Factor 1 - 2.25x8.

(1 - 1.5x 4) 2
(1.5 + x 4)(1.5 - x 4)
(1 + 1.5x 4)(1 - 1.5x 4)

A. The probability that a randomly selected person aged 40 years or older is female and smokes is 0.05841.

B. No, it would not be unusual to randomly select a person aged 40 years or older who is female and smokes.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

When given an event A and an event B, the conditional probability that A will occur given than B has occurred is calculated using this formula -

P(A|B) = P(A and B) / P(B)

Let A be that the person is female and B be that they smoke. It is known that P(B) = 0.295 and let P(A|B) = 0.198.

Use the formula for conditional probability -

0.198 = P(A and B) / 0.295

P(A and B) = 0.198 × 0.295

P(A and B) = 0.05841

The probability that a person aged 40 years or older is female and smokes would happen is 0.05841, which is not less than the usual benchmark of 0.05 to be considered unusual.

Therefore, no, this would not be unusual.

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Suppose there is a 29.5% probability that a randomly selected person aged 40 years or older is a smoker. In addition, there is a 19.8% probability that a randomly selected person aged 40 years or older is a smoker. A. What is the probability that a randomly selected person aged 40 years or older is female and smokes? B. Would it be unusual to randomly select a person aged 40 years or older who is female and smokes?

The solution to the given equation 5x - 2 + x = 9 + 3x + 10 is x = 7.

Given the equation in the question;

5x - 2 + x = 9 + 3x + 10

Solve for x, first collect and add like terms

5x - 2 + x = 9 + 3x + 10

5x + x - 2 = 3x + 10 + 9

Add 5x and x

6x - 2 = 3x + 10 + 9

Add 10 and 9

6x - 2 = 3x + 19

Add 2 to both sides

6x - 2 + 2 = 3x + 19 + 2

6x = 3x + 21

Subtract 3x from both sides

6x - 3x = 3x - 3x + 21

3x = 21

Divide both sides by 3

3x/3 = 21/3

x = 21/3

x = 7

Therefore, the value of x is 7.

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The minimum monthly income of full time worker  is $6112.

Full time worker = 4 weeks of 40 hour per week.

Part time worker = 2 weeks of 40 hour per week.

The full time hourly wage will be:

= $6112/(4 × 40)

= $6112/160

= $38.2

The part time hourly wage will be:

= $6112/(2 × 40)

= $6112/80

= $76.4

An additional child will impact the family budget as it will lead to lesser amount of money spent by each person.

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Graph A is not a function as its ordered pairs have the same first coordinate for different y coordinates.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is not a function if two distinct ordered pairs have the same first coordinate, (a, b), (a, c) is not a function.

The graph of A has an x value of - 3 and has different y values hence it is not a function.

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To derive the distribution of W, we need to find the cumulative distribution function (CDF) of W, F_W(w), and then find its probability density function (PDF), f_W(w).

a) The distribution of the random variable W = Y^2:

The cumulative distribution function (CDF) of W is given by F_W(w) = P(W <= w), where W is the random variable defined as W = Y^2.

Since Y has a uniform distribution on the interval (0,1), its CDF is given by:

F_Y(y) = 0, for y < 0.

= y, for 0 <= y <= 1.

= 1, for y > 1.

Therefore, the CDF of W = Y^2 is:

F_W(w) = P(Y^2 <= w)

= P(0 <= Y <= sqrt(w))

= F_Y(sqrt(w))

= sqrt(w), for 0 <= w <= 1.

= 1, for w > 1.

Thus, the CDF of W is a monotonically increasing function that maps the interval [0, 1] to [0, 1].

The probability density function (PDF) of W is given by f_W(w) = dF_W(w)/dw. The PDF of W can be found by differentiating the CDF:

f_W(w) = dF_W(w)/dw

= d(sqrt(w))/dw

= 1/(2*sqrt(w))

f_W(w) is defined only for 0 <= w <= 1.

b) The distribution of the random variable W = Y^(1/2):

The CDF of W = Y^(1/2) is given by F_W(w) = P(W <= w), where W is the random variable defined as W = Y^(1/2).

Using the same argument as in part (a), we have:

F_W(w) = P(Y^(1/2) <= w)

= P(0 <= Y <= w^2)

= F_Y(w^2)

= w^2, for 0 <= w <= 1.

= 1, for w > 1.

The PDF of W = Y^(1/2) can be found by differentiating the CDF:

f_W(w) = dF_W(w)/dw

= d(w^2)/dw

= 2w

f_W(w) is defined only for 0 <= w <= 1.

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The payment (future value), to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is​ R9,338.80.

The future payment to be made at the end of the seventh year is determined by computing the future values in two stages.

The first stage computes the future value before the payment at the end of the first year.  The second stage computes the future value for six years.  

