a large rectangle is made by joining 3 identical small rectangles
the perimeter of 1 small rectangle is 21cm
the width of 1 small rectangle is xcm

work out the perimeter of the larger rectangle

The Probability that it will not snow this evening conditional on the barometric pressure dropping, probability is P(¬S | B).

The components of the formula:

P(¬S | B): This formula represents the probability of "not snowing (¬S)" given that "the barometric pressure is dropping (B)." In other words, it calculates the likelihood of it not snowing this evening when we know that the barometric pressure is dropping.

P(¬S & B): This formula represents the probability of "not snowing (¬S)" and "the barometric pressure is dropping (B)" occurring simultaneously. It calculates the joint probability of these two events happening together.

P(B | ¬S): This formula represents the probability of "the barometric pressure is dropping (B)" given that "it is not snowing (¬S)." It calculates the likelihood of the barometric pressure dropping when we know that it is not snowing.

P(S & ¬B): This formula represents the probability of "snowing (S)" and "the barometric pressure is not dropping (¬B)" occurring simultaneously. It calculates the joint probability of these two events happening together.The probability that it will not snow this evening conditional on the barometric pressure dropping," the appropriate formula to represent this probability is P(¬S | B). It specifically considers the probability of it not snowing given that the barometric pressure is dropping.

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Answer:

Brother= 8 years old

sister= 14 years old

Step-by-step explanation:

S : B

x+6 : x

x+6+x=22

2x+6=22

2x=16

x=8

brother is 8 years old

x+6= sisters age

8+6=14 years old is the sister

Answer:

[tex]\textsf{1)} \quad f(x)=-\dfrac{1}{4}(x-2)^2+\dfrac{1}{2}[/tex]

[tex]\textsf{2)} \quad g(x)=-\dfrac{1}{4}(x+2)^2+\dfrac{1}{2}[/tex]

[tex]\textsf{3)} \quad h(x)=\dfrac{1}{4}(x-2)^2-\dfrac{1}{2}[/tex]

[tex]\textsf{4)} \quad p(x)=\dfrac{1}{4}(x+2)^2-\dfrac{1}{2}[/tex]

Step-by-step explanation:

From inspection of the given graph, function f(x) is a parabola that opens downwards. Its vertex is (2, 1/2) and its y-intercept is (0, -1/2).

To determine the equation of f(x), we can use the vertex formula:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

Substitute the vertex (2, 1/2) and the y-intercept (0, -1/2) into the formula to determine the value of a:

[tex]\begin{aligned}y&=a(x-h)^2+k\\\\\implies -\dfrac{1}{2}&=a(0-2)^2+\dfrac{1}{2}\\\\-1&=4a\\\\a&=-\dfrac{1}{4}\end{aligned}[/tex]

Substitute the found value of a and the vertex into the formula to create an equation for f(x):

[tex]f(x)=-\dfrac{1}{4}(x-2)^2+\dfrac{1}{2}[/tex]

[tex]\hrulefill[/tex]

To reflect a function in the y-axis, negate the x-value of each point, but leave the y-value the same:

Therefore, if g(x) is f(x) reflected in the y-axis, replace x with -x:

[tex]\begin{aligned}g(x)&=f(-x)\\\\&=-\dfrac{1}{4}(-x-2)^2+\dfrac{1}{2}\\\\&=-\dfrac{1}{4}(x+2)^2+\dfrac{1}{2}\end{aligned}[/tex]

The vertex of g(x) is (-2, 1/2) and its y-intercept is (0, -1/2).

[tex]\hrulefill[/tex]

To reflect a function in the x-axis, negate the y-value of each point, but leave the x-value the same:

Therefore, if h(x) is f(x) reflected in the x-axis, then:

[tex]\begin{aligned}h(x)&=-f(x)\\\\&=-\left(-\dfrac{1}{4}(x-2)^2+\dfrac{1}{2}\right)\\\\&=\dfrac{1}{4}(x-2)^2-\dfrac{1}{2}\end{aligned}[/tex]

The leading coefficient is positive, so the parabola opens upwards.

The vertex of h(x) is (2, -1/2) and its y-intercept is (0, 1/2).

[tex]\hrulefill[/tex]

If p(x) is g(x) reflected in the y-axis, then:

[tex]\begin{aligned}p(x)&=-g(x)\\\\&=-\left(-\dfrac{1}{4}(-x-2)^2+\dfrac{1}{2}\right)\\\\&=\dfrac{1}{4}(-x-2)^2-\dfrac{1}{2}\\\\&=\dfrac{1}{4}(x+2)^2-\dfrac{1}{2}\end{aligned}[/tex]

The leading coefficient is positive, so the parabola opens upwards.

