Instructions: Match each equations with correct type of event.
P(A) · P(BA)
P(A) + P(B)
PA and B)
P(A)
P(A) · P(B)
P(A) + P(B) - P(A and B)

The part that represents the solution to the inequality will be Part B shaded below first line and above second line.

From the information given, the equation of the first line will be:

y - 3 = (-3 - 3/2 + 4)(x + 4)

y - 3 = -1(x + 4)

y + x = -4 + 3

x + y = -1

The equation of the second line will be:

y + 3 = -1(x + 4)

y = x + 4 - 3

y = x + 1

This is plotted on the graph attached.

From the systems of equations, the statement that is correct about the two systems of equations is that They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.

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The value of (fg)(x)= 3x³+ x²

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x) = -3x+1

g(x) = [tex]x^{2}[/tex]

Now, (fg)(x)

=f(x) * g(x)

=  (-3x+1) * ([tex]x^{2}[/tex])

=-3x³+ x²

Hence, (fg)(x)= 3x³+ x²

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The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the distance from the man side of the house to the gutter is 15 m, since the drainpipe comes in lengths of 2.5 m, hence:

Number of drainpipe needed = 15 m / 2.5 m = 6

The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.

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The required quantity of drainpipe is mathematically given as six.

L=6

Generally, Let's say the distance from the male side of the house to the gutter is 15 meters. Since the length of the drainpipe typically comes in increments of 2.5 meters, we may reason as follows:

In conclusion, The required quantity of drainpipe is equal to 15 meters divided by 2.5 meters, which is equal to six.

L=15/2.5

L=6

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Answer:

12x^7+15x^6

Step-by-step explanation:

Change 3x^3-2 to 3x

(x^4)(3x)(4x^2+5x)

Multiply your single terms

(3x^5)(4x^2+5x)

Then distribute

12x^7+15x^6

The inequality is represented by y < 5/3(x+1)

Use the information about the straight line and find the equation of the line.

Given coordinates (-3,-4) and (0,1), we can find the slope

Slope,  

Change in y = y2 – y1 = 1-(-4) = 5

Change in x = x2 – x1 = 0-(-3) = 3

Therefore, Slope (m) = Change in y / Change in x = 5/3

Equation of line using m = 5/3 and points (0,1) and (x, y) in form of y = mx + c

Y – 1/ X – 0 =5/3

3(Y-1) = 5(X)

3Y -3 = 5X

3Y = 5X + 3

Y = 5X + 3/3

Y = 5/3(X + 1)

To find the inequality take a point in the shaded region and check it in the above equation.

Given Options

a. y < Five-thirds x – 2

b. y < Negative five-thirds x + 1

c. y > Five-thirds x + 2

d. y > Negative five-thirds x + 2

 Let’s take points (-3,-4) for verification

  Option a: y < 5/3 (x-2)

                     -4 < 5/3(-3-2)

                      --4 < -3.33

-4 is less than -3.33

Thus option a is in the shaded region

 Option b: y < -5/3 (x+1)

                     -4 < -5/3(-3+1)

                      --4 < 3.33

-4 is less than 3.33

Thus option a is in the shaded region

 Option c: y > 5/3 (x+2)

                     -4 > 5/3(-3+2)

                      --4 > -1.67

-4 is NOT GREATER than -1.67

Thus option c is NOT in the shaded region

Option d: y > -5/3 (x+2)

                     -4 > - 5/3(-3+2)

                      --4 > 1.67

-4 is NOT GREATER than 1.67

Thus option d is NOT in the shaded region

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Answer:

y > Five-thirdsx + 2

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

-|1-2|2+7

-|-1|9

-9×1

-9

The income statement illustrates that the net income will be $3530.

The income statement will be:

Revenue

Consulting revenue 18350

Expenses

Miscellaneous expenses 720

Rent expense 4820

Salaries expense 8370

Telephone expenses 910

Total expenses 14820

Net income = 18350 - 14820 = 3530

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Answer:

(x-5)²+(y+7)²=36

or

x²+y²-10x+14y+38=0

The value of the temperature in function notation is gotten as; f(x) = 91 - 11x

Let us first find the relationship between temperature and how long the turkey sits out.

The temperature after the normal 390 minutes  is equal to approximately 6.5 hours.

Let us create a ratio and solve for x, which represents the temperature change during that extra hour after the "normal time sitting out".

Thus;

(7.5/6.5) = (80/80+ x)

Solving for x gives x = -10.7.

This means that for every extra hour it sits out, the turkey cools approximately 11°. When we add that to 80°, we have 91° which is the expected temperature after 390 minutes (6.5 hours) of sitting out.

Thus, the motion as a function of time is;

f(x) = 91 - 11x

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Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For the binomial distribution, the parameters are given as follows:

n = 100, p = 0.5.

Hence the mean and the standard deviation of the approximation are given as follows:

Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is one subtracted by the p-value of Z when X = 66.5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{66.5 - 50}{5}[/tex]

Z = 3.3

Z = 3.3 has a p-value of 0.9995.

