a unit vector lies in the xy plane, at an angle of 158 degrees from the x axis, with a positive y component. what is the unit vector? (it helps to draw a diagram.)

The vertex of the quadratic equation:

f(x) = 2x^2 - 8

is (0, -8)

For a general quadratic equation:

a*x^2 + b*x + c

The vertex is located at the x-value:

x = -b/2a

Here we have the quadratic equation:

f(x) = 2x^2 - 8

Then the values are:

a = 2

b = 0

c = -8

Then the vertex is at:

x = 0/2*2 = 0

To get the y-value of the vertex, we need to evaluate on x = 0.

f(0) = 2*0^2 - 8 = -8

So the vertex is (0, -8).

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The fraction of no selection cars is 1/4 in the parking lot.

A fraction is a portion of a whole and is expressed as a rational number using the in-line notation form a/b or the traditional "display" notation for a and b.

The number is expressed as a quotient in mathematics by dividing the numerator by the denominator.

In the numerator or denominator of a complex fraction is a fraction. A proper fraction has always a numerator that is all the time lower than its denominator. If the numerator is greater, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a proper-fraction remainder divided by a whole-number quotient.

The whole of a fraction is 1

Here parking lot is  ¾ full

So the The lot that is no selection full of cars is

= 1 - ¾

= 4/4 - 3/4

= 1/4

Thus, the fraction of no selection cars is 1/4 in the parking lot.

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The cost of 250 kg of coal is 500 dollars.

One tonne of coal cost $2000. The cost of 250kg of the same coal can be found as follows:

Let's convert the mass of the coal in kilograms to tonnes.

Hence,

1 kilogram = 0.001 tonnes

250 kilogram = ?

cross multiply

mass of the coal in tonnes = 0.001 × 250

mass of the coal in tonnes = 0.25 tonnes

Hence,

1 tonne = 2000 dollars

0.25 tones = ?

cross multiply

mass of 250 kg of coal = 0.25 × 2000

Therefore,

mass of 250 kg of coal = 500 dollars

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if we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time. but the probability that such a coin will come up heads exactly half the time in 16 tosses is 1 in 65536 (2^16).

This can be calculated using the binomial probability formula which states that the probability of getting a certain number of heads in a certain number of tosses is given by (Number of ways to get the desired number of heads) / (Total number of possible outcomes). In this case, the number of ways to get 8 heads in 16 tosses is equal to 16C8, or 120.

The total number of possible outcomes is equal to 2^16, or 65536. Thus, the probability of getting 8 heads in 16 tosses is 120/65536, which is approximately equal to 1/65536.

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The missing sides or angles that makes the triangle ABC congruent to PDF by ASA are ∠A and ∠P, ∠B and ∠D and AB and PD

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal . In other words, two triangles are congruent when the corresponding sides and angles are equal.

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent by ASA(angle side angle)

Therefore, the missing side or the angles that would make the triangle ABC congruent to triangle PDF by ASA is as follows:

AB≅ PD

∠A ≅ ∠P

∠B ≅ ∠D

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Answer: The slope of the line that passes through the points (-8, -6) and (-8, 4) is undefined. This is because the line is a vertical line and the difference in y-coordinates is 0, making the denominator of the slope equation 0. The slope of a vertical line is undefined.

Step-by-step explanation:

Answer:

Step-by-step explanation:

c

Answer: C

Step-by-step explanation:

The rate of change will be the same for all years. The rate of change is 7%. The . basic formula for this equation is: I(1+R)^T, where I = Initial amount, R = Rate of growth, and T = Time. So the R here is 0.07, or 7%. The growth RATE is constant, the growth AMOUNT will increase each year.

Answer:

▪ 20% of 15 ml

(20/100) × 15 ml = 3% pure milk fat

The shaded region of segments is given in the attachment.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The diameter is the length of the line through the center that touches two points on the edge of the circle.

A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord's endpoints.

A sector of a circle is a pie-shaped part of a circle made of the arc along with its two radii.

Hence, the shaded region of segments is given in the attachment.

