Find the echelon form of this augmented matrix, written so there are 1's on the diagonal. 1 - 1 2 400 100 900 1 -3 7 - 300​

Answer:

undefined or no slope.

Step-by-step explanation:

m is slope. slope is always change of y over change of x. this mean. y2-y1 divide by x2-x1. in this case y2 is -8, y1 is 5 and x2 is 6 and x1 is 6. remember the number in front the variable are base. the answer is undefined.

domain = all real numbers

range = y > -2

y=x²-2

range is y is -2

domain is x is

y-intercept(s): (0,−2)

Answer:

2

Step-by-step explanation:

The [tex]x^{2}[/tex] and x terms are made to follow the sequence:

[tex][a-b]^{2} =a^{2} -2ab + b^{2}[/tex]

Therefore the [tex]b^{2}[/tex] term has to be added to complete the [tex][a -b]^{2}[/tex] sequence, but at the same time the [tex]b^{2}[/tex] term has to be balanced as it is not originally present in the equation:

[tex]y = x^{2} - 3x + 2 = [(x)^{2} - 2(x)(\frac{3}{2}) + (\frac{3}{2})^{2}] + 2 - (\frac{3}{2})^{2}[/tex]

  [tex]= [x - \frac{3}{2}]^{2} + 2 - \frac{9}{4}[/tex]

  = [tex][x - \frac{3}{2}]^{2} + \frac{8}{4} - \frac{9}{4}[/tex]

  = [tex][x- \frac{3}{2}]^{2} \frac{+ 8-9}{4}[/tex]

  = [tex][x-\frac{3}{2}]^{2} -\frac{1}{4}[/tex]

y-intercept is the y-value obtained when x = 0 in the equation:

[tex]= [0 - \frac{3}{2}]^{2} -\frac{1}{4}[/tex]

= [tex](-\frac{3}{2})^{2} -\frac{1}{4}[/tex]

= [tex]\frac{9}{4} - \frac{1}{4}[/tex]

= [tex]\frac{8}{4}[/tex]

= 2

The factors of given polynomial are (x+3), (x-3), (x+2) and (x-2).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given polynomial is x⁴-13x²+36

Here, x⁴-13x²+36 can be written as x⁴-9x²-4x²+36

= x²(x²-9)-4(x²-9)

= (x²-9)(x²-4)

= (x²-3²)(x²-2²)

By using the identity a²-b²=(a+b)(a-b)

So, (x+3)(x-3)(x+2)(x-2)

Therefore, the factors are (x+3), (x-3), (x+2) and (x-2).

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The minimum length of the box to hold the smaller mirror is 10 inches for largest mirror fits in a box that is 18 inches wide by 20 inches long her smaller mirror.

What is proportion ?

In mathematics, proportion refers to the equality of two ratios. Two ratios are said to be proportional if they have the same relative size, meaning they represent the same relationship between quantities.

For example, if we have two ratios, such as 2/3 and 4/6, they are proportional because they represent the same relationship between two quantities. We can say that 2 is to 3 as 4 is to 6, and we can simplify both ratios by dividing the numerator and denominator of each by their greatest common factor, which in this case is 2.

Since the smaller mirror is similar in proportion to the larger mirror, the ratio of their corresponding sides is the same. Therefore, the width of the smaller box is half of the width of the larger box (9 inches is half of 18 inches).

To find the minimum length of the smaller box, we need to use the same ratio of sides. The length of the larger box is 20 inches, so the length of the smaller box should be half of 20 inches, which is 10 inches.

Therefore, the minimum length of the box to hold the smaller mirror is 10 inches.

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Answer:

The total number of boats Paul counted is 24 speed boats + 5 sail boats + 1 rowboat = 30 boats.

So, the experimental probability that the next boat he sees will be a sailboat is 5 sail boats / 30 boats = 1/6.

The experimental probability of an event is defined as the ratio of the number of times the event occurs to the total number of trials or observations.

In this case, Paul observed a total of 24 + 5 + 1 = 30 boats, of which 5 were sailboats.

Therefore, the experimental probability that the next boat Paul sees will be a sailboat is:

Experimental probability = number of sailboats / total number of boats

Experimental probability = 5 / 30

Experimental probability = 1/6

So the experimental probability of seeing a sailboat next is 1/6 or approximately 0.167.

A circle graph representing the data presented will show half of the students prefer apple juice; while grape, orange juice, and fruit punch are preferred by a lower ratio of students.