1 - 0.9995 = 0.0005.

0.0005 = 0.05%

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The part of the trinomial that will equal the product of p and q is the constant part

The expression is given as:

(x + p)(x + q)

From the expression, p and q are both constants.

When a constant is multiplied to another, the result is a constant

This means that:

pq = constant

Hence, the part of the trinomial that will equal the product of p and q is the constant part

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The graph that represents h(x) is option B: On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). ....

Using the piecewise function, one can see that;

In x ≤ 0, the slope of the graph of h(x) = 1/4

In 0 < x ≤ 3, the slope of the graph of h(x) = 1/3

In x ≥ 4, the slope of the graph of h(x) = 1/2

Note that the movement is left to right and the slope of h(x) often increases and the slope of the graph is said to become steeper.

Option B shows the graph of h(x) as it best tells the exact point of various aspect of the function.

Therefore, The graph that represents h(x) is option B: On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, 0) and goes up to (6, 1).

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A firm should go out of business in the long run when its price level is less than the average total cost.

The long run is a period where all factors of production are varied. It is known as the planning time of a firm. In the long run, if the if the average total cost is greater than the price, the firm should exit the market.

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The maximum profit will be 956 birrs for both cows and sheep.

The amount of money earned by any seller on the cost price is called the profit.

Given that:-

From the given data we can see that the total number of animals cows and sheep is 16.

C + S = 16

To raise a cow need 2 Br

To raise Sheep need 5 Br

The number of sheep is 12 and cows 4.

So the amount required to raise sheep and cows is:-

Sheeps = 12 x 2 = 24 Br

Cows = 4 x 5 = 20 Br

Total = 44 Br

The selling price of cows and sheep are 100 and 50 Br.

Cows = 100 x 4 = 400Br

Sheeps = 50 x 12 = 600 Br

Total = 1000 Br

So the profit will be calculated as follows:-

P = 1000 - 44 = 956 Br

Therefore the maximum profit will be 956 birrs for both cows and sheep.

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Answer: Option (2)

Step-by-step explanation:

We need the angle to be included between the two mentioned sides.

Also, the sides need to be corresponding for the ratio, and both sides of the triangle need to be in either the numerators or the denominators.

Answer:

B -o.60

Step-by-step explanation:

34 - 40 = -6.  -6 divide by 10 = -3/5 or - 0.6. So answer is B

Answer:

3,36 in^2

Step-by-step explanation:

The geometric shape shown in image is called a trapezoid

to calculate the area of a trapezoid we use the following formula:

1/2*(a+b)*h (a and b are bases, h: height)

bases are 1.3 and 3.5 and height is 1.4

1/2(1.3 + 3.5)*(1.4) = 3,36 the area is stated in square units so the answer is

3,36 in^2

Answer:

[tex] {( \sqrt{ {x}^{ - 3} }) }^{5} = ({( {x}^{ - 3}) }^{ \frac{1}{2} } ) ^{5} \\ \\ = {x}^{ - 3 \times \frac{1}{2} \times 5} = {x}^{ - \frac{15}{2} } = \frac{1}{ {x}^{ \frac{15}{2} } } [/tex]

Or ;

[tex] {( \sqrt{ {x}^{ - 3} } )}^{5} = {( \sqrt{ \frac{1}{ {x}^{3} }} })^{5} = ( { \frac{ \sqrt{1} }{ \sqrt{ {x}^{3} } } })^{5} \\ \\ = ( { \frac{1}{ \sqrt{x} \sqrt{ {x}^{2} } } })^{5} = ({ \frac{1}{ x\sqrt{x} }})^{5} \\ \\ = ( \frac{ {(1)}^{5} }{ {x}^{5} ( \sqrt{x} )^{5} } ) = \frac{1}{ {x}^{5} \times {x}^{ \frac{1}{2} \times 5 } } \\ \\ = \frac{1}{ {x}^{5} \times {x}^{ \frac{5}{2} } } = \frac{1}{ {x}^{5} \sqrt{ {x}^{5} } } \\ \\ = \frac{1}{ {x}^{5} \sqrt{ {x}^{4} {x}^{1} } } = \frac{1}{ {x}^{5} \sqrt{x} \sqrt{( { {x}^{2} })^{2} } } \\ \\ = \frac{1}{ {x}^{5} {x}^{2} \sqrt{x} } = \frac{1}{ {x}^{7} \sqrt{x} } = \frac{ \sqrt{x} }{ {x}^{8} } [/tex]

The correct option regarding the recursively defined strings is given by:

c) Both i) and ii).

First we start with string 101, we have that:

101 -> 1w -> 10w -> 101

Which belongs to alphabet S.

For string 001, we have that:

001 -> 0w -> 00w -> 001.

Which belongs to alphabet S.

Hence statement c is correct.

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The probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is P=0.77.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Events:

S: success

F: failure

MS: market research forecast a success

MF: market research forecast a failure

The information we have is:

P(S)=0.70

P(F)=0.30

P(S|MS)=0.90

P(F|MS)=0.20

If P(F|MS)=0.20, we can derive that P(F|MF)=0.80. That is, the failed products were predicted to be a failure based on market research 80 per cent of the time.

