Tim has to mow his lawn in under two hours. If "t" represents the time it takes to mow the lawn, how can you express this as an inequality?.

Answer:

832.2

Step-by-step explanation:

730 x 0.028 = (assuming per year) 20.44

20.44 x 5 = 102.2

102.2 + 730 = 832.2

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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A) The probability that all 100 lights will last 2 years is 0.9048.

B) The probability that at least one bulb will burn out in 2 years is 0.0952.

A) To find the probability that all 100 lights will last 2 years, we assume that the success or failure of each bulb is independent.

The probability of a single bulb lasting 2 years is 0.995, so the probability of all 100 bulbs lasting 2 years is:

P(all 100 bulbs last 2 years) is (0.995)¹⁰⁰ ≈ 0.9048

B) The probability that at least one bulb will burn out in 2 years is determined using the complement rule.

P(at least one bulb burns out) = 1 - P(no bulbs burn out)

Since the probability of a single bulb lasting 2 years is 0.995, the probability of a single bulb burning out in 2 years is 1 - 0.995 = 0.005.

The probability of at least one bulb burning out in 2 years is:

P(at least one bulb burns out) = 1 - P(no bulbs burn out)

P(at least one bulb burns out) = 1 - 0.9048

P(at least one bulb burns out) ≈ 0.0952

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Answer:

13, 39

Step-by-step explanation:

H +J =52

H =3J

3J +J =52

4J =52

J =52 :4 =13 (Jane is 13

H =3 ×13 =39 (Harvey is 39

Answer:

Jane is 13 and Harvey is 39

Step-by-step explanation:

To prove that secθ + 1 / tanθ = tanθ / secθ−1, we can use trigonometric identities.

First, we will define secθ as 1/cosθ and tanθ as sinθ/cosθ.

Now, we can substitute these definitions into the equation to get:

secθ + 1 / tanθ = (1/cosθ) + 1 / (sinθ/cosθ)

And, tanθ / secθ−1 = (sinθ/cosθ) / (1/cosθ) - 1

Expanding both sides using basic algebraic manipulations, we get:

(1/cosθ) + 1 / (sinθ/cosθ) = (1/cosθ) * ((sinθ/cosθ) + cosθ/cosθ)

= (sinθ/cosθ) / (1/cosθ) - 1

= (sinθ/cosθ) * (cosθ/1) - 1

= (sinθ) / 1 - 1

= sinθ.

Therefore, secθ + 1 / tanθ = tanθ / secθ−1 has been proven.

The equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).

The area of mixed shapes is the area that is covered by any hybrid shape. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These forms or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.

A composite form is essentially a combination of fundamental shapes. A "composite" or "complex" shape is another name for it.

The area of the rectangle is given as:

A = (l)(w)

A = 10(8)

A = 80 sq. units

The area of the triangle is:

A = 1/2(b)(h)

In the figure:

b = 16 - 10 = 6 and h = 8.

A = 1/2(6)(8)

A = 24 sq. units

The total area of the figure is:

Area = area of rectangle + area of triangle

Area = 80 + 24

Area = 104 sq. units

Hence, the equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).

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To hang 18 napkins one after another in a way that two napkins share the same clip, we need to determine the number of clips required.

If each napkin is hung separately, we would need 18 clips. However, we want to find the number of clips needed when two napkins share the same clip. To accomplish this, we can think of each clip as a separator between two napkins. So, if we have 18 napkins, we will have 17 separators (clips) between them.

Therefore, the number of clips needed to hang 18 napkins such that two napkins share the same clip is 17. By using 17 clips, we can create 18 sections, with each section consisting of two adjacent napkins sharing the same clip.

It's important to note that if we had fewer clips, we wouldn't be able to ensure that two napkins share the same clip. Similarly, if we had more clips, some clips would remain unused. Hence, 17 clips are necessary and sufficient to achieve the desired arrangement.

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Answer:

Step-by-step explanation:

1/5 of 115= 23

so in 15mins he reads 23 pages.

15mins x 4=60mins

23x4=92

Have a nice day sunshine

Answer:

\(a_n = 432 \cdot \left(\frac{1}{6}\right)^n\) OR \(a_n = 72 \cdot \left(\frac{1}{6}\right)^{n-1}\)

Step-by-step explanation:

The first term is 72, and each term is equal to the previous term multiplied by 1/6. This yields the expression \(a_n = 72 \cdot \left(\frac{1}{6}\right)^{n-1}\), which is equivalent to \(a_n = 432 \cdot \left(\frac{1}{6}\right)^n\).