A circle graph also known as a pie graph is a visual representation of data based on a circle and its fractions of it. In this way, if 20 out of the 40 students prefer apple juice this means in the circle graph half of it would be for students preferring apple juice.

Based on this, a possible circle graph that represents the data is shown below:

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In the triangle, the nearest whole number of the side t is 28.

The sine rule states that the ratios of the sides to their corresponding opposite angles are equal to a particular value. This value gives the circumradius of that triangle.

The sum of three angles in a triangle is 180°.

Find the angle ∠T for ∠A=46° and ∠D=84°.

∠A+∠D+∠T=180°

46°+84°+∠T=180°

130°+∠T=180°

∠T=50°

The sine rule for triangle ABC is [tex]\[\frac{a}{{\sin A }} = \frac{{37}}{{\sin B }} = \frac{c}{{\sin C }} = 2R\][/tex], where R is the circumradius and a, b, and c are the opposite sides of the angles ∠A, ∠B, and ∠C, respectively.

On applying the sine rule to triangle ADT, the result becomes [tex]\[\frac{a}{{\sin 46^\circ }} = \frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }} = 2R\][/tex].

Take the equation [tex]\frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }}[/tex] and find t.

[tex]\[\begin{array}{l}t = \frac{{37\sin 50^\circ }}{{\sin 84^\circ }}\\ \approx 28.4997\\ \approx 28\end{array}\][/tex]

Therefore, the nearest round whole number of t is 28.

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Answer: Given the ratio of boys to girls at the park is 4 to 5, then there are 4 boys for every 5 girls. If there are 45 girls at the park, then there are 4 * 45 / 5 = 36 boys at the park.

So, the answer is B) 36.

Step-by-step explanation:

Oliver's number is bigger than that of Chen.

It is a number equal to 10 times 10.

Given is that Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds, my number must be bigger.

Oliver number can be written as follows -

8 x 10 x 10

Chens number can be written as follows -

3 x 10 x 10

It can be concluded that Oliver's number is bigger than that of Chen.

Therefore, Oliver's number is bigger than that of Chen.

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The mean, variance, and standard deviation of this sample is 377.5, 7007.5 meters^2 and 83.7 metres respectively. The 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters. we find that the p-value for a t-statistic of -3.61 is less than 0.01.

To calculate the mean, variance, and standard deviation of this sample, we can use the following formulas:

Using the formulas, we get:

Mean = (365 + 350 + 380 + 400 + 395 + 375 + 385 + 380 + 390 + 370 + 360 + 370 + 380 + 370 + 400 + 385 + 375 + 385 + 380 + 375) / 20

= 377.5 meters

Variance = [(365-377.5)^2 + (350-377.5)^2 + (380-377.5)^2 + ... + (380-377.5)^2 + (375-377.5)^2] / (20-1)

= 7007.5 meters^2

Standard deviation = square root of variance = sqrt(7007.5) = 83.7 meters

Therefore, the mean skidding distance is 377.5 meters, the variance is 7007.5 meters^2, and the standard deviation is 83.7 meters.

To estimate the true mean skidding distance of the road with a 95% confidence interval, we can use the following formula:

Confidence interval = sample mean ± (t-value * (standard deviation / sqrt(sample size)))

Here, the sample mean is 377.5 meters, the standard deviation is 83.7 meters, and the sample size is 20. To find the t-value, we need to look it up in a t-distribution table with 19 degrees of freedom. From the table, we find that the t-value for a 95% confidence interval is 2.093.

substituting the values, we get:

Confidence interval = 377.5 ± (2.093 * (83.7 / sqrt(20)))

= 377.5 ± 37.0

Therefore, the 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters.

The assumptions needed for this inference to be valid are:

The sample is a random sample from the population of skidding distances along the road.

The skidding distances follow a normal distribution in the population.

The sample size is large enough (at least 30) or the population standard deviation is known.

To check these assumptions, we can use a normal probability plot to check for normality and calculate the sample size to see if it is large enough. We can also use previous studies or expert knowledge to check if the assumption of normality is reasonable.

To test the logger's claim that the mean skidding distance is at least 425 meters, we can perform a one-sample t-test. The null hypothesis is that the mean skidding distance is 425 meters, and the alternative hypothesis is that it is less than 425 meters.

