What information do you need to know to write the equation of a line?
the slope of the line in quadrant 2
the location of two ordered pairs that lie along the line
the slope of the line and the location of the origin
the location of 1 ordered pair the lies along the line

Based on the table, the equation that can be used to determine the number of pages (p) Lenny can read in t minutes is B. p = 1.8t.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

For this equation, the slope, unit rate, or pages per minute is the quotient of the total number of pages read and the total time (in minutes) used.

Equations are depicted using the equation symbol (=) to show that two or more mathematical expressions are equal to one another.

Lenny's Reading Rate    

Time (minutes)    Pages Read     Pages per Minute

 60                            108                  1.8 (108/60)

 90                            162                  1.8 (162/90)

135                            243                  1.8 (243/135)

Thus, we can conclude that we can find the number of pages Lenny can read in t minutes using the equation provided by Option B.

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Answer:

p=1.8

Step-by-step explanation:

unit rate 108/60=1.8

The Venn Diagram is shown at the end of the answer.

Then the amounts are given as follows:

The Venn Diagram is filled starting at the intervals involving most variables, that is, the intersections.

286 students took all three courses, hence:

V = 286.

629 students were taking history and dance, hence:

VI + V = 629

VI + 286 = 629

VI = 343.

605 students took history and math, hence:

IV + V = 605

IV = 605 - 286

IV = 319.

604 students took dance and math, hence:

II + V = 604

II = 318.

1236 students took dance, hence:

III + II + VI + V = 1236

III + 318 + 343 + 286 = 1236

III = 1236 - (318 + 343 + 286)

III = 289

1295 students took math, hence:

VIII + IV + V + VI = 1295

VIII + 319 + 286 + 343 = 1295

VIII = 1295 - (319 + 286 + 343)

VII = 347

1174 students took history, hence:

I + II + IV + V = 1174

I + 318 + 319 + 286 = 1174

I = 1174 - (318 + 319 + 286)

I = 251

Then the number of students who took at least one of the subjects is of:

251 + 318 + 289 + 319 + 286 + 343 + 347 = 2153.

The number of students who took none of the subjects is of:

2401 - 2153 = 248.

(VIII = 248 on the diagram).

The remaining amounts are then calculated as follows:

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the probability that the time between consecutive customers is less than 15 seconds is 0.4327

Mean u=0.59

We are supposed to find the probability that the time between consecutive customers is less than 15 seconds

u=1/λ

0.59min=1/λ

0.59*60=1/λ

λ=1/0.59*60

λ=0.02824

The cumulative distribution function is used to describe the probability distribution of random variables.

The cumulative distribution function :P(X≤x)=F(x)=1-e^-λx

We are supposed to find the probability that the time between consecutive customers is less than 15 seconds

P(X≤15)=F(15)=1.e^-0.02824*15

P(X≤15)=F(15)=0.4327

Hence the probability that the time between consecutive customers is less than 15 seconds is 0.4327

The probability that the time between consecutive customers is between ten and fifteen seconds is 0.9000.

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Based on the null hypotheses, the type of error is Decrease the significance level to decrease the probability of Type I error.

According to the given question, the null hypothesis is that the new diagnostic tool is not effective in detecting the condition.

Here the more consequential error described is that the diagnostic tool is not effective, but the significance test indicated that it is effective. This is a type I error.

And in Hypothesis testing, a type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.

Therefore, it involves saying there is significant evidence to show that the new diagnostic tool is effective in detecting the condition when in reality, it isn't.

When the level of significance (α) of a hypothesis test directly gives the probability of a type I error. So, by setting it lower, we reduce the chances of a type I error.

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Answer:

21x^2 - 25x - 28

Step-by-step explanation:

= -3x (4 - 5x) + (3x + 4)(2x - 7)

= -12x + 15x^2 + 6x^2 - 21x + 8x - 28

= 21x^2 - 25x - 28

I hope my answer helps you.

The first statement is false and the rest of the options are true.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

1. 25% of 512 is equal to 1/4 x 500, false due to 500.

2. 90% of 133 is equal to 0.9 x 133, true because 90% is equal to 0.90.

3. 30% of 44 is equal to 3% of 440, true because the value of both is the same.

