P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
What is P(J)?
O 0.1105
O 0.8143
O 0.8895
O 0.1857

Answer:

Set your calculator to degree mode.

Please sketch the figure to confirm my answer.

cos(38°) = 320/d

d•cos(38°) = 320

d = 320/cos(38°) = 406.1 feet

The State Cash Flow Statement using the direct method.

                                                         OP                       INV                  FIN

Personnel emolument                  2,000,000

CRF charges                                 1,000,000

Statutory revenue allocation       20,000,000

Proceeds from sale of fixed assets                          100,000

Purchase of marketable securities                           50,000

Purchase & construction of fixed assets                  500,000

Share of VAT                                 200,000

Share of excess crude oil            100,000

Internally generated revenue    10,000,000

Gratuities and pension              15,000,000

Miscellaneous income                50,000

Overhead expenses                   36,000

Recurrent grant made                20,000

Miscellaneous expenses          10,000

Servicing & repayment of public debts                                            100,000

Grants & subventions from NGO                                                     200,000

Proceeds from loan & other borrowings                                         300,000

Dividends received                                                                           100,000

                                            12,234,000             -450,000              500,000  

  Net Cash Flow for the year ended 31 December 2006: 12,284,000  

To prepare the State Cash Flow Statement using the direct method, we'll classify cash flows into three categories: Operating Activities (OP), Investing Activities (INV), and Financing Activities (FIN). Then, we'll calculate the net cash flow for each category and add them together to find the net cash flow for the year.

Operating Activities:

(-2,000,000 - 1,000,000 + 20,000,000 + 200,000 + 100,000 + 10,000,000 - 15,000,000 + 50,000 - 36,000 - 20,000 - 10,000) = 12,234,000

Investing Activities:

(100,000 - 50,000 - 500,000) = -450,000

Financing Activities:

(-100,000 + 200,000 + 300,000 + 100,000) = 500,000

Net Cash Flow for the year ended 31 December 2006:

12,234,000 (Operating Activities) - 450,000 (Investing Activities) + 500,000 (Financing Activities) = 12,284,000

The above answer is in response to the question below;

The following information has been extracted from the records of WELFARE STATE of Nigeria for the year ended 31 December 2006:

Personnel emolument                  2,000,000

CRF charges                                 1,000,000

Statutory revenue allocation       20,000,000

Proceeds from sale of fixed assets  100,000

Purchase of marketable securities  50,000

Purchase & construction of fixed assets  500,000

Share of VAT                                 200,000

Share of excess crude oil            100,000

Internally generated revenue    10,000,000

Gratuities and pension              15,000,000

Miscellaneous income                50,000

Overhead expenses                   36,000

Recurrent grant made                20,000

Miscellaneous expenses          10,000

Servicing & repayment of public debts      100,000

Grants & subventions from NGO               200,000

Proceeds from loan & other borrowings       300,000

Dividends received                                       100,000

You are required to:

Prepare the State Cash Flow Statements for the year ended 31 December 2006 using the direct method approach (ICAN May 2008)

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The matrix formed by performing the row operation 4R₂ + R₃ — R₃ will result to R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

performing the row operation 4R₂ + R₃ — R₃, we have;

4(-6) + (-9) = -33 {row 3 column 1}

4(5) + 4 = 24 {row 3 column 2}

4(-1) + (-5) = -9 {row 3 column 3}

4(8) + 0 = 32 {row 3 column 4}

Therefore, the matrix formed by performing the row operation 4R₂ + R₃ — R₃ will give a new one with R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]

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Answer:

[tex]=\left(x-2\right)\left(x-3\right)\\[/tex]

Step-by-step explanation:

Given:

[tex]x^2-5x\:+6[/tex]

To find:

Equivalent to x^2-5x+6

Explanation:

[tex]x^2-5x+6\\=\left(x^2-2x\right)+\left(-3x+6\right)\\=x\left(x-2\right)-3\left(x-2\right)\\\mathrm{Factor\:out\:common\:term\:}x-2\\=\left(x-2\right)\left(x-3\right)[/tex]

Final Answer:

(x-2)(x-3)

The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.

