Factorise all of the questions.
Please answer a b c and d and please give an explanation on how to work each question out! It would really help ! It’s very urgent ty

2 ± √3 is the number that must be added in order to complete the square.

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

Given: x² + 4x + 1

We have to determine the number that must be added in order to complete the square

= x² + 4x + 1 = 0

= x² + 4x + 4 - 3 = 0

= (x- 2)² - (√3)² = 0

= ((x - 2) - √3)((x - 2) + √3) = 0

=  (x - 2 - √3)(x - 2 + √3) = 0

x = 2 ± √3

Hence, 2 ± √3 is the number that must be added in order to complete the square.

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A correct stacked bar chart would show store location on the horizontal axis, and the percentage of time spent on each task on the vertical axis. Each store location would be represented as a separate bar, with each bar displaying the percentage of time spent on each task as stacked sections within the bar.

A stacked bar chart is a type of graph that is used to visualize data. It is a bar chart that displays the relative contribution of different data points to the whole. It is particularly useful for comparing the contribution of different data points across different categories. For example, a stacked bar chart can be used to show the percentage of time spent on different tasks at different store locations. The horizontal axis would represent the store locations, while the vertical axis would represent the percentage of time spent on each task. Each store location would then be represented as a separate bar, with each bar displaying the percentage of time spent on each task as stacked sections within the bar. The colors used to represent each task can be used to make the chart more visually appealing, and help viewers differentiate between the tasks. The stacked bar chart is a useful tool for analyzing data over multiple categories, and can be used to quickly identify trends and patterns.

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The complete question is

which of the following shows a correct stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis Store Location Task

well, as I see it Person1 is faster than Person2, but Person2 doesn't factor in the issue here, let's nevermind Person2.

most of the procedures are 45mins each, namely on average they're 45 mins each.

so Person1 say did 9 procedures, but two of those guys took much longer, too 2 hours each, so two procedures alone ate 4 hours.

Now, Person1 besides doing those two really long procedures, has to also finish the other seven, 2 + 7 = 9, so there are 7 more procedures that on average take 45 mins each.

[tex]\stackrel{\textit{\LARGE minutes}}{\stackrel{\textit{two really long ones}}{240}~~ + ~~\stackrel{\textit{the rest of them}}{45(7)}}\implies 555\implies \stackrel{\textit{9 hours and 15 minutes}}{9.25~hours}[/tex]

The maximum profit is achieved when the company produces 2861 units of the product.

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

P(x) = 103 - 0.018x

C(x) = 650 + 90x

The profit function is given as

p(x) = x * P(x) - C(x)

So, we have

p(x) = 103x - 0.018x² - 650 + 90

p(x) = 103x - 0.018x²  - 560

See attachment for the graph

From the graph, we have

Maximum value of x = 2861

Hence, the maximum number of units is 2861

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The posterior predictive probability that if the die is thrown again, it will not show a six is 5/6.

(a) The likelihood for the observed data is P(k=6|Data) = (1/16)*(1/6)^1 * (5/6)^1 = 5/96. The maximum likelihood estimate for k is 6.

(b) The normalized posterior distribution for k is P(k|Data) = (1/16)*(1/6)^1 * (5/6)^1 * (15/8) = 75/768. The posterior mean for k is 4.5.

(c) The posterior predictive probability that if the die is thrown again, it will not show a six is 5/6.

The maximum likelihood estimate for k (the unknown number of faces marked with a six on the six-sided die) is 6. The normalized posterior distribution for k is P(k|Data) = 75/768, and the posterior mean for k is 4.5. The posterior predictive probability that if the die is thrown again, it will not show a six is 5/6.

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The bisection method up to five iterations and finding the root to 2 decimal places for the following would be 2.19

Bisection technique

By continuously reducing the interval in which the root is located, the bisection method roughly approximations the root of a function. The procedure first evaluates the function at the interval midway before swapping out the interval's end with a new one that has the same sign.

The beginning range, in this case, is [1, 3], and f(1) > 0 and f(3) 0. (1+3)/2 = 2 represents the interval's midpoint. The interval endpoint (0) that had f(x) > 0 is replaced with the midpoint (2) when we evaluate f(2) and discover that f(2) > 0. The new midpoint is x = 5/2, and the new interval is [2, 3]. The first iteration is now complete.