4. The percentage of 21 is 28 is equal to the percentage of 30 is 40, true because the percentage of both cases is identical.

The first statement is false and the rest of the options are true.

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The difference between the two candidates who voted is less than the margin of error, so the result cannot be predicted.

The difference between the two candidates voted is less than the margin of error

4% of 2052 is 4/100 x 2052 = 82.08

44% of 2052 is 902.88

46% of 2052 is 943.92

It increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter the larger the margin of error.

The race was too close to call means it is within the margin of error for one candidate to receive 44% of the popular vote and for the other candidate to receive 46​%, the poll cannot predict the winner.

Therefore, The result cannot be predicted as the race was too close to call.

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Part A

p = number of levels

8p = amount of points lost for passing a level

3p = amount of points lost for catching a flower

(6x3)p = multiply the previous expression by 6 since there are 6 flowers per level. This represents the total number of points lost after catching 6 flowers. This expression is equivalent to (3 x 6)p, both of which simplify to 18p.

The quantities 8p and (3 x 6)p are subtracted from the total 100. Then we set that less than 20 to end up with the inequality of

100-8p - (3 x 6)p < 20

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

Part B

Refer to the inequality set up in part A.

We'll solve for p.

100-8p - (3 x 6)p < 20

100-8p-18p < 20

100-26p < 20

-26p < 20-100

-26p < -80

p > -80/(-26) ..... inequality sign flips

p > 3.077

The decimal result is approximate. The inequality sign flips because we divided both sides by a negative number.

Round this value up to the nearest integer.

So p = 3.077 rounds up to p = 4. We do not go to p = 3 because

100-26p = 100-26*3 = 22

which is not under 20.

But p = 4 will work

100-26p = 100-26*4 = -4

Answer: Tina must complete at least 4 levels.

She can purchase 3 blue towels and 5 green towels.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

8 x 5 = 40

10 x 3 = 30

40 + 30 = 70

Hence, She can purchase 3 blue towels and 5 green towels.

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Answer:(4, 4), (7, 0), (4,-2)

Step-by-step explanation: The median of a triangle is the line segment connecting a vertex to the midpoint of the opposite side. In this triangle, the vertex at (7, 4) is connected to the midpoint of the side opposite it, which is the midpoint of the line segment between (1, 4) and (7, -2). This midpoint is located at (4, 0). Therefore, the median through (7, 4) will consist of the points (4, 4), (7, 0), and (4, -2).

2. The Equation for  value x is, x= 13 sin 52.

3. The value of m, m = l cos <N

4. The length of Hypotenuse is 7.92 m.

The branch of mathematics concerned with specific functions of angles and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).

Given:

2. P= x

H= 13 cm

Using Trigonometry

sin 52 = P/ H

sin 52 = x/ 13

x= 13 sin 52.

3. P = n, B= m and H= l

Using Trigonometry

cos <N= B/H

cos <N=  m / l

m = l cos <N

and, using Pythagoras theorem

H² = P² + B²

l²= m² + n²

m= √( l² - n²)

4. P = 7m

angle= 62

Using Trigonometry

sin 62 = 7/ H

0.88295 = 7/ H

H = 7/ 0.88295

H = 7.92 m

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The tank needs 5 more liters of water to be filled.

Subtraction is one of the basic operations of mathematics where we remove numbers or expressions or objects away from a given value.

Amount of water needed to fill the tank = 8 liters

Amount of water Alejandro filled = 2 liters

Amount of water Anthony filled = 1 less than Alejandro = 2 - 1 = 1 liter.

Total amount of water filled = 2 liters + 1 liter = 3 liters

Remaining space can be filled with 8 liter - 3 liter = 5 liters.

Hence tank still need 5 liters of water to be filled.

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Answer:

500 grams

Step-by-step explanation:

6 weigh 750 so multiply them:
6 × 750 = 4500

4500 grams is equivalent to 4.5 kilograms

the total of all blocks of ice was 5 kg
therefore the remaining one is 0.5kg which is 500g

Answer:

90

Step-by-step explanation:

First, we would need to figure out the multiples of 18.

18, 36, 54, 72, 90, 108, 126, 144, 162, 180.

Now, let's figure out the multiples of 30.

