]y=x^2+x-30[/tex]

by setting y to 0, then solving for x.

To do this, we need to factor the right side of the equation.

[tex]0=x^2+x-30[/tex]

[tex]0=(x + 6)(x - 5)[/tex]

We can see that (x + 6) and (x - 5) are the two parts of this factorization because 6 and -5 add to 1 (which is the coefficient of the middle term), and they multiply to -30 (the constant term).

From this factored form, we can split the equation into two because we know that:

IF [tex]ab = 0[/tex],

THEN [tex]a=0[/tex]  OR  [tex]b=0[/tex]

So, we can solve for x in the following two equations:

[tex]x + 6 = 0[/tex]             [tex]x - 5 = 0[/tex]

[tex]\boxed{x = -6}[/tex]    OR   [tex]\boxed{x = 5}[/tex]

__

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When printing a newspaper, you are most likely to use a line screen setting of 85 lpi (lines per inch).

(i) The probability of both events A and B happening, P(A and B), is 0.12. (ii) The probability of either event A or event B happening, P (A or B), is 0.58.

First, let's define what it means for events to be independent. Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In other words, the probability of both events occurring together is equal to the product of their individual probabilities: P (A and B) = P(A) x P(B).

Using this formula, we can find the probability of both events occurring together:
P (A and B) = P (A) x P(B) = 0.3 x 0.4 = 0.12

Now let's find the probability of either event occurring. We can use the formula P (A or B) = P (A) + P(B) - P(A and B).
We already know that P(A) = 0.3 and P(B) = 0.4, and we just found that P (A and B) = 0.12. Plugging those values into the formula, we get:
P (A or B) = 0.3 + 0.4 - 0.12 = 0.58
So, the probability of either event occurring is 0.58.
In summary:
(i) P (A and B) = 0.12
(ii) P (A or B) = 0.58

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Answer:

Dependent

Step-by-step explanation:

This event is dependent, because the probability of grabbing a second shoe depends on whether or not you've already grabbed a shoe. If you haven't grabbed a shoe yet, the probability of grabbing a second shoe is zero. If you have already grabbed a shoe, the probability of grabbing a second shoe is 1 (assuming you have at least two shoes in your closet).

Answer:  Modern dance is a team-based practise that needs participants to move in rhythmic sequences. Choreographed routines in modern dance frequently entail dancers synchronising and coordinating their movements, which are frequently rhythmical and expressive. Baseball, downhill skiing, and competitive swimming all demand teamwork and coordination, yet these sports don't frequently incorporate rhythmic movement patterns.

Step-by-step explanation:

The probability of selecting all three infielders is relatively low, with only a 1.73% chance of happening.

We can use the formula for probability of an event as the ratio of favorable outcomes to total outcomes. In this case, we want to find the probability that all three selected players are infielders, which means we need to select three infielders from the total number of players.

The total number of ways to select 3 players out of 24 (8 pitchers + 7 infielders + 9 other players) is given by the combination formula:

C(24, 3) = (24!)/(3!21!) = 2024

The number of ways to select 3 infielders out of 7 infielders is given by:

C(7, 3) = (7!)/(3!4!) = 35

Therefore, the probability that all 3 selected players are infielders is:

P(all 3 infielders) = favorable outcomes/total outcomes

= C(7, 3) / C(24, 3)

= 35/2024

= 0.0173 or 1.73%

So, the probability of selecting all three infielders is relatively low, with only a 1.73% chance of happening.

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According to the data in the table, blue and gold are the two colors most likely to be the school colors of Amarjit's high school.

The table displays the results of a survey in which 600 students were asked to choose their school colors. Out of the six options presented, blue was the most popular choice with 210 students selecting it, while gold was the second most popular with 180 students selecting it. While other colors were also selected, none of them were chosen by more than 100 students, making it unlikely that they would be the primary school colors. However, it is important to note that there may be other factors that influence the selection of school colors, such as tradition or community preferences, which are not reflected in the survey data.

