Pre calc

Solve e^2x +3e^x- 28=0

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 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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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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Cap rate (going in) = 5.6%

The estimated value of this property = 17,85,714.2 $

The needed rate of return is the rate of return that investors are looking for on assets that are similar. The value of the property and the needed rate of return are inversely related. Property value will fall as the needed rate of return rises, and the opposite is also true.

given cash flow is $100,000 and it increases by 5400$ every year hence growth rate would be 5.4 %.

Cash flows = $1,000,00

Growth rate = 5.4%

Required rate of return = 11%

the required rate of the property = cash flow / ( Required rate of return - growth)

the required rate of the property = 100,000 / (11 -5.4 ) = 17,85,714.2 $

Cap rate (going in) = Required rate of return - a growth rate of the property

Cap rate (going in) = (11 - 5.4) %

Cap rate (going in) = 5.6%

Thus, it can be concluded that the decrease in the required rate of return is the cause of the increase in the value of the property.

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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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Answer:

Step-by-step explanation:

-3x - 2y = -20

3x + y =    10

-y = -10

y = 10

3x + 10 = 10

3x = 0

x = 0

(0, 10)

The composite solid has a volume equal to 2268π cubic feet.

In this problem we have the case of a solid as a result of the combination of a cylinder and a hemisphere. The volume formulas for the cylinder and the hemisphere are, respectively:

Volume of cylinder

V = π · r² · h

Volume of hemisphere

V = (2π / 3) · r³

Where:

Volume of the composite solid:

V' = π · r² · h + (2π / 3) · r³

If we know that r = 9 ft and h = 22 ft, then the volume of the composite solid is:

V' = π · (9 ft)² · (22 ft) + (2π / 3) · (9 ft)³

V' = 2268π ft³

The volume of the composite solid is equal to 1053π cubic feet.

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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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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

Answer: B, Percent

Step-by-step explanation: The formula to find a whole after a percent is:

Worth = Part percent * Wole number / 100

This is the same as the definition says, "the amount or part that results from the base multiplied by the rate."

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.

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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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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The time it takes for the stone to fall in the air is 7 seconds, and it takes 5 seconds for the stone to fall in the water in the seabed.

The average speed of the stone in air is shown here as 16 m/s.

The average speed of the stone in water is 3 meters per second.

The total distance from the top of the cliff to the seabed is 127 meters.

Total fall time = 12 seconds

Therefore

Let t1 represent the time spent by the stone in the air and

t2 = time spent by the stone in water

Now using the equations of motion we get :

Therefore, t₁ + t₂ = 12 s........(1)

16·t₁ + 3·t₂ = 127............(2)

From (1) t₁ = 12 - t₂

16×(12 - t₂) + 3×t₂ = 127

13t2 = 65 is the result.

and t2 equals 5 seconds

t1 = 12 - t2 = 12 - 5 = 7 sec

The time it takes for the stone to fall in the air is t1 = 7 seconds.

The time it takes for the stone to fall into the water is t2 = 5 seconds.

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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:

26

Step-by-step explanation:

One leg measures 7.

One leg measures 8.

a² + b² = c²

7² + 8² = c²

c² = √113 = 10.630 = 11

perimeter = 7 + 8 + 11

perimeter = 26

Answer:

Step-by-step explanation:

2. Unit Rate: 1:2

3. A class has 26 kids. Johnny is trying to figure out the number of ears everyone has in total. You can use the ration 1:2. For every kid there are 2 ears. Therefore there are 52 ears total. [tex]\frac{1}{2}=\frac{26}{52}[/tex]

4. Multiplication

5. No, you can't have half an ear

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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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.

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.

M(x, c) M(x, d) dx is equivalent to = b M(x, c) dx + M(x, d) dx. So, by demonstrating that the two sides of a rectangle are equal, we have established Green's Theorem. The sum of rectangles theorem. Since each region can be as nearly approximated by a sum of rectangles as desired, Green's Theorem must apply to all regions.

It looks like the integral is

[tex]\int\limits^0_c {xy} + x^{2} y^{3} \, dy[/tex]

Let's close the loop by adding a line integral over the line segment joining (1, 4) to (0, 0). Then the closed loop is the triangular region

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x}

Since the integrand has no singularities over or on the boundary of T, we have by Green's theorem

Compute the double integral:

From this result, we subtract the line integral over the extra line segment we added. Parameterize this path by

C' : {(1 - t, 4 - 4t) : 0 ≤ t ≤ 1}

The line integral over C' is

[tex]\int\limits^1_0 {(256t^{5} }+1280t^{4}+ 2560t^{3} - 2564t^{2} + 1288t - 260) \, dt[/tex]

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.

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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 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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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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An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function f(x) = x^2.

This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous. At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.

The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.

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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:(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).

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:

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 desired equation is then y -4 = 12/15 (x -9)

Equations of degree 1 are linear equations. It is the straight line's equation. A linear equation with parameters a and b equal to zero has the conventional form ax+by+c = 0.where a ≠ 0 and b ≠ 0.

We need this line's equation in the point-slope form, y - k = m. (x - h).

The point (h, k) in the point-slope form shown above can be chosen at random from the two points (9, 4) and (-6, -8). In the above point slope form, the other point is thus denoted by (x, y):

Let (x, y) be and (h, k) be (9,4). (-6,-8). Consequently, y - k = m(x - h) becomes

-8-4 = m (-6-9), so that -12 = m(-15), and the slope is thus m = 12/15

The desired equation is then y -4 = 12/15 (x -9) (which is in point-slope form).  

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