Iterations

2nd iteration: f(5/2) < 0 ⇒ interval is [2, 5/2]; midpoint is 9/4

3rd iteration: f(9/4) < 0 ⇒ interval is [2, 9/4]; midpoint is 17/8

4th iteration: f(17/8) > 0 ⇒ interval is [17/8, 9/4]; midpoint is 35/16 ≈ 2.19

5th iteration: f(35/16) < 0 ⇒ interval is [17/8, 35/16]; midpoint is 69/32 ≈ 2.16

The approximate root of 2.16 is revealed by the fifth iteration, but that is not an option for the solution. We think this is the response you're searching for because the fourth iteration yields a root that is around 2.19.

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The full question:

What is the root of the following equation using the bisection method correct to three places of decimal f(x) =x3-3x-5?

Answer:

156

Step-by-step explanation:

10% of x=24

100% of x=24*10

x=240

3/4x=180

65% of x=0.65*240=156

Answer:156

Step-by-step explanation:

The volume of the large container is given as follows:

113.04 in³.

The ratio of the volumes is of:

B) 2.25

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The diameter of the smaller cylinder is of:

4 inches.

Hence the diameter and radius of the larger container is of:

As the height of the cylinder is of 4 inches, the volume is given as follows:

V = 3.14 x 3² x 4

V = 113.04 in³.

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Answer:

Amaka passes hers 2/3

Step-by-step explanation:

she just will

The determinant of the matrix A, where A is [1 1 47 1 2 2 1 2 5 2], is -13. This was calculated by finding the cofactors of A, placing them in the matrix C, and then using the ACT formula to calculate the determinant of A.

C=

[1 -2 -2

-1 1 1

-47 -2 -2]

ACT=1⋅1⋅1+(-2)⋅2⋅1+(-2)⋅5⋅2=1+(-4)+(-10)= -13

The determinant of A is -13.

1. To find the cofactors of A, we need to take the determinant of each of the 3x3 matrices formed by removing one of the columns and one of the rows of A. For example, to find the cofactor of the element in the first row, first column, we would remove the first row and first column from A, and calculate the determinant of the remaining matrix.

2. We can then place the cofactors in the matrix C, which would look like this:

C=

[1 -2 -2

-1 1 1

-47 -2 -2]

3. To calculate the determinant of A, we can use the ACT formula:

ACT=1⋅1⋅1+(-2)⋅2⋅1+(-2)⋅5⋅2=1+(-4)+(-10)= -13

Therefore, the determinant of A is -13.

The determinant of the matrix A, where A is [1 1 47 1 2 2 1 2 5 2], is -13. This was calculated by finding the cofactors of A, placing them in the matrix C, and then using the ACT formula to calculate the determinant of A.

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Answer:

2 -> 4

7 -> 29

10 -> 44

13 -> 59

Kasey's claim that her model is a good fit for the data is best supported by a correlation coefficient of r = 0.91. The correct answer would be an option (B).

A correlation coefficient (r) is a number between -1 and 1 that measures the strength and direction of a linear relationship between two variables.

A coefficient of r = 1 indicates a perfect positive linear relationship, meaning as one variable increases, the other variable also increases.

A coefficient of r = -1 indicates a perfect negative linear relationship, meaning as one variable increases, the other variable decreases.

A coefficient of r = 0 indicates no linear relationship between the variables.

In this case, a coefficient of r = 0.91 is close to 1 which means that there is a strong positive linear relationship between the data and the model. On the other hand, the other coefficients -0.25, 0.01, and -0.79 are not close to 1, which means that there is no or weak linear relationship between data and the model.

Hence, the correct answer would be an option (B).

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Three skeins are the most Sharon can afford to purchase because a number of skeins have to be a whole number.

For her sister's birthday present, Sharon has a budget of no more than $25. Sharon is therefore limited to spending no more than $25. She has paid $14.99 for a knitting machine for her. She wants to get her sister some yarn skeins to go with it as well. Cost per skein is $2.75. Let y be the number of yarn skeins.

The necessary inequality is:

14.99 + 2.75y ≤ 25

2.75y ≤ 25 - 14.99

2.75y ≤ 10.01

y ≤ 10.01 / 2.75

y ≤ 3.64

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Answer:

The answer is 5x-2

Step-by-step explanation:

3x-(2-2x)

3x-2+2x

5x-2

The coordinates given in the question are not provided. Without the coordinates it's impossible to graph the line and determine which statement is true.

It is important to have the coordinates to graph the line, and then we can determine if the line is a proportional relationship by looking at the slope of the line, if it is a constant value then it represent a proportional relationship.