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Answer:

6/5

Step-by-step explanation:

easy as pie because 3/5x2=6/5

Answer:

Step-by-step explanation:

Answer: The sale price would be 225.00

The selling price of the trampoline will be $225.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that there is a 25% discount on the price $300. The discounted price will be calculated as:-

Discounted price = 300 x 0.75

Discounted price = $225

Therefore, the selling price of the trampoline will be $225.

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The probability distribution of X is given as follows:

A probability is defined as the division of the number of desired outcomes by the number of total outcomes.

A probability distribution gives the probability of all the possible outcomes in the context of a problem.

There are two outcomes for this problem, listed as follows:

Only one of the 1000 combinations are a winning combination, hence the probability distribution of X is given as follows:

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(a) Mean of given sample = 75

(b) Mean (60, 80) = 70

(c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.

The given sample is (60, 70, 80, 90)

(a) Mean of sample = (60+70+80+90)/4 = 300/4 = 75

(b) Mean of any 2 of scores

let's take (60,80)

mean(60,80) = (60+80)/2 = 70

(c) All possible samples of size 2 are

(60,70), mean(60,70) = 65

(60,80), mean(60,80) = 70

(60,90), mean(60,90) = 75

(70,80), mean(70,80) = 75

(70,90), mean(70,90) = 80

(80,90), mean(80,90) = 85

Therefore, for the given sample (a) Mean of the sample = 75, (b) Mean (60, 80) = 70, (c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.

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The complete question is:

How did the Chapter 6 test go? Today, we will be taking a sample from a population. We will use the average from the sample to estimate the average for the population. Let's start with a very simple example. My 5th period is very small. There were only 4 students who took the chapter 6 test. Their scores were: 60, 70, 80, and 90. Answer the following questions:

(a) Find the mean of the sample

(b) Take a sample of any 2 of the scores. Find the mean of your sample.

(c) Figure out all of the possible samples of size two. Calculate a sample mean for each sample of 2.

The area of the triangle is given by the equation A = 35.1 feet²

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

The area of the triangle = ( 1/2 ) x Length x Base

An equilateral triangle is a triangle in which all three sides have the same length.

Let the triangle be ΔABC , and

∠A = ∠B = ∠C = 60° and AB = BC = CA

Given data ,

Let the triangle be represented as ABC

Now , the triangle ABC is an equilateral triangle

So , AB = BC = CA

The perimeter of the triangle is P = 27 feet

So , the base length of the triangle AB = 27/3 = 9 feet

The height of the triangle = 7.8 feet

Now , area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

The area of the triangle A = ( 1/2 ) x 7.8 x 9

The area of the triangle A = 35.1 feet²

Hence , the area of the triangle is 35.1 feet²

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Answer:

D. 88.47 in3

Step-by-step explanation:

The volume of a single coin would be the volume of a cylinder with a radius of 1.4 inches and a height of 0.0625 inches. The formula for the volume of a cylinder is V = πr^2h. So, V = 3.14 * (1.4^2) * 0.0625 = 0.38 in^3

Since there are 230 coins, the total volume of the coins would be 230* 0.38 = 87.40 in^3

So, the answer would be 87.40, which is closest to D. 88.47 in3

Answer: D: 88.47 in³​

Step-by-step explanation:

So what you want to do is first find the individual volume of the coins. Use the volume formula: V = πr^2h

Take 1.4 and times it by itself

1.4 x 1.4 = 1.96

Now multiply 1.96 by 0.0625

1.96 x 0.0625 = 0.1225

And times 0.1225 by pi, or in this case, 3.14

0.1225 x 3.14 = 0.38465

Now you have found the individual volume of each coin. You are trying to find how much space all of the coins take up together. The question says that there is 230 coins in total. So times 0.38465 by 230 to find how much space all the coins take up.

0.38465 x 230 = 88.4695 in³

Now round it to the nearest hundredth: 88.47 in³

That is your answer.

Also I took the same test and I picked 88.47 inches cubed and got it right.

Proof:

Have a good day :)))

The square matrix can be formed using this system of equations option second is correct.

Matrix:

A matrix is ​​a rectangular array of numbers, variables, symbols, or expressions defined for operations such as subtraction, addition, and multiplication. The size of a matrix (called matrix order) is determined by the number of rows and columns in the matrix. The order of a matrix with 6 rows and 4 columns is expressed as 6×4 and read as 6×4.

