What is the slope of the line that passes through the points (1, 6)(1,6) and (13, 2)(13,2)? write your answer in simplest form.

The probability that  on a randomly selected​ day, he wrote at least one check is 0.3843

A year is made up of 365 days

The number of checks written = 177

λ = 177 / 365

= 0.4849

P(x ≥ 1) = 1 - p(x < 1)

p(x < 1) is going to be 0

so we would have 1 - p(x = 0)

the Poisson distribution is given as

P = e^-λ (λκ) / κ!

This is written as

1 - e^-0.485 x 0.485⁰ / 0!

1 - 0.6157

= 0.3843

The probability that  on a randomly selected​ day, he wrote at least one check is 0.3843

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The median of the following numbers

8, 10, 8, 5, 4, 7, 5, 10, 88, 10, 8, 5, 4, 7, 5, 10, 8 is 8.

Given numbers is

8, 10, 8, 5, 4, 7, 5, 10, 88,10, 8, 5, 4, 7, 5, 10, 8

First you have to organize them in least to greatest order,

4, 5, 5, 7, 8, 8, 8, 10, 10

Second now take these numbers and climate one from each side until you have 1 or 2 numbers left.

that is the

4   5   5   7  8  8    8  10  10

x    x   x   x   !   x    x    x    x

So, the middle number will be the median of the given numbers.

Hence the answer is the median of the following numbers

8, 10, 8, 5, 4, 7, 5, 10, 88, 10, 8, 5, 4, 7, 5, 10, 8 is 8.

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If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Given,

We have to state that the triangles are congruent;

Here,

Congruent state;-

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Conditions for congruent triangles;-

If two triangles satisfy one of the following conditions, they are congruent:

That is,

If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.

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The value of y after solving the pair of similar triangle is 15.

Similar shapes are enlargements of each other using a scale factor.

To find the value of y from the similar triangle below, we use the formula below.

Note: The ratio of the corresponding sides of two similar triangle are equal

Formula:

make y the subject of the equation above

Hence, the value of y is 15

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On testing the hypothesis , We fail to reject the null hypothesis at 5% level of significance.

In the question ,

it is given that ,

sample size (n) is = 50 ,

sample proportion(â) = 18/50 = 0.36

The null hypothesis is given as H₀ : p = 0.3

and the alternate hypothesis is [tex]H_{\alpha }[/tex] : p ≠ 0.3

The z - test statistics can be calculated using the formula

z = (â - p) / √(p(1-p)/n)

Substituting the value â = 0.36 , p = 0.3 and n = 50 ,

we get ,

z = (0.36 - 0.3) / √(0.3(1-0.3)/50)

On simplifying ,

we get ,

z = 0.93

the excel function for the critical value ,

=NORMINV(0.05/2,0,1)

we get , the critical value as 1.96

we can see that the critical value is greater than test statistic value ,

So , we fail to reject null hypothesis at 5% level of significance .

Therefore , On testing given hypothesis , We fail to reject the null hypothesis at 5% level of significance.

The given question is incomplete , the complete question is

A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.

Test the hypotheses H₀ : p = 0.3 versus H₁ : p ≠ 0.3 with α = 0.05  .

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The number that will complete the square to solve equation is 1/36.

What is completing the square?

For some values of h and k, completing the square is an elementary algebraic method for changing a quadratic polynomial of the form

ax^2 + bx + c to the form a^2 + k. In other words, the quadratic expression is completed by inserting a perfect square trinomial.

Consider, the given polynomial

3w^2 - w - 24 = 0

Rewrite the polynomial in the form ax^2 + bx = c

Add 24 on both sides,

3w^2 - w - 24 + 24 = 24

⇒ 3w^2 - w = 24

Divide both sides by 3,

[tex]w^2-\frac{1}{3}w = 8[/tex]

To complete the square x^2 + bx, we add [tex](\frac{b}{2} )^2[/tex]

Here, b = -1/3

So, [tex](\frac{b}{2})^2 = (\frac{-1/3}{2})^2 = (-\frac{1}{6})^2 = \frac{1}{36}[/tex]

Adding to both sides of the equation, we have

[tex]w^2-\frac{1}{3}w+\frac{1}{36} = 8+\frac{1}{36}[/tex]

Hence, the number that will complete the square to solve an equation is 1/36.