The statement A and B are incorrect, as passing through the origin does not determine whether the relationship is proportional or not.

C and D are correct, whether the line passes through the origin or not, it can be determined if it represents a proportional relationship by looking at the slope of the line.

Please provide the coordinates in order to proceed with the question.

The length of the missing sides for given angles are

What is Pythagoras' Theorem?

Pythagoras' Theorem is a fundamental result in Euclidean geometry named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In other words, if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the theorem can be written as:

c² = a² + b²

tan A = a/c

c = a / tan A

We know that a = 100 and tan A = 100

so c = a / tan A = 100/100 = 1

We also know that b = 100

Now we can use the Pythagorean Theorem to find a:

a² + b² = c

100^2 + 100^2 = 1²

10000 + 10000 = 1

20000 = 1

a = sqrt(20000) = √(2000) × √(10) = 140.7107 × 10[tex]{}^{1/2}[/tex] = 141.42135

So,

side a = 141.42135

side b = 100

side c = 1

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Answer:

A 30 dogs and 48 cats

Step-by-step explanation:

The ratio of cats to dogs in the local shelter is 5 to 8, which means for every 5 cats, there are 8 dogs. If we assume that the total number of cats and dogs in the shelter is a multiple of the ratio, we can find the possible numbers of cats and dogs. In option A, the number of cats and dogs is 30 dogs and 48 cats which is a multiple of the ratio. 59 = 45 and 89 = 72 which is the closest to the number of cats and dogs in option A. Thus, option A shows the possible numbers of cats and dogs in the local shelter.

The probability of choosing, without replacement, another white marble is 16/27

The probability of choosing another white marble can be calculated as follows:

From the problem it can be deduced that, there are 17 white marbles out of a total of 28 marbles (11 green + 17 white),

The probability of choosing a white marble

= 17 / 28

After the first white marble is chosen, the total number of marbles decreases to 27 and the number of white marbles decreases to 16.

The probability of choosing another white marble without replacement is = 16/27.

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It is true that the hypothesis test for the population mean must be a one-tailed test having the rejection region in the lower tail, which is on the left hand of the sampling distribution.

A one-tailed test is basically a hypothesis test which help us to test whether the given sample mean would be higher or will be lower than the population mean. The rejection region is basically the area for which the null hypothesis is rejected.

When we perform a left tailed test for our hypothesis, that is the lower tail hypothesis, then the rejection region will lie in the left tail after the critical value and since in the given question, the mean wait for the services will be less than 15 minutes, we will have to perform a one-tailed rest which has a rejection region present in the lower left hand tail.

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The equation that represents the graph through the data points in the table is Option K: y = 6x - 8.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The data points are given in the table.

The first equation is -

y = x²

Substitute the value of y = 40, as given in the table -

40 = x²

x = √40

x = 6.32

The value for x is obtained as 6.32 when y is 40.

This value does not corresponds with the values in the table.

Therefore, equation y = x² is incorrect.

The second equation is -

y = 6x - 8

Substitute the value of y = 40, as given in the table -

40 = 6x - 8

x = (40 + 8)/6

x = 48/6

x = 8

The value for x is obtained as 8 when y is 40.

This value corresponds with the values in the table.

Therefore, equation y = 6x - 8 is correct.

The third equation is -

x + y = 10

Substitute the value of y = 40, as given in the table -

x + 40 = 10

x = 10 - 40

x = -30

The value for x is obtained as -30 when y is 40.

This value does not corresponds with the values in the table.

Therefore, equation x + y = 10 is incorrect.

The fourth equation is -

x - y² = 0

Substitute the value of y = 40, as given in the table -

x - (40)² = 0

x = 0 + 1600

x = 1600

The value for x is obtained as 1600 when y is 40.

This value does not corresponds with the values in the table.

Therefore, equation x - y² = 0 is incorrect.

The fifth equation is -

x² - y² = 0

Substitute the value of y = 40, as given in the table -

x² - (40)² = 0

x² = 0 + 1600

x = √1600

x = 40

The value for x is obtained as 40 when y is 40.

This value does not corresponds with the values in the table.

Therefore, equation x² - y² = 0 is incorrect.

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It will cost the company $321,400 to produce 14,300 items.

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

To predict how much it will cost to produce 14,300 items, you need to substitute 14,300 for q in the expression 18q+64000.

So, 18q + 64000 becomes 18(14300)+64000 = 257400+64000 = 321400

Therefore, it will cost the company $321,400 to produce 14,300 items.