The future value is computed by compounding the present value at an interest rate.

Current debt = R6,421,00

Compound interest rate = 11% per year

Compounding period = Quarterly

N (# of periods) = 4 quarters (1 year x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R6,421.00

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R7,156.98

Total Interest = R735.98

Future Value (FV) = R7,156.98

Payment in one year's time = R2,287.00

Balance = R4,869.98

N (# of periods) = 24 quarters (6 years x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R4,869.98

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R9,338.80

Total Interest = R4,468.82

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Answer:

3 dollars for

Step-by-step explanation:

The cost of a donut is $0.5.

The cost of donut holes is $0.041

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 6 is an equation.

We have,

x = cost of a donut

y = cost of donut holes

Cleo:

$25 to purchase 2 bags of donut holes and 4 dozen donuts.

This can be written as,

(2 x 12)y + (4 x 12)x = 25

24y + 48x = 25 ______(1)

Gavin:

$20 to buy 4 bags of donut holes and 3 dozen donuts.

This can be written as,

(4 x 12)y + (3 x 12)x = 20

48y + 36x = 20 ________(2)

Now,

From (1) and (2),

Multiplying 2 on (1).

48y + 96x = 50

48y + 36x = 20

(-)     (-)       (-)

        60x = 30

             x = 30/60 = 1/2 = 0.5

Now,

24y + 48x = 25

Substituting x = 1/2

24y + 48 x 1/2 = 25

24y + 24 = 25

24y = 25- 24

y = 1/24

y = 0.042

Thus,

$0.5 = cost of a donut

$0.042 = cost of donut holes

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Answer:

60th term is 347

Step-by-step explanation:

This is an arithmetic sequence with common difference = -1 - (-7) = 5 - (-1) = 11 -5 = 6

The nth term for such a series is given by
aₙ = a₁ + d(n-1) where d = common difference and a₁ is the first term

Here d = 6, a₁ = -7

So

aₙ = -7 + 6(n-1)

aₙ = -7 + 6n-6

aₙ = 6n-13

60th term is

a₆₀ = 6(60) - 13 = 360 - 13 = 347

The lifeguard covered distance of 14 feet to save the victim. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, also referred to as "arithmetic operations," are said by mathematicians to be able to describe all real numbers. The four mathematical operations of division, multiplication, addition, and subtraction result in the terms quotient, product, sum, and difference, respectively.

We are given that a life guard is sitting 8 feet on the observation chair and he notices someone struggling at 6 feet beneath the pool.

So, the total distance he travelled is 8 + 6 = 14 feet

Hence, the lifeguard covered distance of 14 feet to save the victim.

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Order of fractions from smallest to largest:

If sorted we first equate the denominator to 40.

21/40, 29/40, 34/40, 30/40, 32/40

So if sorted from smallest to largest, the order becomes:

21/40, 29/40, 3/4, 4/5, 17/20

If sorted we first equate the denominator to 35. it becomes:

40/35, 65/35, 84/35, 98/36, 37/35

So if sorted from smallest to largest, the order becomes:

37/35, 8/7, 13/7, 12/5, 14/5

If sorted we first equate the denominator to 30. it becomes:

20/30, 24/30, 12/30, 21/30, 27/30

So if sorted from smallest to largest, the order becomes:

2/5, 2/3, 7/10, 4/5, 9/10

If sorted we first equate the denominator to 30. it becomes:

126/30, 65/30, 125/30, 66/30, 39/30

So if sorted from smallest to largest, the order becomes:

13/10, 13/6, 11/5, 25/6, 21/5

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The value of the angle m/G is 118 degrees

It is important to note that the sum of the angles in a triangle is equivalent to 180 degrees.

From the information given, we have that;

Add the angles, we get;

8x + 14 + 3x - 6 + x + 16 = 180

collect like terms

8x + 3x + x = 180- 14 + 6 - 16

add or subtract like terms, we get;

12x = 156

Make 'x' the subject of formula by dividing both sides by the coefficient

x = 156/12

Divide the values

x = 13

m/G = 8(13) + 14

m/G = 118 degrees

Hence, the angle is 118 degrees

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Answer:

  no

Step-by-step explanation:

You want to know if the equation y = 3x +1/5 represents a proportional relation.

A proportional relation has the equation ...

  y = kx

for some constant of proportionality k.

The added constant +1/5 in the given equation means the relation is Not Proportional.

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Answer: 35%

Explanation:

1 - 0.65 = 0.35

0.35 in percentage is 35%

The required, we end up paying 60% of the original price.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
If an item is marked down by 25%, then its sale price is 75% of its original price.

If the sale offers an additional 20% off clearance items, then the final sale price is 80% of the sale price.