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The given statements are true or false as following:

We have given some statements about matrix and subspace and we have to check whether the statements are true or false .

1. True

The columns of U are linearly independent and thus form an orthonormal basis for Col U. So, projcolU y = UU^T*y for all y in R^n.

2. True

The statement is true because y can be written uniquely in the form y = projw y+z where y − projw y is in W and Z is in W⊥ and it follows that Z = projw y

3. True

since z is orthogonal to u1 and to u2 it is orthogonal to every vector in W = Span{u1, u2}, a set that spans W.

4. False

The uniqueness property of the orthogonal decomposition y = y^ + z indicates that, no matter the basis used to find it, it will always be the same.

5. True

For an orthogonal basis of W, B = u1, ..., uP y and projw y can be written as linear combinations of vectors in B with equal weights.

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The Three Kinds of Outliers

All outliers fit into one of three well recognized groups in statistics and data science:

1 Global outliers, type 1 (aka Point Anomalies)

2 Contextual outliers, type 2 (aka Conditional Anomalies)

3 Collective outliers, type 3

Global outliers, type 1

In the same way that "global variables" in a computer program can be accessed by any function in the program, a data point is considered to be a global outlier if its value is significantly outside the bounds of the data set in which it is found.

Contextual (Conditional) Outliers, Type 2

Data points that dramatically differ from other data within the same context are known as contextual outliers. When it comes to time-series data, such as records of a certain number across time, the "context" is nearly always temporal.

Collective outliers, type 3

If a subset of data points inside a data set exhibits values that considerably differ from the overall data set, but the values of the individual data points do not exhibit abnormal behavior either globally or contextually, then the subset is said to be anomalous.

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The change in the accounts receivable is -$373,816.23 if the firm's management wanted its to be done in 35 days.

Here we have to find the change in the accounts receivable.

The given data:

Sales = $ 9,745,923

inventory = $ 2,237,435

cash = $ 755,071

day's sales outstanding(DSO) = 49 days

Formula to find DSO:

DSO = 365/ accounts receivable turnover

        = 365/ ( net sales/ accounts receivable)

        = 365 × accounts receivable/ net sales

Account receivables = DSO × net sales / 365

                                 = 49 × 9,745,923 / 365

                                 = $1,308,356.70

Target DSO = 35 days

Net accounts received = DSO × net sales / 365

                                      = 35 × 9,745,923 / 365

                                      = $934,540.56

ΔAccounts received = $1,308,356.79 - $ 934,540.56

                                  = - $373,816.23

Therefore change in accounts received is -$373,816.23.

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The lower bound and upper bound for Helen's value would be;  3.165, and 3.065.

The circumference is the perimeter of the circle.

Given that the circumference of circle C, at 405 mm to three significant numbers.

Helen correctly estimates the diameter of circle, d, to be 130 mm to two significant numbers.

She wants to find the value of Pi using the formula π=C/D

We have, the circumference of the circle, C = 405 mm

The diameter of the circle, d = 130 mm

π=C/D

π= 405 mm / 130 mm

= 405 / 130

π= 3.115 measured to the nearest 0.1.

The degree of accuracy is nearest 0.1.

Then;

0.1/2 = 0.05

Therefore, Upper bound = 3.115 + 0.05 = 3.165

Lower bound = 3.115 - 0.05 = 3.065

Therefore, the lower bound and upper bound for Helen's value would be;  3.165, and 3.065.

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The value of |x - y| which is not possible is 8.

Here we have to find the value of | x - y| which is not possible.

Given data:

The sides of a triangle are 4,6 and x and the other sides of a triangle are 4, 6, and y.

We know the fact that the sum of the lengths of two sides of a triangle is always greater than the third side.

Let us take the minimum and maximum values of the third side as x and y.

Minimum value is ≥ 6 - 4 that is ≥ 2

Maximum value is ≤ 6 + 4 that is ≤ 10

So, | x - y | ≤ | 10 - 2| that is ≤ 8.

The smallest positive number that is not the possible value of | x - y| is 8.

Therefore the value of | x-y| which is not possible is 8.

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Answer: -2x + 7.20

Step-by-step explanation: This equation is in simplified form, given the fraction is already a mixed number. Since 7 1/5 is a mixed number, we can find the equivalent expression by identifying 1/5 of 100.  