We have three linear equations:

3x - 2y = -2

7x + 3y = 26

-x  -11y = 46

To solve the above equations we can use the matrix concept:

The matrix will be:

[tex]\left[\begin{array}{ccc}3&-2&-2\\7&3&26\\-1&-11&-46\end{array}\right][/tex]

The above matrix is a square matrix.

Square Matrix:

A square matrix is ​​a matrix that has the same number of rows and columns. Its order is of the form n x n. The product of these rows and columns also gives the number of elements in a square matrix, so the number of elements in it is always a perfect square.

Thus, the square matrix can be formed using this system of equations option second is correct.

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The number of in-state undergraduates could not be 200.

International or foreign students are students who migrate to another country to pursue their studies and complete all or a portion of their postsecondary education there.

Each nation has its unique national educational system, which affects how "foreign students" and "international students" are defined.

If foreign students comprise exactly 1/8 of the number of out-of-state undergraduates, then the number of in-state undergraduates would have to be a value that yields an integer value for the number of foreign students.

In-state undergraduates are 55% of 60% of the total, or (.55)(.6) = (.33) of the total.

If 330 is the number of in-state undergraduates, which comprise 33% of the total, then you can calculate the total number of admitted students:

(0.33) (total) = 200

⇒ total = 200/0.33

⇒ total = 200*100/33

⇒ total = 606.06

So that The number of in-state undergraduates could not be 200.

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The correct question is with graph

For 2011, if foreign students comprise exactly 1/8 of the number of out-of-state undergraduates, indicate which could not be the number of in-state undergraduates.

200

330

1320

There are only 2 possible solutions for B, 1 and 3, so that the number forms the two-digit numbers 16 and 36, which are the positive squares of the positive integers 4 and 6.

Now, we have been given a two-digit number, B6.

The numbers whose squares are 2 digit numbers are:

1, 4, 9, 16, 25, 36, 49, 64, 81

From this list, it is evident that there are 2 numbers that end with 6 and are perfect positive squares of a number, in this case, 4 and 6.

4x4 = 16, 6x6 = 36.

Therefore, B can take 2 values, 1 and 3. These are the only distinct possible values of positive integers for B to take.

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Answer:

To find out how many minutes Susanna paid for, we need to convert the fraction of an hour to minutes.

There are 60 minutes in an hour. So, to find out how many minutes 3/5 of an hour is, we can multiply 3/5 by 60:

3/5 * 60 = 36

Therefore, Susanna paid for 36 minutes of parking.

Answer:

36 minutes

Step-by-step explanation:

We need to convert hours to minutes and then multiply by a fraction.

1 hour = 60 minutes

3/5 of 60 minutes

3/5 * 60

180/5

36 minutes

Answer:

Step-by-step explanation:

8(3y + 0.5) so first we do 8 * 3 = 24y and 8 * 0.5 = 4. Then that becomes 24y = 4. so now we do 24y / 24 = y bc 24 cancels out, 4 / 24 = 0.166. So y = 0.166. HOPE THIS HELPS!!!

Answer:

  4.0 km

Step-by-step explanation:

You want the distance between two boats after 45 minutes if they left at the same time and traveled 10 km/h at N47E, and 8 km/h at N79E.

The distances the boats traveled in 3/4 hour can be found by multiplying the speed by the time:

  distance = speed · time

  distance = {10 km/h, 8 km/h} · (3/4 h) = {7.5 km, 6 km}

The distance between their positions can be found from the law of cosines:

  c² = a² +b² -2ab·cos(C)

Here, the angle between the vectors is 79° -47° = 32°, so the distance is given by ...

  c² = 7.5² +6² -2·7.5·6·cos(32°) ≈ 15.925671

  c ≈ √15.925671 ≈ 3.9907

To the nearest tenth km, the distance between the boats is 4.0 km.

__

Additional comment

It can be helpful to draw a diagram. A geometry app can measure the distance for you (attachment 1), or a calculator app can calculate it based on the speed vectors (attachment 2).

The probability that the first girl is the first to flip a head is; 1/2.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that if the number of toss required is odd as in one attempt represent odd number , we have following sequence of events

H, TTH, TTTTH.....

The required probability P will be as;

P = 1/2 + (1/2)³ + (1/2)⁵..........