30, 60, 90, 120, 150, 180.

The numbers match up! This means that in 90 days the soccer team and football team will practice together, and the same happens on day 180.

The fitted regression model is  y = 0.96+0.38x1 + 1.27 x2, and  Fitted regression model is y = 1.87+0.29x1 + 1.11 x2 -0.61 x3.

a) simple linear regression equation is y=a+bx1+cx2

last maintenance service (x1), repair time (y) given the type of repair (x2).

If x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical. The Fitted regression model is y = 0.96+0.38x1 + 1.27 x2

b) Since R2 is 0.84.hence we say that x1 and x2 are 84% variation on. Hence we conclude that the above equation is best fit for the data.

c) simple linear regression equation is y=a+bx1+cx2+dx3

last maintenance service (x1), repair time (y) given the type of repair (x2).

If x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical. and x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.

The Fitted regression model is y = 1.87+0.29x1 + 1.11 x2 -0.61 x3

d) Since R2 is 0.89.hence we say that x1 and x2 are 89% variation on y. Hence we conclude that the above equation is best fit for the data. compare to part (b).

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The probability density function (pdf) for the uniform distribution has the basic formula: f(x) = 1/ (B-A) for A x B.

A continuous probability distribution, the uniform distribution is concerned with equally likely outcomes. It is referred to as having a rectangular distribution on the interval [a,b] or having a uniform distribution for the continuous random variable X. Above is a representation of the probability density function of a continuous uniform distribution. The probability of drawing a heart, club, diamond, or spade is equally likely; hence, the area under the curve is 1, which makes sense given that the total of all probabilities in a probability distribution is 1.

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About -$10.15 that is, on average you lose about 15 cents.

Using the principle of discrete probability, the expected value, which is a measure of the mean amount after many plays is - 2/13

Calculating the required probabilities :

P(winning) = P(drawing an Ace) = 4/52 = 1/13

Hence, P(losing) = 1 - 1/13 = 12/13

X :____ 10 _____ - 1

P(X) : _ 1/13_____ 12/13

The expected value :

E(X) = 10 × (1/13) + - 1(12/13)

E(X) = 10/13 - 12/13

E(X) = - 2/13

Hence, the measure of the mean amount is -2/13.

The victory value is $10, and the loss value is $-1.

Out of a total of 52 cards, this deck has 4 aces.

The probability can then be defined as the ratio of the number of desirable outcomes to the number of possible outcomes.

P(win) = number of favorable outcome/number of the possible outcome

= 4/52

= 1/13

P(loss) = number of favorable outcome/number of the possible outcome

= 48/52

= 12/13

Then we have

$10x1/13 + (-1)x12/13

= 10/13-12/13

= -2/13 dollars

= -$0.15

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The following rational functions is graphed below is D . F ( x ) = 1 / x^2 .

Given :

f the following rational functions is graphed below

we know that ,

Rational functions in the form a / b

y = 1 / x^2

Table :

x    -2     -1      1       2

y   1 / 4    1      1       1 / 4

on plotting the above points we get the graph which is shown in figure .

here vertical asymptote x = 0 and

Horizontal asymptote y = 0

Therefore F ( x ) = 1 / x^2 is the rational function graphed below .

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Assume that the basis for a subspace V in Rn is v1,..., vp. Show that a vector in Rn is orthogonal to a vector in V if and only if it is orthogonal to every vector v1,..., vp.

An orthogonal vector , In mathematics, orthogonality is an extension of perpendicularity, particularly in vector calculus and linear algebra. Basic geometry dictates that two lines or line segments are only perpendicular if they form a straight angle.

It makes sense to think of vectors as arrows, such as R 2 and R 3, when discussing orthogonal vectors in an inner product space (a real or complex vector space with a notion of vector multiplication).

There are inner product spaces where it makes no sense to conceive of vectors as arrows, yet one still needs to have some understanding of what it means when discussing orthogonal vs. perpendicular.

Hence, It is orthogonal to every vector in vector space, or o V. Every vector in V is a linear combination of these vectors since v1,..., vp serves as the basis for V.