The percentage increase can be determined by finding the difference or the amount of increase in sales.

This difference is divided by the previous month's sales and multiplied by 100.

The total number of boxes of cookies Molly's Scout Troop sold last month = 148

The total number sold this month = 165

The increase = 17 (165 - 148)

Percentage increase = 11.5% (17 ÷ 148 x 100)

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mean = 11+20+38+5+4/5 = 78/5 = 15.6

Answer:  A and yes

Step-by-step explanation:

1.  A is the answer. You must balance an equation.  Whatever you do to one side you have to do to the other side. There are no like terms to combine on one side so C, D are out.

2.  Yes, because the equations are balance and will get same answers

Answer:

Step-by-step explanation:
To test the null hypothesis that the proportion of red light runners is the same at both intersections, we can use a two-sample z-test for proportions.

Let p1 be the proportion of red light runners at the first intersection, and p2 be the proportion of red light runners at the second intersection. We want to test the null hypothesis:

H0: p1 = p2

against the alternative hypothesis:

Ha: p1 ≠ p2

We can use the following formula to calculate the test statistic:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of red light runners at the two intersections, and n1 and n2 are the sample sizes.

For the first intersection, we have x1 = 24 and n1 = 127. For the second intersection, we have x2 = 29 and n2 = 164.

The pooled sample proportion is:

p_hat = (x1 + x2) / (n1 + n2) = (24 + 29) / (127 + 164) = 0.167

The test statistic is:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2)) = (0.189 - 0.177) / sqrt(0.167 * (1 - 0.167) * (1/127 + 1/164)) = 0.99

Using a standard normal distribution table, we can find that the probability of getting a z-value of 0.99 or greater is 0.160. Since this is greater than the significance level of 0.01, we fail to reject the null hypothesis.

Therefore, we cannot conclude that the proportion of red light runners differs between the two intersections.

According to the information, the dilated rectangle would have the dimensions of 2.66cm on the side and 5cm on the base.

To calculate the dimensions of each side of the dilated figure we must identify the dilation factor. In this case it is 3, so we must divide the length of each side into the number of the expansion factor as shown below:

According to the above, the dilated rectangle would remain with the dimensions of 2.66cm on the side and 5cm on the base.

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3.) The quantity of students that are in the P.E class would be = 31 students.

4.) The number of students that ran 1 mile in under 9 minutes would be = 6 students.

For question 3.)

To calculate the quantity of students, all the values in the frequency column is added together. That is;

Total number of students= 6+2+8+6+9 = 31 students.

For question 4.)

To calculate the number of students that ran 1 mile in less than 9 minutes would be the time range of 8.00-8.59 minutes = 6 students.

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Answer:

2x³-5x² - 2x + 1

Step-by-step explanation:

We are given

f(x) = 2x³ - 5x²

g(x) = 2x - 1

and asked to find (f - g)(x)

(f - g)(x) is nothing but f(x) - g(x)

(f- g)(x) = f(x) - g(x) = 2x³-5x² - (2x - 1)

= 2x³-5x² - 2x + 1

Note that adding one pair does not make the table a function. This is why it is trickly. For the table to be a function, each value of x must be related to only one unique value of y and vice versa.

For the table to become a function, we must eliminate any repeated ordered pairs such as (3, 8) and (7, 8)

For example, we can say (3, 6) and (7, 8) then pick the last to be (5, 10)

So the table becomes a function when you have:

X    Y

6     0

3     6

9     12

7     8
5     10

The word linear function in mathematics refers to two separate but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

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The converse of the statement "A → B: If x = 3, then x + 8 = 11" is Option(c) which is "B → A: If x + 8 = 11, then x = 3."

The "Converse" of a "conditional-statement" can be expressed by interchanging the hypothesis and the conclusion of "original-statement".

In this case, The "conditional-statement" is given to be "A → B: If x = 3, then x+8=11", which is read-as that if "x" is equal to 3, then expression "x + 8" is equal to 11.

So, The converse statement would say that if "x + 8" is equal to 11, then x must be equal to 3.

Therefore, the correct option is (c).

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The percentage of time that the machine will dispense from 7. 5 oz to 7. 9 oz is 62.47% of the time.