Multiplying these two percentages, we get:

Final price = 80% of 75% of the original price

Final price = 0.80 × 0.75 × original price

Final price = 0.6 × original price

So the final price that you pay is 60% of the original price.

Therefore, we end up paying 60% of the original price.

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Answer:

93cm

Step-by-step explanation:

6789 = 73 * length

length = 6789/73=93

Answer:

The length is 93 cm.

Step-by-step explanation:

We know that area is width times height. So, if we don't know what the length is,

Let x = the length

The equation would be

[tex]73x=6789\\[/tex]

We multiply 73 by x because of the formula talked about previously.

Now, lets  divide 73 on both sides

[tex]x = 93[/tex]

As a result, the combo meal includes 4 onion rings and 8 pizza buns.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Let x be the number of onion rings in the combination meal and y be the number of pizza rolls. We can write the following system of equations to represent the given information:

40x + 80y = 800 (the total calories of the meal)

y = x + 4 (the number of pizza rolls is 4 more than the number of onion rings)

We can substitute the second equation into the first equation to solve for x:

40x + 80(x + 4) = 800

40x + 80x + 320 = 800

120x = 480

x = 4

We can use this value to find y:

y = x + 4 = 4 + 4 = 8

So, the combination meal contains 4 onion rings and 8 pizza rolls.

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The farmer should place the two fence pieces at an angle of 90 degrees (perpendicular) against the barn wall to maximize the area of the resulting triangular enclosure.

When all the sides are the same length, or when the object is genuinely a square, the area will be at its greatest for a given perimeter.

But a square is still a rectangle! Therefore, to find the length of each side if you know the perimeter, divide it by four. To get the area, multiply the length by the breadth.

For the problem, a right triangle with legs of equal length will have the maximum area among all right triangles with equal perimeter.

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Answer:

  [9, 9+√18.25] ≈ [9, 13.272]

Step-by-step explanation:

You want the range of f(x)= 9+√(6+7x-x^2), determined algebraically.

The range is the set of values that f(x) may take on. It is the vertical extent of the graph. Here, it will be limited by the possible values the radical may have.

The expression under the radical is a quadratic that opens downward. It will have a maximum at its vertex, and a minimum usable value of 0.

The vertex of the quadratic can be found by putting it in vertex form:

  -x² +7x +6 = -(x² -7x) +6 = -(x² -7x +(7/2)²) +6 +(7/2)² = -(x -7/2)² +18.25

The maximum value the quadratic may have is 18.25.

Then the range of values that f(x) may have is ...

  9 +0 ≤ f(x) ≤ 9 +√18.25

The range is [9, 9+√18.25] ≈ [9, 13.272].

Answer:

-22

Step-by-step explanation:

-9x^0-13

=-9×1-13

=-9-13

=-22

Answer:

-22

Step-by-step explanation:

To solve the expression

Let's start by finding the value of 'x'

[tex] - 9 {x}^{0} - 13[/tex]

Hint: Any number raised to power 0 is always 1.

Therefore x⁰ = 1

let's rewrite the expression by substituting where x is with 1

[tex] - 9(1) - 13[/tex]

[tex] - 9 \times 1 = - 9[/tex]

[tex] - 9 -13 = - 22[/tex]

The required covariance between the variable and correlation coefficient are -2.8 and -0.38.

a. To calculate the covariance, we'll first find the mean of both variables, x and y:

mean of x = (11 + 13 + 27 + 22 + 30) / 5 = 20

mean of y = (28 + 26 + 25 + 20 + 16) / 5 = 22

Next, we'll find the deviations of each x and y value from their respective means:

x deviations: -9, -7, 7, 2, 10

y deviations: 6, 4, 3, -2, -6

Finally, we'll multiply the deviations of x and y for each pair of values and take the average of these products:

covariance = ( (-9 * 6) + (-7 * 4) + (7 * 3) + (2 * -2) + (10 * -6) ) / 5 = -2.8

So, the covariance between the variables x and y is -2.8.

b. To calculate the correlation coefficient, we'll divide the covariance by the standard deviation of x and y:

standard deviation of

x = [tex]\sqrt{\frac{(((11 - 20)^2 + (13 - 20)^2 + (27 - 20)^2 + (22 - 20)^2 + (30 - 20)^2)}{5} }[/tex] = 8.3666

standard deviation of

y = [tex]\sqrt{\frac{(((28 - 22)^2 + (26 - 22)^2 + (25 - 22)^2 + (20 - 22)^2 + (16 - 22)^2)}{5} }[/tex]= 3.87298

correlation coefficient = covariance / (standard deviation of x * standard deviation of y) = -2.8 / (8.3666 * 3.87298) = -0.381

So, the correlation coefficient between the variables x and y is -0.38.

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The y - intercept of the graph is,  5

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 5) and (8, -2).