We also can conclude that P(S|MF)=0.10.

We can calculate the probability of having a forecast of a failure, given that the product is actually unsuccessful as:

[tex]P(MF|F) = \dfrac{P(F|MF)\times P(F)}{P(F|MF)\times P(F)+P(S|MF)\times P(S)}[/tex]

[tex]P(MF|F) =\frac{(0.8\times 0.3)}{0.8\times 0.3)+(0.1\times 0.7}[/tex]

[tex]P(MF|F) =\dfrac{0.24}{0.31}=0.77[/tex]

The probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is P=0.77.

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For the given equation, either 3x + 7 = 0 or x + 7 = 0

Now,

or

So, possible values of x is : -7 and -7/3

[tex](3x + 7)(x + 7) = 0 \\ \\ \\3x + 7 = 0 \\ \\ 3x = - 7 \\ \\ x = \frac{ - 7}{3} . \\ \\ \\ x + 7 = 0 \\ \\ x = - 7.[/tex]

The length of the kitchen in the drawing using the scale factor is: B. 5/6.

We are given a scale factor of 1:24.

Let the length of the kitchen in the drawing = x

Actual length of kitchen = 20 ft.

Using the scale factor, we have:

1/24(20) = 20/24

= 5/6

The length of the kitchen in the drawing is: B. 5/6.

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The total packs the teams bring to each game is 8 packs.

Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷.

Number of packs = 24 ÷ 3 = 8

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The correct answer is option 4 which is f(x) = 2.9|x| is narrower than the parent function f(x) = |x|

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Given parent function is f(x)=|x|

Now we have to find which function from given choices will be narrower than the parent function.

Notice that adding or subtracting some number from the parent function only shifts the graph up, down, and left of the right side.

But that will not make the function narrower or broader.

So f(x) = |x – 2| and f(x) = |x| + 3, can't be the answer.

Multiplying by some positive real number which is more than 1, makes the function narrower.

Only f(x) = 2.9|x| from remaining choices fits that case.

Hence correct answer is option 4 which is f(x) = 2.9|x| is narrower than the parent function f(x) = |x|

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Answer:

D,E

Step-by-step explanation:

Answer:

[tex]\textsf{Zeros}: \quad x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Rewrite the given polynomial in the form ax² + bx + c:

[tex]f(x)=2 \sqrt{3}x^2+5x-4 \sqrt{3}[/tex]

To find the zeros, set the function to zero and solve for x using the quadratic formula.

[tex]\implies 2 \sqrt{3}x^2+5x-4 \sqrt{3}=0[/tex]

Quadratic formula:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore,

Substituting the values into the quadratic formula:

[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2\sqrt{3})(-4\sqrt{3})} }{2(2\sqrt{3})}[/tex]

[tex]\implies x=\dfrac {-5 \pm \sqrt {121}}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {-5 \pm 11}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {6}{4\sqrt{3}}, \:\:x=\dfrac {-16}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {3}{2\sqrt{3}}, \:\:x=-\dfrac {4}{\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]

The sum of the roots of a polynomial is -b/a:

[tex]\implies -\dfrac{b}{a}=-\dfrac{5}{2 \sqrt{3}}=-\dfrac{5\sqrt{3}}{6}[/tex]

The sum of the found roots is:

[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)+\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{5\sqrt{3}}{6}[/tex]

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is:  c/a

[tex]\implies \dfrac{c}{a}=\dfrac{-4\sqrt{3}}{2\sqrt{3}}=-2[/tex]

The product of the found roots is:

[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{12}{6}=-2[/tex]

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.

Answer:

Step-by-step explanation:

Rewrite the given polynomial in the form ax² + bx + c:

To find the zeros, set the function to zero and solve for x using the quadratic formula.

Quadratic formula:

Therefore,

a = 2√3

b = 5

c = - 4√3

Substituting the values into the quadratic formula:

The sum of the roots of a polynomial is -b/a:

The sum of the found roots is:

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is: c/a

The product of the found roots is:

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.

Answer:

[tex]-\frac{3}{10}[/tex]

Step-by-step explanation:

[tex]\frac{2}{5} *-\frac{3}{4} \\=-\frac{6}{20} \\=-\frac{3}{10}[/tex] (Reduced to simplest form.)

Answer:

y= 4x+8

Step-by-step explanation:

Add 12x to both sides.

3y=24+12x

The equation is in standard form.

3y=12x+24

Divide both sides by 3.

3

3y

​

=

3

12x+24

​

Dividing by 3 undoes the multiplication by 3.

y=

3

12x+24

​

Divide 24+12x by 3.

y=4x+8

Using it's concept, it is found that the percentage of his sales that area food costs is of 29.62%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, he has $1643 out of $5546 in food, hence the percentage is given by:

[tex]P = \frac{1643}{5546} \times 100\% = 29.62%[/tex]

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