Using the formula for the t-statistic, we get:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

= (377.5 - 425) / (83.7 / sqrt(20))

= -3.61

From a t-distribution table with 19 degrees of freedom, we find that the p-value for a t-statistic of -3.61 is less than 0.01. Therefore, we reject the null hypothesis and can conclude that there is not enough evidence to support the logger's claim. Therefore, we do not agree with the logger's claim.

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Step-by-step explanation:

you have to be careful when typing questions and particularly formulae and expressions here. automatic text conversion has the habit of transforming e.g. fractions into one line divisions without any brackets.

what your wrote here :

575,000/1 + 4000e^-T = 575,000 + 4000e^-T

that cannot be the function.

I am sure it must be

F(T) = 575,000/(1 + 4000e^-T)

right ?

I am basing the rest of my answer on that assumption.

how many people became ill, when the outbreak began ? that means T = 0.

F(0) = 575,000/(1 + 4000e^-0) =

= 575,000/(1 + 4000×1) =

= 575,000/(4001) = 143.7140715... ≈ 144 people

6 weeks after the outbreak

F(6) = 575,000/(1 + 4000e^-6) =

= 575,000/(1 + 4000/(e^6)) =

= 575,000/(1 + 9.915008707...) =

= 575,000/10.915008707... =

= 52,679.75642... ≈ 52,680 people

limit t -> infinity

F(infinity) = 575,000/(1 + 4000e^-infinity) =

= 575,000/(1 + 4000/(e^infinity)) =

= 575,000/(1 + 0) = 575,000 people

The range of set 1 is 11. The range of set 2 is  208

The wider range of set 2, set 2 contains a wider spread of the given data.

The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.

The set is given in the question, as follows:

Set 1: 1, 4, 6, 8, 10, 12

The maximum value = 12

The minimum value = 1

The range of the set 1 = maximum value - minimum value

Substitute the values in the above formula,

The range of the  set 1  = 12 - 1

Apply the subtraction operation to get the answer

The range of the set 1 = 11

Set 2: 230, 24, 33, 22, 41

Now, the range of the  set 2  = 230 - 22 = 208

Data set 1 has a range of 11, whereas data set 2 has a range of 208.

Therefore, the wider range of set 2, set 2 contains a wider dispersion of data.

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Answer:

t = 21 + (-4)h

Step-by-step explanation:

t = temp. at hour h

h = # of hours past midnight

t = 21° + (-4°/hr)h

The measure of ∠B of the right angle is 152°

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°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

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

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ABC

Now , the measure of ∠A = 2x - 8

The measure of ∠B = 3x + 5

And , angle A and angle B make a right angle

On simplifying the equation , we get

2x - 8 = 90

Adding 8 on both sides of the equation , we get

2x = 98

Divide by 2 on both sides of the equation , we get

x = 49

Substitute the value of x in equation , we get

∠B = 3 ( 49 ) + 5

The measure of ∠B = 152°

Hence , the angle is ∠B = 152°

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The solution is:  (A) y+4=-3(x+6), is the equation of the line in point-slope form.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The point-slope form of the equation of a line whose slope is m and passes through the point (x1,y1) is:

y-y1 = m (x-x1)

Given the point:

(x1,y1) = (-6, -4)

Slope, m= -3

x1 = -6,

y1 =-4

Substituting these values into: y-y1 = m (x-x1) , we obtain the point slope form of the equation:

we get,

y+4=-3(x+6)

The correct option is A.

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complete question:

The graph of a line has a slope of -3 and passes through the point (-6,-4).

What is the equation of the line in point-slope form?

Oy + 4 = -3(x + 6)

y + 6 = -3(x + 4)

y-4 = -3(x-6)

y-6 = -3(x – 4)

The graph of the points on a coordinate plane is added as an attachment

From the question, we have the following parameters that can be used in our computation:

(0.5, -1.5) and (3,5) on the coordinate plane

The description of the points are:

Using the above as a guide, we have the graph as an attachment

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The distance of the point P to the plane is 42/√629 units. The solution has been obtained by using vectors.

What are vectors?

An item with both magnitude and direction is said to contain a vector. An object's motion from one point to another is described by a vector.

We are given three points Q, R and S. So, we will find equation of the plane defined by the three points.

Vector RQ = < 5, 1, -4 >  and RS = < 7, 6, -7>  and their cross product

RQ x RS = < 5, 1, -4 > x < 7, 6, -7> = < 17 , 7, 23>  = n  

This is a vector normal to the plane.