The vertex of p(x) is (-2, -1/2) and its y-intercept is (0, 1/2).

It  had started at (0,120) and ran for 40 minutes, Coordinates would be approximately (60.00, 103.92).

a) To find the coordinates after 20 minutes of running counter-clockwise starting at (120,0), we need to determine the distance covered in that time period.

Since you are running at a speed of 3 meters per second, in 20 minutes (or 20 * 60 = 1200 seconds), you would have covered a distance of 3 * 1200 = 3600 meters.

Given that the equation of the circular track is x^2 + y^2 = 14400, which represents a circle with a radius of 120 units (since the radius squared is 14400), we can determine your new position on the track.

Starting from (120,0) and moving counter-clockwise, you would have traveled a distance of 3600 meters along the circumference of the circle. This corresponds to a fraction of 3600 / (2 * π * 120) = 15 / π of the circle's circumference.

Using this fraction, we can calculate the angle in radians by multiplying it by 2π. Therefore, the angle is 2π * (15 / π) = 30 radians.

To find the new coordinates, we can use the polar coordinates formula:

x = r * cos(θ)

y = r * sin(θ)

Plugging in the values:

x = 120 * cos(30) ≈ 103.92

y = 120 * sin(30) ≈ 60.00

So, after 20 minutes of running counter-clockwise, your coordinates would be approximately (103.92, 60.00).

b) If you had started at (0,120) and ran for 40 minutes, the process is similar. Since you are running at a speed of 3 meters per second, in 40 minutes (or 40 * 60 = 2400 seconds), you would have covered a distance of 3 * 2400 = 7200 meters.

Using the same circle equation x^2 + y^2 = 14400, we determine the new position on the track.

Starting from (0,120) and moving counter-clockwise, you would have traveled a distance of 7200 meters along the circumference of the circle. This corresponds to a fraction of 7200 / (2 * π * 120) = 30 / π of the circle's circumference.

The angle in radians is given by 2π * (30 / π) = 60 radians.

Using the polar coordinates formula:

x = r * cos(θ)

y = r * sin(θ)

Plugging in the values:

x = 120 * cos(60) ≈ 60.00

y = 120 * sin(60) ≈ 103.92

So, if you had started at (0,120) and ran for 40 minutes, your coordinates would be approximately (60.00, 103.92).

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The logarithmic eqaution log₂ 4 + log₂ (c-9) = 5 has its solution to be 17

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

log₂ 4 + log₂ (c-9) = 5

Apply the product rule of logarithm

So, we have

log₂(4 * (c-9)) = 5

This can then be expressed as

(4 * (c-9)) = 2⁵

Divide both sides by 4

c - 9 = 2³

So, we have

c - 9 = 8

When evaluated, we have

c = 17

Hence, the logarithmic eqaution has its solution to be 17

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Answer:the probability that event A or event B takes place is 12/19.

The difference in design and fit between left and right shoes is essential for providing comfort, support, and functionality during physical activities such as training for an obstacle course.

If Helena accidentally purchased two left shoes instead of a left and a right shoe, the comparison between the shoes would change. Instead of the right shoe looking like a reflection of the left shoe, both shoes would look the same, with neither shoe resembling a reflection of the other.

When placing the shoes on the floor next to each other, Helena would notice that both shoes have the same design, structure, and orientation. The left shoe and the right shoe would be identical, and there would be no visual distinction between them.

When Helena initially placed the shoes on the floor and observed that the right shoe looked like a reflection of the left shoe, it implied that there was a clear distinction between the left and right shoes. The right shoe would have mirrored the design and features of the left shoe, creating a symmetrical appearance.

However, if Helena had purchased two left shoes, there would be no mirror image effect or reflection between the shoes. Both shoes would appear identical and would lack the characteristic differences between left and right shoes. This means that both shoes would have the same design, features, and overall appearance.

As a result, Helena would notice that there is no shoe that corresponds to the opposite foot. When trying to wear the shoes, she would find that both shoes fit on the same foot, causing discomfort and impracticality.

In this scenario, Helena would likely realize her mistake and need to exchange or return the shoes for a proper pair with a left shoe and a right shoe. The difference in design and fit between left and right shoes is essential for providing comfort, support, and functionality during physical activities such as training for an obstacle course.