Find the Z-scores for both 7. 5 oz and 7. 9 oz :

Z = ( X - μ ) / σ

For 7. 5 oz :

Z = ( 7.5 - 7.6 ) / 0.2

Z = -0. 1 / 0. 2

Z = -0. 5

For 7.9 oz:

Z =  (7. 9 - 7.6 ) / 0.2

Z = 0. 3 / 0. 2

Z = 1. 5

Using the z - values from the table, the percentage of time is:

0.9332 - 0.3085 = 0.6247

= 62. 47 %

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The solution of the inequality, log₂ 2m > log₂ (m + 5) is {m | m > 5 / 2}.

An inequality is an expression that have <, >, ≤ and ≥ . Therefore, let's solve the logarithmic inequality for the variable m.

Hence,

log₂ 2m > log₂ (m + 5)

Therefore, let's divide both sides by log₂.

Hence,

2m > m + 5

subtract m from both sides of the inequality

2m > m + 5

2m - m > m - m + 5

2m > 5

divide both sides by 2

2m / 2 > 5 / 2

Therefore,

m > 5 / 2

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The correct answers are:

They are inverses of one another

They are symmetric over the line y=x

When a number is too big or too little, exponential notation can express it as a single number and 10 increased to the power of the appropriate exponent.

The exponential form [tex]y=5^x[/tex]

The logarithmic form [tex]y = log_5\ x[/tex] are inverse functions of each other.

If we [tex]y = 5^x[/tex], then [tex]x = log_5\ y[/tex].

As long as x is a real number and y is positive, this is true for any value of x and y.

The graphs of [tex]y = 5^x[/tex] and [tex]y = log_5\ x[/tex] are symmetric over the line y = x.

We obtain the other graph by reflecting the first graph across this line.

Over the line y = x, the inverse functions are always symmetric.

If we swap the x and y coordinates of any point on one graph, we get a comparable position on the other graph.

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a) If two similar solids have a scale factor of 2 : 5, the ratio of their volumes is 8:125, expressed in the lowest terms.

b) If cone with volume 2625 m³ is dilated by a scale factor of 15, the volume of the resulting cone is 10,640,625 m³.

(a) When two solids are similar, their corresponding linear dimensions are in the same ratio, which is known as the scale factor. For example, if two similar solids have a scale factor of 2:5, it means that the corresponding sides of the two solids are in the ratio 2:5.

The volume of a solid is proportional to the cube of its linear dimensions. Therefore, if the linear dimensions of two similar solids are in the ratio 2:5, the ratio of their volumes would be:

(2/5)³ = 8/125

(b) The volume of a cone is given by the formula:

V = (1/3)πr²h

where V is the volume, r is the radius, and h is the height of the cone.

When a cone is dilated by a scale factor of k, its linear dimensions increase by a factor of k, and its volume increases by a factor of k³. Therefore, if the volume of a cone is V and it is dilated by a scale factor of k, the volume of the resulting cone would be:

V' = k³V

In this case, the volume of the original cone is given as 2625 m³, and it is dilated by a scale factor of 15. Substituting these values in the formula, we get:

V' = 15³(2625)

V' = 15³(2625/1)

V' = 10640625

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Answer: C: 5/8

Step-by-step explanation:

Simply 5/8 of the bar is filled in

Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.

Here, we have,

Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.

Positive Outcomes/Total Results = x/n = Probability(Event)

Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.

Here in the question,

Total region = 8.

Shaded region = 5

So, probability of falling in the shaded region = 5/8

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Answer:

Phone dies in 6 hours

Step-by-step explanation:

The value of the length of line segment AB, in feet, that corresponds to the width of the television is,

⇒ 12 feet

We have to given that;

A new curved projection system for a small media room states the optimal viewing angle is 74° (m/ACB = 74°) when you sit 10 feet from the center of the TV (length of CD = 10 ft). The depth of the curved screen is 2 feet (length of DE = 2 ft).