So, the equation of the plane is 17x + 4y + 18z = 139

The distance is calculated using

⇒d = (|A·Mx + B·My + C·Mz + D| )/(√A² + B² + C²)

⇒d = (|-17·3 + (-4)·1 + (-18)·7 + 139|)/((-17)² + (-4)² + (-18)²)

⇒d = 42/√629

Hence, the distance is 42/√629 units.

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The complete question:

Evaluate the expression. 0.3 = -5 - (-0.4 - -0.6) Write your answer as an integer or a decimal. Do not round.​

Solution:

The value of the expression in a decimal form is, -17.33.

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

We have,

0.3x = -5 - (-0.4 - (-0.6))

0.3x = -5 - (-0.4 + 0.6)

0.3x = -5 - 0.2

0.3x = -5.2

x = -5.2/0.3

x = -17.33

Therefore, the value of x is -17.33.

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Answer:

E is a major arc

C is a minor sector

A is a major segment

Major segment is the portion (or part) of the circular region enclosed between a chord and the corresponding major arc.

Major arc is the longer arc connecting two endpoints on a circle.

A sector with a central angle less than 180° is called a minor sector.

Applying the triangle proportionality theorem, QR = 17½.

The triangle proportionality theorem states that when a line is constructed parallel to one side of a triangle and intersects the remaining two sides at two different points, the two sides of the triangle will be divided in equivalent proportions.

Therefore:

SQ/PS = TQ/TR

SQ = 5

PS = 2

TQ = ?

TR = 5

Plug in the values:

5/2 = TQ/5

Cross multiply:

2TQ = 25

TQ = 25/2

TQ = 12½.

QR = TQ + TR

QR = 12½ + 5

QR = 17½

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Answer:

Step-by-step explanation:

The number of Dr. Pepper cans are 39.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Julia bought a total of 52 cans of Dr. Pepper and Sprite.

There were three times as many cans of Dr. Pepper as Sprite.

Let number of sprite cans be x.

Then, the number of Dr. Pepper cans will be 3x.

Now, x+3x=52

4x=52

x=13

So, 3x=39

Therefore, the number of Dr. Pepper cans are 39.

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Answer:

              Based on the measures of the following triangle's angles, the triangle can be classified as an obtuse triangle.

Step-by-step explanation:

              In order to decide which type of triangle this is, first we must understand what an acute, right, and obtuse triangle are. Acute triangles are triangles with all three of its angles less than 90°, right triangles are triangles with one angle that is exactly 90°, and obtuse triangles are triangles with one angle that is greater than 90°. Overall, we can determine the type of this triangle by looking at its angles.

             The given triangle has the angles 25°, 136°, and 19°. Now we can compare it to the rules above and see whether this triangle is acute, right, or obtuse. As the given triangle has an angle that is greater than 90°, we can conclude that the following triangle is an obtuse triangle.

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Answer: [tex]x-75\geq 420[/tex]

Step-by-step explanation:

... as it say...

Answer:

x -75 ⩾ 420

Step-by-step explanation:

we take away 75 from the value of X and compare it to 420 using the greater than or equal sign.

Answer: 4x = 64 or -32/-2

Step-by-step explanation:

you could multiply both sides by 2.

4x = 64

4x/4 = 64/4

x = 16

OR

-2x or -32 to both sides

-32 = -2x

divide both sides by -2

x = -32/-2

x = 16

hope this helps

Answer:(4,-1)

Step-by-step explanation: The vertex is the highest point of the parabola (curved line). The vertex is the point where the parabola crosses its axis of symmetry.

(a) Randomized experiment, (b) There are three criteria for a randomized experiment

a) This is a randomized experiment.

b) The three criteria for a randomized experiment are:

Random assignment, the children were randomly assigned to the xylitol or placebo group.

Control group, a placebo group was used as a control.

Manipulation, the children were given different forms and doses of xylitol or placebo.

c) The explanatory variable is the form and dose of xylitol or placebo given to the children. The response variable is the incidence of ear infections.

d) Diagram of the randomized comparative experiment:

Population of healthy children in daycare centers

↓

Random assignment to xylitol or placebo group

↓

Intervention group: given xylitol in syrup, gum or lozenge form

Control group: given a placebo in gum, syrup or lozenge form

↓

Comparison of incidence of ear infections in intervention and control groups

↓

Analysis of results to determine the effectiveness of xylitol in reducing ear infections.

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