1/5 × 100 = 100/5 ⇒ 20

Finally, we substitute 20 in for 1/5 to find the equivalent expression:

-2x + 7 1/5 ⇒ -2x + 7.20

The birth weight of newborns, measured in grams, is an example of quantitative data. So the option a is correct.

In the given question,

The birth weight of newborns, measured in grams, is an example of .

a. quantitative data

b. either categorical or quantitative data

c. neither categorical nor quantitative data

d. categorical data

The quantitative data means data that is explain in the subjective ways. It is  also explain quantity, amount and range.

Categorical data is a body of knowledge that is organised into categories. For instance, the data obtained when an organisation or agency tries to collect the biodata of its employees is referred to as categorical data.

The birth weight of newborns measured in grams, is an example of quantitative data.

Birth weight is quantitative because it can take on multiple numerical values. So the option a is correct.

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Before buying Christmas presents for her family, Mother had Php 1,025 initially.

How to calculate total money before spending?

To calculate the initial amount before spending add the amount spent and left after spending.

According to the given question:

Mother spent 134.25 on chocolate box, 385.75 on pair of slippers and 235.50 for a shirt.

Therefore total money spent = 134.25 + 385.75 + 235.50 = 755.50

Money left after spending = 269.50

So, the total money mother had initially = 755.50 + 269.50 = 1025

The actual amount mother had was Php 1,025

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An equation for a parabola with x-intercept (-3,0) and (2,0) which pass through the point (1,-20) is  "[tex]5x^2+5x-30[/tex]".

parabola is a major conic section that has wide applications in science and technology. know according to the condition by following intercepts we begin with an equation

                            [tex]y=a(x+3)(x-2)[/tex]

where a is any number that restricts the parabola to pass through (1,-20)

know we have to choose a for what the above equation got its require achievements. substitute (1,-20) in   [tex]y=a(x+3)(x-2)[/tex] we get

                           [tex]-20=a(1+3)(1-2)\\\\-20=a(4)(-1)\\\\a=5[/tex]

substituting a back in the first equation we get the equation of the parabola. so, the parabola has an equation  y= f(x)=[tex]5x^2+5x-30[/tex].

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The probability that there are not enough seats left is given by:

0.15 = 15%.

The probabilities in this problem are given from the discrete probability table, as follows:

There will not be enough seats if:

Exactly 39 or 40 passengers show up.

Hence the probability is given as follows:

p = P(X = 39) + P(X = 40) = 0.1 + 0.05 = 0.15.

The problem asks for the probability that there are not enough sets left.

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If the scale factor is greater than 1, the image is larger than the preimage

Increasing the size of a figure without changing its shape is a process known as dilatation. Dilation can result in a figure growing or shrinking. Preimage is the name for the earliest figure in dilatation. A figure has been magnified  Figures are warped from the center of dilatation, which is a fixed point.

By enlarging or contracting a figure, the scale factor indicates how much the image will change in size.

1) If the scaling factor is between 0 and 1, the picture is smaller than the preimage. With a scale factor of between 0 and 1, reductions are known as dilations.

2) If the scale factor is more than 1, the picture will be bigger than the preimage. When a dilatation has a scale factor higher than 1, it is said to be an enlargement. Each new point in a dilated figure may be located using the prime symbol, ". The dilated version of point, which stands for "prime," would be point'.

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The equation of the line is -3x - y + 2 = 0.

Here, we are given a graph of a line as shown in the image below.

From the graph we can see that the line cuts the y axis at -2. This means that when x = 0, y = -2.

Thus, we get one point, that is, (0, -2)

Similarly, the line cuts x axis at 2/3.

Thus, we get another point, that is, (2/3, 0)

Thus, the slope of the line will be-

(0 + 2)/ (2/3 - 0)

= 2*3/2

= 6/2

= 3

The equation of a line is given as y = mx + c, where m is the slope and c is the y intercept.

Here, m = 3 and c = -2

Thus, equation of the line will be-

y = 3(x) - 2

y = 3x - 2

-3x - y + 2 = 0

Thus, the equation of the line is -3x - y + 2 = 0.

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Your question was incomplete. Check for the missing figure below.