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The expanded form of log4(4 / [7x^2]) is 1 - log4(7) - 2 * log4(x)

To expand the expression log4(4 / [7x^2]), we can use logarithmic properties to simplify it. First, we can rewrite the numerator as a power of the base 4:

log4(4) - log4(7x^2)

Since log4(4) is equal to 1 (since 4 raised to the power of 1 equals 4), the expression becomes:

1 - log4(7x^2)

Next, we can apply the logarithmic property log_a(b^c) = c * log_a(b) to simplify the logarithm of a product:

1 - (log4(7) + log4(x^2))

Using another logarithmic property log_a(b^c) = c * log_a(b), we can simplify the expression further:

1 - (log4(7) + 2 * log4(x))

Therefore, the expanded form of log4(4 / [7x^2]) is:

1 - log4(7) - 2 * log4(x)

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Length of the base of the building from the wall is, 1.68 m

We have to given that;

A ladder 8 m long leans against the wall of a building.

And, the foot of the ladder makes an angle of 78 degrees with the ground.

Now, We know that;

cos x = Base / Hypotenuse

Here, Hypotenuse = 8 m

And, Length of the base of the building from the wall = Base = x

Hence, We get;

cos 78 = x / 8

0.21 = x / 8

x = 0.21  x 8

x = 1.68 m

Thus, Length of the base of the building from the wall is, 1.68 m

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The correct order from least to greatest is log₂ 26, log₂ 33, log 26, eln 4, the correct option is D.

We are given that;

The logs log, 26, log, 33 and log3 26

Now,

We can simplify these expressions using the following identities:

eln x = x

log a a = 1

log a (b × c) = log a b + log a c

log a (b / c) = log a b - log a c

Using these identities and the properties of logarithms listed above, we can compare the given expressions as follows:

A. eln 4 = 4; log 26 < log 33; so we have:

4 < log 26 < log 33

B. eln 4 = 4; so we have:

log 33 < 4 < log 26 < log 26

C. eln 4 = 4; so we have

log₂ 26 < log 26 < log 33 < 4

D. eln 4 = 4; so we have:

log₂ 26 < log₂ 33 < log 26 < 4

Therefore, by logarithm the answer will be log₂ 26, log₂ 33, log 26, eln 4.

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Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer:

8750

Step-by-step explanation:

the original price was really "x", which oddly enough is the 100%, but today the collar is on sale at 15% off, that means the sale price is 100% - 15% = 85% of the original price, and we happen to know that's $3.91, so

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 3.91& 85 \end{array} \implies \cfrac{x}{3.91}~~=~~\cfrac{100}{85} \\\\\\ \cfrac{x}{3.91} ~~=~~ \cfrac{20}{17}\implies 17x=78.2\implies x=\cfrac{78.2}{17}\implies x=4.6[/tex]

The comparison of each expression is completed as shown below

7/5 x 11 / 10 > 7 / 5

7/5 x 3 / 3 = 7 / 5

7/5 x 4 / 9 < 7 / 5

In mathematics, inequality signs are symbols used to compare the relative size or value of two numbers or expressions. The most common inequality signs are:

Greater than: ">"

This symbol indicates that the number or expression on the left side is greater than the number or expression on the right side. For example, 5 > 3 means "5 is greater than 3."

Less than: "<"

This symbol indicates that the number or expression on the left side is less than the number or expression on the right side. For example, 2 < 7 means "2 is less than 7."

Greater than or equal to: "≥"

This symbol indicates that the number or expression on the left side is greater than or equal to the number or expression on the right side. For example, 4 ≥ 4 means "4 is greater than or equal to 4."

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Answer:

Step-by-step explanation: Compound interest formula = P*(1+r/n)^n*t, where:

- P = principal amount (initial investment amount).

- r = nominal annual interest rate.

- n = number of times interest is principally entered per year.

- t = number of years borrowed money.

Applying the above compound interest formula, after 10 years, you will get the amount:

= 15,000 * (1+4%/12)^(12*10) = 22363.49024

If Brenda deposits `₱15,000.00` in a savings account that pays `4%` interest compounded monthly, the accumulated interest after `10` years can be calculated using the formula for compound interest: `A = P(1 + r/n)^(nt)`, where `A` is the future value of the investment, `P` is the initial principal amount, `r` is the annual interest rate (as a decimal), `n` is the number of times the interest is compounded per year, and `t` is the number of years the money is invested for.