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Based on the data in the table, which two colors are most likely the school colors of Amarjit's high school?

The type of scale used to evaluate the food at a new restaurant on 7-point scales with bipolar adjectives such as good-bad and inexpensive-expensive is known as a Likert scale.

This type of scale is commonly used in surveys to measure attitudes and opinions towards a particular topic, in this case, the food at a new restaurant. A Likert scale consists of a series of statements or adjectives that respondents are asked to rate on a scale that ranges from strongly disagree to strongly agree or, in this case, from bad to good and from inexpensive to expensive.

The bipolar adjectives used in the scale allow for a clear distinction between the positive and negative aspects of the food, which helps to ensure that the responses are more accurate and meaningful. The 7-point scale provides a wider range of options than a binary scale, which allows for more nuanced and detailed responses.

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Donald will have $210 at the end of the year

Given that the principal amount Donald is having at the start of the year is $200 and the rate of interest per annum is 5%.

Since the interest is not compounded, at the end of the year the amount of interest he will be earning = 0.05 x 200 = $10 (since interest is not compounded)

From, the above analysis, Donald is earning $10 of interest per annum from $200.

Now, Total money Donald will be having in 1 year = principal amount + interest earned money = $200 + $10 = $210

From the above solution, we can conclude that Donals is having $210 in total for one year.

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Answer:

Order from greatest to least: 25, 24, 23, 2 1/2

Step-by-step explanation:

Numbers: 23, 24, 25, 2 1/2

2 1/2 = 5/2 = 2.5

Order from greatest to least: 25, 24, 23, 2 1/2

Based on the limited information, it can be deduced that 1/5 of the ribbon is not in view.

In order to show the complete ribbon, we need to understand that in mathematical terms:

Since 4/5 of the ribbon is showing

This means that about 1- 4/5

= 1/5 of the ribbon is not in view.

With this knowledge, you can go ahead to complete your drawing, knowing that a full ribbon has a rectangular shape.

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Homoscedasticity refers to the pattern of covariation that is constant around the regression line, whether the values are small, medium, or large.

Regression line is defined as the line which is used to estimate the unknown relationship between two variables and the relationship is linear.

The equation of this line is used to find or predict the value of one of the variable from the other.

Homoscedasticity is something which assumes that the variances are equal for different groups.

So, this refers to the pattern of covariation that is constant around the regression line, whether the values are small, medium, or large.

Hence the correct term is Homoscedasticity.

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The answers are explained in the solution.

Given that, a bus and a car have speed of 100km/hr and 120km/hr.

They are covering a distance of 340 km, they started travelling at 7:00 am,

Speed = distance / time

A) Bus travelled in 30 minutes = 100 × 0.5 = 20 km

After 30 minutes = 100 × 0.5 = 20 km

Total distance by bus in 1 hour = 40 km

Car covered in 30 minutes = 120 × 0.5 = 60 km

Distance between them = 60-40 = 20 km

Relative speed = 120-100 = 20 km/h

Time to catch up = 20/20 = 1 hour

Distance from Nairobi = 60 + (1 × 120) = 180 km

Therefore, the car catches up with the bus 180 km from Nairobi,

B) Time taken = 30 + 30 + 1 = 2 hours.

7:00am + 2 hours = 9:00 am

C) Time taken by bus to reach the destination = 340 / 100

= 3.4 hours

Hence, bus took 3.4 hours to reach the destination.

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Answer:

a= 5.7

Step-by-step explanation:

Ok, when solving problems like this, it is important to do it step by step to minimize any mistakes.

Original Equation:

[tex]\frac{10a}{3} -1.5=17.5[/tex]

Then we add 1.5 to both sides

[tex]\frac{10a}{3} -1.5+1.5=17.5+1.5[/tex]

Simplify:

[tex]\frac{10a}{3}=19[/tex]

Multiply both sides by 3 to get rid of the denominator in the left side.