Answer:

\(n _{th} = n _{1} {r}^{n - 1} \\ n _{th} = 72 \times 12 {}^{(n - 1)} \\ n _{th} = 72 \times ( {12}^{n} .12^(-1)) \\ n _{th} = 6 × {12}^{n} \)

the probability of Andrea breaking the record in the next race is 0.002555

The probability that Ashley beats Andrea in their next race is 0.2661

Andrea has mean 62 and sd, so P(x <= 60) = P(z <= (60-62)/.8) = P(z <= 2.5) = norm.s.dist(-2.5,1) = .00621

Ashley has mean 62.8 and sd 1, so P(x <= 60) = P(z <= (60-62.8)/1) = P(z <= -2.8) = norm.s.dist(-2.8,1) = 0.002555

The mean difference for Ashley - Andrea = 62.8 - 62 = 0.8

The variance of the difference, given independence, is .8^2 + 1^2 = 1.64

Ashley is faster if the difference is less than 0.

Then, P(x <= 0)  = P(z <= (0 - 0.8)/sqrt(1.64) ) = norm.s.dist(-.8/sqrt(1.64),1) = 0.2661

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a.)  Based on the scatter plot, the estimated average daily maximum temperature in Fort Frances in July is  around 25°C.

b) There are four communities with average daily maximum temperatures greater than 22°C. Their latitudes are approximately:

Toronto: 44°N

Windsor: 42°N

London: 43°N

Ottawa: 45°N

c.)

. Based on the scatter plot, there seems to be a relationship between  latitude and temperature .

As latitude increases, temperature generally decreases  because places closer to the equator receive more direct sunlight and therefore tend to be warmer, while places farther away receive less direct sunlight and tend to be cooler.

Latitude is described as a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body.

there are some exceptions to this general trend that states that as latitude increases, temperature  decreases  because places closer to the equator receive more direct sunlight and therefore tend to be warmer, while places farther away receive less direct sunlight and tend to be cooler. which could be due to other factors such as elevation, proximity to water, or local weather patterns.

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Answer:

20% of 70 is 14

Step-by-step explanation:

l

If you're comparing 1.435 * 10^(-3) mm to 1.435 * 10^3 mm, then the more reasonable measurement is 1.435 * 10^3 mm since,

1.435 * 10^3 mm = 1435 mm = 1.435 meters

1 meter is about 3.28 feet approximately

So 1.435 meters is slightly larger (about 4.708 feet) which is a fairly reasonable distance between the tracks on a railroad.

-------------------

Something like 1.435 * 10^(-3) mm is equal to 0.001435 mm, which is far less than 1 mm.

These tests would allow us to determine if the observed sample mean of $934 is significantly different from the claimed average of $1250, providing evidence to support or reject the alternative hypothesis.

To test the claim made by the IRS representative that the average deduction for medical care is $1250, we can formulate the null and alternative hypotheses as follows:

Null Hypothesis (H0): The average deduction for medical care is $1250.

Alternative Hypothesis (H1): The average deduction for medical care is lower than $1250.

In this case, the taxpayer who believes that the real figure is lower has collected a sample of 32 random families. The sample mean is $934, and the sample standard deviation is $619. The null hypothesis assumes that the average deduction is $1250, while the alternative hypothesis suggests that it is lower than $1250.

To statistically test these hypotheses, we can use a one-sample t-test or a z-test, depending on the sample size and whether the population standard deviation is known.

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Answer:

Yes they both are equal

The minimum number of hard disks that can be used for implementing a RAID 10 solution is four (option c).  

The minimum number of hard disks that can be used for implementing a RAID 10 solution on the video editor's desktop workstation is four (option c). RAID 10, also known as RAID 1+0, combines elements of RAID 1 (mirroring) and RAID 0 (striping) to provide both data redundancy and improved performance.

In RAID 10, data is mirrored across multiple drives to ensure redundancy. To implement RAID 10, we need at least two sets of mirrored drives, where each set contains a minimum of two hard disks.

The data is striped across these mirrored sets to enhance performance.

With four hard disks, you can create two mirrored sets, each consisting of two drives.

The data is then striped across these mirrored sets, providing both redundancy and improved read/write speeds.

If one drive fails in each mirrored set, the system can still function without data loss due to the mirroring.

This setup provides a balance between data protection and performance.

While more hard disks can be used in RAID 10 for larger capacities and better performance, the minimum requirement is four hard disks.

Using fewer drives would not allow for the necessary mirrored sets and striping required for RAID 10.

By implementing a RAID 10 solution with four hard disks on the video editor's workstation, you can help safeguard against data loss in case of drive failure, ensuring the integrity and availability of important video editing data.  

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Answer:

(c) is correct.

Step-by-step explanation:

(c) 9 + 2(4) = 9 + 8 = 17

The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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the total amount is 9000

Answer:

its 42÷2= 21 i think

Step-by-step explanation:

because dana has twice the nb of cans erica has so it dana has 48 then erica has the half number

the speed of the private airplane is approximately 214.3 miles per hour. Rounding to one decimal place is not necessary but if you round it the answer will be 214 miles.