In this case, `P = 15000`, `r = 0.04`, `n = 12` (since the interest is compounded monthly), and `t = 10`. Plugging these values into the formula, we get:

```

A = 15000(1 + 0.04/12)^(12 * 10)

A ≈ 22265.07

```

So after `10` years, the accumulated interest would be `A - P = 22265.07 - 15000 = ₱7265.07`.

As an assessor, it is essential to objectively evaluate the Bonus payment, taking into account industry standards, the relationship between Dawa and Zeko, and compliance with tax laws.

As an assessor, it is important to approach this case with objectivity and fairness. The key factors to consider are the nature of the bonus payment, the relationship between Dawa and Zeko, and any relevant tax laws or regulations.

Firstly, it is necessary to determine if the bonus payment was reasonable and consistent with industry standards. Assessors often compare the bonus amounts given by similar enterprises in the same industry to establish a benchmark. If the bonus amount falls within a reasonable range, it is more likely to be considered as a legitimate business expense.

Secondly, the relationship between Dawa and Zeko should be evaluated. In this case, Dawa is identified as the son of Zeko, which raises questions about potential conflicts of interest or nepotism. Assessors must carefully examine whether the bonus payment to Dawa was based on his merit and contribution to the enterprise or if it was primarily due to their familial relationship. If there is evidence of favoritism or the bonus is disproportionate to Dawa's role and responsibilities, it could be deemed as personal income rather than a legitimate business expense.

Lastly, assessors need to adhere to relevant tax laws and regulations. The bonus payment should be assessed in accordance with the tax code of the jurisdiction where Zeko Enterprise operates. This involves ensuring that the appropriate taxes are paid on the bonus amount and that it is properly reported in the company's financial records.

Overall, as an assessor, it is essential to objectively evaluate the bonus payment, taking into account industry standards, the relationship between Dawa and Zeko, and compliance with tax laws. The focus should be on determining the legitimacy of the bonus payment as a business expense and ensuring that proper taxes are paid.

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The probability that a randomly chosen battery will last more than 3.664 years is 0.9673.

(a) The probability that a randomly chosen battery will last fewer than 5 years is 0.8413. This is calculated by subtracting the cumulative probability of 4.2 years (the mean life of the battery) from the cumulative probability of 5 years. We can calculate the cumulative probability using the z-score formula: z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. We can also use the standard normal table to find the cumulative probability.

Z = (5 - 4.2) / 0.8 = 0.75

Cumulative probability of 5 years = 0.7734 (from the standard normal table)

Cumulative probability of 4.2 years = 0.7257 (from the standard normal table)

Therefore, the probability that a randomly chosen battery will last fewer than 5 years = 0.7734 - 0.7257 = 0.8413

(b) The probability that a randomly chosen battery will last between 1.8 and 6.6 years is 0.9545. This is calculated by subtracting the cumulative probability of 1.8 years from the cumulative probability of 6.6 years.

Z = (1.8 - 4.2) / 0.8 = -1.5

Cumulative probability of 1.8 years = 0.0668 (from the standard normal table)

Z = (6.6 - 4.2) / 0.8 = 1.75

Cumulative probability of 6.6 years = 0.9619 (from the standard normal table)

Therefore, the probability that a randomly chosen battery will last between 1.8 and 6.6 years = 0.9619 - 0.0668 = 0.9545

(c) The probability that a randomly chosen battery will last more than 3.664 years is 0.9673. This is calculated by subtracting the cumulative probability of 3.664 years from the cumulative probability of 1.

Z = (3.664 - 4.2) / 0.8 = -0.55

Cumulative probability of 3.664 years = 0.7118 (from the standard normal table)

Cumulative probability of 1 = 0.8413 (from the standard normal table)

Thus, 0.8413 - 0.7118 = 0.9673

Therefore, the probability that a randomly chosen battery will last more than 3.664 years is 0.9673.

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Answer:

Score                      Frequency

68                              02

69                              03

70                              01

71                               02

72                              02

73                              01

74                              02

75                              02

76                              01

Answer:

y=2/3x

Step-by-step explanation:

Since they cross at (3,2) the formula would be y=2/3x

Answer:

(x, y) = (4, 3)

Step-by-step explanation:

y = x - 1 (Equation 1)

2x - 3y = -1 (Equation 2)

We can use substitution method:

Substitute the expression for y from Equation 1 into Equation 2 and solve for x:

2x - 3(x - 1) = -1

2x - 3x + 3 = -1

-x = -4

x = 4

Now that we have found the value of x, we can substitute it back into Equation 1 to find y:

y = x - 1

y = 4 - 1

y = 3

Therefore, the solution to the system of equations is (x, y) = (4, 3).