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cash dividends paid that should be recorded in the financing section of the statement of cash flow is $ 148300

With regards to the above, information, the amount of cash dividends paid that should be recorded is computed as;

= Cash dividends payable at the beginning of the year + Cash dividends declared for the year - Cash dividends payable at the end of the year

= $27,100 + $67,000 - $54,200

= $ 148 300

Therefore, cash dividends paid that should be recorded in the financing section of the statement of cash flow is $ 148300

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The greatest integer that does not exceed 1000x is 1. the value of x is approximately 0.001.

What is the area?

The area of a shadow is the amount of surface area that is covered by the shadow. It is the two-dimensional projection of an object onto a surface.

Let the distance between the point source of light and the horizontal surface be h. Since the shadow is a projection of the cube onto the horizontal surface, the shadow has the same proportions as the cube. Therefore, the height of the shadow is h/x times the length of the shadow, which is 48x. The area of the shadow is then:

48x * h/x = 48h

Since the area of the shadow is 48x^2, we have:

48h = 48x^2

h = x^2

We are asked to find the greatest integer that does not exceed 1000x. Substituting the expression for h into the equation, we get:

1000x = 1000x^2

x = 1/1000

Hence, The greatest integer that does not exceed 1000x is 1. the value of x is approximately 0.001.

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Your's check would be $198 for two weeks with 9 hours of work from Sunday-Friday.

In a word problem, the mathematical operations are written in text format. To solve such a problem, the text should be understood and simple basic arithmetic operations are applied.

It is given that,

He/She makes $11 for 1 hour and works for 9 hours from Sunday to Friday.

For 9 hours of work, he/she gets, $11 × 9 = $99

Then, for two weeks, the payment = $99 + $99 = $198

So, he gets a biweekly check with $198.

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In triangle ABC, where AD = DB , BC = 18 units then length of DE is equal to 9 units.

As given in the question,

In the given triangle ABC,

BC = 18 units

AD = DB

⇒ 'D' is the mid-point of AB.

From the given figure of triangle ABC,

DE is parallel to BC.

⇒E is the midpoint of AC.

Using mid-point theorem,

'D' and 'E' are midpoint of AB and AC and parallel to the opposite side BC then DE is half the measure of BC.

DE = ( 1/2) BC.

⇒ DE = ( 1/2) (18)

⇒ DE = 9 units

Therefore, in the given triangle ABC, the length of DE is equal to 9 units.

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The answer to the sum is: ∑ k⁴ (k  ranges from 1 to 6)

Express the sum in sigma notation :

According to the question,

1 = lower limit of summation

k = the index of summation

1 + 16 + 81 + 256 + 625 + 1296 = 1² + 4² + 9² + 16² + 25² + 36²

                                                 = 1⁴ + 2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ ( i.e 16 = 4²=(2²)²)

                                                 = ∑ k⁴ (k ranges from 1 to 6)

 So, The answer to the sum is - ∑ k⁴ (k ranges from 1 to 6).    

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Answer:

Step-by-step explanation:

To find a least squares solution using the normal equations, compute AT A and AT b, then solve the new system AT Ax = AT b. Each solution will be a least squares solution x to Ax = b.

What is least square method with example?

By reducing the total of the offsets or residuals of points from the plotted curve, the least squares method is a statistical technique for determining the best fit for a set of data points. In order to forecast the behavior of dependent variables, least squares regression is performed.

The least squares approach, sometimes referred to as the linear or simple least squares method, typically fits a straight line across the provided points. The sum of squares of the distances from the points is reduced along this line, which is known as the line of best fit.

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The total cost of all the items he wants to buy with the applied discount and before tax is $9.9.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Bashir has a loyalty card good for a 10% discount at his local hardware store.

So, Each good he buys at (100 - 10)% = 90% of the value before tax.

He wants to buy some items that cost $11  before the discount and tax.

Therefore the amount he has to pay is,

= (90/100)×11.

= $9.9

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Answer:

Step-by-step explanation:

the sum of the interior angles in a triangle is 180°

take off from 180° the know angles and you will find "x".

180 - 68 - 66 =

46°

Answer:

Step-by-step explanation:

-3x - 2y = -20

3x + y =    10

-y = -10

y = 10

3x + 10 = 10

3x = 0

x = 0

(0, 10)