Now,

Since, The equation of line passes through the points (0, 5) and (8, -2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 2 - 5) / ( 8 - 0)

m = - 7 / 8

Thus, The equation of line with slope - 7/8 is,

⇒ y - 5 = - 7/8 (x - 0)

⇒ y - 5 = - 7/8x

⇒ y = - 7/8x + 5

Therefore, The y - intercept of the graph is,  5

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[tex](3-2)^2+(7+5)(3-2)=(3-2)(3-2)+(7+5)(3-2)=(3-2)(3-2+7+5)=1*13=13[/tex]

Answer: The statement "d. The total cost is $4,950.00 since $27.50×180 = $4,950.00" is incorrect.

The first step is to convert the dimensions of the floor from feet to yards. Since 1 yard = 3 feet, the length of the floor is 15 feet / 3 feet/yard = 5 yards, and the width of the floor is 12 feet / 3 feet/yard = 4 yards. The total area of the floor is 5 yards * 4 yards = 20 square yards.

The total cost per square yard for carpet and installation is $27.50 + $4.15 = $31.65.

The total cost for carpet and installation for the entire floor is 20 square yards * $31.65/square yard = $633.00.

So, the statement "b. The total cost is $633.00 since $31.65×20 = $633.00" is correct.

Step-by-step explanation:

As a result, the volume of the revolution solid is roughly -62.83π cubic units.

Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. As a result, the fish tank has a volume of 6 cubic feet.

Here,

The region R is the upper half of a circle centered at the origin with a radius of 5. By the method of washers, the volume of the solid of revolution obtained by revolving R about the x-axis can be found by subtracting the volume of a cylinder of height "h" and radius "x" from the volume of a cylinder of height "h" and radius "sqrt(25-x²)".

The volume of a cylinder of height "h" and radius "r" is given by V = πr²h.

So, the volume of the solid of revolution can be expressed as:

V = ∫π(sqrt(25-x²)²- x²) dx from x=0 to x=5

Evaluating this integral, we get:

V = π(∫(25-x²)*0.5 dx - ∫x² dx) from x=0 to x=5

Using substitution and integrating, we can obtain the volume:

V = π * (5 * (2 * sqrt(25 - x²) - x²/2))

Evaluating the expression at x=5, we get:

V = π * (5 * (2 * sqrt(25 - 25) - 25/2))

V = π * (5 * (0 - 25/2))

V = -62.83π cubic units.

So, the volume of the solid of revolution is approximately -62.83π cubic units.

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The sinusoidal function have the following features:

Amplitude: 1

Period: 2π

Frequency: ω = 2π / 2π = 1

Herein we find an example of a sinusoidal function, whose definition is shown below:

f(x) = A · sin (2π · x / T + Φ) + x'

Where:

The frequency (ω) is equal to the following formula:

ω = 2π / T

If we know that the sinusoidal function f(x) = sin (x + π / 2) - 2, then the amplitude, the period and the frequency, that is, the features of the sinusoidal function, are, respectively:

Amplitude: 1

Period: 2π

Frequency: ω = 2π / 2π = 1

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The expression for the number of sundaes shop owner needs to sell in September is 3x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, the ice cream shop owner wants to triple her sale of sundaes from August to September.

If the ice cream shop owner sold x sundaes in August, then she will sell

3×x=3x sundaes in September.

Therefore, number of sundaes shop owner sold in September is 3x.

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Answer: B = 9 cm, C = 15 cm

Step-by-step explanation:

If the ratio of A to B to C is 2:3:5, we can write:

A = 2x

B = 3x

C = 5x

and all we have to do is solve for x.

Since we know A = 2x = 6, we have 2x = 6 and x = 3.

So for B we can plug in 3x = 3(3) = 9 cm

And for C we can plug in 5x = 5(3) = 15 cm

If you put these numbers in a ration, 6:9:15 and reduce as much as possible, you'll see you get 2:3:5.

The average velocity is 0.1 meters per second.

The displacement of a body during a period of time divided by the passage of time yields the average velocity of the body during that period. Therefore, if a particle travels along a specific displacement vector AB between times t₁ and t₂, its average speed is:

Here we have

At time t in seconds, a particle's distance s(t), in cm, from a point is given in the table.  

t     0    3     6    10     13

s(t)  0   72   92   144  180    

As we know

Average velocity = [ Total distance ]/[ Total time]    

From the given table,

The total distance traveled up to t = 10, = 144 - 72 = 72

As we know 100 cm = 1 meter

=>  72 cm = 72 × 1/100 = 0.72 m

The total time from t = 3 to t = 10, = 10 - 3 = 7  

Average distance = 0.72/7 = 0.10 meter per sec  

Therefore,

The average velocity is 0.1 meters per second.  

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