The solutions to the equation 8x^3 - 1 = 0 are x = 1/2, x = (-2 + 2√2i)/8, and x = (-2 - 2√2i)/8.None of the given Values is NOT a solution of the equation.

The solution(s) of the equation 8x^3 - 1 = 0, we need to determine the values of x that satisfy the equation. We can solve this equation by setting it equal to zero and factoring:

8x^3 - 1 = 0

(2x)^3 - 1^3 = 0

(2x - 1)(4x^2 + 2x + 1) = 0

Now we can find the values of x that make each factor equal to zero:

2x - 1 = 0

x = 1/2

4x^2 + 2x + 1 = 0

Using the quadratic formula, we can solve for x and find two additional solutions:

x = (-2 ± √(-8))/8

x = (-2 ± 2√2i)/8

Therefore, the solutions to the equation 8x^3 - 1 = 0 are x = 1/2, x = (-2 + 2√2i)/8, and x = (-2 - 2√2i)/8.None of the given values is NOT a solution of the equation.

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The correct answer is (b) 54 in.², which Matches just performed.

The area of a triangle, we use the formula:

Area = (1/2) * base * height

Given that the base (b) is 9 inches and the height (h) is 12 inches, we can substitute these values into the formula:

Area = (1/2) * 9 * 12

Simplifying the equation:

Area = (1/2) * 108

Area = 54

Therefore, the area of the triangle with a base of 9 inches and a height of 12 inches is 54 square inches.

Among the options given:

(a) 90 in.²

(b) 54 in.²

(c) 10.5 in.²

(d) 162 in.²

The correct answer is (b) 54 in.², which matches the calculation we just performed.

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The solution is 768  is the correct answer, is the 9th term of the geometric sequence 3,6,12,24.

Given:

The geometric sequence 3,6,12,24.

Required:

Find the 6th term of the geometric sequence.

Explanation:

The given sequence is 3,6,12,24.

The nth term of the sequence is given by the formula:

an = a* r^n-1

Where a = first term and r = common ratio

From the given sequence

a = 3, r = 6/3 = 2

Then 9th term is:

a9 = 3 * 2^9-1

    = 3* 2^8

    =768

Final answer:

The solution is 768  is the correct answer, is the 9th term of the geometric sequence 3,6,12,24.

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The area of the given rectangular frame is: 352 in²

The formula for the area of a rectangle is expressed as:

A = L * W

Where:

A is Area

L is Length

W is width

Now, we are told that the parameters are:

Width of frame = 16 inches

Length of frame = 22 inches

Thus:

Area of frame = 22 * 16

Area = 352 in²

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Harvey bought a frame in which he put his family's picture. Frame is 16 inches wide and 22 inches length. Picture area is 12 inches wide and 18 inches length. What is the area of the frame

The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

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Step-by-step explanation:

Let's break down the information provided and write out the mathematical statement step by step.

The electrician purchased 15 dimmer switches, each costing $20. This can be represented as:

Cost of dimmer switches = 15 * $20

The electrician also received a credit of $8 for each of the two duplex receptacles she returned. The total credit received can be calculated as:

Total credit = 2 * $8

To find the total amount of money she spent, we need to subtract the total credit from the cost of the dimmer switches:

Total amount spent = (Cost of dimmer switches) - (Total credit)

Now, let's calculate the total amount of money she spent:

Cost of dimmer switches = 15 * $20 = $300

Total credit = 2 * $8 = $16

Total amount spent = $300 - $16 = $284

Therefore, the electrician spent a total of $284.

The solution to the given system of equations is (-158/85, 57/17).

The system of linear equations are 5x-2y=-16 ------(i) and 4x -5y=-23 ------(ii).

Multiply equation (i) by 4, we get

20x-8y= -48 -----(iii)

Multiply equation (ii) by 5, we get

20x-25y=-105 -----(iv)

Subtract equation (iii) from equation (iv), we get

20x-25y-(20x-8y)=-105+48

-17y=-57

y=57/17

Substitute y=57/17 in equation (i), we get

5x-2(57/17)=-16

5x-114/17=-16

5x=-16+114/17

5x=(-272+114)/17

x= -158/85

Therefore, the solution to the given system of equations is (-158/85, 57/17).

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