Let's call the speed of the private airplane "s". According to the problem, the speed of the commercial jet is 103 miles per hour faster than the speed of the private airplane. So, the speed of the commercial jet is:

s + 103

We know that the distance from Denver to Phoenix is the same for both planes. Let's call this distance "d".

Using the formula distance = rate x time, we can set up two equations:

For the private airplane:

d = s × 4

For the commercial jet:

d = (s + 103) × 2.7

Since both equations represent the same distance, we can set them equal to each other and solve for s:

s × 4 = (s + 103) × 2.7

4s = 2.7s + 278.1

1.3s = 278.1

s = 278.1 / 1.3

s = 214.3

Therefore, the speed of the private airplane is approximately 214.3 miles per hour.

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the point P_0(2,1,2) lies on the tangent plane, we can use it to find the equation of the normal line:

x - 2 = 2

We start by finding the characteristic equation:

r^2 + 4r + 3 = 0

Solving for r, we get:

r = -1 or r = -3

So the complementary solution is:

y_c(t) = c_1 e^{-t} + c_2 e^{-3t}

Next, we need to find the transfer function H(s):

s^2 Y(s) - s y(0) - y'(0) + 4s Y(s) - 4y(0) + 3Y(s) = 1/s + 1/(s-1)

Applying the initial conditions y(0) = 0 and y'(0) = 1, we get:

(s^2 + 4s + 3) Y(s) = 1/s + 1/(s-1) + 4

Y(s) = [1/(s+1) + 1/(s+3) + 4/(s^2 + 4s + 3)] / (s^2 + 4s + 3)

We can factor the denominator of the second term in the numerator:

Y(s) = [1/(s+1) + 1/(s+3) + 4/((s+1)(s+3))] / [(s+1)(s+3)]

Using partial fraction decomposition, we get:

Y(s) = [2/(s+1) - 1/(s+3) + 1/((s+1)(s+3))] / (s+1) + [-1/(s+1) + 2/(s+3) - 1/((s+1)(s+3))] / (s+3)

Taking the inverse Laplace transform, we get:

y(t) = 2e^{-t} - e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

So the general solution is:

y(t) = y_c(t) + y_p(t) = c_1 e^{-t} + c_2 e^{-3t} + 2e^{-t} - e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

To find a particular solution, we need to solve for the unknown coefficients. Using the initial conditions y(0) = 1 and y'(0) = 0, we get:

c_1 + c_2 + 3/2 = 1

-c_1 - 3c_2 - 1/2 = 0

Solving this system of equations, we get:

c_1 = -2/5

c_2 = 9/10

So the particular solution is:

y_p(t) = (-2/5) e^{-t} + (9/10) e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

Finally, the tangent plane at P_0(2,1,2) is given by the equation:

2x + 4y + 3z = 24

which corresponds to option (B) in the given choices.

To find the normal line, we first need to find the normal vector to the tangent plane, which is simply:

n = <2, 4, 3>

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The value of the modulus function |5x| = 3 is x = 3/5 or x = -3/5.

In  mathematics modulus function is the absolute or numerical value of the function irrespective of the sign.It represents magnitude.We modulus functions when we want length, mass and for other variables when we want to represent their weight.

According to the given question |5x| = 3.

We know |x| = a implies x = a or x = -a.

∴ |5x| = 3 is

5x = 3

x = 3/5

Or

5x = -3.

x = -3/5.

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Answer:

Step-by-step explanation:

a line is 180° so we subtract 109 from 180 to find mLUE

180-109=

71

a triangle is also 180° so we add up the angles we have so far and subtract that from 180°

180-(71+49)

180-(120)

mULE = 60°

Answer:

Step-by-step explanation:

1.  48 96 192      (multiplying by 2)

2. 30 37 44        ( adding 7)

3. 25 18 11          ( subtracting 7)

4. 110 232 456  ( adding 7, 14, 28, 56  and so on)

5. 230 470 950  (adding 15, 30, 60 120 and so on)

Answer:

the number is 11

Step-by-step explanation:

"Diminished" is another word for subtraction, so our equation is : 9x - 4 = 95

Add 4 on each side: 9x = 99

Divide each side by 9: x = 11

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Answer:

Step-by-step explanation:

Let a number be X

So

Nine times a number, diminished by 4, is 95

9x-4=95

9x=95+4

9x=99

X=99/9

X=11

So the number is 11

Answer:  x = -11, x = 11

Step-by-step explanation:

   x² = 121

 \(\sqrt{x^2}=\sqrt{121}\)

   x = ±11

  x = -11, x = 11