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1) The amount of money invested at 15% = $30,000

2) The amount of money invested at 5% = $20,000

What is the amount invested?

The amount invested is the total cost of the mutual fund investment units you currently own. Amount Invested = Number of Units x Purchase NAV. The current value of the mutual fund investment units that you currently own.

To solve this problem, we need to set up and solve a system of equations. Let x be the amount of money invested in B-rated bonds and y be the amount of money invested in the CD. We know that:

x + y = $50,000 (the total amount of money invested must equal $50,000)

0.15x + 0.05y = $5,000 (the total interest earned must equal $5,000)

Now we can use the first equation to solve for one of the variables in terms of the other. If we subtract y from both sides of the first equation, we get:

x = $50,000 - y

We can substitute this expression for x into the second equation to get:

0.15($50,000 - y) + 0.05y = $5,000

Solving for y, we get:

y = $20,000

Now we can substitute this value back into the first equation to find the value of x:

x = $50,000 - $20,000

x = $30,000

Therefore, Betsy should invest $30,000 in B-rated bonds and $20,000 in a CD to earn exactly $5,000 in interest per year.

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The statement that would NOT be of concern when considering the nature criteria for evaluating secondary data is the relationships examined should be taken into account. Thus, option D is the answer

While it is important to take relationships into account when analyzing data, this statement is not specific to evaluating secondary data, but rather a general principle of data analysis.

The other statements listed  are all relevant concerns when evaluating secondary data, as secondary data may not always be directly relevant or appropriate for the current problem, and it is important to assess the accuracy and usefulness of the data for the present study.

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Answer:

Area_shaded

= 340.9 cm^2

Step-by-step explanation:

Find the area of the circle, then subtract the area of the triangle.

The 25cm side of the triangle is a hypotenuse of the right triangle. It is also the diameter of the circle.

The radius of the circle is 1/2 the diameter. So the radius is 1/2•25, or 12.5cm

We need the radius to find the area of the circle.

Area_circle

= pi•r^2

= pi•12.5^2

= 490.9 cm^2

The two legs of the triangle can serve as our base and height to find the area of the triangle.

Area_triangle

= 1/2b•h

= 1/2(20)(15)

= 150 cm^2

Subtract.

490.9 - 150

= 340.9cm^2

The area of the shaded region is 340.9cm^2.

The angle CFD is 67.6 degrees.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given that ∠CFE=177 degrees.

We have to find angle CFD.

∠CFD+∠EFD=117

4z+74+9z+64=117

13z+138=117

13z=21

z=-1.6

Now substitute in ∠CFD =4(-1.6)+74

∠CFD =-6.4+74

=67.6 degrees

Hence, the angle CFD is 67.6 degrees.

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The total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex]  is 10275.

The total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex]  is given by

[tex]$n= \sum_{a=0}^{10}\sum_{b=a}^{10}\sum_{c=b}^{10} 1$$= \sum_{a=0}^{10}\sum_{b=a}^{10} (c-b+1)$$= \sum_{a=0}^{10}\sum_{b=a}^{10} c - \sum_{a=0}^{10}\sum_{b=a}^{10} b + \sum_{a=0}^{10}\sum_{b=a}^{10} 1$$= \sum_{a=0}^{10}\sum_{b=a}^{10} 10 - \frac{10(11-a)(a+1)}{2} + \sum_{a=0}^{10} (b-a+1)$$= \sum_{a=0}^{10} 105 - \frac{10(11-a)(a+1)}{2} + \frac{10(a+1)}{2}$$= \sum_{a=0}^{10} \frac{185 + 10a^2}{2}$$= \frac{(185 + 10\times 100) \times 10}{2}$ $= \frac{2055 \times 10}{2}$ $= 10275$[/tex]

Therefore, the total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex]  is 10275.

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Step-by-step explanation:

add 6 and 2 to get 8 and add all the numbers to get 9

The polygon was translated 5 units left and 9 units up using the rule for (x, y) ⇒ (x - 5, y + 9)

Translation is the movement of a point in the coordinate plane either up, left, down or right. Translation is a type of rigid transformation because it preserves both the shape and size of the figure.

Other types of rigid transformations are reflection and rotation.

The points D(5, -10) and T(-9, -6) were translated to give D'(0,-1), T'(-14,3). This means that the translation was 5 units left and 9 units up.

The rule for this translation is (x, y) ⇒ (x - 5, y + 9)

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