Now, We can formulate;

CE = 10 - 2 = 8 feet

∠ACD = 74/2 = 37°

Hence, We can formulate;

tan 37° = AE / CE

0.75 = AE / 8

AE = 0.75 × 8

AE = 6

Hence, The value of the length of line segment AB, in feet, that corresponds to the width of the television is,

⇒ AB = 6 x 2

⇒ AB = 12 feet

Thus, The value of the length of line segment AB, in feet, that corresponds to the width of the television is,

⇒ 12 feet

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Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Graphical methods are commonly used for determining whether the data support an interpretation of mixing of two potential sources or fractionation of a single source.

A graphic solution can be done by hand (on graph paper), or with the use of a graphing calculator. Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross).

GIVE NICE GUY BRAINLINEST PLEASE

We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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The sum of both numbers is 107/12

One number is 6 3/4

The other smaller number is 2 1/6

The sum of both numbers can be calculated as follows

= 6 3/4 + 2 1/6

= 27/4 + 13/6

= 162 + 52/24

= 214/24

= 107/12

Hence the sum of both numbers is 107/12

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Answer:

5,340x.095=507.3

507.3÷5=101.46

101.46÷12=$8.45 interest

5,340÷5=1068

1068÷12= $89

89+8.45=$97.45

answer $97.45 a month

The weight of the empty tank is given as follows:

4 pounds.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The weight of the empty tank is the intercept of the function, which is of b = 4, hence:

4 pounds.

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Answer:

4/5

Step-by-step explanation:

Answer:

[tex]\dfrac{\left(12x-56\right)x}{\left(x-4\right)\left(-x^2+20x-32\right)}[/tex]

Step-by-step explanation:

Simplify

[tex]\dfrac{\dfrac{16}{x-2}-\dfrac{4}{x-4}}{\dfrac{16}{x}-\dfrac{x-4}{x-2}}[/tex]

The first-level numerator is
[tex]\dfrac{16}{x-4}-\dfrac{4}{x-2}\\\\\\= \dfrac{16(x-4) - 4(x - 2)}{(x-2)(x-4)}\\\\\\= \dfrac{16x -64 - 4x + 8}{(x-2)(x-4)}\\\\\\= \dfrac{12x -56}{(x-2)(x-4)}[/tex]

The first-level denominator is
[tex]\dfrac{16}{x}-\dfrac{x-4}{x-2}\\\\\\= \dfrac{16(x-2) - x(x-4)}{x(x-2)}\\\\\\\\= \dfrac{16x - 32 -x^2 +4x}{x(x-2)}[/tex]

[tex]= \dfrac{-x^2+20x-32}{x\left(x-2\right)}[/tex]

Therefore
[tex]\dfrac{\dfrac{16}{x-2}-\dfrac{4}{x-4}}{\dfrac{16}{x}-\dfrac{x-4}{x-2}}\\\\\\= \dfrac{12x -56}{(x-2)(x-4)} \div\dfrac{-x^2+20x-32}{x\left(x-2\right)} \\\\\\[/tex]

Use the fraction rule: [tex]\dfrac{a}{b} \div \dfrac{d}{c} = \dfrac{a}{b} \cdot \dfrac{d}{c}[/tex]

[tex]= \dfrac{12x -56}{(x-2)(x-4)} \cdot \dfrac{x(x-2)}{-x^2 +20x -32}}[/tex]

The (x-2) term cancels out resulting in:
[tex]\dfrac{\left(12x-56\right)x}{\left(x-4\right)\left(-x^2+20x-32\right)}[/tex]

The circumference of the circle with a radius of 10 cm is 20π cm, option (C) is correct.

A circle's perimeter, or the distance encircling it, is known as its circumference. It is determined by multiplying the circle's diameter by pi. But in this case, we are given the radius of the circle, which is half of the diameter.

To get a circle's circumference, use the following formula:

C = 2πr

where;

r = radius of the circle

π = mathematical constant pi (approximately equal to 3.14).

Given the radius of the circle as 10 cm, we can use the formula to find its circumference:

C = 2πr

C = 2π(10 cm)

C = 20π cm

Hence, option C is correct.

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The correct question is:

What is the circumference of the circle with radius = 10 cm (leave your answer of π).

A) 10π cm

B) 5π cm

C) 20π cm

D) 10π cm