[tex]\frac{10a}{3} *3 = 19*3[/tex]

Simplify:

[tex]10a=57[/tex]

Divide both sides by 10 to isolate a

[tex]a = 5.7[/tex]

We can check our answer by plugging our value into the original equation!

Original equation:

[tex]\frac{10a}{3}-1.5=17.5[/tex]

New equation:

[tex]\frac{10(5.7)}{3}-1.5=17.5[/tex]

Multiply the numerator:

[tex]\frac{57}{3}-1.5=17.5[/tex]

Divide the fraction:

[tex]19-1.5= 17.5[/tex]

Subtract:

[tex]17.5=17.5[/tex]

as you can see, the values on both sides of the equation match.

So, a = 5.7

This is a false statement because y-coordinates are different.

In mathematics, an ordered pair is a pair of elements, usually written in the form (x,y), where x and y are two values that are related in some way. In the case of (8,8), this represents an ordered pair where the value of x is 8 and the value of y is 8.

On the other hand, (9-1, 6+3) can be simplified using basic arithmetic operations. We first evaluate the expressions inside the parentheses, 9-1 and 6+3, which give us 8 and 9 respectively. Then we combine them into an ordered pair to get (8,9).

When we compare the two ordered pairs, we can see that the x-coordinates are the same, but the y-coordinates are different. Therefore, (8,8) is not equal to (9-1,6+3) and the statement "True or False(8,8) = (9-1,6+3)" is false.

Let's evaluate each side of the equation separately:

(8,8) represents an ordered pair with 8 as the x-coordinate and 8 as the y-coordinate.

(9-1, 6+3) evaluates to (8,9), since 9-1 = 8 and 6+3 = 9.

So we have:

(8,8) = (8,9)

This is a false statement, since the y-coordinates are different. Therefore, the answer is False.

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The vertex form of the parabola is y = 2(x-1)² + 3.

We have,

Vertex = (1, 3)

passing point (-1, 11)

Use the vertex form of the quadratic:

y = a(x - h)² + k

Here h = 1 and k = 3

So, 11 = a(-1 -1)² + 3

11 = 4a² + 3

8 = 4a²

a² = 8/4

a² = 4

a =2

Then, the vertex form of parabola is

y = 2(x-1)² + 3

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When solving a system of linear equations, the technique you're thinking of is called the "elimination method" or "adding/subtracting method."

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

The method you are referring to is known as the "elimination method" or "adding/subtracting method" for solving a system of linear equations.

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Answer: To find the area of the walkway surrounding the circular garden, we need to subtract the area of the circular garden from the area of the larger circle that includes the garden and the walkway.

The diameter of the larger circle is equal to the diameter of the garden plus the width of the walkway on both sides, which is 1 meter on each side. So the diameter of the larger circle is:

10 + 1 + 1 = 12 meters

The radius of the larger circle is half of its diameter, which is:

12 / 2 = 6 meters

The area of the larger circle is:

πr^2 = π(6)^2 = 36π square meters

The radius of the circular garden is half of its diameter, which is:

10 / 2 = 5 meters

The area of the circular garden is:

πr^2 = π(5)^2 = 25π square meters

Therefore, the area of the walkway surrounding the circular garden is the difference between the area of the larger circle and the area of the circular garden:

Area of walkway = Area of larger circle - Area of circular garden

= 36π - 25π

= 11π square meters

So the area of the walkway is 11π square meters.

The equation of the scatter plot is given by the curve fitting of parabola equation y = -3.54x² + 41.7x + 73

Given data ,

Let the cleaning company models its profits be plotted on the graph

where the points are given by

A ( 1 , 100 ) , B ( 2 , 175 ) , C ( 3 , 150 ) , D ( 3 , 175 ) , E ( 5 , 175 ) , F ( 6 , 225 ) , G ( 7 , 175 ) , H ( 8 , 200 ) , I ( 9 , 150 )

Using the curve fitting model , we can plot the graph as

y = -3.54x² + 41.7x + 73

Hence , the equation of graph is y = -3.54x² + 41.7x + 73

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The complete question is attached below :