The Formula of Area of Obtuse Triangle is equal to ½ × b× h .

and by using Heron's formula,

A = √(S(S-a)(S-b)(S-c)) ; S = (a+b+c)/2

A closed two-dimensional figure with three sides of equal or unequal length and three corners of equal or unequal angles is called a triangle.

Obtuse triangle: A type of triangle with the following properties:

Area formula of obtuse triangle :

Area of obtuse triangle = ½ × b × h

where b --> base of triangle

h ---> height of triangle.

The area of a triangle can also be found using Heron's formula.

A = √(S(S-a)(S-b)(S-c)),

where s is half the perimeter of the triangle and a, b, c are the three sides of the triangle.

the perimeter of the triangle = a + b + c cm then

S = (a + b + c)/2

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-0.5 < µd< 4.5 are the limits of the given data.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given,

The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores

Before 70 80 92 99 93 97 76 63 68 71 74

After 69 79 90 96 91 95 75 64 62 64 76

Mean        SD          SEM     N

80.27       12.76       3.85     11

78.27       12.92        3.89    11

df = 10

standard error of difference = 0.798

The mean of Before minus After equals 2.00

Given a=0.01, |t(0.005, df=10)|=3.17 (check student t table)

So 99% confidence interval is 2±ts

2±3.17(0.798)

-0.5 < µd< 4.5

Hence, -0.5 < µd< 4.5 are the limits of the given data.

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This study is not well designed because formulas A and B are not compared with the original formula.

Given:

A company famous for its nacho-flavored corn chips has developed two new formulas, A and B, which they hope their customers will like even more than the original formula. To determine whether customers prefer one of the new formulas over the current nacho flavoring, a sample of 50 customers is obtained. Each customer tastes both formula A and formula B in a randomly assigned order and indicates which one they prefer more.

sample customers = 50

But here there is not given a relation or comparing between A and B so we cannot predict which one is prefer more.

Therefore This study is not well designed because formulas A and B are not compared with the original formula.

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All integers higher than or equal to 10 and less than or equal to 20 are included in the domain.

The domain of a function is the set of all possible inputs. The set of all potential values that can be used as inputs, or alternatively, the entire range of possible values for independent variables, constitutes the domain of a function.

As, The domain of a function is the set of all values that can be put into it while assuring that it exists and accepts a real number as a value.

The domain of a function is understood to be the set of values that we are permitted to enter into our function.

This set consists of the x values for a function like f(x).

Hence, the correct answer is the domain consists of all integers greater than or equal to 10 and less than or equal to 20.

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The Complete Question is:

Every day Isabel swims 10 to 20 laps in a 50-meter pool. She tracks the numbers of laps she swims and how long it takes her to complete the laps, in

minutes

Choose the correct answer below.

O A. The domain consists of all integers greater than or equal to 0.

OB. The domain consists of all integers greater than 0 and less than or equal to 20.

OC. The domain consists of all integers greater than or equal to 0 and less than or equal to 20

D. The domain consists of all integers greater than or equal to 10 and less than or equal to 20.

E. The domain consists of all integers less than or equal to 20.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

1 x 96 = 96 (1, 96)

2 x 48 = 96 (2, 48)

3 x 32 = 96 (3, 32)

4 x 24 = 96 (4, 24)

6 x 16 = 96 (6, 16)

8 x 12= 96 (8, 18)

The value of the digit 3 in 3808000 is 3 million.

What are population digits?

A population is a distinct group of individuals, animals, or objects that can be distinguished from one another for the purposes of data collection and analysis in statistics and other branches of mathematics. Data is typically collected from a sample in order to learn more about a large population.

Here, we have

The population of the town is 3808000.

We have to find the value of the digit 3 in 3808000.

We concluded from the given statement is the value of the digit 3 in 3808000 is 3 million.

Hence, the value of the digit 3 in 3808000 is 3 million.

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the dilation factor will change the square of the side 2 units.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

A square with a side length of 2 units is drawn on the coordinate plane with a vertex at the origin.

If a scale factor of 2 is applied to the given square, with point D serving as the centre of dilation

A point is enlarged by a scale factor k according to the following rule:

(x, y) → (kx, ky)

According to this rule, k =2

A(-2, 0) → A'(-4, 0)

B(-2, 2) → B'(-4, 4)

C(0, 2) → C'(0, 4)

D(0, 0) → D'(0, 0)

Hence the dilation factor will change the square of the side 2 units.