As she flipped it in first go the probability is 1/2.

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On solving the provided question, we can say that probability that a four or higher number will first emerge on the third or fourth roll.= 4/27 + 8/81 = 20/21

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

On a dice, the numbers 5 and 6 are the ones above 4. The likelihood of receiving a number higher than 4 (i.e., 5 or 6) is = 2/6 = 1/3

and as a result, the likelihood of receiving 4 or less is= 1-1/3 = 2/3

The likelihood that a number larger than 4 will show up on the third roll is equal to

2/3* 2/3 * 1/3 = 4/27

The likelihood that a number larger than 4 will emerge on the fourth roll is equal to =2/3*2/3* 2/3 * 1/3 = 8/81

probability that a four or higher number will first emerge on the third or fourth roll.= 4/27 + 8/81 = 20/21

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Simplifying √75 the answer is option D. 5√3.

An expression of a number which has a square root is termed surd. Some procedures are required to solve any given question on surd, especially when the given expression involves numbers that do not have a whole root.

To simplify √75 as required in the question, we have to look for a two numbers. One of these numbers must have a whole square root.

So that we can use 3 and 25.

Thus,

√75 = √(3 x 25)

       = √3 * √25

       = √3 * 5

       = 5√3

√75 = 5√3

The answer is option D. 5√3

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Answer: [tex]3:2[/tex]

Step-by-step explanation:

Using the zero-product property, we know that [tex]2x-3y=0[/tex] or [tex]x+5y=0[/tex]. We can rearrange these cases to yield [tex]x=\frac{3}{2}y[/tex] and [tex]x=-5y[/tex].

However, since [tex]x[/tex] and [tex]y[/tex] have the same sign, we neglect the case [tex]x=-5y[/tex]. This means [tex]x=\frac{3}{2}y[/tex].

[tex]x=\frac{3}{2}y \implies \frac{x}{y}=\frac{3}{2} \implies x:y=3:2[/tex]

Answer: We can use the distributive property to expand the left side of the equation:

2xx + 2x5y - 3yx - 3y5y = 0

Then, combine like terms:

2x^2 + 10xy - 3xy - 15y^2 = 0

Now we can add 3xy + 15y^2 on both sides of the equation to get:

2x^2 + 10xy = 0

We know that x and y are positive, so we can divide both sides by 2:

x^2 + 5xy = 0

and since x>0, we can divide both sides by x:

x + 5y = 0

So the ratio x:y = x/(-5y) = -x/5y.

To simplify we can divide x by -x and 5y by 5y and get the final answer as

x:y = -1:

Step-by-step explanation:

Answer:

La circunferencia es 245.044 mm

The distance formula for a triangle is the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The distance formula for a triangle is the Pythagorean Theorem, which outlines a relationship between the three sides of a right triangle. Specifically, the theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. To find the distance between two points in a triangle, you must first determine the length of all three sides. Once you know the lengths of all three sides, you can use the Pythagorean Theorem to calculate the distance between the two points. To use the theorem, you must first calculate the square of the hypotenuse. Then, you must square the lengths of the other two sides and add them together. Finally, you can take the square root of the sum of the squares to calculate the distance between the two points.

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On solving the provided question, we can say that by statistical data each week, loads would be transported a total of 3,100 meters.        

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration

First we arrange the workflow of the departments in descending order while the distance will be in ascending order.

TRIPS  -    DISTANCE(metres)

1 -11     -       10

11 - 111     -   10

1 - 111     -    20

DEPARTMENTAL PAIR       WORKFLOW

Y-Z   -       150

Z-Y    -        130  

Z-X -     100

X-Z     - 80

Y-X     -           30  

In light of the assignment of departments X, Y, and Z to areas 1, 2, and 3 in turn. Decide on the distance for each acceptable departmental pair while keeping that in mind;

DEPARTMENTAL PAIR     WORKFLOW     DISTANCE    TOTAL DISTANCE                                    

Y-Z           150         10       1500

Z-Y        130       -

Z-X        100        10     1000

X-Z        80            -

Y-X              30          20        600

This means that each week, loads would be transported a total of 3,100 meters.                    

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hi

Step-by-step explanation:

Answer: If you are bored, try Khan Academy, or answer questions on brainly.