A cleaning company models its profits on the graph.

p(t)

Profit ($ thousands)

Answer:

1539/4 (improper fraction) or 384 3/4 (simplified fraction)

Step-by-step explanation:

To find the improper fraction, write 384.75 as a fraction:

384.75/1

Then, since you have 2 decimal places after the ., multiply the entire fraction by 100:

38475/100

Next, find the GCF, which is 25, and simplify this fraction to find the final improper fraction:

1539/4

To find the simplified fraction, we already have the whole number, 384, so we have to convert 0.75 to a fraction which is 3/4, because 0.75 is 3/4 of 100:

384 3/4

Hope this helps :)

Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

The equation of the parabola in vertex form is y = (1/20)(x + 7)^2 + 1.

To write the equation of a parabola in vertex form, we use the equation:

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

where (h, k) represents the vertex of the parabola.

Given that the vertex is (-7, 1), we have h = -7 and k = 1. Substituting these values into the equation, we get:

y = a(x + 7)^2 + 1

Now, we need to find the value of 'a' to complete the equation. Since the parabola passes through the point (10, 309/20), we can substitute these coordinates into the equation:

309/20 = a(10 + 7)^2 + 1

309/20 = a(17)^2 + 1

309/20 = a(289) + 1

309/20 = 289a + 1

To simplify the fraction, we multiply both sides by 20:

309 = 20(289a + 1)

309 = 5780a + 20

Now, we solve for 'a':

5780a = 309 - 20

5780a = 289

a = 289/5780

a = 1/20

Substituting this value of 'a' back into the equation, we have:

y = (1/20)(x + 7)^2 + 1

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Answer:

110°

Step-by-step explanation:

Sum of interior angles : 360

360-120-130 = 110

The number of F ratios which calculated in a 3 way ANOVA is 7.

So, the correct answer is C.

In a three-way ANOVA, which involves three independent variables, a total of 7 F ratios are calculated.

This includes the main effect of each independent variable (3 F ratios), the two-way interactions between the independent variables (3 F ratios), and the three-way interaction between all three independent variables (1 F ratio).

Thus, the correct answer is c. 7 F ratios.

These F ratios help in determining the significance of each factor and interaction effect on the dependent variable in the analysis.

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The number of randomly presented items that children can repeat immediately after the items are presented is called their immediate memory span or short-term memory capacity.

The number of randomly presented items that children can repeat immediately after the items are presented is called their immediate memory span or short-term memory capacity.

The capacity of short-term memory is limited and varies from person to person and depending on the complexity of the information being presented.

The typical range of immediate memory span for children is around 5 to 9 items, with older children and adults having a slightly larger capacity.

However,

Some individuals with exceptional memory abilities, such as memory athletes, can recall significantly more items in short-term memory.

Factors that can affect short-term memory capacity include the nature of the items being presented their familiarity or meaningfulness, the duration of the presentation and the individual's level of attention and working memory capacity.

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The seventh-grade class supplied 175 bags of snacks and 225 beverages for the school dance.

Finding the number of bags of snacks and beverages:

Let's assume that the number of bags of snacks supplied by the seventh-grade class is represented by 'x'. Since the number of beverages supplied is 50 more than the number of bags of snacks, we can represent the number of beverages supplied as 'x + 50'.

The total number of items supplied is 400, so we can write:

x + (x + 50) = 400

Simplifying this equation, we get:

2x + 50 = 400

Subtracting 50 from both sides, we get:

2x = 350

Dividing both sides by 2, we get:

x = 175

Therefore, the number of bags of snacks supplied by the seventh-grade class is 175. Using the fact that the number of beverages supplied is 50 more than the number of bags of snacks, we can calculate the number of beverages supplied as:

x + 50 = 175 + 50 = 225

Therefore, the number of beverages supplied by the seventh-grade class is 225.

So, the seventh-grade class supplied 175 bags of snacks and 225 beverages for the school dance.

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