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These are the following steps you should follow to create a function table:

By rule since [tex]X^{2} = Y[/tex] or square of input = output

By output since [tex]\frac{x}{5}[/tex] = output

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The probability that the card is greater than 2 but less than 9 is 6 / 13.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.

P ( E )   =   Number of favourable outcomes / Total number of outcomes → 1

In an ordinary deck of cards,

                                                       Queen, King

As per the question,

A card is drawn from an ordinary deck and that is red.

⇒ Total number of red cards in an ordinary deck = 26 cards

∴   Total number of outcomes  = 26

The card that is greater than 2 but less than 9,

⇒ Number of cards that are greater than 2 but less than 9 in red suite = 12

∴  Number of favourable outcomes = 12

Substitute the values in 1,

P ( E )   =   Number of favourable outcomes / Total number of outcomes

            =  12 /26

P ( E )    =  6 / 13

Therefore, 6 / 13 is the probability that the card is drawn in a red suite greater than 2 but less than 9.

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The complete question is

A card is drawn from an ordinary deck and we are told that it is red. What is the probability that the card is greater than 2 but less than 9?

A bacterial culture that starts with 8000 bacteria of population and doubles every 20 minutes will reach 33000 bacteria in 40.887 minutes.

Calculate t in 33,000

33,000 = 8000 (2)^t/20

33,000/8000 = 2^t/20

log(33,000/8000) = (t/20) log2

t = 20 log(33,000/8000) / log 2 = 40.887 minutes.

Hence the time taken to reach 33000 population is 40.877mins.

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The given trigonometric identities can be evaluated as (a) sin(x + y) = (-15 + 6√7)/4√61, (b) cos(x - y) =(5√7 - 18)/4√61  and  (c) tan(x - y) = (-15 - 6√7)/(5√7 - 18).

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

Given that,

The value sin(x) = 3/ 4 for  π/2 < x < π.

And, cot(y) = 5/6  for  π < y < 3π/2.

Since x is given in the second quadrant cos(x) is negative such that,

cos(x) = -√ (1 - sin²(x) )

          = - √(1 - (3/4)²

          = -√7/4

Since, y is in third quadrant sin(y) and cos(y) is negative.

sin(y) = -1/√(1 + cot²(y))

         = -1/√(1 + (5/6)²)

         = -6/√61

Cos(y) =  -√ (1 - sin²(y))

           =  - √(1 - (-6/√61)²

           = -5/√61

tan(x) = sin(x)/cos(x)

         = -3/√7

tan(y) = sin(y)/cos(y)

         = 6/5

Now, the following trigonometric identities can be evaluated as follows,

(a)

sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

Substitute the respective values to get,

sin(x + y) = 3/4 × -5/√61 + -√7/4 × -6/√61

              = (-15 + 6√7)/4√61

(b) cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

                    = -√7/4 × -5/√61 +  3/4 × -6/√61

                    = (5√7 - 18)/4√61

(c) tan(x - y) = (tan(x) - tan(y))/(1 +tan(x)tan(y))

                   = (-3/√7- 6/5)/(1 +-3/√7 × 6/5)

                   = (-15 - 6√7)/(5√7 - 18)

Hence, the required values are sin(x + y) = (-15 + 6√7)/4√61, cos(x - y) =(5√7 - 18)/4√61 and tan(x - y) = (-15 - 6√7)/(5√7 - 18).

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If  she will need to start 2 inches in then total length of ribbon is 25.2 needs.

In the given question, Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3.

2 inches are frayed at one end of the ribbon, she will need to start 2 inches.

Total length of ribbon is 60-inches.

Ratio of pieces = 2:3

Let the one piece length is 2x and other piece is 3x.

So 2x+3x=60

5x=60

Divide by 5, we get

x = 12

Now the length of one piece = 2*12 = 24

Other piece length = 3*12 = 36

Since, 2 inches are frayed at one end of the ribbon, she will need to start 2 inches.

So

=2* (3/2+3)

=2* 3/5

=1.2 inches

So the total length = 24+1.2 = 25.2

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Answer: A (25.2 in)

Step-by-step explanation:
:3